subroutine comp_next ( n, k, a, more, h, t ) !*****************************************************************************80 ! !! comp_next() computes the compositions of the integer N into K parts. ! ! Discussion: ! ! A composition of the integer N into K parts is an ordered sequence ! of K nonnegative integers which sum to N. The compositions (1,2,1) ! and (1,1,2) are considered to be distinct. ! ! The routine computes one composition on each call until there are no more. ! For instance, one composition of 6 into 3 parts is ! 3+2+1, another would be 6+0+0. ! ! On the first call to this routine, set MORE = FALSE. The routine ! will compute the first element in the sequence of compositions, and ! return it, as well as setting MORE = TRUE. If more compositions ! are desired, call again, and again. Each time, the routine will ! return with a new composition. ! ! However, when the LAST composition in the sequence is computed ! and returned, the routine will reset MORE to FALSE, signaling that ! the end of the sequence has been reached. ! ! There are 28 compositions of 6 into three parts. This routine will ! produce those compositions in the following order: ! ! I A ! - --------- ! 1 6 0 0 ! 2 5 1 0 ! 3 4 2 0 ! 4 3 3 0 ! 5 2 4 0 ! 6 1 5 0 ! 7 0 6 0 ! 8 5 0 1 ! 9 4 1 1 ! 10 3 2 1 ! 11 2 3 1 ! 12 1 4 1 ! 13 0 5 1 ! 14 4 0 2 ! 15 3 1 2 ! 16 2 2 2 ! 17 1 3 2 ! 18 0 4 2 ! 19 3 0 3 ! 20 2 1 3 ! 21 1 2 3 ! 22 0 3 3 ! 23 2 0 4 ! 24 1 1 4 ! 25 0 2 4 ! 26 1 0 5 ! 27 0 1 5 ! 28 0 0 6 ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 02 July 2008 ! ! Author: ! ! Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf. ! FORTRAN90 version by John Burkardt. ! ! Reference: ! ! Albert Nijenhuis, Herbert Wilf, ! Combinatorial Algorithms for Computers and Calculators, ! Second Edition, ! Academic Press, 1978, ! ISBN: 0-12-519260-6, ! LC: QA164.N54. ! ! Parameters: ! ! Input, integer N, the integer whose compositions are desired. ! ! Input, integer K, the number of parts in the composition. ! ! Input/output, integer A(K), the parts of the composition. ! ! Input/output, logical MORE, set by the user to start the computation, ! and by the routine to terminate it. ! ! Input/output, integer H, T, two internal parameters needed ! for the computation. The user should allocate space for these in the ! calling program, include them in the calling sequence, but never alter ! them! ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer k integer a(k) integer h logical more integer n integer t ! ! The first computation. ! if ( .not. more ) then t = n h = 0 a(1) = n a(2:k) = 0 ! ! The next computation. ! else ! ! If the first entry A(1) is positive, then set H to zero, ! so that when we increment H, it points to A(1); we will decrement A(1) by 1 ! and increment A(2). ! if ( 1 < t ) then h = 0 end if ! ! Otherwise, A(1) is 0. Then by H + 1 is the entry we incremented last time. ! Set H = H + 1, zero A(H), adding all but one of its value to A(1), ! and incrementing A(H+1) by 1. ! h = h + 1 t = a(h) a(h) = 0 a(1) = t - 1 a(h+1) = a(h+1) + 1 end if ! ! This is the last element of the sequence if all the ! items are in the last slot. ! more = ( a(k) /= n ) return end subroutine monomial_value ( d, n, e, x, v ) !*****************************************************************************80 ! !! monomial_value() evaluates a monomial. ! ! Discussion: ! ! This routine evaluates a monomial of the form ! ! product ( 1 <= i <= d ) x(i)^e(i) ! ! The combination 0.0^0, if encountered, is treated as 1.0. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 16 May 2023 ! ! Author: ! ! John Burkardt ! ! Input: ! ! integer D, the spatial dimension. ! ! integer N, the number of evaluation points. ! ! integer E(D), the exponents. ! ! real ( kind = rk ) X(N,D), the point coordinates. ! ! Output: ! ! real ( kind = rk ) V(N), the monomial values. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer d integer n integer e(d) integer j real ( kind = rk ) v(n) real ( kind = rk ) x(n,d) v(1:n) = 1.0D+00 do j = 1, d if ( 0 /= e(j) ) then v(1:n) = v(1:n) * x(1:n,j) ** e(j) end if end do return end subroutine rule_order ( p, n ) !*****************************************************************************80 ! !! rule_order() returns the order of a rule. ! ! Licensing: ! ! This code is distributed under the GNU GPL license. ! ! Modified: ! ! 10 June 2023 ! ! Author: ! ! John Burkardt. ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient quadrature ! rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer p: the precision of the quadrature. ! 0 <= p <= 50. ! ! Output: ! ! integer n: the number of nodes. ! implicit none integer n integer nnodes(0:50) integer p save nnodes data nnodes / & 1, & 1, 3, 6, 6, 7, 12, 15, 16, 19, 25, & 28, 33, 37, 42, 49, 55, 60, 67, 73, 79, & 87, 96, 103, 112, 120, 130, 141, 150, 159, 171, & 181, 193, 204, 214, 228, 243, 252, 267, 282, 295, & 309, 324, 339, 354, 370, 385, 399, 423, 435, 453 / if ( 0 <= p .and. p <= 50 ) then n = nnodes(p) else write ( *, '(a)' ) '' write ( *, '(a)' ) 'rule_order(): Fatal error!' write ( *, '(a)' ) ' Precision p must be between 0 and 50.' stop 1 end if return end subroutine rule00 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule00() returns the rule of precision 0. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 10 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3333333333333333D+00 /) b = (/ & 0.3333333333333334D+00 /) c = (/ & 0.3333333333333333D+00 /) w = (/ & 1.0000000000000000D+00 /) return end subroutine rule01 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule01() returns the rule of precision 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3333333333333333D+00 /) b = (/ & 0.3333333333333334D+00 /) c = (/ & 0.3333333333333333D+00 /) w = (/ & 1.0000000000000000D+00 /) return end subroutine rule02 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule02() returns the rule of precision 2. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1666666666666666D+00, & 0.6666666666666665D+00, & 0.1666666666666669D+00 /) b = (/ & 0.1666666666666668D+00, & 0.1666666666666667D+00, & 0.6666666666666667D+00 /) c = (/ & 0.6666666666666665D+00, & 0.1666666666666668D+00, & 0.1666666666666664D+00 /) w = (/ & 0.3333333333333333D+00, & 0.3333333333333333D+00, & 0.3333333333333333D+00 /) return end subroutine rule03 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule03() returns the rule of precision 3. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4459484909159648D+00, & 0.4459484909159649D+00, & 0.1081030181680702D+00, & 0.0915762135097707D+00, & 0.8168475729804584D+00, & 0.0915762135097710D+00 /) b = (/ & 0.1081030181680703D+00, & 0.4459484909159649D+00, & 0.4459484909159651D+00, & 0.0915762135097709D+00, & 0.0915762135097707D+00, & 0.8168475729804585D+00 /) c = (/ & 0.4459484909159649D+00, & 0.1081030181680702D+00, & 0.4459484909159647D+00, & 0.8168475729804585D+00, & 0.0915762135097709D+00, & 0.0915762135097705D+00 /) w = (/ & 0.2233815896780115D+00, & 0.2233815896780115D+00, & 0.2233815896780115D+00, & 0.1099517436553219D+00, & 0.1099517436553219D+00, & 0.1099517436553219D+00 /) return end subroutine rule04 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule04() returns the rule of precision 4. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4459484909159648D+00, & 0.4459484909159649D+00, & 0.1081030181680702D+00, & 0.0915762135097707D+00, & 0.8168475729804584D+00, & 0.0915762135097710D+00 /) b = (/ & 0.1081030181680703D+00, & 0.4459484909159649D+00, & 0.4459484909159651D+00, & 0.0915762135097709D+00, & 0.0915762135097707D+00, & 0.8168475729804585D+00 /) c = (/ & 0.4459484909159649D+00, & 0.1081030181680702D+00, & 0.4459484909159647D+00, & 0.8168475729804585D+00, & 0.0915762135097709D+00, & 0.0915762135097705D+00 /) w = (/ & 0.2233815896780115D+00, & 0.2233815896780115D+00, & 0.2233815896780115D+00, & 0.1099517436553219D+00, & 0.1099517436553219D+00, & 0.1099517436553219D+00 /) return end subroutine rule05 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule05() returns the rule of precision 5. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1012865073234563D+00, & 0.7974269853530872D+00, & 0.1012865073234565D+00, & 0.4701420641051151D+00, & 0.4701420641051151D+00, & 0.0597158717897698D+00, & 0.3333333333333333D+00 /) b = (/ & 0.1012865073234565D+00, & 0.1012865073234562D+00, & 0.7974269853530874D+00, & 0.0597158717897699D+00, & 0.4701420641051151D+00, & 0.4701420641051153D+00, & 0.3333333333333334D+00 /) c = (/ & 0.7974269853530873D+00, & 0.1012865073234566D+00, & 0.1012865073234560D+00, & 0.4701420641051151D+00, & 0.0597158717897698D+00, & 0.4701420641051149D+00, & 0.3333333333333333D+00 /) w = (/ & 0.1259391805448272D+00, & 0.1259391805448272D+00, & 0.1259391805448272D+00, & 0.1323941527885062D+00, & 0.1323941527885062D+00, & 0.1323941527885062D+00, & 0.2250000000000000D+00 /) return end subroutine rule06 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule06() returns the rule of precision 6. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2194299825497829D+00, & 0.5611400349004340D+00, & 0.2194299825497830D+00, & 0.4801379641122150D+00, & 0.4801379641122151D+00, & 0.0397240717755699D+00, & 0.1416190159239681D+00, & 0.8390092597147910D+00, & 0.0193717243612410D+00, & 0.8390092597147911D+00, & 0.1416190159239681D+00, & 0.0193717243612406D+00 /) b = (/ & 0.2194299825497831D+00, & 0.2194299825497830D+00, & 0.5611400349004342D+00, & 0.0397240717755700D+00, & 0.4801379641122150D+00, & 0.4801379641122153D+00, & 0.0193717243612408D+00, & 0.1416190159239681D+00, & 0.8390092597147911D+00, & 0.0193717243612408D+00, & 0.8390092597147912D+00, & 0.1416190159239684D+00 /) c = (/ & 0.5611400349004340D+00, & 0.2194299825497831D+00, & 0.2194299825497829D+00, & 0.4801379641122150D+00, & 0.0397240717755699D+00, & 0.4801379641122148D+00, & 0.8390092597147911D+00, & 0.0193717243612409D+00, & 0.1416190159239679D+00, & 0.1416190159239681D+00, & 0.0193717243612407D+00, & 0.8390092597147910D+00 /) w = (/ & 0.1713331241529810D+00, & 0.1713331241529810D+00, & 0.1713331241529810D+00, & 0.0807310895930310D+00, & 0.0807310895930310D+00, & 0.0807310895930310D+00, & 0.0406345597936607D+00, & 0.0406345597936607D+00, & 0.0406345597936607D+00, & 0.0406345597936607D+00, & 0.0406345597936607D+00, & 0.0406345597936607D+00 /) return end subroutine rule07 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule07() returns the rule of precision 7. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4731956536892510D+00, & 0.4731956536892510D+00, & 0.0536086926214978D+00, & 0.0577976400545063D+00, & 0.8844047198909870D+00, & 0.0577976400545066D+00, & 0.2593390118657857D+00, & 0.6936897820041288D+00, & 0.0469712061300856D+00, & 0.6936897820041288D+00, & 0.2593390118657857D+00, & 0.0469712061300854D+00, & 0.2416636063972473D+00, & 0.5166727872055051D+00, & 0.2416636063972475D+00 /) b = (/ & 0.0536086926214979D+00, & 0.4731956536892511D+00, & 0.4731956536892513D+00, & 0.0577976400545066D+00, & 0.0577976400545063D+00, & 0.8844047198909872D+00, & 0.0469712061300856D+00, & 0.2593390118657857D+00, & 0.6936897820041289D+00, & 0.0469712061300856D+00, & 0.6936897820041289D+00, & 0.2593390118657859D+00, & 0.2416636063972475D+00, & 0.2416636063972474D+00, & 0.5166727872055052D+00 /) c = (/ & 0.4731956536892511D+00, & 0.0536086926214979D+00, & 0.4731956536892509D+00, & 0.8844047198909871D+00, & 0.0577976400545067D+00, & 0.0577976400545062D+00, & 0.6936897820041288D+00, & 0.0469712061300855D+00, & 0.2593390118657856D+00, & 0.2593390118657857D+00, & 0.0469712061300854D+00, & 0.6936897820041287D+00, & 0.5166727872055050D+00, & 0.2416636063972475D+00, & 0.2416636063972473D+00 /) w = (/ & 0.0531808332967605D+00, & 0.0531808332967605D+00, & 0.0531808332967605D+00, & 0.0409181703940569D+00, & 0.0409181703940569D+00, & 0.0409181703940569D+00, & 0.0557545405406911D+00, & 0.0557545405406911D+00, & 0.0557545405406911D+00, & 0.0557545405406911D+00, & 0.0557545405406911D+00, & 0.0557545405406911D+00, & 0.1277252485611338D+00, & 0.1277252485611338D+00, & 0.1277252485611338D+00 /) return end subroutine rule08 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule08() returns the rule of precision 8. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1705693077517601D+00, & 0.6588613844964795D+00, & 0.1705693077517604D+00, & 0.4592925882927231D+00, & 0.4592925882927231D+00, & 0.0814148234145537D+00, & 0.3333333333333333D+00, & 0.0505472283170309D+00, & 0.8989055433659379D+00, & 0.0505472283170313D+00, & 0.2631128296346381D+00, & 0.7284923929554042D+00, & 0.0083947774099577D+00, & 0.7284923929554042D+00, & 0.2631128296346381D+00, & 0.0083947774099575D+00 /) b = (/ & 0.1705693077517604D+00, & 0.1705693077517602D+00, & 0.6588613844964796D+00, & 0.0814148234145537D+00, & 0.4592925882927232D+00, & 0.4592925882927233D+00, & 0.3333333333333334D+00, & 0.0505472283170312D+00, & 0.0505472283170309D+00, & 0.8989055433659381D+00, & 0.0083947774099577D+00, & 0.2631128296346381D+00, & 0.7284923929554045D+00, & 0.0083947774099577D+00, & 0.7284923929554044D+00, & 0.2631128296346383D+00 /) c = (/ & 0.6588613844964796D+00, & 0.1705693077517604D+00, & 0.1705693077517599D+00, & 0.4592925882927231D+00, & 0.0814148234145537D+00, & 0.4592925882927231D+00, & 0.3333333333333333D+00, & 0.8989055433659380D+00, & 0.0505472283170313D+00, & 0.0505472283170306D+00, & 0.7284923929554042D+00, & 0.0083947774099577D+00, & 0.2631128296346378D+00, & 0.2631128296346381D+00, & 0.0083947774099575D+00, & 0.7284923929554041D+00 /) w = (/ & 0.1032173705347182D+00, & 0.1032173705347182D+00, & 0.1032173705347182D+00, & 0.0950916342672846D+00, & 0.0950916342672846D+00, & 0.0950916342672846D+00, & 0.1443156076777872D+00, & 0.0324584976231981D+00, & 0.0324584976231981D+00, & 0.0324584976231981D+00, & 0.0272303141744350D+00, & 0.0272303141744350D+00, & 0.0272303141744350D+00, & 0.0272303141744350D+00, & 0.0272303141744350D+00, & 0.0272303141744350D+00 /) return end subroutine rule09 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule09() returns the rule of precision 9. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4896825191987376D+00, & 0.4896825191987376D+00, & 0.0206349616025247D+00, & 0.3333333333333333D+00, & 0.1882035356190326D+00, & 0.6235929287619344D+00, & 0.1882035356190329D+00, & 0.2219629891607657D+00, & 0.7411985987844980D+00, & 0.0368384120547364D+00, & 0.7411985987844980D+00, & 0.2219629891607658D+00, & 0.0368384120547361D+00, & 0.4370895914929366D+00, & 0.4370895914929366D+00, & 0.1258208170141267D+00, & 0.0447295133944526D+00, & 0.9105409732110945D+00, & 0.0447295133944530D+00 /) b = (/ & 0.0206349616025248D+00, & 0.4896825191987377D+00, & 0.4896825191987378D+00, & 0.3333333333333334D+00, & 0.1882035356190329D+00, & 0.1882035356190327D+00, & 0.6235929287619346D+00, & 0.0368384120547363D+00, & 0.2219629891607657D+00, & 0.7411985987844981D+00, & 0.0368384120547363D+00, & 0.7411985987844981D+00, & 0.2219629891607660D+00, & 0.1258208170141268D+00, & 0.4370895914929367D+00, & 0.4370895914929368D+00, & 0.0447295133944529D+00, & 0.0447295133944525D+00, & 0.9105409732110946D+00 /) c = (/ & 0.4896825191987376D+00, & 0.0206349616025246D+00, & 0.4896825191987374D+00, & 0.3333333333333333D+00, & 0.6235929287619345D+00, & 0.1882035356190329D+00, & 0.1882035356190325D+00, & 0.7411985987844980D+00, & 0.0368384120547363D+00, & 0.2219629891607655D+00, & 0.2219629891607657D+00, & 0.0368384120547361D+00, & 0.7411985987844979D+00, & 0.4370895914929366D+00, & 0.1258208170141267D+00, & 0.4370895914929366D+00, & 0.9105409732110946D+00, & 0.0447295133944530D+00, & 0.0447295133944524D+00 /) w = (/ & 0.0313347002271391D+00, & 0.0313347002271391D+00, & 0.0313347002271391D+00, & 0.0971357962827989D+00, & 0.0796477389272103D+00, & 0.0796477389272103D+00, & 0.0796477389272103D+00, & 0.0432835393772894D+00, & 0.0432835393772894D+00, & 0.0432835393772894D+00, & 0.0432835393772894D+00, & 0.0432835393772894D+00, & 0.0432835393772894D+00, & 0.0778275410047743D+00, & 0.0778275410047743D+00, & 0.0778275410047743D+00, & 0.0255776756586980D+00, & 0.0255776756586980D+00, & 0.0255776756586980D+00 /) return end subroutine rule10 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule10() returns the rule of precision 10. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4951734598011704D+00, & 0.4951734598011704D+00, & 0.0096530803976590D+00, & 0.0191394152428411D+00, & 0.9617211695143175D+00, & 0.0191394152428416D+00, & 0.1337347551008691D+00, & 0.8315416244168033D+00, & 0.0347236204823275D+00, & 0.8315416244168033D+00, & 0.1337347551008692D+00, & 0.0347236204823273D+00, & 0.3333333333333333D+00, & 0.3266931362813369D+00, & 0.6357241363774715D+00, & 0.0375827273411917D+00, & 0.6357241363774714D+00, & 0.3266931362813369D+00, & 0.0375827273411916D+00, & 0.1844850126852464D+00, & 0.6310299746295069D+00, & 0.1844850126852466D+00, & 0.4282348209437188D+00, & 0.4282348209437188D+00, & 0.1435303581125623D+00 /) b = (/ & 0.0096530803976591D+00, & 0.4951734598011706D+00, & 0.4951734598011707D+00, & 0.0191394152428414D+00, & 0.0191394152428411D+00, & 0.9617211695143175D+00, & 0.0347236204823275D+00, & 0.1337347551008691D+00, & 0.8315416244168037D+00, & 0.0347236204823275D+00, & 0.8315416244168035D+00, & 0.1337347551008694D+00, & 0.3333333333333334D+00, & 0.0375827273411917D+00, & 0.3266931362813369D+00, & 0.6357241363774715D+00, & 0.0375827273411917D+00, & 0.6357241363774715D+00, & 0.3266931362813372D+00, & 0.1844850126852466D+00, & 0.1844850126852465D+00, & 0.6310299746295072D+00, & 0.1435303581125623D+00, & 0.4282348209437189D+00, & 0.4282348209437190D+00 /) c = (/ & 0.4951734598011705D+00, & 0.0096530803976590D+00, & 0.4951734598011703D+00, & 0.9617211695143174D+00, & 0.0191394152428414D+00, & 0.0191394152428409D+00, & 0.8315416244168033D+00, & 0.0347236204823275D+00, & 0.1337347551008689D+00, & 0.1337347551008692D+00, & 0.0347236204823274D+00, & 0.8315416244168033D+00, & 0.3333333333333333D+00, & 0.6357241363774714D+00, & 0.0375827273411916D+00, & 0.3266931362813368D+00, & 0.3266931362813369D+00, & 0.0375827273411916D+00, & 0.6357241363774713D+00, & 0.6310299746295069D+00, & 0.1844850126852466D+00, & 0.1844850126852462D+00, & 0.4282348209437189D+00, & 0.1435303581125623D+00, & 0.4282348209437188D+00 /) w = (/ & 0.0097925904984183D+00, & 0.0097925904984183D+00, & 0.0097925904984183D+00, & 0.0063853592301187D+00, & 0.0063853592301187D+00, & 0.0063853592301187D+00, & 0.0289622814632563D+00, & 0.0289622814632563D+00, & 0.0289622814632563D+00, & 0.0289622814632563D+00, & 0.0289622814632563D+00, & 0.0289622814632563D+00, & 0.0836148743739739D+00, & 0.0387390490860189D+00, & 0.0387390490860189D+00, & 0.0387390490860189D+00, & 0.0387390490860189D+00, & 0.0387390490860189D+00, & 0.0387390490860189D+00, & 0.0786337697463773D+00, & 0.0786337697463773D+00, & 0.0786337697463773D+00, & 0.0752473279685440D+00, & 0.0752473279685440D+00, & 0.0752473279685440D+00 /) return end subroutine rule11 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule11() returns the rule of precision 11. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0308468956355879D+00, & 0.9383062087288239D+00, & 0.0308468956355883D+00, & 0.4987801651784607D+00, & 0.4987801651784607D+00, & 0.0024396696430784D+00, & 0.1593036198376935D+00, & 0.8263297175927509D+00, & 0.0143666625695557D+00, & 0.8263297175927509D+00, & 0.1593036198376935D+00, & 0.0143666625695554D+00, & 0.3333333333333333D+00, & 0.1132078272866939D+00, & 0.7735843454266120D+00, & 0.1132078272866941D+00, & 0.4366550163931761D+00, & 0.4366550163931761D+00, & 0.1266899672136477D+00, & 0.2144834586192693D+00, & 0.5710330827614613D+00, & 0.2144834586192694D+00, & 0.3106312163134631D+00, & 0.6417047167143861D+00, & 0.0476640669721508D+00, & 0.6417047167143860D+00, & 0.3106312163134631D+00, & 0.0476640669721507D+00 /) b = (/ & 0.0308468956355882D+00, & 0.0308468956355879D+00, & 0.9383062087288241D+00, & 0.0024396696430785D+00, & 0.4987801651784608D+00, & 0.4987801651784610D+00, & 0.0143666625695556D+00, & 0.1593036198376935D+00, & 0.8263297175927511D+00, & 0.0143666625695556D+00, & 0.8263297175927511D+00, & 0.1593036198376938D+00, & 0.3333333333333334D+00, & 0.1132078272866941D+00, & 0.1132078272866939D+00, & 0.7735843454266123D+00, & 0.1266899672136478D+00, & 0.4366550163931761D+00, & 0.4366550163931763D+00, & 0.2144834586192694D+00, & 0.2144834586192693D+00, & 0.5710330827614615D+00, & 0.0476640669721508D+00, & 0.3106312163134631D+00, & 0.6417047167143863D+00, & 0.0476640669721508D+00, & 0.6417047167143861D+00, & 0.3106312163134634D+00 /) c = (/ & 0.9383062087288240D+00, & 0.0308468956355883D+00, & 0.0308468956355876D+00, & 0.4987801651784608D+00, & 0.0024396696430785D+00, & 0.4987801651784606D+00, & 0.8263297175927509D+00, & 0.0143666625695556D+00, & 0.1593036198376933D+00, & 0.1593036198376935D+00, & 0.0143666625695554D+00, & 0.8263297175927509D+00, & 0.3333333333333333D+00, & 0.7735843454266120D+00, & 0.1132078272866941D+00, & 0.1132078272866937D+00, & 0.4366550163931761D+00, & 0.1266899672136478D+00, & 0.4366550163931761D+00, & 0.5710330827614614D+00, & 0.2144834586192694D+00, & 0.2144834586192691D+00, & 0.6417047167143861D+00, & 0.0476640669721508D+00, & 0.3106312163134629D+00, & 0.3106312163134632D+00, & 0.0476640669721508D+00, & 0.6417047167143859D+00 /) w = (/ & 0.0122492969507080D+00, & 0.0122492969507080D+00, & 0.0122492969507080D+00, & 0.0124654918738814D+00, & 0.0124654918738814D+00, & 0.0124654918738814D+00, & 0.0145576233378092D+00, & 0.0145576233378092D+00, & 0.0145576233378092D+00, & 0.0145576233378092D+00, & 0.0145576233378092D+00, & 0.0145576233378092D+00, & 0.0814451347093513D+00, & 0.0401292423813083D+00, & 0.0401292423813083D+00, & 0.0401292423813083D+00, & 0.0630948721598987D+00, & 0.0630948721598987D+00, & 0.0630948721598987D+00, & 0.0678451077436951D+00, & 0.0678451077436951D+00, & 0.0678451077436951D+00, & 0.0406428486558865D+00, & 0.0406428486558865D+00, & 0.0406428486558865D+00, & 0.0406428486558865D+00, & 0.0406428486558865D+00, & 0.0406428486558865D+00 /) return end subroutine rule12 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule12() returns the rule of precision 12. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2714625070149260D+00, & 0.4570749859701477D+00, & 0.2714625070149261D+00, & 0.1092578276593542D+00, & 0.7814843446812912D+00, & 0.1092578276593545D+00, & 0.4401116486585931D+00, & 0.4401116486585931D+00, & 0.1197767026828138D+00, & 0.2554542286385173D+00, & 0.6282497516835561D+00, & 0.1162960196779266D+00, & 0.6282497516835561D+00, & 0.2554542286385174D+00, & 0.1162960196779265D+00, & 0.1272797172335894D+00, & 0.8513377925102400D+00, & 0.0213824902561707D+00, & 0.8513377925102400D+00, & 0.1272797172335894D+00, & 0.0213824902561704D+00, & 0.2916556797383409D+00, & 0.6853101639063919D+00, & 0.0230341563552672D+00, & 0.6853101639063919D+00, & 0.2916556797383410D+00, & 0.0230341563552670D+00, & 0.4882037509455415D+00, & 0.4882037509455415D+00, & 0.0235924981089169D+00, & 0.0246463634363355D+00, & 0.9507072731273287D+00, & 0.0246463634363359D+00 /) b = (/ & 0.2714625070149262D+00, & 0.2714625070149261D+00, & 0.4570749859701479D+00, & 0.1092578276593545D+00, & 0.1092578276593542D+00, & 0.7814843446812915D+00, & 0.1197767026828138D+00, & 0.4401116486585931D+00, & 0.4401116486585933D+00, & 0.1162960196779266D+00, & 0.2554542286385174D+00, & 0.6282497516835562D+00, & 0.1162960196779266D+00, & 0.6282497516835562D+00, & 0.2554542286385176D+00, & 0.0213824902561706D+00, & 0.1272797172335893D+00, & 0.8513377925102402D+00, & 0.0213824902561706D+00, & 0.8513377925102402D+00, & 0.1272797172335897D+00, & 0.0230341563552672D+00, & 0.2916556797383410D+00, & 0.6853101639063921D+00, & 0.0230341563552672D+00, & 0.6853101639063920D+00, & 0.2916556797383412D+00, & 0.0235924981089169D+00, & 0.4882037509455416D+00, & 0.4882037509455417D+00, & 0.0246463634363358D+00, & 0.0246463634363355D+00, & 0.9507072731273288D+00 /) c = (/ & 0.4570749859701478D+00, & 0.2714625070149261D+00, & 0.2714625070149260D+00, & 0.7814843446812914D+00, & 0.1092578276593545D+00, & 0.1092578276593540D+00, & 0.4401116486585931D+00, & 0.1197767026828138D+00, & 0.4401116486585929D+00, & 0.6282497516835560D+00, & 0.1162960196779265D+00, & 0.2554542286385172D+00, & 0.2554542286385172D+00, & 0.1162960196779265D+00, & 0.6282497516835559D+00, & 0.8513377925102400D+00, & 0.0213824902561707D+00, & 0.1272797172335890D+00, & 0.1272797172335894D+00, & 0.0213824902561704D+00, & 0.8513377925102400D+00, & 0.6853101639063919D+00, & 0.0230341563552671D+00, & 0.2916556797383407D+00, & 0.2916556797383409D+00, & 0.0230341563552671D+00, & 0.6853101639063917D+00, & 0.4882037509455416D+00, & 0.0235924981089169D+00, & 0.4882037509455414D+00, & 0.9507072731273288D+00, & 0.0246463634363358D+00, & 0.0246463634363353D+00 /) w = (/ & 0.0625412131959027D+00, & 0.0625412131959027D+00, & 0.0625412131959027D+00, & 0.0284860520688775D+00, & 0.0284860520688775D+00, & 0.0284860520688775D+00, & 0.0499183349280609D+00, & 0.0499183349280609D+00, & 0.0499183349280609D+00, & 0.0432273636594142D+00, & 0.0432273636594142D+00, & 0.0432273636594142D+00, & 0.0432273636594142D+00, & 0.0432273636594142D+00, & 0.0432273636594142D+00, & 0.0150836775765114D+00, & 0.0150836775765114D+00, & 0.0150836775765114D+00, & 0.0150836775765114D+00, & 0.0150836775765114D+00, & 0.0150836775765114D+00, & 0.0217835850386075D+00, & 0.0217835850386075D+00, & 0.0217835850386075D+00, & 0.0217835850386075D+00, & 0.0217835850386075D+00, & 0.0217835850386075D+00, & 0.0242668380814520D+00, & 0.0242668380814520D+00, & 0.0242668380814520D+00, & 0.0079316425099736D+00, & 0.0079316425099736D+00, & 0.0079316425099736D+00 /) return end subroutine rule13 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule13() returns the rule of precision 13. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4961358947410461D+00, & 0.4961358947410460D+00, & 0.0077282105179078D+00, & 0.4696086896534919D+00, & 0.4696086896534918D+00, & 0.0607826206930162D+00, & 0.2311102849490822D+00, & 0.5377794301018355D+00, & 0.2311102849490823D+00, & 0.2920786885766364D+00, & 0.6889333070396045D+00, & 0.0189880043837591D+00, & 0.6889333070396045D+00, & 0.2920786885766364D+00, & 0.0189880043837589D+00, & 0.3333333333333333D+00, & 0.2667452533103511D+00, & 0.6355187156236324D+00, & 0.0977360310660165D+00, & 0.6355187156236323D+00, & 0.2667452533103513D+00, & 0.0977360310660164D+00, & 0.4144775702790545D+00, & 0.4144775702790545D+00, & 0.1710448594418908D+00, & 0.1135599125721331D+00, & 0.7728801748557336D+00, & 0.1135599125721334D+00, & 0.1267997757838373D+00, & 0.8512338800096334D+00, & 0.0219663442065294D+00, & 0.8512338800096334D+00, & 0.1267997757838374D+00, & 0.0219663442065290D+00, & 0.0248959314912162D+00, & 0.9502081370175671D+00, & 0.0248959314912167D+00 /) b = (/ & 0.0077282105179079D+00, & 0.4961358947410461D+00, & 0.4961358947410462D+00, & 0.0607826206930162D+00, & 0.4696086896534920D+00, & 0.4696086896534921D+00, & 0.2311102849490824D+00, & 0.2311102849490823D+00, & 0.5377794301018356D+00, & 0.0189880043837590D+00, & 0.2920786885766364D+00, & 0.6889333070396048D+00, & 0.0189880043837590D+00, & 0.6889333070396046D+00, & 0.2920786885766367D+00, & 0.3333333333333334D+00, & 0.0977360310660166D+00, & 0.2667452533103512D+00, & 0.6355187156236326D+00, & 0.0977360310660166D+00, & 0.6355187156236323D+00, & 0.2667452533103514D+00, & 0.1710448594418909D+00, & 0.4144775702790546D+00, & 0.4144775702790547D+00, & 0.1135599125721333D+00, & 0.1135599125721331D+00, & 0.7728801748557337D+00, & 0.0219663442065293D+00, & 0.1267997757838373D+00, & 0.8512338800096335D+00, & 0.0219663442065293D+00, & 0.8512338800096335D+00, & 0.1267997757838377D+00, & 0.0248959314912165D+00, & 0.0248959314912162D+00, & 0.9502081370175673D+00 /) c = (/ & 0.4961358947410460D+00, & 0.0077282105179078D+00, & 0.4961358947410459D+00, & 0.4696086896534919D+00, & 0.0607826206930161D+00, & 0.4696086896534917D+00, & 0.5377794301018354D+00, & 0.2311102849490823D+00, & 0.2311102849490821D+00, & 0.6889333070396045D+00, & 0.0189880043837590D+00, & 0.2920786885766361D+00, & 0.2920786885766364D+00, & 0.0189880043837589D+00, & 0.6889333070396044D+00, & 0.3333333333333333D+00, & 0.6355187156236323D+00, & 0.0977360310660164D+00, & 0.2667452533103509D+00, & 0.2667452533103511D+00, & 0.0977360310660164D+00, & 0.6355187156236322D+00, & 0.4144775702790546D+00, & 0.1710448594418909D+00, & 0.4144775702790545D+00, & 0.7728801748557337D+00, & 0.1135599125721334D+00, & 0.1135599125721329D+00, & 0.8512338800096335D+00, & 0.0219663442065293D+00, & 0.1267997757838371D+00, & 0.1267997757838373D+00, & 0.0219663442065291D+00, & 0.8512338800096333D+00, & 0.9502081370175672D+00, & 0.0248959314912166D+00, & 0.0248959314912159D+00 /) w = (/ & 0.0099414763610726D+00, & 0.0099414763610726D+00, & 0.0099414763610726D+00, & 0.0327812416037230D+00, & 0.0327812416037230D+00, & 0.0327812416037230D+00, & 0.0460624095927782D+00, & 0.0460624095927782D+00, & 0.0460624095927782D+00, & 0.0181254986462009D+00, & 0.0181254986462009D+00, & 0.0181254986462009D+00, & 0.0181254986462009D+00, & 0.0181254986462009D+00, & 0.0181254986462009D+00, & 0.0516226466642908D+00, & 0.0372119604572615D+00, & 0.0372119604572615D+00, & 0.0372119604572615D+00, & 0.0372119604572615D+00, & 0.0372119604572615D+00, & 0.0372119604572615D+00, & 0.0469470955421552D+00, & 0.0469470955421552D+00, & 0.0469470955421552D+00, & 0.0309030979757598D+00, & 0.0309030979757598D+00, & 0.0309030979757598D+00, & 0.0153930726837822D+00, & 0.0153930726837822D+00, & 0.0153930726837822D+00, & 0.0153930726837822D+00, & 0.0153930726837822D+00, & 0.0153930726837822D+00, & 0.0080293997952584D+00, & 0.0080293997952584D+00, & 0.0080293997952584D+00 /) return end subroutine rule14 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule14() returns the rule of precision 14. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4176447193404539D+00, & 0.4176447193404539D+00, & 0.1647105613190921D+00, & 0.2983728821362577D+00, & 0.6869801678080878D+00, & 0.0146469500556545D+00, & 0.6869801678080878D+00, & 0.2983728821362577D+00, & 0.0146469500556543D+00, & 0.0617998830908725D+00, & 0.8764002338182547D+00, & 0.0617998830908729D+00, & 0.3368614597963450D+00, & 0.5702222908466831D+00, & 0.0929162493569718D+00, & 0.5702222908466831D+00, & 0.3368614597963450D+00, & 0.0929162493569718D+00, & 0.2734775283088386D+00, & 0.4530449433823227D+00, & 0.2734775283088388D+00, & 0.1772055324125434D+00, & 0.6455889351749130D+00, & 0.1772055324125437D+00, & 0.0193909612487009D+00, & 0.9612180775025979D+00, & 0.0193909612487014D+00, & 0.4889639103621786D+00, & 0.4889639103621787D+00, & 0.0220721792756427D+00, & 0.1722666878213555D+00, & 0.7706085547749963D+00, & 0.0571247574036480D+00, & 0.7706085547749965D+00, & 0.1722666878213556D+00, & 0.0571247574036478D+00, & 0.1189744976969568D+00, & 0.8797571713701711D+00, & 0.0012683309328722D+00, & 0.8797571713701712D+00, & 0.1189744976969569D+00, & 0.0012683309328719D+00 /) b = (/ & 0.1647105613190922D+00, & 0.4176447193404541D+00, & 0.4176447193404541D+00, & 0.0146469500556545D+00, & 0.2983728821362578D+00, & 0.6869801678080880D+00, & 0.0146469500556545D+00, & 0.6869801678080880D+00, & 0.2983728821362580D+00, & 0.0617998830908728D+00, & 0.0617998830908724D+00, & 0.8764002338182548D+00, & 0.0929162493569719D+00, & 0.3368614597963451D+00, & 0.5702222908466833D+00, & 0.0929162493569719D+00, & 0.5702222908466833D+00, & 0.3368614597963452D+00, & 0.2734775283088388D+00, & 0.2734775283088387D+00, & 0.4530449433823228D+00, & 0.1772055324125436D+00, & 0.1772055324125434D+00, & 0.6455889351749131D+00, & 0.0193909612487012D+00, & 0.0193909612487009D+00, & 0.9612180775025979D+00, & 0.0220721792756428D+00, & 0.4889639103621786D+00, & 0.4889639103621788D+00, & 0.0571247574036480D+00, & 0.1722666878213556D+00, & 0.7706085547749967D+00, & 0.0571247574036480D+00, & 0.7706085547749966D+00, & 0.1722666878213558D+00, & 0.0012683309328721D+00, & 0.1189744976969568D+00, & 0.8797571713701712D+00, & 0.0012683309328721D+00, & 0.8797571713701712D+00, & 0.1189744976969572D+00 /) c = (/ & 0.4176447193404539D+00, & 0.1647105613190921D+00, & 0.4176447193404539D+00, & 0.6869801678080878D+00, & 0.0146469500556544D+00, & 0.2983728821362575D+00, & 0.2983728821362577D+00, & 0.0146469500556543D+00, & 0.6869801678080877D+00, & 0.8764002338182547D+00, & 0.0617998830908728D+00, & 0.0617998830908723D+00, & 0.5702222908466831D+00, & 0.0929162493569718D+00, & 0.3368614597963449D+00, & 0.3368614597963450D+00, & 0.0929162493569716D+00, & 0.5702222908466831D+00, & 0.4530449433823226D+00, & 0.2734775283088386D+00, & 0.2734775283088385D+00, & 0.6455889351749130D+00, & 0.1772055324125436D+00, & 0.1772055324125432D+00, & 0.9612180775025979D+00, & 0.0193909612487012D+00, & 0.0193909612487008D+00, & 0.4889639103621786D+00, & 0.0220721792756427D+00, & 0.4889639103621784D+00, & 0.7706085547749965D+00, & 0.0571247574036481D+00, & 0.1722666878213553D+00, & 0.1722666878213555D+00, & 0.0571247574036479D+00, & 0.7706085547749963D+00, & 0.8797571713701712D+00, & 0.0012683309328721D+00, & 0.1189744976969566D+00, & 0.1189744976969567D+00, & 0.0012683309328719D+00, & 0.8797571713701708D+00 /) w = (/ & 0.0327883535441254D+00, & 0.0327883535441254D+00, & 0.0327883535441254D+00, & 0.0144363081135338D+00, & 0.0144363081135338D+00, & 0.0144363081135338D+00, & 0.0144363081135338D+00, & 0.0144363081135338D+00, & 0.0144363081135338D+00, & 0.0144336996697767D+00, & 0.0144336996697767D+00, & 0.0144336996697767D+00, & 0.0385715107870607D+00, & 0.0385715107870607D+00, & 0.0385715107870607D+00, & 0.0385715107870607D+00, & 0.0385715107870607D+00, & 0.0385715107870607D+00, & 0.0517741045072916D+00, & 0.0517741045072916D+00, & 0.0517741045072916D+00, & 0.0421625887369930D+00, & 0.0421625887369930D+00, & 0.0421625887369930D+00, & 0.0049234036024001D+00, & 0.0049234036024001D+00, & 0.0049234036024001D+00, & 0.0218835813694289D+00, & 0.0218835813694289D+00, & 0.0218835813694289D+00, & 0.0246657532125637D+00, & 0.0246657532125637D+00, & 0.0246657532125637D+00, & 0.0246657532125637D+00, & 0.0246657532125637D+00, & 0.0246657532125637D+00, & 0.0050102288385007D+00, & 0.0050102288385007D+00, & 0.0050102288385007D+00, & 0.0050102288385007D+00, & 0.0050102288385007D+00, & 0.0050102288385007D+00 /) return end subroutine rule15 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule15() returns the rule of precision 15. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1299782299330778D+00, & 0.7400435401338442D+00, & 0.1299782299330779D+00, & 0.3333333333333333D+00, & 0.4600769492970597D+00, & 0.4600769492970597D+00, & 0.0798461014058805D+00, & 0.1823217834071913D+00, & 0.7330839951106168D+00, & 0.0845942214821919D+00, & 0.7330839951106169D+00, & 0.1823217834071914D+00, & 0.0845942214821916D+00, & 0.1502003840652387D+00, & 0.8337725261484157D+00, & 0.0160270897863456D+00, & 0.8337725261484158D+00, & 0.1502003840652388D+00, & 0.0160270897863453D+00, & 0.3231113151637127D+00, & 0.5792382424060449D+00, & 0.0976504424302423D+00, & 0.5792382424060449D+00, & 0.3231113151637127D+00, & 0.0976504424302423D+00, & 0.4916858166302972D+00, & 0.4916858166302972D+00, & 0.0166283667394055D+00, & 0.2215323407951419D+00, & 0.5569353184097160D+00, & 0.2215323407951421D+00, & 0.3969337374090606D+00, & 0.3969337374090606D+00, & 0.2061325251818788D+00, & 0.3079476814836729D+00, & 0.6735980666116939D+00, & 0.0184542519046332D+00, & 0.6735980666116940D+00, & 0.3079476814836729D+00, & 0.0184542519046331D+00, & 0.0563419176961000D+00, & 0.8873161646077997D+00, & 0.0563419176961004D+00, & 0.0380352293011093D+00, & 0.9608512354248769D+00, & 0.0011135352740139D+00, & 0.9608512354248770D+00, & 0.0380352293011093D+00, & 0.0011135352740135D+00 /) b = (/ & 0.1299782299330780D+00, & 0.1299782299330778D+00, & 0.7400435401338445D+00, & 0.3333333333333334D+00, & 0.0798461014058806D+00, & 0.4600769492970598D+00, & 0.4600769492970599D+00, & 0.0845942214821918D+00, & 0.1823217834071913D+00, & 0.7330839951106169D+00, & 0.0845942214821918D+00, & 0.7330839951106171D+00, & 0.1823217834071916D+00, & 0.0160270897863455D+00, & 0.1502003840652387D+00, & 0.8337725261484159D+00, & 0.0160270897863455D+00, & 0.8337725261484159D+00, & 0.1502003840652391D+00, & 0.0976504424302424D+00, & 0.3231113151637127D+00, & 0.5792382424060452D+00, & 0.0976504424302424D+00, & 0.5792382424060450D+00, & 0.3231113151637129D+00, & 0.0166283667394056D+00, & 0.4916858166302973D+00, & 0.4916858166302975D+00, & 0.2215323407951421D+00, & 0.2215323407951420D+00, & 0.5569353184097161D+00, & 0.2061325251818789D+00, & 0.3969337374090606D+00, & 0.3969337374090607D+00, & 0.0184542519046332D+00, & 0.3079476814836729D+00, & 0.6735980666116942D+00, & 0.0184542519046332D+00, & 0.6735980666116941D+00, & 0.3079476814836731D+00, & 0.0563419176961003D+00, & 0.0563419176960999D+00, & 0.8873161646077998D+00, & 0.0011135352740137D+00, & 0.0380352293011093D+00, & 0.9608512354248772D+00, & 0.0011135352740137D+00, & 0.9608512354248772D+00, & 0.0380352293011096D+00 /) c = (/ & 0.7400435401338443D+00, & 0.1299782299330780D+00, & 0.1299782299330775D+00, & 0.3333333333333333D+00, & 0.4600769492970597D+00, & 0.0798461014058806D+00, & 0.4600769492970595D+00, & 0.7330839951106168D+00, & 0.0845942214821918D+00, & 0.1823217834071911D+00, & 0.1823217834071912D+00, & 0.0845942214821916D+00, & 0.7330839951106169D+00, & 0.8337725261484158D+00, & 0.0160270897863456D+00, & 0.1502003840652385D+00, & 0.1502003840652387D+00, & 0.0160270897863453D+00, & 0.8337725261484157D+00, & 0.5792382424060450D+00, & 0.0976504424302423D+00, & 0.3231113151637125D+00, & 0.3231113151637127D+00, & 0.0976504424302423D+00, & 0.5792382424060449D+00, & 0.4916858166302972D+00, & 0.0166283667394055D+00, & 0.4916858166302970D+00, & 0.5569353184097159D+00, & 0.2215323407951420D+00, & 0.2215323407951418D+00, & 0.3969337374090605D+00, & 0.2061325251818788D+00, & 0.3969337374090605D+00, & 0.6735980666116940D+00, & 0.0184542519046332D+00, & 0.3079476814836727D+00, & 0.3079476814836729D+00, & 0.0184542519046330D+00, & 0.6735980666116937D+00, & 0.8873161646077997D+00, & 0.0563419176961003D+00, & 0.0563419176960998D+00, & 0.9608512354248770D+00, & 0.0011135352740138D+00, & 0.0380352293011089D+00, & 0.0380352293011092D+00, & 0.0011135352740136D+00, & 0.9608512354248769D+00 /) w = (/ & 0.0073975040670461D+00, & 0.0073975040670461D+00, & 0.0073975040670461D+00, & 0.0297304197480713D+00, & 0.0215940879364384D+00, & 0.0215940879364384D+00, & 0.0215940879364384D+00, & 0.0242300087831256D+00, & 0.0242300087831256D+00, & 0.0242300087831256D+00, & 0.0242300087831256D+00, & 0.0242300087831256D+00, & 0.0242300087831256D+00, & 0.0112285042988781D+00, & 0.0112285042988781D+00, & 0.0112285042988781D+00, & 0.0112285042988781D+00, & 0.0112285042988781D+00, & 0.0112285042988781D+00, & 0.0310752204705109D+00, & 0.0310752204705109D+00, & 0.0310752204705109D+00, & 0.0310752204705109D+00, & 0.0310752204705109D+00, & 0.0310752204705109D+00, & 0.0158322763500218D+00, & 0.0158322763500218D+00, & 0.0158322763500218D+00, & 0.0462872861051981D+00, & 0.0462872861051981D+00, & 0.0462872861051981D+00, & 0.0463360413912072D+00, & 0.0463360413912072D+00, & 0.0463360413912072D+00, & 0.0164367620928279D+00, & 0.0164367620928279D+00, & 0.0164367620928279D+00, & 0.0164367620928279D+00, & 0.0164367620928279D+00, & 0.0164367620928279D+00, & 0.0150844742475971D+00, & 0.0150844742475971D+00, & 0.0150844742475971D+00, & 0.0024752660145579D+00, & 0.0024752660145579D+00, & 0.0024752660145579D+00, & 0.0024752660145579D+00, & 0.0024752660145579D+00, & 0.0024752660145579D+00 /) return end subroutine rule16 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule16() returns the rule of precision 16. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4137694858270852D+00, & 0.5765655597692547D+00, & 0.0096649544036603D+00, & 0.5765655597692546D+00, & 0.4137694858270852D+00, & 0.0096649544036602D+00, & 0.3041794482294797D+00, & 0.6655146084153339D+00, & 0.0303059433551864D+00, & 0.6655146084153339D+00, & 0.3041794482294798D+00, & 0.0303059433551863D+00, & 0.0666744722402382D+00, & 0.8666510555195234D+00, & 0.0666744722402385D+00, & 0.0896090890227058D+00, & 0.8995779382011904D+00, & 0.0108129727761038D+00, & 0.8995779382011904D+00, & 0.0896090890227059D+00, & 0.0108129727761035D+00, & 0.2966153724003829D+00, & 0.5967314670634685D+00, & 0.1066531605361485D+00, & 0.5967314670634686D+00, & 0.2966153724003830D+00, & 0.1066531605361483D+00, & 0.2413216807013783D+00, & 0.5173566385972432D+00, & 0.2413216807013784D+00, & 0.4127980959552237D+00, & 0.4127980959552237D+00, & 0.1744038080895526D+00, & 0.1697633551502897D+00, & 0.7788823295056971D+00, & 0.0513543153440132D+00, & 0.7788823295056972D+00, & 0.1697633551502898D+00, & 0.0513543153440130D+00, & 0.1500637365870350D+00, & 0.6998725268259297D+00, & 0.1500637365870353D+00, & 0.2140487799258473D+00, & 0.7822542773667971D+00, & 0.0036969427073556D+00, & 0.7822542773667971D+00, & 0.2140487799258473D+00, & 0.0036969427073554D+00, & 0.4695480309966850D+00, & 0.4695480309966850D+00, & 0.0609039380066300D+00, & 0.3333333333333333D+00, & 0.0170416294057183D+00, & 0.9659167411885631D+00, & 0.0170416294057187D+00 /) b = (/ & 0.0096649544036603D+00, & 0.4137694858270852D+00, & 0.5765655597692547D+00, & 0.0096649544036603D+00, & 0.5765655597692547D+00, & 0.4137694858270854D+00, & 0.0303059433551864D+00, & 0.3041794482294797D+00, & 0.6655146084153342D+00, & 0.0303059433551864D+00, & 0.6655146084153339D+00, & 0.3041794482294800D+00, & 0.0666744722402385D+00, & 0.0666744722402381D+00, & 0.8666510555195236D+00, & 0.0108129727761038D+00, & 0.0896090890227058D+00, & 0.8995779382011906D+00, & 0.0108129727761038D+00, & 0.8995779382011906D+00, & 0.0896090890227062D+00, & 0.1066531605361485D+00, & 0.2966153724003830D+00, & 0.5967314670634687D+00, & 0.1066531605361485D+00, & 0.5967314670634686D+00, & 0.2966153724003832D+00, & 0.2413216807013785D+00, & 0.2413216807013784D+00, & 0.5173566385972433D+00, & 0.1744038080895527D+00, & 0.4127980959552238D+00, & 0.4127980959552238D+00, & 0.0513543153440131D+00, & 0.1697633551502898D+00, & 0.7788823295056972D+00, & 0.0513543153440131D+00, & 0.7788823295056971D+00, & 0.1697633551502900D+00, & 0.1500637365870353D+00, & 0.1500637365870350D+00, & 0.6998725268259298D+00, & 0.0036969427073556D+00, & 0.2140487799258473D+00, & 0.7822542773667974D+00, & 0.0036969427073556D+00, & 0.7822542773667972D+00, & 0.2140487799258476D+00, & 0.0609039380066301D+00, & 0.4695480309966850D+00, & 0.4695480309966852D+00, & 0.3333333333333334D+00, & 0.0170416294057186D+00, & 0.0170416294057182D+00, & 0.9659167411885633D+00 /) c = (/ & 0.5765655597692546D+00, & 0.0096649544036601D+00, & 0.4137694858270851D+00, & 0.4137694858270851D+00, & 0.0096649544036601D+00, & 0.5765655597692544D+00, & 0.6655146084153339D+00, & 0.0303059433551863D+00, & 0.3041794482294794D+00, & 0.3041794482294797D+00, & 0.0303059433551863D+00, & 0.6655146084153338D+00, & 0.8666510555195234D+00, & 0.0666744722402385D+00, & 0.0666744722402378D+00, & 0.8995779382011905D+00, & 0.0108129727761038D+00, & 0.0896090890227056D+00, & 0.0896090890227059D+00, & 0.0108129727761035D+00, & 0.8995779382011904D+00, & 0.5967314670634686D+00, & 0.1066531605361485D+00, & 0.2966153724003828D+00, & 0.2966153724003829D+00, & 0.1066531605361484D+00, & 0.5967314670634685D+00, & 0.5173566385972432D+00, & 0.2413216807013784D+00, & 0.2413216807013782D+00, & 0.4127980959552237D+00, & 0.1744038080895526D+00, & 0.4127980959552236D+00, & 0.7788823295056971D+00, & 0.0513543153440131D+00, & 0.1697633551502895D+00, & 0.1697633551502896D+00, & 0.0513543153440131D+00, & 0.7788823295056969D+00, & 0.6998725268259297D+00, & 0.1500637365870353D+00, & 0.1500637365870349D+00, & 0.7822542773667971D+00, & 0.0036969427073556D+00, & 0.2140487799258469D+00, & 0.2140487799258473D+00, & 0.0036969427073555D+00, & 0.7822542773667970D+00, & 0.4695480309966850D+00, & 0.0609039380066300D+00, & 0.4695480309966847D+00, & 0.3333333333333333D+00, & 0.9659167411885632D+00, & 0.0170416294057187D+00, & 0.0170416294057180D+00 /) w = (/ & 0.0081822105532221D+00, & 0.0081822105532221D+00, & 0.0081822105532221D+00, & 0.0081822105532221D+00, & 0.0081822105532221D+00, & 0.0081822105532221D+00, & 0.0139836071246536D+00, & 0.0139836071246536D+00, & 0.0139836071246536D+00, & 0.0139836071246536D+00, & 0.0139836071246536D+00, & 0.0139836071246536D+00, & 0.0124254255955610D+00, & 0.0124254255955610D+00, & 0.0124254255955610D+00, & 0.0057518699704972D+00, & 0.0057518699704972D+00, & 0.0057518699704972D+00, & 0.0057518699704972D+00, & 0.0057518699704972D+00, & 0.0057518699704972D+00, & 0.0316460616819832D+00, & 0.0316460616819832D+00, & 0.0316460616819832D+00, & 0.0316460616819832D+00, & 0.0316460616819832D+00, & 0.0316460616819832D+00, & 0.0411840410697925D+00, & 0.0411840410697925D+00, & 0.0411840410697925D+00, & 0.0409852197868154D+00, & 0.0409852197868154D+00, & 0.0409852197868154D+00, & 0.0176530810471033D+00, & 0.0176530810471033D+00, & 0.0176530810471033D+00, & 0.0176530810471033D+00, & 0.0176530810471033D+00, & 0.0176530810471033D+00, & 0.0287834967027489D+00, & 0.0287834967027489D+00, & 0.0287834967027489D+00, & 0.0046146906397291D+00, & 0.0046146906397291D+00, & 0.0046146906397291D+00, & 0.0046146906397291D+00, & 0.0046146906397291D+00, & 0.0046146906397291D+00, & 0.0270936694677105D+00, & 0.0270936694677105D+00, & 0.0270936694677105D+00, & 0.0462279103141913D+00, & 0.0037891352382642D+00, & 0.0037891352382642D+00, & 0.0037891352382642D+00 /) return end subroutine rule17 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule17() returns the rule of precision 17. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4171034443615992D+00, & 0.4171034443615992D+00, & 0.1657931112768016D+00, & 0.0725054707990024D+00, & 0.9159193532978169D+00, & 0.0115751759031809D+00, & 0.9159193532978169D+00, & 0.0725054707990024D+00, & 0.0115751759031804D+00, & 0.1803581162663705D+00, & 0.6392837674672587D+00, & 0.1803581162663708D+00, & 0.4154754592952291D+00, & 0.5712948679446841D+00, & 0.0132296727600869D+00, & 0.5712948679446841D+00, & 0.4154754592952290D+00, & 0.0132296727600868D+00, & 0.2717918700553548D+00, & 0.7150722591106424D+00, & 0.0131358708340029D+00, & 0.7150722591106424D+00, & 0.2717918700553550D+00, & 0.0131358708340026D+00, & 0.2992189424769703D+00, & 0.5432755795961597D+00, & 0.1575054779268699D+00, & 0.5432755795961597D+00, & 0.2992189424769702D+00, & 0.1575054779268698D+00, & 0.2857065024365866D+00, & 0.4285869951268267D+00, & 0.2857065024365867D+00, & 0.3062815917461865D+00, & 0.6263690303864522D+00, & 0.0673493778673613D+00, & 0.6263690303864522D+00, & 0.3062815917461865D+00, & 0.0673493778673612D+00, & 0.1687225134952594D+00, & 0.7532351459364581D+00, & 0.0780423405682825D+00, & 0.7532351459364581D+00, & 0.1687225134952594D+00, & 0.0780423405682823D+00, & 0.0666540634795968D+00, & 0.8666918730408060D+00, & 0.0666540634795971D+00, & 0.1591922874727927D+00, & 0.8247900701650880D+00, & 0.0160176423621194D+00, & 0.8247900701650880D+00, & 0.1591922874727927D+00, & 0.0160176423621192D+00, & 0.0147554916607538D+00, & 0.9704890166784920D+00, & 0.0147554916607542D+00, & 0.4655978716188903D+00, & 0.4655978716188902D+00, & 0.0688042567622194D+00 /) b = (/ & 0.1657931112768017D+00, & 0.4171034443615993D+00, & 0.4171034443615994D+00, & 0.0115751759031807D+00, & 0.0725054707990024D+00, & 0.9159193532978170D+00, & 0.0115751759031807D+00, & 0.9159193532978170D+00, & 0.0725054707990027D+00, & 0.1803581162663707D+00, & 0.1803581162663706D+00, & 0.6392837674672588D+00, & 0.0132296727600870D+00, & 0.4154754592952291D+00, & 0.5712948679446843D+00, & 0.0132296727600870D+00, & 0.5712948679446841D+00, & 0.4154754592952293D+00, & 0.0131358708340028D+00, & 0.2717918700553549D+00, & 0.7150722591106425D+00, & 0.0131358708340028D+00, & 0.7150722591106424D+00, & 0.2717918700553552D+00, & 0.1575054779268700D+00, & 0.2992189424769703D+00, & 0.5432755795961599D+00, & 0.1575054779268700D+00, & 0.5432755795961599D+00, & 0.2992189424769705D+00, & 0.2857065024365867D+00, & 0.2857065024365867D+00, & 0.4285869951268269D+00, & 0.0673493778673613D+00, & 0.3062815917461865D+00, & 0.6263690303864524D+00, & 0.0673493778673613D+00, & 0.6263690303864524D+00, & 0.3062815917461867D+00, & 0.0780423405682825D+00, & 0.1687225134952594D+00, & 0.7532351459364584D+00, & 0.0780423405682825D+00, & 0.7532351459364582D+00, & 0.1687225134952597D+00, & 0.0666540634795971D+00, & 0.0666540634795968D+00, & 0.8666918730408062D+00, & 0.0160176423621193D+00, & 0.1591922874727927D+00, & 0.8247900701650882D+00, & 0.0160176423621193D+00, & 0.8247900701650882D+00, & 0.1591922874727930D+00, & 0.0147554916607541D+00, & 0.0147554916607538D+00, & 0.9704890166784922D+00, & 0.0688042567622194D+00, & 0.4655978716188904D+00, & 0.4655978716188905D+00 /) c = (/ & 0.4171034443615991D+00, & 0.1657931112768015D+00, & 0.4171034443615990D+00, & 0.9159193532978169D+00, & 0.0115751759031807D+00, & 0.0725054707990022D+00, & 0.0725054707990024D+00, & 0.0115751759031805D+00, & 0.9159193532978168D+00, & 0.6392837674672587D+00, & 0.1803581162663707D+00, & 0.1803581162663704D+00, & 0.5712948679446841D+00, & 0.0132296727600869D+00, & 0.4154754592952288D+00, & 0.4154754592952289D+00, & 0.0132296727600869D+00, & 0.5712948679446839D+00, & 0.7150722591106424D+00, & 0.0131358708340027D+00, & 0.2717918700553547D+00, & 0.2717918700553548D+00, & 0.0131358708340026D+00, & 0.7150722591106422D+00, & 0.5432755795961598D+00, & 0.1575054779268700D+00, & 0.2992189424769702D+00, & 0.2992189424769703D+00, & 0.1575054779268699D+00, & 0.5432755795961597D+00, & 0.4285869951268267D+00, & 0.2857065024365867D+00, & 0.2857065024365865D+00, & 0.6263690303864522D+00, & 0.0673493778673613D+00, & 0.3062815917461863D+00, & 0.3062815917461865D+00, & 0.0673493778673611D+00, & 0.6263690303864521D+00, & 0.7532351459364580D+00, & 0.0780423405682825D+00, & 0.1687225134952591D+00, & 0.1687225134952594D+00, & 0.0780423405682823D+00, & 0.7532351459364579D+00, & 0.8666918730408061D+00, & 0.0666540634795972D+00, & 0.0666540634795967D+00, & 0.8247900701650880D+00, & 0.0160176423621193D+00, & 0.1591922874727923D+00, & 0.1591922874727927D+00, & 0.0160176423621191D+00, & 0.8247900701650878D+00, & 0.9704890166784921D+00, & 0.0147554916607542D+00, & 0.0147554916607536D+00, & 0.4655978716188903D+00, & 0.0688042567622194D+00, & 0.4655978716188902D+00 /) w = (/ & 0.0273109265281021D+00, & 0.0273109265281021D+00, & 0.0273109265281021D+00, & 0.0045843484017359D+00, & 0.0045843484017359D+00, & 0.0045843484017359D+00, & 0.0045843484017359D+00, & 0.0045843484017359D+00, & 0.0045843484017359D+00, & 0.0263126305880180D+00, & 0.0263126305880180D+00, & 0.0263126305880180D+00, & 0.0103984399558395D+00, & 0.0103984399558395D+00, & 0.0103984399558395D+00, & 0.0103984399558395D+00, & 0.0103984399558395D+00, & 0.0103984399558395D+00, & 0.0086922145010012D+00, & 0.0086922145010012D+00, & 0.0086922145010012D+00, & 0.0086922145010012D+00, & 0.0086922145010012D+00, & 0.0086922145010012D+00, & 0.0261716259353370D+00, & 0.0261716259353370D+00, & 0.0261716259353370D+00, & 0.0261716259353370D+00, & 0.0261716259353370D+00, & 0.0261716259353370D+00, & 0.0377162371527953D+00, & 0.0377162371527953D+00, & 0.0377162371527953D+00, & 0.0224877725466911D+00, & 0.0224877725466911D+00, & 0.0224877725466911D+00, & 0.0224877725466911D+00, & 0.0224877725466911D+00, & 0.0224877725466911D+00, & 0.0205578983204545D+00, & 0.0205578983204545D+00, & 0.0205578983204545D+00, & 0.0205578983204545D+00, & 0.0205578983204545D+00, & 0.0205578983204545D+00, & 0.0124590008023054D+00, & 0.0124590008023054D+00, & 0.0124590008023054D+00, & 0.0079783002059296D+00, & 0.0079783002059296D+00, & 0.0079783002059296D+00, & 0.0079783002059296D+00, & 0.0079783002059296D+00, & 0.0079783002059296D+00, & 0.0027738875776376D+00, & 0.0027738875776376D+00, & 0.0027738875776376D+00, & 0.0250194509504974D+00, & 0.0250194509504974D+00, & 0.0250194509504974D+00 /) return end subroutine rule18 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule18() returns the rule of precision 18. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3850440344131636D+00, & 0.5245289252324958D+00, & 0.0904270403543406D+00, & 0.5245289252324957D+00, & 0.3850440344131637D+00, & 0.0904270403543405D+00, & 0.4749182113240457D+00, & 0.4749182113240458D+00, & 0.0501635773519085D+00, & 0.1516385069726047D+00, & 0.6967229860547902D+00, & 0.1516385069726050D+00, & 0.0472761418326517D+00, & 0.9402249256838527D+00, & 0.0124989324834957D+00, & 0.9402249256838527D+00, & 0.0472761418326518D+00, & 0.0124989324834952D+00, & 0.3333333333333333D+00, & 0.3020619577128708D+00, & 0.6439263069481050D+00, & 0.0540117353390243D+00, & 0.6439263069481049D+00, & 0.3020619577128708D+00, & 0.0540117353390241D+00, & 0.2565061597742415D+00, & 0.7329888214065164D+00, & 0.0105050188192420D+00, & 0.7329888214065166D+00, & 0.2565061597742415D+00, & 0.0105050188192418D+00, & 0.4110671018759194D+00, & 0.4110671018759194D+00, & 0.1778657962481610D+00, & 0.1784791255658876D+00, & 0.7553984164057089D+00, & 0.0661224580284036D+00, & 0.7553984164057089D+00, & 0.1784791255658877D+00, & 0.0661224580284032D+00, & 0.2656146099053742D+00, & 0.4687707801892516D+00, & 0.2656146099053743D+00, & 0.0037589443410682D+00, & 0.9924821113178632D+00, & 0.0037589443410687D+00, & 0.2685733063960138D+00, & 0.5823597834782123D+00, & 0.1490669101257739D+00, & 0.5823597834782123D+00, & 0.2685733063960138D+00, & 0.1490669101257737D+00, & 0.4110656686746184D+00, & 0.5772425066507145D+00, & 0.0116918246746671D+00, & 0.5772425066507145D+00, & 0.4110656686746185D+00, & 0.0116918246746671D+00, & 0.1327788302713893D+00, & 0.8528896449496687D+00, & 0.0143315247789422D+00, & 0.8528896449496688D+00, & 0.1327788302713893D+00, & 0.0143315247789417D+00, & 0.0724387055673328D+00, & 0.8551225888653341D+00, & 0.0724387055673332D+00 /) b = (/ & 0.0904270403543407D+00, & 0.3850440344131637D+00, & 0.5245289252324959D+00, & 0.0904270403543407D+00, & 0.5245289252324958D+00, & 0.3850440344131639D+00, & 0.0501635773519086D+00, & 0.4749182113240458D+00, & 0.4749182113240459D+00, & 0.1516385069726050D+00, & 0.1516385069726048D+00, & 0.6967229860547904D+00, & 0.0124989324834955D+00, & 0.0472761418326518D+00, & 0.9402249256838529D+00, & 0.0124989324834955D+00, & 0.9402249256838529D+00, & 0.0472761418326521D+00, & 0.3333333333333334D+00, & 0.0540117353390243D+00, & 0.3020619577128708D+00, & 0.6439263069481052D+00, & 0.0540117353390243D+00, & 0.6439263069481049D+00, & 0.3020619577128710D+00, & 0.0105050188192420D+00, & 0.2565061597742415D+00, & 0.7329888214065168D+00, & 0.0105050188192420D+00, & 0.7329888214065168D+00, & 0.2565061597742418D+00, & 0.1778657962481611D+00, & 0.4110671018759195D+00, & 0.4110671018759197D+00, & 0.0661224580284034D+00, & 0.1784791255658876D+00, & 0.7553984164057090D+00, & 0.0661224580284034D+00, & 0.7553984164057090D+00, & 0.1784791255658879D+00, & 0.2656146099053743D+00, & 0.2656146099053742D+00, & 0.4687707801892517D+00, & 0.0037589443410685D+00, & 0.0037589443410682D+00, & 0.9924821113178633D+00, & 0.1490669101257739D+00, & 0.2685733063960138D+00, & 0.5823597834782125D+00, & 0.1490669101257739D+00, & 0.5823597834782125D+00, & 0.2685733063960140D+00, & 0.0116918246746672D+00, & 0.4110656686746184D+00, & 0.5772425066507147D+00, & 0.0116918246746672D+00, & 0.5772425066507145D+00, & 0.4110656686746186D+00, & 0.0143315247789420D+00, & 0.1327788302713893D+00, & 0.8528896449496687D+00, & 0.0143315247789420D+00, & 0.8528896449496690D+00, & 0.1327788302713896D+00, & 0.0724387055673330D+00, & 0.0724387055673327D+00, & 0.8551225888653343D+00 /) c = (/ & 0.5245289252324957D+00, & 0.0904270403543405D+00, & 0.3850440344131635D+00, & 0.3850440344131636D+00, & 0.0904270403543405D+00, & 0.5245289252324956D+00, & 0.4749182113240457D+00, & 0.0501635773519085D+00, & 0.4749182113240456D+00, & 0.6967229860547902D+00, & 0.1516385069726050D+00, & 0.1516385069726046D+00, & 0.9402249256838529D+00, & 0.0124989324834955D+00, & 0.0472761418326515D+00, & 0.0472761418326518D+00, & 0.0124989324834953D+00, & 0.9402249256838527D+00, & 0.3333333333333333D+00, & 0.6439263069481050D+00, & 0.0540117353390242D+00, & 0.3020619577128706D+00, & 0.3020619577128708D+00, & 0.0540117353390243D+00, & 0.6439263069481048D+00, & 0.7329888214065166D+00, & 0.0105050188192420D+00, & 0.2565061597742413D+00, & 0.2565061597742415D+00, & 0.0105050188192417D+00, & 0.7329888214065164D+00, & 0.4110671018759195D+00, & 0.1778657962481610D+00, & 0.4110671018759194D+00, & 0.7553984164057089D+00, & 0.0661224580284035D+00, & 0.1784791255658874D+00, & 0.1784791255658876D+00, & 0.0661224580284032D+00, & 0.7553984164057088D+00, & 0.4687707801892514D+00, & 0.2656146099053742D+00, & 0.2656146099053741D+00, & 0.9924821113178633D+00, & 0.0037589443410686D+00, & 0.0037589443410680D+00, & 0.5823597834782123D+00, & 0.1490669101257739D+00, & 0.2685733063960136D+00, & 0.2685733063960138D+00, & 0.1490669101257737D+00, & 0.5823597834782122D+00, & 0.5772425066507145D+00, & 0.0116918246746671D+00, & 0.4110656686746181D+00, & 0.4110656686746183D+00, & 0.0116918246746670D+00, & 0.5772425066507143D+00, & 0.8528896449496688D+00, & 0.0143315247789421D+00, & 0.1327788302713891D+00, & 0.1327788302713892D+00, & 0.0143315247789417D+00, & 0.8528896449496687D+00, & 0.8551225888653342D+00, & 0.0724387055673332D+00, & 0.0724387055673325D+00 /) w = (/ & 0.0153282581945531D+00, & 0.0153282581945531D+00, & 0.0153282581945531D+00, & 0.0153282581945531D+00, & 0.0153282581945531D+00, & 0.0153282581945531D+00, & 0.0131070274917388D+00, & 0.0131070274917388D+00, & 0.0131070274917388D+00, & 0.0203183388454584D+00, & 0.0203183388454584D+00, & 0.0203183388454584D+00, & 0.0042175167747444D+00, & 0.0042175167747444D+00, & 0.0042175167747444D+00, & 0.0042175167747444D+00, & 0.0042175167747444D+00, & 0.0042175167747444D+00, & 0.0307485212391159D+00, & 0.0163659084139866D+00, & 0.0163659084139866D+00, & 0.0163659084139866D+00, & 0.0163659084139866D+00, & 0.0163659084139866D+00, & 0.0163659084139866D+00, & 0.0077298352800062D+00, & 0.0077298352800062D+00, & 0.0077298352800062D+00, & 0.0077298352800062D+00, & 0.0077298352800062D+00, & 0.0077298352800062D+00, & 0.0334719940598479D+00, & 0.0334719940598479D+00, & 0.0334719940598479D+00, & 0.0169116539174801D+00, & 0.0169116539174801D+00, & 0.0169116539174801D+00, & 0.0169116539174801D+00, & 0.0169116539174801D+00, & 0.0169116539174801D+00, & 0.0311163966020061D+00, & 0.0311163966020061D+00, & 0.0311163966020061D+00, & 0.0005320056169478D+00, & 0.0005320056169478D+00, & 0.0005320056169478D+00, & 0.0275928864885795D+00, & 0.0275928864885795D+00, & 0.0275928864885795D+00, & 0.0275928864885795D+00, & 0.0275928864885795D+00, & 0.0275928864885795D+00, & 0.0095861244743615D+00, & 0.0095861244743615D+00, & 0.0095861244743615D+00, & 0.0095861244743615D+00, & 0.0095861244743615D+00, & 0.0095861244743615D+00, & 0.0076417049727196D+00, & 0.0076417049727196D+00, & 0.0076417049727196D+00, & 0.0076417049727196D+00, & 0.0076417049727196D+00, & 0.0076417049727196D+00, & 0.0137902866047669D+00, & 0.0137902866047669D+00, & 0.0137902866047669D+00 /) return end subroutine rule19 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule19() returns the rule of precision 19. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1424222825711269D+00, & 0.8525725750765226D+00, & 0.0050051423523504D+00, & 0.8525725750765226D+00, & 0.1424222825711269D+00, & 0.0050051423523502D+00, & 0.0525262798541034D+00, & 0.8949474402917929D+00, & 0.0525262798541039D+00, & 0.0600838999627024D+00, & 0.9301390385986208D+00, & 0.0097770614386771D+00, & 0.9301390385986208D+00, & 0.0600838999627025D+00, & 0.0097770614386767D+00, & 0.1307006699605345D+00, & 0.8301568806048565D+00, & 0.0391424494346090D+00, & 0.8301568806048566D+00, & 0.1307006699605346D+00, & 0.0391424494346087D+00, & 0.3113183832239869D+00, & 0.5593688070080342D+00, & 0.1293128097679790D+00, & 0.5593688070080342D+00, & 0.3113183832239869D+00, & 0.1293128097679789D+00, & 0.1114480557169985D+00, & 0.7771038885660025D+00, & 0.1114480557169988D+00, & 0.0116390273279224D+00, & 0.9767219453441548D+00, & 0.0116390273279229D+00, & 0.2551621331531247D+00, & 0.4896757336937503D+00, & 0.2551621331531249D+00, & 0.2214339418891134D+00, & 0.7040048688065315D+00, & 0.0745611893043552D+00, & 0.7040048688065313D+00, & 0.2214339418891134D+00, & 0.0745611893043550D+00, & 0.4039697179663860D+00, & 0.4039697179663860D+00, & 0.1920605640672278D+00, & 0.3540259269997119D+00, & 0.6050857585353100D+00, & 0.0408883144649781D+00, & 0.6050857585353100D+00, & 0.3540259269997119D+00, & 0.0408883144649780D+00, & 0.1781710060796274D+00, & 0.6436579878407451D+00, & 0.1781710060796276D+00, & 0.4591943889568276D+00, & 0.4591943889568276D+00, & 0.0816112220863447D+00, & 0.3333333333333333D+00, & 0.4925124498658742D+00, & 0.4925124498658742D+00, & 0.0149751002682516D+00, & 0.2418941040068926D+00, & 0.7431822570856689D+00, & 0.0149236389074385D+00, & 0.7431822570856689D+00, & 0.2418941040068927D+00, & 0.0149236389074383D+00, & 0.3646204143387100D+00, & 0.6333104818121875D+00, & 0.0020691038491024D+00, & 0.6333104818121876D+00, & 0.3646204143387101D+00, & 0.0020691038491022D+00 /) b = (/ & 0.0050051423523504D+00, & 0.1424222825711269D+00, & 0.8525725750765228D+00, & 0.0050051423523504D+00, & 0.8525725750765228D+00, & 0.1424222825711273D+00, & 0.0525262798541037D+00, & 0.0525262798541034D+00, & 0.8949474402917930D+00, & 0.0097770614386769D+00, & 0.0600838999627023D+00, & 0.9301390385986208D+00, & 0.0097770614386769D+00, & 0.9301390385986208D+00, & 0.0600838999627027D+00, & 0.0391424494346089D+00, & 0.1307006699605346D+00, & 0.8301568806048567D+00, & 0.0391424494346089D+00, & 0.8301568806048567D+00, & 0.1307006699605348D+00, & 0.1293128097679790D+00, & 0.3113183832239869D+00, & 0.5593688070080343D+00, & 0.1293128097679790D+00, & 0.5593688070080343D+00, & 0.3113183832239870D+00, & 0.1114480557169988D+00, & 0.1114480557169985D+00, & 0.7771038885660028D+00, & 0.0116390273279228D+00, & 0.0116390273279224D+00, & 0.9767219453441548D+00, & 0.2551621331531249D+00, & 0.2551621331531249D+00, & 0.4896757336937504D+00, & 0.0745611893043552D+00, & 0.2214339418891134D+00, & 0.7040048688065317D+00, & 0.0745611893043552D+00, & 0.7040048688065317D+00, & 0.2214339418891137D+00, & 0.1920605640672279D+00, & 0.4039697179663861D+00, & 0.4039697179663862D+00, & 0.0408883144649781D+00, & 0.3540259269997119D+00, & 0.6050857585353102D+00, & 0.0408883144649781D+00, & 0.6050857585353101D+00, & 0.3540259269997121D+00, & 0.1781710060796276D+00, & 0.1781710060796274D+00, & 0.6436579878407452D+00, & 0.0816112220863448D+00, & 0.4591943889568277D+00, & 0.4591943889568278D+00, & 0.3333333333333334D+00, & 0.0149751002682516D+00, & 0.4925124498658743D+00, & 0.4925124498658744D+00, & 0.0149236389074385D+00, & 0.2418941040068926D+00, & 0.7431822570856692D+00, & 0.0149236389074385D+00, & 0.7431822570856690D+00, & 0.2418941040068929D+00, & 0.0020691038491024D+00, & 0.3646204143387101D+00, & 0.6333104818121877D+00, & 0.0020691038491024D+00, & 0.6333104818121877D+00, & 0.3646204143387103D+00 /) c = (/ & 0.8525725750765227D+00, & 0.0050051423523504D+00, & 0.1424222825711267D+00, & 0.1424222825711269D+00, & 0.0050051423523502D+00, & 0.8525725750765225D+00, & 0.8949474402917929D+00, & 0.0525262798541037D+00, & 0.0525262798541032D+00, & 0.9301390385986208D+00, & 0.0097770614386769D+00, & 0.0600838999627021D+00, & 0.0600838999627024D+00, & 0.0097770614386767D+00, & 0.9301390385986207D+00, & 0.8301568806048566D+00, & 0.0391424494346090D+00, & 0.1307006699605343D+00, & 0.1307006699605345D+00, & 0.0391424494346087D+00, & 0.8301568806048565D+00, & 0.5593688070080340D+00, & 0.1293128097679789D+00, & 0.3113183832239867D+00, & 0.3113183832239868D+00, & 0.1293128097679789D+00, & 0.5593688070080340D+00, & 0.7771038885660027D+00, & 0.1114480557169989D+00, & 0.1114480557169985D+00, & 0.9767219453441548D+00, & 0.0116390273279228D+00, & 0.0116390273279222D+00, & 0.4896757336937503D+00, & 0.2551621331531249D+00, & 0.2551621331531247D+00, & 0.7040048688065315D+00, & 0.0745611893043551D+00, & 0.2214339418891131D+00, & 0.2214339418891135D+00, & 0.0745611893043550D+00, & 0.7040048688065313D+00, & 0.4039697179663861D+00, & 0.1920605640672278D+00, & 0.4039697179663860D+00, & 0.6050857585353100D+00, & 0.0408883144649781D+00, & 0.3540259269997117D+00, & 0.3540259269997119D+00, & 0.0408883144649780D+00, & 0.6050857585353098D+00, & 0.6436579878407449D+00, & 0.1781710060796274D+00, & 0.1781710060796272D+00, & 0.4591943889568276D+00, & 0.0816112220863447D+00, & 0.4591943889568275D+00, & 0.3333333333333333D+00, & 0.4925124498658742D+00, & 0.0149751002682516D+00, & 0.4925124498658741D+00, & 0.7431822570856689D+00, & 0.0149236389074385D+00, & 0.2418941040068923D+00, & 0.2418941040068927D+00, & 0.0149236389074383D+00, & 0.7431822570856688D+00, & 0.6333104818121876D+00, & 0.0020691038491024D+00, & 0.3646204143387098D+00, & 0.3646204143387100D+00, & 0.0020691038491022D+00, & 0.6333104818121874D+00 /) w = (/ & 0.0029256924878801D+00, & 0.0029256924878801D+00, & 0.0029256924878801D+00, & 0.0029256924878801D+00, & 0.0029256924878801D+00, & 0.0029256924878801D+00, & 0.0071093936227949D+00, & 0.0071093936227949D+00, & 0.0071093936227949D+00, & 0.0033273888405939D+00, & 0.0033273888405939D+00, & 0.0033273888405939D+00, & 0.0033273888405939D+00, & 0.0033273888405939D+00, & 0.0033273888405939D+00, & 0.0096955190816242D+00, & 0.0096955190816242D+00, & 0.0096955190816242D+00, & 0.0096955190816242D+00, & 0.0096955190816242D+00, & 0.0096955190816242D+00, & 0.0263462647074454D+00, & 0.0263462647074454D+00, & 0.0263462647074454D+00, & 0.0263462647074454D+00, & 0.0263462647074454D+00, & 0.0263462647074454D+00, & 0.0152349565170048D+00, & 0.0152349565170048D+00, & 0.0152349565170048D+00, & 0.0017651924183085D+00, & 0.0017651924183085D+00, & 0.0017651924183085D+00, & 0.0317528545875300D+00, & 0.0317528545875300D+00, & 0.0317528545875300D+00, & 0.0181080745904305D+00, & 0.0181080745904305D+00, & 0.0181080745904305D+00, & 0.0181080745904305D+00, & 0.0181080745904305D+00, & 0.0181080745904305D+00, & 0.0315373586452396D+00, & 0.0315373586452396D+00, & 0.0315373586452396D+00, & 0.0161022094609394D+00, & 0.0161022094609394D+00, & 0.0161022094609394D+00, & 0.0161022094609394D+00, & 0.0161022094609394D+00, & 0.0161022094609394D+00, & 0.0246519810535848D+00, & 0.0246519810535848D+00, & 0.0246519810535848D+00, & 0.0229835709771232D+00, & 0.0229835709771232D+00, & 0.0229835709771232D+00, & 0.0344691608509053D+00, & 0.0103218821824189D+00, & 0.0103218821824189D+00, & 0.0103218821824189D+00, & 0.0084559248390935D+00, & 0.0084559248390935D+00, & 0.0084559248390935D+00, & 0.0084559248390935D+00, & 0.0084559248390935D+00, & 0.0084559248390935D+00, & 0.0032821375148397D+00, & 0.0032821375148397D+00, & 0.0032821375148397D+00, & 0.0032821375148397D+00, & 0.0032821375148397D+00, & 0.0032821375148397D+00 /) return end subroutine rule20 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule20() returns the rule of precision 20. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1862949977445409D+00, & 0.6274100045109180D+00, & 0.1862949977445411D+00, & 0.0373108805988846D+00, & 0.9253782388022305D+00, & 0.0373108805988850D+00, & 0.4762456115404990D+00, & 0.4762456115404990D+00, & 0.0475087769190019D+00, & 0.0640905856084340D+00, & 0.9310544767839422D+00, & 0.0048549376076240D+00, & 0.9310544767839422D+00, & 0.0640905856084341D+00, & 0.0048549376076235D+00, & 0.2156070573900944D+00, & 0.6781657378896355D+00, & 0.1062272047202701D+00, & 0.6781657378896355D+00, & 0.2156070573900943D+00, & 0.1062272047202699D+00, & 0.4455510569559248D+00, & 0.4455510569559248D+00, & 0.1088978860881503D+00, & 0.1591337076570672D+00, & 0.8332955118382362D+00, & 0.0075707805046966D+00, & 0.8332955118382362D+00, & 0.1591337076570672D+00, & 0.0075707805046964D+00, & 0.3178601238357719D+00, & 0.5423318041724280D+00, & 0.1398080719918000D+00, & 0.5423318041724280D+00, & 0.3178601238357719D+00, & 0.1398080719917999D+00, & 0.2545792676733390D+00, & 0.4908414646533217D+00, & 0.2545792676733392D+00, & 0.3333333333333333D+00, & 0.1985181322287882D+00, & 0.7549215028635475D+00, & 0.0465603649076644D+00, & 0.7549215028635474D+00, & 0.1985181322287882D+00, & 0.0465603649076642D+00, & 0.3934253478170998D+00, & 0.3934253478170998D+00, & 0.2131493043658002D+00, & 0.0999522962881386D+00, & 0.8616840189364867D+00, & 0.0383636847753748D+00, & 0.8616840189364866D+00, & 0.0999522962881387D+00, & 0.0383636847753744D+00, & 0.4200237588162241D+00, & 0.5701446928909734D+00, & 0.0098315482928025D+00, & 0.5701446928909734D+00, & 0.4200237588162241D+00, & 0.0098315482928025D+00, & 0.3331348173095874D+00, & 0.6118777035474257D+00, & 0.0549874791429869D+00, & 0.6118777035474257D+00, & 0.3331348173095874D+00, & 0.0549874791429867D+00, & 0.2805814114236652D+00, & 0.7086813757203236D+00, & 0.0107372128560111D+00, & 0.7086813757203237D+00, & 0.2805814114236653D+00, & 0.0107372128560110D+00, & 0.0109761410283976D+00, & 0.9780477179432044D+00, & 0.0109761410283981D+00, & 0.1093835967117145D+00, & 0.7812328065765708D+00, & 0.1093835967117148D+00 /) b = (/ & 0.1862949977445411D+00, & 0.1862949977445409D+00, & 0.6274100045109182D+00, & 0.0373108805988849D+00, & 0.0373108805988846D+00, & 0.9253782388022306D+00, & 0.0475087769190020D+00, & 0.4762456115404990D+00, & 0.4762456115404993D+00, & 0.0048549376076238D+00, & 0.0640905856084340D+00, & 0.9310544767839423D+00, & 0.0048549376076238D+00, & 0.9310544767839423D+00, & 0.0640905856084343D+00, & 0.1062272047202701D+00, & 0.2156070573900944D+00, & 0.6781657378896357D+00, & 0.1062272047202701D+00, & 0.6781657378896357D+00, & 0.2156070573900946D+00, & 0.1088978860881504D+00, & 0.4455510569559249D+00, & 0.4455510569559250D+00, & 0.0075707805046966D+00, & 0.1591337076570672D+00, & 0.8332955118382365D+00, & 0.0075707805046966D+00, & 0.8332955118382364D+00, & 0.1591337076570676D+00, & 0.1398080719918000D+00, & 0.3178601238357721D+00, & 0.5423318041724282D+00, & 0.1398080719918000D+00, & 0.5423318041724282D+00, & 0.3178601238357722D+00, & 0.2545792676733392D+00, & 0.2545792676733392D+00, & 0.4908414646533218D+00, & 0.3333333333333334D+00, & 0.0465603649076644D+00, & 0.1985181322287882D+00, & 0.7549215028635476D+00, & 0.0465603649076644D+00, & 0.7549215028635476D+00, & 0.1985181322287885D+00, & 0.2131493043658003D+00, & 0.3934253478171000D+00, & 0.3934253478171000D+00, & 0.0383636847753747D+00, & 0.0999522962881386D+00, & 0.8616840189364868D+00, & 0.0383636847753747D+00, & 0.8616840189364868D+00, & 0.0999522962881389D+00, & 0.0098315482928026D+00, & 0.4200237588162241D+00, & 0.5701446928909736D+00, & 0.0098315482928026D+00, & 0.5701446928909735D+00, & 0.4200237588162243D+00, & 0.0549874791429869D+00, & 0.3331348173095875D+00, & 0.6118777035474259D+00, & 0.0549874791429869D+00, & 0.6118777035474258D+00, & 0.3331348173095877D+00, & 0.0107372128560111D+00, & 0.2805814114236653D+00, & 0.7086813757203239D+00, & 0.0107372128560111D+00, & 0.7086813757203237D+00, & 0.2805814114236655D+00, & 0.0109761410283979D+00, & 0.0109761410283976D+00, & 0.9780477179432047D+00, & 0.1093835967117148D+00, & 0.1093835967117145D+00, & 0.7812328065765709D+00 /) c = (/ & 0.6274100045109180D+00, & 0.1862949977445411D+00, & 0.1862949977445406D+00, & 0.9253782388022306D+00, & 0.0373108805988850D+00, & 0.0373108805988843D+00, & 0.4762456115404990D+00, & 0.0475087769190020D+00, & 0.4762456115404988D+00, & 0.9310544767839422D+00, & 0.0048549376076238D+00, & 0.0640905856084338D+00, & 0.0640905856084340D+00, & 0.0048549376076236D+00, & 0.9310544767839422D+00, & 0.6781657378896355D+00, & 0.1062272047202700D+00, & 0.2156070573900941D+00, & 0.2156070573900944D+00, & 0.1062272047202699D+00, & 0.6781657378896354D+00, & 0.4455510569559248D+00, & 0.1088978860881503D+00, & 0.4455510569559247D+00, & 0.8332955118382361D+00, & 0.0075707805046965D+00, & 0.1591337076570670D+00, & 0.1591337076570672D+00, & 0.0075707805046964D+00, & 0.8332955118382360D+00, & 0.5423318041724281D+00, & 0.1398080719918000D+00, & 0.3178601238357718D+00, & 0.3178601238357720D+00, & 0.1398080719917999D+00, & 0.5423318041724279D+00, & 0.4908414646533217D+00, & 0.2545792676733392D+00, & 0.2545792676733390D+00, & 0.3333333333333333D+00, & 0.7549215028635475D+00, & 0.0465603649076643D+00, & 0.1985181322287879D+00, & 0.1985181322287882D+00, & 0.0465603649076641D+00, & 0.7549215028635474D+00, & 0.3934253478170998D+00, & 0.2131493043658002D+00, & 0.3934253478170998D+00, & 0.8616840189364867D+00, & 0.0383636847753747D+00, & 0.0999522962881384D+00, & 0.0999522962881387D+00, & 0.0383636847753744D+00, & 0.8616840189364866D+00, & 0.5701446928909732D+00, & 0.0098315482928025D+00, & 0.4200237588162239D+00, & 0.4200237588162241D+00, & 0.0098315482928024D+00, & 0.5701446928909732D+00, & 0.6118777035474258D+00, & 0.0549874791429869D+00, & 0.3331348173095873D+00, & 0.3331348173095875D+00, & 0.0549874791429869D+00, & 0.6118777035474255D+00, & 0.7086813757203236D+00, & 0.0107372128560111D+00, & 0.2805814114236650D+00, & 0.2805814114236652D+00, & 0.0107372128560109D+00, & 0.7086813757203236D+00, & 0.9780477179432044D+00, & 0.0109761410283980D+00, & 0.0109761410283972D+00, & 0.7812328065765708D+00, & 0.1093835967117147D+00, & 0.1093835967117144D+00 /) w = (/ & 0.0183469259485058D+00, & 0.0183469259485058D+00, & 0.0183469259485058D+00, & 0.0043225508213312D+00, & 0.0043225508213312D+00, & 0.0043225508213312D+00, & 0.0142036506068169D+00, & 0.0142036506068169D+00, & 0.0142036506068169D+00, & 0.0022597392042517D+00, & 0.0022597392042517D+00, & 0.0022597392042517D+00, & 0.0022597392042517D+00, & 0.0022597392042517D+00, & 0.0022597392042517D+00, & 0.0154452156441985D+00, & 0.0154452156441985D+00, & 0.0154452156441985D+00, & 0.0154452156441985D+00, & 0.0154452156441985D+00, & 0.0154452156441985D+00, & 0.0189047998664649D+00, & 0.0189047998664649D+00, & 0.0189047998664649D+00, & 0.0044057948371170D+00, & 0.0044057948371170D+00, & 0.0044057948371170D+00, & 0.0044057948371170D+00, & 0.0044057948371170D+00, & 0.0044057948371170D+00, & 0.0233834914636555D+00, & 0.0233834914636555D+00, & 0.0233834914636555D+00, & 0.0233834914636555D+00, & 0.0233834914636555D+00, & 0.0233834914636555D+00, & 0.0281664026150405D+00, & 0.0281664026150405D+00, & 0.0281664026150405D+00, & 0.0278202214029062D+00, & 0.0119727971579094D+00, & 0.0119727971579094D+00, & 0.0119727971579094D+00, & 0.0119727971579094D+00, & 0.0119727971579094D+00, & 0.0119727971579094D+00, & 0.0275761012581409D+00, & 0.0275761012581409D+00, & 0.0275761012581409D+00, & 0.0082914230552277D+00, & 0.0082914230552277D+00, & 0.0082914230552277D+00, & 0.0082914230552277D+00, & 0.0082914230552277D+00, & 0.0082914230552277D+00, & 0.0073913630005106D+00, & 0.0073913630005106D+00, & 0.0073913630005106D+00, & 0.0073913630005106D+00, & 0.0073913630005106D+00, & 0.0073913630005106D+00, & 0.0173344511344387D+00, & 0.0173344511344387D+00, & 0.0173344511344387D+00, & 0.0173344511344387D+00, & 0.0173344511344387D+00, & 0.0173344511344387D+00, & 0.0071564004769154D+00, & 0.0071564004769154D+00, & 0.0071564004769154D+00, & 0.0071564004769154D+00, & 0.0071564004769154D+00, & 0.0071564004769154D+00, & 0.0015976815821332D+00, & 0.0015976815821332D+00, & 0.0015976815821332D+00, & 0.0156604615521491D+00, & 0.0156604615521491D+00, & 0.0156604615521491D+00 /) return end subroutine rule21 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule21() returns the rule of precision 21. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2989362353149825D+00, & 0.4021275293700348D+00, & 0.2989362353149825D+00, & 0.2891894960785947D+00, & 0.5055149445862437D+00, & 0.2052955593351616D+00, & 0.5055149445862437D+00, & 0.2891894960785947D+00, & 0.2052955593351615D+00, & 0.4970078754686856D+00, & 0.4970078754686856D+00, & 0.0059842490626288D+00, & 0.2378733825979940D+00, & 0.7551948083705379D+00, & 0.0069318090314683D+00, & 0.7551948083705379D+00, & 0.2378733825979941D+00, & 0.0069318090314680D+00, & 0.4036175865463851D+00, & 0.4036175865463851D+00, & 0.1927648269072297D+00, & 0.3188653107948282D+00, & 0.5573552887996790D+00, & 0.1237794004054928D+00, & 0.5573552887996790D+00, & 0.3188653107948283D+00, & 0.1237794004054926D+00, & 0.2318736253704010D+00, & 0.7291350120063786D+00, & 0.0389913626232204D+00, & 0.7291350120063788D+00, & 0.2318736253704010D+00, & 0.0389913626232202D+00, & 0.1331671229413703D+00, & 0.8572966295289191D+00, & 0.0095362475297107D+00, & 0.8572966295289192D+00, & 0.1331671229413703D+00, & 0.0095362475297104D+00, & 0.3468079798099110D+00, & 0.6001398284888722D+00, & 0.0530521917012168D+00, & 0.6001398284888722D+00, & 0.3468079798099111D+00, & 0.0530521917012167D+00, & 0.1189885776227193D+00, & 0.7620228447545612D+00, & 0.1189885776227196D+00, & 0.1902887180912784D+00, & 0.6194225638174430D+00, & 0.1902887180912786D+00, & 0.2165996231899825D+00, & 0.6829423567359030D+00, & 0.1004580200741146D+00, & 0.6829423567359030D+00, & 0.2165996231899825D+00, & 0.1004580200741143D+00, & 0.4815978686532166D+00, & 0.4815978686532166D+00, & 0.0368042626935668D+00, & 0.4498127917753624D+00, & 0.4498127917753624D+00, & 0.1003744164492752D+00, & 0.1288298079620515D+00, & 0.8217191264694078D+00, & 0.0494510655685407D+00, & 0.8217191264694079D+00, & 0.1288298079620517D+00, & 0.0494510655685403D+00, & 0.0536275755461449D+00, & 0.8927448489077100D+00, & 0.0536275755461453D+00, & 0.3609534080189222D+00, & 0.6287919561081534D+00, & 0.0102546358729245D+00, & 0.6287919561081533D+00, & 0.3609534080189222D+00, & 0.0102546358729244D+00, & 0.0107424564328283D+00, & 0.9785150871343431D+00, & 0.0107424564328287D+00, & 0.0557195650723719D+00, & 0.9339785312842042D+00, & 0.0103019036434240D+00, & 0.9339785312842040D+00, & 0.0557195650723720D+00, & 0.0103019036434236D+00 /) b = (/ & 0.2989362353149826D+00, & 0.2989362353149826D+00, & 0.4021275293700349D+00, & 0.2052955593351616D+00, & 0.2891894960785948D+00, & 0.5055149445862438D+00, & 0.2052955593351616D+00, & 0.5055149445862438D+00, & 0.2891894960785949D+00, & 0.0059842490626289D+00, & 0.4970078754686856D+00, & 0.4970078754686857D+00, & 0.0069318090314681D+00, & 0.2378733825979940D+00, & 0.7551948083705379D+00, & 0.0069318090314681D+00, & 0.7551948083705379D+00, & 0.2378733825979943D+00, & 0.1927648269072298D+00, & 0.4036175865463852D+00, & 0.4036175865463852D+00, & 0.1237794004054928D+00, & 0.3188653107948283D+00, & 0.5573552887996791D+00, & 0.1237794004054928D+00, & 0.5573552887996791D+00, & 0.3188653107948285D+00, & 0.0389913626232203D+00, & 0.2318736253704010D+00, & 0.7291350120063789D+00, & 0.0389913626232203D+00, & 0.7291350120063789D+00, & 0.2318736253704013D+00, & 0.0095362475297106D+00, & 0.1331671229413703D+00, & 0.8572966295289193D+00, & 0.0095362475297106D+00, & 0.8572966295289193D+00, & 0.1331671229413706D+00, & 0.0530521917012168D+00, & 0.3468079798099111D+00, & 0.6001398284888723D+00, & 0.0530521917012168D+00, & 0.6001398284888722D+00, & 0.3468079798099113D+00, & 0.1189885776227196D+00, & 0.1189885776227193D+00, & 0.7620228447545613D+00, & 0.1902887180912786D+00, & 0.1902887180912785D+00, & 0.6194225638174431D+00, & 0.1004580200741145D+00, & 0.2165996231899825D+00, & 0.6829423567359031D+00, & 0.1004580200741145D+00, & 0.6829423567359032D+00, & 0.2165996231899828D+00, & 0.0368042626935668D+00, & 0.4815978686532166D+00, & 0.4815978686532168D+00, & 0.1003744164492753D+00, & 0.4498127917753625D+00, & 0.4498127917753625D+00, & 0.0494510655685406D+00, & 0.1288298079620515D+00, & 0.8217191264694079D+00, & 0.0494510655685406D+00, & 0.8217191264694079D+00, & 0.1288298079620518D+00, & 0.0536275755461451D+00, & 0.0536275755461448D+00, & 0.8927448489077101D+00, & 0.0102546358729245D+00, & 0.3609534080189222D+00, & 0.6287919561081535D+00, & 0.0102546358729245D+00, & 0.6287919561081534D+00, & 0.3609534080189224D+00, & 0.0107424564328286D+00, & 0.0107424564328283D+00, & 0.9785150871343433D+00, & 0.0103019036434239D+00, & 0.0557195650723719D+00, & 0.9339785312842044D+00, & 0.0103019036434239D+00, & 0.9339785312842044D+00, & 0.0557195650723723D+00 /) c = (/ & 0.4021275293700349D+00, & 0.2989362353149825D+00, & 0.2989362353149826D+00, & 0.5055149445862437D+00, & 0.2052955593351615D+00, & 0.2891894960785947D+00, & 0.2891894960785947D+00, & 0.2052955593351614D+00, & 0.5055149445862436D+00, & 0.4970078754686856D+00, & 0.0059842490626288D+00, & 0.4970078754686854D+00, & 0.7551948083705379D+00, & 0.0069318090314681D+00, & 0.2378733825979938D+00, & 0.2378733825979940D+00, & 0.0069318090314680D+00, & 0.7551948083705377D+00, & 0.4036175865463850D+00, & 0.1927648269072297D+00, & 0.4036175865463850D+00, & 0.5573552887996789D+00, & 0.1237794004054927D+00, & 0.3188653107948280D+00, & 0.3188653107948282D+00, & 0.1237794004054926D+00, & 0.5573552887996789D+00, & 0.7291350120063786D+00, & 0.0389913626232204D+00, & 0.2318736253704008D+00, & 0.2318736253704009D+00, & 0.0389913626232201D+00, & 0.7291350120063785D+00, & 0.8572966295289192D+00, & 0.0095362475297107D+00, & 0.1331671229413700D+00, & 0.1331671229413702D+00, & 0.0095362475297104D+00, & 0.8572966295289191D+00, & 0.6001398284888720D+00, & 0.0530521917012167D+00, & 0.3468079798099110D+00, & 0.3468079798099110D+00, & 0.0530521917012168D+00, & 0.6001398284888719D+00, & 0.7620228447545612D+00, & 0.1189885776227195D+00, & 0.1189885776227192D+00, & 0.6194225638174429D+00, & 0.1902887180912785D+00, & 0.1902887180912783D+00, & 0.6829423567359030D+00, & 0.1004580200741145D+00, & 0.2165996231899824D+00, & 0.2165996231899825D+00, & 0.1004580200741143D+00, & 0.6829423567359030D+00, & 0.4815978686532166D+00, & 0.0368042626935668D+00, & 0.4815978686532165D+00, & 0.4498127917753624D+00, & 0.1003744164492751D+00, & 0.4498127917753622D+00, & 0.8217191264694078D+00, & 0.0494510655685407D+00, & 0.1288298079620513D+00, & 0.1288298079620515D+00, & 0.0494510655685404D+00, & 0.8217191264694079D+00, & 0.8927448489077100D+00, & 0.0536275755461452D+00, & 0.0536275755461446D+00, & 0.6287919561081533D+00, & 0.0102546358729244D+00, & 0.3609534080189220D+00, & 0.3609534080189222D+00, & 0.0102546358729244D+00, & 0.6287919561081532D+00, & 0.9785150871343432D+00, & 0.0107424564328287D+00, & 0.0107424564328280D+00, & 0.9339785312842042D+00, & 0.0103019036434239D+00, & 0.0557195650723716D+00, & 0.0557195650723720D+00, & 0.0103019036434236D+00, & 0.9339785312842040D+00 /) w = (/ & 0.0214511219291323D+00, & 0.0214511219291323D+00, & 0.0214511219291323D+00, & 0.0174954161557631D+00, & 0.0174954161557631D+00, & 0.0174954161557631D+00, & 0.0174954161557631D+00, & 0.0174954161557631D+00, & 0.0174954161557631D+00, & 0.0044378296970659D+00, & 0.0044378296970659D+00, & 0.0044378296970659D+00, & 0.0042061202881497D+00, & 0.0042061202881497D+00, & 0.0042061202881497D+00, & 0.0042061202881497D+00, & 0.0042061202881497D+00, & 0.0042061202881497D+00, & 0.0230007046532839D+00, & 0.0230007046532839D+00, & 0.0230007046532839D+00, & 0.0184474848479328D+00, & 0.0184474848479328D+00, & 0.0184474848479328D+00, & 0.0184474848479328D+00, & 0.0184474848479328D+00, & 0.0184474848479328D+00, & 0.0104699041853248D+00, & 0.0104699041853248D+00, & 0.0104699041853248D+00, & 0.0104699041853248D+00, & 0.0104699041853248D+00, & 0.0104699041853248D+00, & 0.0044808131219015D+00, & 0.0044808131219015D+00, & 0.0044808131219015D+00, & 0.0044808131219015D+00, & 0.0044808131219015D+00, & 0.0044808131219015D+00, & 0.0145003059189710D+00, & 0.0145003059189710D+00, & 0.0145003059189710D+00, & 0.0145003059189710D+00, & 0.0145003059189710D+00, & 0.0145003059189710D+00, & 0.0136560324522302D+00, & 0.0136560324522302D+00, & 0.0136560324522302D+00, & 0.0194552418607507D+00, & 0.0194552418607507D+00, & 0.0194552418607507D+00, & 0.0159040367054280D+00, & 0.0159040367054280D+00, & 0.0159040367054280D+00, & 0.0159040367054280D+00, & 0.0159040367054280D+00, & 0.0159040367054280D+00, & 0.0122144101633844D+00, & 0.0122144101633844D+00, & 0.0122144101633844D+00, & 0.0196144752278240D+00, & 0.0196144752278240D+00, & 0.0196144752278240D+00, & 0.0098119718225504D+00, & 0.0098119718225504D+00, & 0.0098119718225504D+00, & 0.0098119718225504D+00, & 0.0098119718225504D+00, & 0.0098119718225504D+00, & 0.0071520851012837D+00, & 0.0071520851012837D+00, & 0.0071520851012837D+00, & 0.0068398848579343D+00, & 0.0068398848579343D+00, & 0.0068398848579343D+00, & 0.0068398848579343D+00, & 0.0068398848579343D+00, & 0.0068398848579343D+00, & 0.0015086992723787D+00, & 0.0015086992723787D+00, & 0.0015086992723787D+00, & 0.0032654285840441D+00, & 0.0032654285840441D+00, & 0.0032654285840441D+00, & 0.0032654285840441D+00, & 0.0032654285840441D+00, & 0.0032654285840441D+00 /) return end subroutine rule22 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule22() returns the rule of precision 22. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3851845246273021D+00, & 0.3851845246273021D+00, & 0.2296309507453957D+00, & 0.4577694113676721D+00, & 0.4577694113676721D+00, & 0.0844611772646559D+00, & 0.0698421694674436D+00, & 0.9222815483109740D+00, & 0.0078762822215824D+00, & 0.9222815483109740D+00, & 0.0698421694674436D+00, & 0.0078762822215821D+00, & 0.2945582590299500D+00, & 0.4108834819400997D+00, & 0.2945582590299501D+00, & 0.1885105236302838D+00, & 0.6229789527394320D+00, & 0.1885105236302841D+00, & 0.4219818887935349D+00, & 0.4219818887935349D+00, & 0.1560362224129301D+00, & 0.0903988311664077D+00, & 0.8648488844852564D+00, & 0.0447522843483360D+00, & 0.8648488844852564D+00, & 0.0903988311664079D+00, & 0.0447522843483357D+00, & 0.4113417640205587D+00, & 0.5503830012785774D+00, & 0.0382752347008638D+00, & 0.5503830012785774D+00, & 0.4113417640205588D+00, & 0.0382752347008637D+00, & 0.3321061050074464D+00, & 0.5651468190056221D+00, & 0.1027470759869314D+00, & 0.5651468190056222D+00, & 0.3321061050074463D+00, & 0.1027470759869313D+00, & 0.3625762804324673D+00, & 0.6300234783328220D+00, & 0.0074002412347108D+00, & 0.6300234783328220D+00, & 0.3625762804324673D+00, & 0.0074002412347107D+00, & 0.2900668241166688D+00, & 0.5188518779166110D+00, & 0.1910812979667201D+00, & 0.5188518779166110D+00, & 0.2900668241166688D+00, & 0.1910812979667200D+00, & 0.4961611784097086D+00, & 0.4961611784097086D+00, & 0.0076776431805827D+00, & 0.2879318028241718D+00, & 0.6680765517823724D+00, & 0.0439916453934559D+00, & 0.6680765517823722D+00, & 0.2879318028241718D+00, & 0.0439916453934557D+00, & 0.2167869333649411D+00, & 0.6745231247723867D+00, & 0.1086899418626721D+00, & 0.6745231247723867D+00, & 0.2167869333649412D+00, & 0.1086899418626718D+00, & 0.1458737198735252D+00, & 0.8449815687515108D+00, & 0.0091447113749641D+00, & 0.8449815687515108D+00, & 0.1458737198735252D+00, & 0.0091447113749638D+00, & 0.1762974348245001D+00, & 0.7754476410608585D+00, & 0.0482549241146414D+00, & 0.7754476410608585D+00, & 0.1762974348245001D+00, & 0.0482549241146412D+00, & 0.2439906460394931D+00, & 0.7468454447123216D+00, & 0.0091639092481853D+00, & 0.7468454447123217D+00, & 0.2439906460394931D+00, & 0.0091639092481851D+00, & 0.0291084706708074D+00, & 0.9417830586583850D+00, & 0.0291084706708079D+00, & 0.1154315382192049D+00, & 0.7691369235615900D+00, & 0.1154315382192052D+00, & 0.0179343210529390D+00, & 0.9802672139581126D+00, & 0.0017984649889486D+00, & 0.9802672139581127D+00, & 0.0179343210529391D+00, & 0.0017984649889481D+00 /) b = (/ & 0.2296309507453958D+00, & 0.3851845246273022D+00, & 0.3851845246273022D+00, & 0.0844611772646559D+00, & 0.4577694113676721D+00, & 0.4577694113676722D+00, & 0.0078762822215824D+00, & 0.0698421694674436D+00, & 0.9222815483109743D+00, & 0.0078762822215824D+00, & 0.9222815483109743D+00, & 0.0698421694674439D+00, & 0.2945582590299502D+00, & 0.2945582590299502D+00, & 0.4108834819400998D+00, & 0.1885105236302840D+00, & 0.1885105236302839D+00, & 0.6229789527394323D+00, & 0.1560362224129302D+00, & 0.4219818887935350D+00, & 0.4219818887935351D+00, & 0.0447522843483359D+00, & 0.0903988311664078D+00, & 0.8648488844852564D+00, & 0.0447522843483359D+00, & 0.8648488844852564D+00, & 0.0903988311664081D+00, & 0.0382752347008638D+00, & 0.4113417640205588D+00, & 0.5503830012785776D+00, & 0.0382752347008638D+00, & 0.5503830012785775D+00, & 0.4113417640205590D+00, & 0.1027470759869314D+00, & 0.3321061050074464D+00, & 0.5651468190056224D+00, & 0.1027470759869314D+00, & 0.5651468190056224D+00, & 0.3321061050074466D+00, & 0.0074002412347108D+00, & 0.3625762804324673D+00, & 0.6300234783328221D+00, & 0.0074002412347108D+00, & 0.6300234783328221D+00, & 0.3625762804324675D+00, & 0.1910812979667202D+00, & 0.2900668241166688D+00, & 0.5188518779166111D+00, & 0.1910812979667202D+00, & 0.5188518779166111D+00, & 0.2900668241166690D+00, & 0.0076776431805828D+00, & 0.4961611784097087D+00, & 0.4961611784097089D+00, & 0.0439916453934559D+00, & 0.2879318028241719D+00, & 0.6680765517823725D+00, & 0.0439916453934559D+00, & 0.6680765517823725D+00, & 0.2879318028241721D+00, & 0.1086899418626720D+00, & 0.2167869333649412D+00, & 0.6745231247723870D+00, & 0.1086899418626720D+00, & 0.6745231247723870D+00, & 0.2167869333649414D+00, & 0.0091447113749641D+00, & 0.1458737198735252D+00, & 0.8449815687515109D+00, & 0.0091447113749641D+00, & 0.8449815687515109D+00, & 0.1458737198735255D+00, & 0.0482549241146414D+00, & 0.1762974348245001D+00, & 0.7754476410608587D+00, & 0.0482549241146414D+00, & 0.7754476410608587D+00, & 0.1762974348245004D+00, & 0.0091639092481852D+00, & 0.2439906460394931D+00, & 0.7468454447123218D+00, & 0.0091639092481852D+00, & 0.7468454447123218D+00, & 0.2439906460394934D+00, & 0.0291084706708077D+00, & 0.0291084706708073D+00, & 0.9417830586583850D+00, & 0.1154315382192051D+00, & 0.1154315382192049D+00, & 0.7691369235615901D+00, & 0.0017984649889484D+00, & 0.0179343210529390D+00, & 0.9802672139581127D+00, & 0.0017984649889484D+00, & 0.9802672139581129D+00, & 0.0179343210529393D+00 /) c = (/ & 0.3851845246273021D+00, & 0.2296309507453957D+00, & 0.3851845246273020D+00, & 0.4577694113676721D+00, & 0.0844611772646559D+00, & 0.4577694113676719D+00, & 0.9222815483109740D+00, & 0.0078762822215824D+00, & 0.0698421694674433D+00, & 0.0698421694674436D+00, & 0.0078762822215821D+00, & 0.9222815483109740D+00, & 0.4108834819400998D+00, & 0.2945582590299501D+00, & 0.2945582590299501D+00, & 0.6229789527394320D+00, & 0.1885105236302841D+00, & 0.1885105236302836D+00, & 0.4219818887935349D+00, & 0.1560362224129300D+00, & 0.4219818887935349D+00, & 0.8648488844852564D+00, & 0.0447522843483358D+00, & 0.0903988311664076D+00, & 0.0903988311664077D+00, & 0.0447522843483357D+00, & 0.8648488844852562D+00, & 0.5503830012785774D+00, & 0.0382752347008638D+00, & 0.4113417640205586D+00, & 0.4113417640205587D+00, & 0.0382752347008637D+00, & 0.5503830012785773D+00, & 0.5651468190056222D+00, & 0.1027470759869314D+00, & 0.3321061050074462D+00, & 0.3321061050074463D+00, & 0.1027470759869313D+00, & 0.5651468190056220D+00, & 0.6300234783328220D+00, & 0.0074002412347107D+00, & 0.3625762804324671D+00, & 0.3625762804324672D+00, & 0.0074002412347106D+00, & 0.6300234783328218D+00, & 0.5188518779166110D+00, & 0.1910812979667201D+00, & 0.2900668241166687D+00, & 0.2900668241166688D+00, & 0.1910812979667200D+00, & 0.5188518779166110D+00, & 0.4961611784097086D+00, & 0.0076776431805827D+00, & 0.4961611784097084D+00, & 0.6680765517823724D+00, & 0.0439916453934558D+00, & 0.2879318028241716D+00, & 0.2879318028241719D+00, & 0.0439916453934558D+00, & 0.6680765517823722D+00, & 0.6745231247723869D+00, & 0.1086899418626721D+00, & 0.2167869333649409D+00, & 0.2167869333649412D+00, & 0.1086899418626718D+00, & 0.6745231247723867D+00, & 0.8449815687515108D+00, & 0.0091447113749641D+00, & 0.1458737198735250D+00, & 0.1458737198735252D+00, & 0.0091447113749640D+00, & 0.8449815687515108D+00, & 0.7754476410608585D+00, & 0.0482549241146414D+00, & 0.1762974348244998D+00, & 0.1762974348245001D+00, & 0.0482549241146412D+00, & 0.7754476410608585D+00, & 0.7468454447123217D+00, & 0.0091639092481853D+00, & 0.2439906460394928D+00, & 0.2439906460394931D+00, & 0.0091639092481851D+00, & 0.7468454447123216D+00, & 0.9417830586583850D+00, & 0.0291084706708077D+00, & 0.0291084706708072D+00, & 0.7691369235615899D+00, & 0.1154315382192051D+00, & 0.1154315382192047D+00, & 0.9802672139581126D+00, & 0.0017984649889485D+00, & 0.0179343210529387D+00, & 0.0179343210529390D+00, & 0.0017984649889481D+00, & 0.9802672139581127D+00 /) w = (/ & 0.0134930838836107D+00, & 0.0134930838836107D+00, & 0.0134930838836107D+00, & 0.0138613995242342D+00, & 0.0138613995242342D+00, & 0.0138613995242342D+00, & 0.0025954384742313D+00, & 0.0025954384742313D+00, & 0.0025954384742313D+00, & 0.0025954384742313D+00, & 0.0025954384742313D+00, & 0.0025954384742313D+00, & 0.0210757639574522D+00, & 0.0210757639574522D+00, & 0.0210757639574522D+00, & 0.0160212991251489D+00, & 0.0160212991251489D+00, & 0.0160212991251489D+00, & 0.0188530925538413D+00, & 0.0188530925538413D+00, & 0.0188530925538413D+00, & 0.0075175778177884D+00, & 0.0075175778177884D+00, & 0.0075175778177884D+00, & 0.0075175778177884D+00, & 0.0075175778177884D+00, & 0.0075175778177884D+00, & 0.0111973134719628D+00, & 0.0111973134719628D+00, & 0.0111973134719628D+00, & 0.0111973134719628D+00, & 0.0111973134719628D+00, & 0.0111973134719628D+00, & 0.0177190934895102D+00, & 0.0177190934895102D+00, & 0.0177190934895102D+00, & 0.0177190934895102D+00, & 0.0177190934895102D+00, & 0.0177190934895102D+00, & 0.0049042603975570D+00, & 0.0049042603975570D+00, & 0.0049042603975570D+00, & 0.0049042603975570D+00, & 0.0049042603975570D+00, & 0.0049042603975570D+00, & 0.0217064195555090D+00, & 0.0217064195555090D+00, & 0.0217064195555090D+00, & 0.0217064195555090D+00, & 0.0217064195555090D+00, & 0.0217064195555090D+00, & 0.0052893396659844D+00, & 0.0052893396659844D+00, & 0.0052893396659844D+00, & 0.0116622228673430D+00, & 0.0116622228673430D+00, & 0.0116622228673430D+00, & 0.0116622228673430D+00, & 0.0116622228673430D+00, & 0.0116622228673430D+00, & 0.0157101626225703D+00, & 0.0157101626225703D+00, & 0.0157101626225703D+00, & 0.0157101626225703D+00, & 0.0157101626225703D+00, & 0.0157101626225703D+00, & 0.0041066870715756D+00, & 0.0041066870715756D+00, & 0.0041066870715756D+00, & 0.0041066870715756D+00, & 0.0041066870715756D+00, & 0.0041066870715756D+00, & 0.0105635849677469D+00, & 0.0105635849677469D+00, & 0.0105635849677469D+00, & 0.0105635849677469D+00, & 0.0105635849677469D+00, & 0.0105635849677469D+00, & 0.0050540768975846D+00, & 0.0050540768975846D+00, & 0.0050540768975846D+00, & 0.0050540768975846D+00, & 0.0050540768975846D+00, & 0.0050540768975846D+00, & 0.0035691091658564D+00, & 0.0035691091658564D+00, & 0.0035691091658564D+00, & 0.0144157131281046D+00, & 0.0144157131281046D+00, & 0.0144157131281046D+00, & 0.0006404285311714D+00, & 0.0006404285311714D+00, & 0.0006404285311714D+00, & 0.0006404285311714D+00, & 0.0006404285311714D+00, & 0.0006404285311714D+00 /) return end subroutine rule23 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule23() returns the rule of precision 23. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1595037989247572D+00, & 0.8166259474208891D+00, & 0.0238702536543537D+00, & 0.8166259474208892D+00, & 0.1595037989247573D+00, & 0.0238702536543534D+00, & 0.1141013603223645D+00, & 0.8807088179167908D+00, & 0.0051898217608446D+00, & 0.8807088179167909D+00, & 0.1141013603223646D+00, & 0.0051898217608443D+00, & 0.0390072687570320D+00, & 0.9219854624859357D+00, & 0.0390072687570324D+00, & 0.0955398781717349D+00, & 0.8717190926395586D+00, & 0.0327410291887065D+00, & 0.8717190926395587D+00, & 0.0955398781717349D+00, & 0.0327410291887062D+00, & 0.3111622680517019D+00, & 0.6863901320923316D+00, & 0.0024475998559664D+00, & 0.6863901320923317D+00, & 0.3111622680517019D+00, & 0.0024475998559662D+00, & 0.2056172320580521D+00, & 0.7856574783566395D+00, & 0.0087252895853085D+00, & 0.7856574783566393D+00, & 0.2056172320580521D+00, & 0.0087252895853083D+00, & 0.0472616294497253D+00, & 0.9455758306400303D+00, & 0.0071625399102447D+00, & 0.9455758306400303D+00, & 0.0472616294497255D+00, & 0.0071625399102442D+00, & 0.3585095935696251D+00, & 0.5729634522431619D+00, & 0.0685269541872131D+00, & 0.5729634522431619D+00, & 0.3585095935696250D+00, & 0.0685269541872129D+00, & 0.4803288773373085D+00, & 0.4803288773373085D+00, & 0.0393422453253830D+00, & 0.2404827720350127D+00, & 0.6577888986377031D+00, & 0.1017283293272843D+00, & 0.6577888986377032D+00, & 0.2404827720350126D+00, & 0.1017283293272841D+00, & 0.0868410482076331D+00, & 0.8263179035847337D+00, & 0.0868410482076334D+00, & 0.3943235060115415D+00, & 0.3943235060115415D+00, & 0.2113529879769169D+00, & 0.2662513178772472D+00, & 0.4674973642455053D+00, & 0.2662513178772474D+00, & 0.1729323031292240D+00, & 0.7687161216332605D+00, & 0.0583515752375156D+00, & 0.7687161216332605D+00, & 0.1729323031292240D+00, & 0.0583515752375153D+00, & 0.3163043076538381D+00, & 0.5288655369406456D+00, & 0.1548301554055163D+00, & 0.5288655369406456D+00, & 0.3163043076538382D+00, & 0.1548301554055161D+00, & 0.1371293873116475D+00, & 0.7257412253767047D+00, & 0.1371293873116478D+00, & 0.4989594312095863D+00, & 0.4989594312095863D+00, & 0.0020811375808273D+00, & 0.3977585768030076D+00, & 0.5874824534670471D+00, & 0.0147589697299451D+00, & 0.5874824534670471D+00, & 0.3977585768030076D+00, & 0.0147589697299450D+00, & 0.4446924421277275D+00, & 0.4446924421277275D+00, & 0.1106151157445449D+00, & 0.1987498063965361D+00, & 0.6025003872069274D+00, & 0.1987498063965363D+00, & 0.2787941698141023D+00, & 0.6882121219933649D+00, & 0.0329937081925328D+00, & 0.6882121219933649D+00, & 0.2787941698141023D+00, & 0.0329937081925327D+00, & 0.0090164402055982D+00, & 0.9819671195888033D+00, & 0.0090164402055986D+00, & 0.3333333333333333D+00 /) b = (/ & 0.0238702536543536D+00, & 0.1595037989247572D+00, & 0.8166259474208892D+00, & 0.0238702536543536D+00, & 0.8166259474208892D+00, & 0.1595037989247576D+00, & 0.0051898217608445D+00, & 0.1141013603223645D+00, & 0.8807088179167911D+00, & 0.0051898217608445D+00, & 0.8807088179167911D+00, & 0.1141013603223648D+00, & 0.0390072687570323D+00, & 0.0390072687570320D+00, & 0.9219854624859359D+00, & 0.0327410291887064D+00, & 0.0955398781717349D+00, & 0.8717190926395588D+00, & 0.0327410291887064D+00, & 0.8717190926395588D+00, & 0.0955398781717352D+00, & 0.0024475998559664D+00, & 0.3111622680517020D+00, & 0.6863901320923319D+00, & 0.0024475998559664D+00, & 0.6863901320923319D+00, & 0.3111622680517022D+00, & 0.0087252895853085D+00, & 0.2056172320580521D+00, & 0.7856574783566396D+00, & 0.0087252895853085D+00, & 0.7856574783566396D+00, & 0.2056172320580524D+00, & 0.0071625399102445D+00, & 0.0472616294497253D+00, & 0.9455758306400303D+00, & 0.0071625399102445D+00, & 0.9455758306400303D+00, & 0.0472616294497257D+00, & 0.0685269541872130D+00, & 0.3585095935696251D+00, & 0.5729634522431620D+00, & 0.0685269541872130D+00, & 0.5729634522431620D+00, & 0.3585095935696253D+00, & 0.0393422453253830D+00, & 0.4803288773373086D+00, & 0.4803288773373087D+00, & 0.1017283293272843D+00, & 0.2404827720350127D+00, & 0.6577888986377033D+00, & 0.1017283293272843D+00, & 0.6577888986377033D+00, & 0.2404827720350129D+00, & 0.0868410482076333D+00, & 0.0868410482076330D+00, & 0.8263179035847338D+00, & 0.2113529879769170D+00, & 0.3943235060115416D+00, & 0.3943235060115416D+00, & 0.2662513178772474D+00, & 0.2662513178772473D+00, & 0.4674973642455055D+00, & 0.0583515752375155D+00, & 0.1729323031292239D+00, & 0.7687161216332608D+00, & 0.0583515752375155D+00, & 0.7687161216332608D+00, & 0.1729323031292242D+00, & 0.1548301554055163D+00, & 0.3163043076538382D+00, & 0.5288655369406458D+00, & 0.1548301554055163D+00, & 0.5288655369406458D+00, & 0.3163043076538383D+00, & 0.1371293873116478D+00, & 0.1371293873116475D+00, & 0.7257412253767048D+00, & 0.0020811375808274D+00, & 0.4989594312095864D+00, & 0.4989594312095865D+00, & 0.0147589697299452D+00, & 0.3977585768030077D+00, & 0.5874824534670474D+00, & 0.0147589697299452D+00, & 0.5874824534670473D+00, & 0.3977585768030079D+00, & 0.1106151157445450D+00, & 0.4446924421277276D+00, & 0.4446924421277277D+00, & 0.1987498063965364D+00, & 0.1987498063965362D+00, & 0.6025003872069277D+00, & 0.0329937081925328D+00, & 0.2787941698141023D+00, & 0.6882121219933651D+00, & 0.0329937081925328D+00, & 0.6882121219933650D+00, & 0.2787941698141025D+00, & 0.0090164402055985D+00, & 0.0090164402055982D+00, & 0.9819671195888034D+00, & 0.3333333333333334D+00 /) c = (/ & 0.8166259474208892D+00, & 0.0238702536543536D+00, & 0.1595037989247570D+00, & 0.1595037989247572D+00, & 0.0238702536543535D+00, & 0.8166259474208891D+00, & 0.8807088179167910D+00, & 0.0051898217608447D+00, & 0.1141013603223643D+00, & 0.1141013603223646D+00, & 0.0051898217608443D+00, & 0.8807088179167908D+00, & 0.9219854624859357D+00, & 0.0390072687570323D+00, & 0.0390072687570316D+00, & 0.8717190926395586D+00, & 0.0327410291887065D+00, & 0.0955398781717347D+00, & 0.0955398781717349D+00, & 0.0327410291887062D+00, & 0.8717190926395585D+00, & 0.6863901320923317D+00, & 0.0024475998559664D+00, & 0.3111622680517018D+00, & 0.3111622680517019D+00, & 0.0024475998559662D+00, & 0.6863901320923316D+00, & 0.7856574783566395D+00, & 0.0087252895853084D+00, & 0.2056172320580519D+00, & 0.2056172320580521D+00, & 0.0087252895853084D+00, & 0.7856574783566393D+00, & 0.9455758306400301D+00, & 0.0071625399102445D+00, & 0.0472616294497251D+00, & 0.0472616294497253D+00, & 0.0071625399102443D+00, & 0.9455758306400301D+00, & 0.5729634522431619D+00, & 0.0685269541872129D+00, & 0.3585095935696249D+00, & 0.3585095935696251D+00, & 0.0685269541872130D+00, & 0.5729634522431618D+00, & 0.4803288773373085D+00, & 0.0393422453253830D+00, & 0.4803288773373083D+00, & 0.6577888986377031D+00, & 0.1017283293272842D+00, & 0.2404827720350124D+00, & 0.2404827720350126D+00, & 0.1017283293272840D+00, & 0.6577888986377031D+00, & 0.8263179035847337D+00, & 0.0868410482076333D+00, & 0.0868410482076328D+00, & 0.3943235060115415D+00, & 0.2113529879769168D+00, & 0.3943235060115414D+00, & 0.4674973642455054D+00, & 0.2662513178772473D+00, & 0.2662513178772471D+00, & 0.7687161216332605D+00, & 0.0583515752375155D+00, & 0.1729323031292237D+00, & 0.1729323031292240D+00, & 0.0583515752375152D+00, & 0.7687161216332604D+00, & 0.5288655369406456D+00, & 0.1548301554055162D+00, & 0.3163043076538380D+00, & 0.3163043076538381D+00, & 0.1548301554055161D+00, & 0.5288655369406455D+00, & 0.7257412253767047D+00, & 0.1371293873116478D+00, & 0.1371293873116474D+00, & 0.4989594312095863D+00, & 0.0020811375808273D+00, & 0.4989594312095861D+00, & 0.5874824534670472D+00, & 0.0147589697299452D+00, & 0.3977585768030075D+00, & 0.3977585768030077D+00, & 0.0147589697299451D+00, & 0.5874824534670471D+00, & 0.4446924421277275D+00, & 0.1106151157445449D+00, & 0.4446924421277273D+00, & 0.6025003872069276D+00, & 0.1987498063965363D+00, & 0.1987498063965361D+00, & 0.6882121219933649D+00, & 0.0329937081925328D+00, & 0.2787941698141020D+00, & 0.2787941698141023D+00, & 0.0329937081925327D+00, & 0.6882121219933648D+00, & 0.9819671195888033D+00, & 0.0090164402055985D+00, & 0.0090164402055980D+00, & 0.3333333333333333D+00 /) w = (/ & 0.0025281660553823D+00, & 0.0025281660553823D+00, & 0.0025281660553823D+00, & 0.0025281660553823D+00, & 0.0025281660553823D+00, & 0.0025281660553823D+00, & 0.0022250197297245D+00, & 0.0022250197297245D+00, & 0.0022250197297245D+00, & 0.0022250197297245D+00, & 0.0022250197297245D+00, & 0.0022250197297245D+00, & 0.0039157402590329D+00, & 0.0039157402590329D+00, & 0.0039157402590329D+00, & 0.0053280304311948D+00, & 0.0053280304311948D+00, & 0.0053280304311948D+00, & 0.0053280304311948D+00, & 0.0053280304311948D+00, & 0.0053280304311948D+00, & 0.0022811036762558D+00, & 0.0022811036762558D+00, & 0.0022811036762558D+00, & 0.0022811036762558D+00, & 0.0022811036762558D+00, & 0.0022811036762558D+00, & 0.0041147503444161D+00, & 0.0041147503444161D+00, & 0.0041147503444161D+00, & 0.0041147503444161D+00, & 0.0041147503444161D+00, & 0.0041147503444161D+00, & 0.0019525913278907D+00, & 0.0019525913278907D+00, & 0.0019525913278907D+00, & 0.0019525913278907D+00, & 0.0019525913278907D+00, & 0.0019525913278907D+00, & 0.0149811133931992D+00, & 0.0149811133931992D+00, & 0.0149811133931992D+00, & 0.0149811133931992D+00, & 0.0149811133931992D+00, & 0.0149811133931992D+00, & 0.0113978892678008D+00, & 0.0113978892678008D+00, & 0.0113978892678008D+00, & 0.0161212416370172D+00, & 0.0161212416370172D+00, & 0.0161212416370172D+00, & 0.0161212416370172D+00, & 0.0161212416370172D+00, & 0.0161212416370172D+00, & 0.0089599170255135D+00, & 0.0089599170255135D+00, & 0.0089599170255135D+00, & 0.0236746084631280D+00, & 0.0236746084631280D+00, & 0.0236746084631280D+00, & 0.0238078628874998D+00, & 0.0238078628874998D+00, & 0.0238078628874998D+00, & 0.0104702564931301D+00, & 0.0104702564931301D+00, & 0.0104702564931301D+00, & 0.0104702564931301D+00, & 0.0104702564931301D+00, & 0.0104702564931301D+00, & 0.0208443958589688D+00, & 0.0208443958589688D+00, & 0.0208443958589688D+00, & 0.0208443958589688D+00, & 0.0208443958589688D+00, & 0.0208443958589688D+00, & 0.0145594493927417D+00, & 0.0145594493927417D+00, & 0.0145594493927417D+00, & 0.0024075446041814D+00, & 0.0024075446041814D+00, & 0.0024075446041814D+00, & 0.0070977788345218D+00, & 0.0070977788345218D+00, & 0.0070977788345218D+00, & 0.0070977788345218D+00, & 0.0070977788345218D+00, & 0.0070977788345218D+00, & 0.0189519506693389D+00, & 0.0189519506693389D+00, & 0.0189519506693389D+00, & 0.0199352778801050D+00, & 0.0199352778801050D+00, & 0.0199352778801050D+00, & 0.0101755746567070D+00, & 0.0101755746567070D+00, & 0.0101755746567070D+00, & 0.0101755746567070D+00, & 0.0101755746567070D+00, & 0.0101755746567070D+00, & 0.0010653612328293D+00, & 0.0010653612328293D+00, & 0.0010653612328293D+00, & 0.0252530603230362D+00 /) return end subroutine rule24 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule24() returns the rule of precision 24. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3333333333333333D+00, & 0.4188909749106027D+00, & 0.4188909749106027D+00, & 0.1622180501787944D+00, & 0.1623606337169263D+00, & 0.6752787325661472D+00, & 0.1623606337169265D+00, & 0.2414797600735940D+00, & 0.5881529574639622D+00, & 0.1703672824624437D+00, & 0.5881529574639622D+00, & 0.2414797600735940D+00, & 0.1703672824624436D+00, & 0.3289758089242263D+00, & 0.5012643952150375D+00, & 0.1697597958607360D+00, & 0.5012643952150376D+00, & 0.3289758089242264D+00, & 0.1697597958607359D+00, & 0.0409856290011169D+00, & 0.9180287419977657D+00, & 0.0409856290011174D+00, & 0.0067312708878883D+00, & 0.9865374582242232D+00, & 0.0067312708878887D+00, & 0.0931674097798811D+00, & 0.8685143643990995D+00, & 0.0383182258210195D+00, & 0.8685143643990995D+00, & 0.0931674097798812D+00, & 0.0383182258210191D+00, & 0.3945202798001943D+00, & 0.5128232386790481D+00, & 0.0926564815207574D+00, & 0.5128232386790481D+00, & 0.3945202798001944D+00, & 0.0926564815207574D+00, & 0.1626774163944774D+00, & 0.7961338693570472D+00, & 0.0411887142484756D+00, & 0.7961338693570472D+00, & 0.1626774163944775D+00, & 0.0411887142484752D+00, & 0.2535890142188795D+00, & 0.7068400808109625D+00, & 0.0395709049701581D+00, & 0.7068400808109625D+00, & 0.2535890142188795D+00, & 0.0395709049701579D+00, & 0.3622522413177913D+00, & 0.5991550585073127D+00, & 0.0385927001748961D+00, & 0.5991550585073125D+00, & 0.3622522413177913D+00, & 0.0385927001748960D+00, & 0.2816225777061608D+00, & 0.6238424605572400D+00, & 0.0945349617365990D+00, & 0.6238424605572401D+00, & 0.2816225777061608D+00, & 0.0945349617365988D+00, & 0.3832726649926592D+00, & 0.6093393403750466D+00, & 0.0073879946322942D+00, & 0.6093393403750464D+00, & 0.3832726649926592D+00, & 0.0073879946322941D+00, & 0.2737503525162605D+00, & 0.7187036443214266D+00, & 0.0075460031623129D+00, & 0.7187036443214266D+00, & 0.2737503525162606D+00, & 0.0075460031623126D+00, & 0.4962552776757351D+00, & 0.4962552776757351D+00, & 0.0074894446485297D+00, & 0.0941213427973660D+00, & 0.8986440987448518D+00, & 0.0072345584577822D+00, & 0.8986440987448518D+00, & 0.0941213427973661D+00, & 0.0072345584577819D+00, & 0.2642313154382725D+00, & 0.4715373691234548D+00, & 0.2642313154382727D+00, & 0.1803961518867657D+00, & 0.7240375785858689D+00, & 0.0955662695273654D+00, & 0.7240375785858689D+00, & 0.1803961518867657D+00, & 0.0955662695273650D+00, & 0.4806125617925032D+00, & 0.4806125617925033D+00, & 0.0387748764149934D+00, & 0.1747373462828057D+00, & 0.8172747318363464D+00, & 0.0079879218808480D+00, & 0.8172747318363462D+00, & 0.1747373462828057D+00, & 0.0079879218808478D+00, & 0.0963284955992151D+00, & 0.8073430088015696D+00, & 0.0963284955992154D+00, & 0.0372914720512912D+00, & 0.9546336170785000D+00, & 0.0080749108702090D+00, & 0.9546336170785000D+00, & 0.0372914720512914D+00, & 0.0080749108702085D+00, & 0.3753529267020863D+00, & 0.3753529267020863D+00, & 0.2492941465958274D+00 /) b = (/ & 0.3333333333333334D+00, & 0.1622180501787945D+00, & 0.4188909749106028D+00, & 0.4188909749106029D+00, & 0.1623606337169265D+00, & 0.1623606337169263D+00, & 0.6752787325661475D+00, & 0.1703672824624437D+00, & 0.2414797600735941D+00, & 0.5881529574639625D+00, & 0.1703672824624437D+00, & 0.5881529574639625D+00, & 0.2414797600735942D+00, & 0.1697597958607361D+00, & 0.3289758089242264D+00, & 0.5012643952150377D+00, & 0.1697597958607361D+00, & 0.5012643952150377D+00, & 0.3289758089242266D+00, & 0.0409856290011173D+00, & 0.0409856290011169D+00, & 0.9180287419977659D+00, & 0.0067312708878885D+00, & 0.0067312708878882D+00, & 0.9865374582242232D+00, & 0.0383182258210194D+00, & 0.0931674097798812D+00, & 0.8685143643990996D+00, & 0.0383182258210194D+00, & 0.8685143643990996D+00, & 0.0931674097798815D+00, & 0.0926564815207575D+00, & 0.3945202798001944D+00, & 0.5128232386790483D+00, & 0.0926564815207575D+00, & 0.5128232386790482D+00, & 0.3945202798001946D+00, & 0.0411887142484754D+00, & 0.1626774163944774D+00, & 0.7961338693570472D+00, & 0.0411887142484754D+00, & 0.7961338693570472D+00, & 0.1626774163944777D+00, & 0.0395709049701581D+00, & 0.2535890142188795D+00, & 0.7068400808109626D+00, & 0.0395709049701581D+00, & 0.7068400808109626D+00, & 0.2535890142188797D+00, & 0.0385927001748961D+00, & 0.3622522413177914D+00, & 0.5991550585073128D+00, & 0.0385927001748961D+00, & 0.5991550585073127D+00, & 0.3622522413177915D+00, & 0.0945349617365990D+00, & 0.2816225777061609D+00, & 0.6238424605572404D+00, & 0.0945349617365990D+00, & 0.6238424605572404D+00, & 0.2816225777061611D+00, & 0.0073879946322942D+00, & 0.3832726649926593D+00, & 0.6093393403750468D+00, & 0.0073879946322942D+00, & 0.6093393403750467D+00, & 0.3832726649926595D+00, & 0.0075460031623128D+00, & 0.2737503525162605D+00, & 0.7187036443214270D+00, & 0.0075460031623128D+00, & 0.7187036443214267D+00, & 0.2737503525162608D+00, & 0.0074894446485298D+00, & 0.4962552776757352D+00, & 0.4962552776757354D+00, & 0.0072345584577821D+00, & 0.0941213427973660D+00, & 0.8986440987448521D+00, & 0.0072345584577821D+00, & 0.8986440987448520D+00, & 0.0941213427973664D+00, & 0.2642313154382727D+00, & 0.2642313154382726D+00, & 0.4715373691234549D+00, & 0.0955662695273653D+00, & 0.1803961518867657D+00, & 0.7240375785858691D+00, & 0.0955662695273653D+00, & 0.7240375785858693D+00, & 0.1803961518867660D+00, & 0.0387748764149935D+00, & 0.4806125617925033D+00, & 0.4806125617925034D+00, & 0.0079879218808480D+00, & 0.1747373462828057D+00, & 0.8172747318363466D+00, & 0.0079879218808480D+00, & 0.8172747318363466D+00, & 0.1747373462828060D+00, & 0.0963284955992153D+00, & 0.0963284955992151D+00, & 0.8073430088015697D+00, & 0.0080749108702088D+00, & 0.0372914720512912D+00, & 0.9546336170785000D+00, & 0.0080749108702088D+00, & 0.9546336170785000D+00, & 0.0372914720512916D+00, & 0.2492941465958275D+00, & 0.3753529267020864D+00, & 0.3753529267020864D+00 /) c = (/ & 0.3333333333333333D+00, & 0.4188909749106028D+00, & 0.1622180501787945D+00, & 0.4188909749106027D+00, & 0.6752787325661472D+00, & 0.1623606337169265D+00, & 0.1623606337169260D+00, & 0.5881529574639622D+00, & 0.1703672824624437D+00, & 0.2414797600735938D+00, & 0.2414797600735940D+00, & 0.1703672824624435D+00, & 0.5881529574639621D+00, & 0.5012643952150376D+00, & 0.1697597958607361D+00, & 0.3289758089242263D+00, & 0.3289758089242263D+00, & 0.1697597958607359D+00, & 0.5012643952150375D+00, & 0.9180287419977659D+00, & 0.0409856290011173D+00, & 0.0409856290011167D+00, & 0.9865374582242232D+00, & 0.0067312708878886D+00, & 0.0067312708878881D+00, & 0.8685143643990995D+00, & 0.0383182258210194D+00, & 0.0931674097798809D+00, & 0.0931674097798811D+00, & 0.0383182258210192D+00, & 0.8685143643990995D+00, & 0.5128232386790481D+00, & 0.0926564815207574D+00, & 0.3945202798001942D+00, & 0.3945202798001943D+00, & 0.0926564815207574D+00, & 0.5128232386790480D+00, & 0.7961338693570472D+00, & 0.0411887142484754D+00, & 0.1626774163944772D+00, & 0.1626774163944774D+00, & 0.0411887142484753D+00, & 0.7961338693570471D+00, & 0.7068400808109625D+00, & 0.0395709049701580D+00, & 0.2535890142188794D+00, & 0.2535890142188795D+00, & 0.0395709049701579D+00, & 0.7068400808109623D+00, & 0.5991550585073125D+00, & 0.0385927001748960D+00, & 0.3622522413177912D+00, & 0.3622522413177913D+00, & 0.0385927001748960D+00, & 0.5991550585073124D+00, & 0.6238424605572401D+00, & 0.0945349617365990D+00, & 0.2816225777061607D+00, & 0.2816225777061608D+00, & 0.0945349617365988D+00, & 0.6238424605572401D+00, & 0.6093393403750466D+00, & 0.0073879946322942D+00, & 0.3832726649926591D+00, & 0.3832726649926593D+00, & 0.0073879946322941D+00, & 0.6093393403750464D+00, & 0.7187036443214266D+00, & 0.0075460031623129D+00, & 0.2737503525162601D+00, & 0.2737503525162606D+00, & 0.0075460031623127D+00, & 0.7187036443214266D+00, & 0.4962552776757350D+00, & 0.0074894446485297D+00, & 0.4962552776757349D+00, & 0.8986440987448518D+00, & 0.0072345584577821D+00, & 0.0941213427973657D+00, & 0.0941213427973660D+00, & 0.0072345584577819D+00, & 0.8986440987448517D+00, & 0.4715373691234548D+00, & 0.2642313154382726D+00, & 0.2642313154382724D+00, & 0.7240375785858690D+00, & 0.0955662695273653D+00, & 0.1803961518867655D+00, & 0.1803961518867658D+00, & 0.0955662695273650D+00, & 0.7240375785858690D+00, & 0.4806125617925033D+00, & 0.0387748764149934D+00, & 0.4806125617925031D+00, & 0.8172747318363464D+00, & 0.0079879218808480D+00, & 0.1747373462828054D+00, & 0.1747373462828058D+00, & 0.0079879218808477D+00, & 0.8172747318363462D+00, & 0.8073430088015696D+00, & 0.0963284955992153D+00, & 0.0963284955992149D+00, & 0.9546336170785000D+00, & 0.0080749108702088D+00, & 0.0372914720512910D+00, & 0.0372914720512912D+00, & 0.0080749108702086D+00, & 0.9546336170784999D+00, & 0.3753529267020862D+00, & 0.2492941465958273D+00, & 0.3753529267020862D+00 /) w = (/ & 0.0125456898456003D+00, & 0.0131105327018852D+00, & 0.0131105327018852D+00, & 0.0131105327018852D+00, & 0.0103790160564002D+00, & 0.0103790160564002D+00, & 0.0103790160564002D+00, & 0.0141450458064848D+00, & 0.0141450458064848D+00, & 0.0141450458064848D+00, & 0.0141450458064848D+00, & 0.0141450458064848D+00, & 0.0141450458064848D+00, & 0.0152744426013246D+00, & 0.0152744426013246D+00, & 0.0152744426013246D+00, & 0.0152744426013246D+00, & 0.0152744426013246D+00, & 0.0152744426013246D+00, & 0.0038336997309292D+00, & 0.0038336997309292D+00, & 0.0038336997309292D+00, & 0.0006172545054966D+00, & 0.0006172545054966D+00, & 0.0006172545054966D+00, & 0.0053662714541678D+00, & 0.0053662714541678D+00, & 0.0053662714541678D+00, & 0.0053662714541678D+00, & 0.0053662714541678D+00, & 0.0053662714541678D+00, & 0.0150318543497413D+00, & 0.0150318543497413D+00, & 0.0150318543497413D+00, & 0.0150318543497413D+00, & 0.0150318543497413D+00, & 0.0150318543497413D+00, & 0.0072041341747974D+00, & 0.0072041341747974D+00, & 0.0072041341747974D+00, & 0.0072041341747974D+00, & 0.0072041341747974D+00, & 0.0072041341747974D+00, & 0.0089048769281636D+00, & 0.0089048769281636D+00, & 0.0089048769281636D+00, & 0.0089048769281636D+00, & 0.0089048769281636D+00, & 0.0089048769281636D+00, & 0.0099472518756824D+00, & 0.0099472518756824D+00, & 0.0099472518756824D+00, & 0.0099472518756824D+00, & 0.0099472518756824D+00, & 0.0099472518756824D+00, & 0.0143523515781575D+00, & 0.0143523515781575D+00, & 0.0143523515781575D+00, & 0.0143523515781575D+00, & 0.0143523515781575D+00, & 0.0143523515781575D+00, & 0.0042421492668038D+00, & 0.0042421492668038D+00, & 0.0042421492668038D+00, & 0.0042421492668038D+00, & 0.0042421492668038D+00, & 0.0042421492668038D+00, & 0.0040812750771165D+00, & 0.0040812750771165D+00, & 0.0040812750771165D+00, & 0.0040812750771165D+00, & 0.0040812750771165D+00, & 0.0040812750771165D+00, & 0.0043432467221707D+00, & 0.0043432467221707D+00, & 0.0043432467221707D+00, & 0.0025892123823980D+00, & 0.0025892123823980D+00, & 0.0025892123823980D+00, & 0.0025892123823980D+00, & 0.0025892123823980D+00, & 0.0025892123823980D+00, & 0.0205200086715098D+00, & 0.0205200086715098D+00, & 0.0205200086715098D+00, & 0.0118435621425431D+00, & 0.0118435621425431D+00, & 0.0118435621425431D+00, & 0.0118435621425431D+00, & 0.0118435621425431D+00, & 0.0118435621425431D+00, & 0.0103524947708526D+00, & 0.0103524947708526D+00, & 0.0103524947708526D+00, & 0.0037072267642463D+00, & 0.0037072267642463D+00, & 0.0037072267642463D+00, & 0.0037072267642463D+00, & 0.0037072267642463D+00, & 0.0037072267642463D+00, & 0.0100273930673889D+00, & 0.0100273930673889D+00, & 0.0100273930673889D+00, & 0.0017969475854466D+00, & 0.0017969475854466D+00, & 0.0017969475854466D+00, & 0.0017969475854466D+00, & 0.0017969475854466D+00, & 0.0017969475854466D+00, & 0.0189945865173527D+00, & 0.0189945865173527D+00, & 0.0189945865173527D+00 /) return end subroutine rule25 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule25() returns the rule of precision 25. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3876420304045634D+00, & 0.3876420304045634D+00, & 0.2247159391908731D+00, & 0.2110045080614966D+00, & 0.5779909838770066D+00, & 0.2110045080614967D+00, & 0.4404169274793433D+00, & 0.5577642058863823D+00, & 0.0018188666342743D+00, & 0.5577642058863823D+00, & 0.4404169274793434D+00, & 0.0018188666342743D+00, & 0.2994923158045084D+00, & 0.4010153683909830D+00, & 0.2994923158045084D+00, & 0.1590079061973279D+00, & 0.8040319522230005D+00, & 0.0369601415796716D+00, & 0.8040319522230007D+00, & 0.1590079061973279D+00, & 0.0369601415796713D+00, & 0.0372229259924406D+00, & 0.9255541480151184D+00, & 0.0372229259924410D+00, & 0.1773537967572529D+00, & 0.7437881352371117D+00, & 0.0788580680056354D+00, & 0.7437881352371118D+00, & 0.1773537967572530D+00, & 0.0788580680056351D+00, & 0.1451092435745002D+00, & 0.7097815128509992D+00, & 0.1451092435745006D+00, & 0.2700667358209594D+00, & 0.6610857347475426D+00, & 0.0688475294314979D+00, & 0.6610857347475427D+00, & 0.2700667358209594D+00, & 0.0688475294314977D+00, & 0.3413910330211499D+00, & 0.5426091593378899D+00, & 0.1159998076409602D+00, & 0.5426091593378899D+00, & 0.3413910330211499D+00, & 0.1159998076409601D+00, & 0.3739379797195844D+00, & 0.5777445859930386D+00, & 0.0483174342873769D+00, & 0.5777445859930387D+00, & 0.3739379797195845D+00, & 0.0483174342873768D+00, & 0.0991330633416822D+00, & 0.8937386221570603D+00, & 0.0071283145012576D+00, & 0.8937386221570603D+00, & 0.0991330633416823D+00, & 0.0071283145012572D+00, & 0.2995064186296745D+00, & 0.4968006707860745D+00, & 0.2036929105842510D+00, & 0.4968006707860745D+00, & 0.2995064186296745D+00, & 0.2036929105842509D+00, & 0.4247593045405747D+00, & 0.4247593045405746D+00, & 0.1504813909188505D+00, & 0.1786298486036162D+00, & 0.8141339896484356D+00, & 0.0072361617479482D+00, & 0.8141339896484356D+00, & 0.1786298486036164D+00, & 0.0072361617479479D+00, & 0.3620688018959720D+00, & 0.6250173148539955D+00, & 0.0129138832500325D+00, & 0.6250173148539954D+00, & 0.3620688018959721D+00, & 0.0129138832500325D+00, & 0.0887929154893665D+00, & 0.8735191347263743D+00, & 0.0376879497842592D+00, & 0.8735191347263743D+00, & 0.0887929154893666D+00, & 0.0376879497842588D+00, & 0.2336228101417152D+00, & 0.6293704957712137D+00, & 0.1370066940870710D+00, & 0.6293704957712138D+00, & 0.2336228101417152D+00, & 0.1370066940870708D+00, & 0.4622087087487061D+00, & 0.4622087087487061D+00, & 0.0755825825025877D+00, & 0.2565954097090198D+00, & 0.7188645300434557D+00, & 0.0245400602475245D+00, & 0.7188645300434559D+00, & 0.2565954097090199D+00, & 0.0245400602475242D+00, & 0.0929497017007698D+00, & 0.8141005965984600D+00, & 0.0929497017007701D+00, & 0.0410688191117846D+00, & 0.9517423526265223D+00, & 0.0071888282616933D+00, & 0.9517423526265224D+00, & 0.0410688191117848D+00, & 0.0071888282616928D+00, & 0.0078353442826036D+00, & 0.9843293114347924D+00, & 0.0078353442826041D+00, & 0.4890393696603955D+00, & 0.4890393696603955D+00, & 0.0219212606792090D+00, & 0.2794161886492607D+00, & 0.7196923470332411D+00, & 0.0008914643174981D+00, & 0.7196923470332411D+00, & 0.2794161886492608D+00, & 0.0008914643174980D+00 /) b = (/ & 0.2247159391908732D+00, & 0.3876420304045635D+00, & 0.3876420304045636D+00, & 0.2110045080614968D+00, & 0.2110045080614966D+00, & 0.5779909838770069D+00, & 0.0018188666342744D+00, & 0.4404169274793434D+00, & 0.5577642058863825D+00, & 0.0018188666342744D+00, & 0.5577642058863823D+00, & 0.4404169274793436D+00, & 0.2994923158045086D+00, & 0.2994923158045085D+00, & 0.4010153683909831D+00, & 0.0369601415796715D+00, & 0.1590079061973279D+00, & 0.8040319522230007D+00, & 0.0369601415796715D+00, & 0.8040319522230007D+00, & 0.1590079061973282D+00, & 0.0372229259924409D+00, & 0.0372229259924406D+00, & 0.9255541480151186D+00, & 0.0788580680056353D+00, & 0.1773537967572529D+00, & 0.7437881352371120D+00, & 0.0788580680056353D+00, & 0.7437881352371120D+00, & 0.1773537967572532D+00, & 0.1451092435745005D+00, & 0.1451092435745003D+00, & 0.7097815128509993D+00, & 0.0688475294314979D+00, & 0.2700667358209594D+00, & 0.6610857347475428D+00, & 0.0688475294314979D+00, & 0.6610857347475428D+00, & 0.2700667358209596D+00, & 0.1159998076409602D+00, & 0.3413910330211499D+00, & 0.5426091593378901D+00, & 0.1159998076409602D+00, & 0.5426091593378900D+00, & 0.3413910330211500D+00, & 0.0483174342873770D+00, & 0.3739379797195844D+00, & 0.5777445859930388D+00, & 0.0483174342873770D+00, & 0.5777445859930387D+00, & 0.3739379797195846D+00, & 0.0071283145012574D+00, & 0.0991330633416822D+00, & 0.8937386221570605D+00, & 0.0071283145012574D+00, & 0.8937386221570605D+00, & 0.0991330633416825D+00, & 0.2036929105842510D+00, & 0.2995064186296746D+00, & 0.4968006707860746D+00, & 0.2036929105842510D+00, & 0.4968006707860746D+00, & 0.2995064186296747D+00, & 0.1504813909188506D+00, & 0.4247593045405748D+00, & 0.4247593045405749D+00, & 0.0072361617479482D+00, & 0.1786298486036162D+00, & 0.8141339896484358D+00, & 0.0072361617479482D+00, & 0.8141339896484358D+00, & 0.1786298486036166D+00, & 0.0129138832500325D+00, & 0.3620688018959721D+00, & 0.6250173148539957D+00, & 0.0129138832500325D+00, & 0.6250173148539956D+00, & 0.3620688018959722D+00, & 0.0376879497842591D+00, & 0.0887929154893666D+00, & 0.8735191347263744D+00, & 0.0376879497842591D+00, & 0.8735191347263744D+00, & 0.0887929154893669D+00, & 0.1370066940870710D+00, & 0.2336228101417153D+00, & 0.6293704957712140D+00, & 0.1370066940870710D+00, & 0.6293704957712140D+00, & 0.2336228101417155D+00, & 0.0755825825025878D+00, & 0.4622087087487062D+00, & 0.4622087087487063D+00, & 0.0245400602475244D+00, & 0.2565954097090198D+00, & 0.7188645300434559D+00, & 0.0245400602475244D+00, & 0.7188645300434559D+00, & 0.2565954097090201D+00, & 0.0929497017007700D+00, & 0.0929497017007698D+00, & 0.8141005965984602D+00, & 0.0071888282616930D+00, & 0.0410688191117846D+00, & 0.9517423526265224D+00, & 0.0071888282616930D+00, & 0.9517423526265224D+00, & 0.0410688191117850D+00, & 0.0078353442826039D+00, & 0.0078353442826036D+00, & 0.9843293114347926D+00, & 0.0219212606792091D+00, & 0.4890393696603955D+00, & 0.4890393696603957D+00, & 0.0008914643174981D+00, & 0.2794161886492607D+00, & 0.7196923470332415D+00, & 0.0008914643174981D+00, & 0.7196923470332413D+00, & 0.2794161886492610D+00 /) c = (/ & 0.3876420304045634D+00, & 0.2247159391908732D+00, & 0.3876420304045634D+00, & 0.5779909838770066D+00, & 0.2110045080614967D+00, & 0.2110045080614965D+00, & 0.5577642058863823D+00, & 0.0018188666342743D+00, & 0.4404169274793431D+00, & 0.4404169274793433D+00, & 0.0018188666342743D+00, & 0.5577642058863822D+00, & 0.4010153683909830D+00, & 0.2994923158045085D+00, & 0.2994923158045085D+00, & 0.8040319522230006D+00, & 0.0369601415796716D+00, & 0.1590079061973276D+00, & 0.1590079061973278D+00, & 0.0369601415796713D+00, & 0.8040319522230005D+00, & 0.9255541480151185D+00, & 0.0372229259924410D+00, & 0.0372229259924404D+00, & 0.7437881352371117D+00, & 0.0788580680056354D+00, & 0.1773537967572526D+00, & 0.1773537967572529D+00, & 0.0788580680056351D+00, & 0.7437881352371117D+00, & 0.7097815128509992D+00, & 0.1451092435745005D+00, & 0.1451092435745002D+00, & 0.6610857347475426D+00, & 0.0688475294314980D+00, & 0.2700667358209593D+00, & 0.2700667358209593D+00, & 0.0688475294314977D+00, & 0.6610857347475426D+00, & 0.5426091593378900D+00, & 0.1159998076409602D+00, & 0.3413910330211497D+00, & 0.3413910330211499D+00, & 0.1159998076409602D+00, & 0.5426091593378899D+00, & 0.5777445859930387D+00, & 0.0483174342873770D+00, & 0.3739379797195843D+00, & 0.3739379797195844D+00, & 0.0483174342873768D+00, & 0.5777445859930385D+00, & 0.8937386221570605D+00, & 0.0071283145012575D+00, & 0.0991330633416820D+00, & 0.0991330633416822D+00, & 0.0071283145012573D+00, & 0.8937386221570603D+00, & 0.4968006707860744D+00, & 0.2036929105842509D+00, & 0.2995064186296744D+00, & 0.2995064186296745D+00, & 0.2036929105842509D+00, & 0.4968006707860744D+00, & 0.4247593045405748D+00, & 0.1504813909188505D+00, & 0.4247593045405746D+00, & 0.8141339896484356D+00, & 0.0072361617479481D+00, & 0.1786298486036161D+00, & 0.1786298486036162D+00, & 0.0072361617479478D+00, & 0.8141339896484355D+00, & 0.6250173148539955D+00, & 0.0129138832500325D+00, & 0.3620688018959718D+00, & 0.3620688018959721D+00, & 0.0129138832500323D+00, & 0.6250173148539954D+00, & 0.8735191347263744D+00, & 0.0376879497842591D+00, & 0.0887929154893663D+00, & 0.0887929154893666D+00, & 0.0376879497842589D+00, & 0.8735191347263743D+00, & 0.6293704957712137D+00, & 0.1370066940870710D+00, & 0.2336228101417150D+00, & 0.2336228101417152D+00, & 0.1370066940870708D+00, & 0.6293704957712137D+00, & 0.4622087087487061D+00, & 0.0755825825025877D+00, & 0.4622087087487059D+00, & 0.7188645300434559D+00, & 0.0245400602475244D+00, & 0.2565954097090196D+00, & 0.2565954097090197D+00, & 0.0245400602475242D+00, & 0.7188645300434557D+00, & 0.8141005965984602D+00, & 0.0929497017007702D+00, & 0.0929497017007697D+00, & 0.9517423526265223D+00, & 0.0071888282616931D+00, & 0.0410688191117844D+00, & 0.0410688191117846D+00, & 0.0071888282616929D+00, & 0.9517423526265223D+00, & 0.9843293114347924D+00, & 0.0078353442826040D+00, & 0.0078353442826032D+00, & 0.4890393696603955D+00, & 0.0219212606792091D+00, & 0.4890393696603952D+00, & 0.7196923470332411D+00, & 0.0008914643174981D+00, & 0.2794161886492604D+00, & 0.2794161886492607D+00, & 0.0008914643174980D+00, & 0.7196923470332410D+00 /) w = (/ & 0.0136898515482722D+00, & 0.0136898515482722D+00, & 0.0136898515482722D+00, & 0.0115872632360106D+00, & 0.0115872632360106D+00, & 0.0115872632360106D+00, & 0.0016748178319347D+00, & 0.0016748178319347D+00, & 0.0016748178319347D+00, & 0.0016748178319347D+00, & 0.0016748178319347D+00, & 0.0016748178319347D+00, & 0.0180176407017015D+00, & 0.0180176407017015D+00, & 0.0180176407017015D+00, & 0.0063114780247593D+00, & 0.0063114780247593D+00, & 0.0063114780247593D+00, & 0.0063114780247593D+00, & 0.0063114780247593D+00, & 0.0063114780247593D+00, & 0.0033972977219047D+00, & 0.0033972977219047D+00, & 0.0033972977219047D+00, & 0.0095150215674558D+00, & 0.0095150215674558D+00, & 0.0095150215674558D+00, & 0.0095150215674558D+00, & 0.0095150215674558D+00, & 0.0095150215674558D+00, & 0.0114915258625648D+00, & 0.0114915258625648D+00, & 0.0114915258625648D+00, & 0.0108843936124369D+00, & 0.0108843936124369D+00, & 0.0108843936124369D+00, & 0.0108843936124369D+00, & 0.0108843936124369D+00, & 0.0108843936124369D+00, & 0.0158403522878984D+00, & 0.0158403522878984D+00, & 0.0158403522878984D+00, & 0.0158403522878984D+00, & 0.0158403522878984D+00, & 0.0158403522878984D+00, & 0.0106401706955088D+00, & 0.0106401706955088D+00, & 0.0106401706955088D+00, & 0.0106401706955088D+00, & 0.0106401706955088D+00, & 0.0106401706955088D+00, & 0.0025452716253490D+00, & 0.0025452716253490D+00, & 0.0025452716253490D+00, & 0.0025452716253490D+00, & 0.0025452716253490D+00, & 0.0025452716253490D+00, & 0.0179138208922761D+00, & 0.0179138208922761D+00, & 0.0179138208922761D+00, & 0.0179138208922761D+00, & 0.0179138208922761D+00, & 0.0179138208922761D+00, & 0.0159113101374584D+00, & 0.0159113101374584D+00, & 0.0159113101374584D+00, & 0.0032637396820492D+00, & 0.0032637396820492D+00, & 0.0032637396820492D+00, & 0.0032637396820492D+00, & 0.0032637396820492D+00, & 0.0032637396820492D+00, & 0.0054546383679744D+00, & 0.0054546383679744D+00, & 0.0054546383679744D+00, & 0.0054546383679744D+00, & 0.0054546383679744D+00, & 0.0054546383679744D+00, & 0.0052725619214294D+00, & 0.0052725619214294D+00, & 0.0052725619214294D+00, & 0.0052725619214294D+00, & 0.0052725619214294D+00, & 0.0052725619214294D+00, & 0.0137400825920226D+00, & 0.0137400825920226D+00, & 0.0137400825920226D+00, & 0.0137400825920226D+00, & 0.0137400825920226D+00, & 0.0137400825920226D+00, & 0.0136542751875280D+00, & 0.0136542751875280D+00, & 0.0136542751875280D+00, & 0.0073143409079328D+00, & 0.0073143409079328D+00, & 0.0073143409079328D+00, & 0.0073143409079328D+00, & 0.0073143409079328D+00, & 0.0073143409079328D+00, & 0.0091828212598200D+00, & 0.0091828212598200D+00, & 0.0091828212598200D+00, & 0.0016929836341273D+00, & 0.0016929836341273D+00, & 0.0016929836341273D+00, & 0.0016929836341273D+00, & 0.0016929836341273D+00, & 0.0016929836341273D+00, & 0.0008065102883246D+00, & 0.0008065102883246D+00, & 0.0008065102883246D+00, & 0.0084440859465211D+00, & 0.0084440859465211D+00, & 0.0084440859465211D+00, & 0.0015117020784589D+00, & 0.0015117020784589D+00, & 0.0015117020784589D+00, & 0.0015117020784589D+00, & 0.0015117020784589D+00, & 0.0015117020784589D+00 /) return end subroutine rule26 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule26() returns the rule of precision 26. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0800716549403165D+00, & 0.9151336840842468D+00, & 0.0047946609754368D+00, & 0.9151336840842468D+00, & 0.0800716549403166D+00, & 0.0047946609754365D+00, & 0.0316436115715308D+00, & 0.9392011922216335D+00, & 0.0291551962068360D+00, & 0.9392011922216333D+00, & 0.0316436115715308D+00, & 0.0291551962068356D+00, & 0.0667371225764661D+00, & 0.8665257548470675D+00, & 0.0667371225764665D+00, & 0.0753800475153987D+00, & 0.8984105884621026D+00, & 0.0262093640224987D+00, & 0.8984105884621026D+00, & 0.0753800475153986D+00, & 0.0262093640224984D+00, & 0.0331000343360323D+00, & 0.9612018477470925D+00, & 0.0056981179168754D+00, & 0.9612018477470925D+00, & 0.0331000343360324D+00, & 0.0056981179168749D+00, & 0.0063401164920767D+00, & 0.9873197670158463D+00, & 0.0063401164920771D+00, & 0.1324861896145673D+00, & 0.8257890876433117D+00, & 0.0417247227421210D+00, & 0.8257890876433117D+00, & 0.1324861896145674D+00, & 0.0417247227421207D+00, & 0.1086871329144021D+00, & 0.7912672079790702D+00, & 0.1000456591065276D+00, & 0.7912672079790704D+00, & 0.1086871329144022D+00, & 0.1000456591065273D+00, & 0.4937530328963848D+00, & 0.4937530328963847D+00, & 0.0124939342072304D+00, & 0.2502723132905265D+00, & 0.6291132845042245D+00, & 0.1206144022052490D+00, & 0.6291132845042245D+00, & 0.2502723132905265D+00, & 0.1206144022052489D+00, & 0.3890220620427617D+00, & 0.5814399954403304D+00, & 0.0295379425169078D+00, & 0.5814399954403304D+00, & 0.3890220620427618D+00, & 0.0295379425169077D+00, & 0.3585092964276616D+00, & 0.5541122384084940D+00, & 0.0873784651638445D+00, & 0.5541122384084940D+00, & 0.3585092964276616D+00, & 0.0873784651638444D+00, & 0.3887874971075940D+00, & 0.3887874971075940D+00, & 0.2224250057848119D+00, & 0.1868691794762216D+00, & 0.7368189190108190D+00, & 0.0763119015129595D+00, & 0.7368189190108190D+00, & 0.1868691794762216D+00, & 0.0763119015129592D+00, & 0.2731471009290787D+00, & 0.4537057981418425D+00, & 0.2731471009290788D+00, & 0.4147059095903063D+00, & 0.5832365594443230D+00, & 0.0020575309653708D+00, & 0.5832365594443230D+00, & 0.4147059095903063D+00, & 0.0020575309653707D+00, & 0.3194153053834387D+00, & 0.5101059661193124D+00, & 0.1704787284972489D+00, & 0.5101059661193124D+00, & 0.3194153053834387D+00, & 0.1704787284972488D+00, & 0.1437376261997640D+00, & 0.8482627657087517D+00, & 0.0079996080914844D+00, & 0.8482627657087517D+00, & 0.1437376261997642D+00, & 0.0079996080914840D+00, & 0.4718285633211660D+00, & 0.4718285633211661D+00, & 0.0563428733576679D+00, & 0.1542014303645442D+00, & 0.6915971392709114D+00, & 0.1542014303645444D+00, & 0.2837881388594704D+00, & 0.6650459874553918D+00, & 0.0511658736851378D+00, & 0.6650459874553918D+00, & 0.2837881388594705D+00, & 0.0511658736851376D+00, & 0.2120431633022055D+00, & 0.5759136733955887D+00, & 0.2120431633022057D+00, & 0.4359854193843832D+00, & 0.4359854193843832D+00, & 0.1280291612312335D+00, & 0.2165466664734771D+00, & 0.7606687342756272D+00, & 0.0227845992508957D+00, & 0.7606687342756272D+00, & 0.2165466664734772D+00, & 0.0227845992508955D+00, & 0.3333333333333333D+00, & 0.3128985030748800D+00, & 0.6776281990129065D+00, & 0.0094732979122136D+00, & 0.6776281990129064D+00, & 0.3128985030748800D+00, & 0.0094732979122134D+00, & 0.2264347974077175D+00, & 0.7731011948601069D+00, & 0.0004640077321757D+00, & 0.7731011948601069D+00, & 0.2264347974077175D+00, & 0.0004640077321755D+00 /) b = (/ & 0.0047946609754367D+00, & 0.0800716549403165D+00, & 0.9151336840842469D+00, & 0.0047946609754367D+00, & 0.9151336840842469D+00, & 0.0800716549403169D+00, & 0.0291551962068358D+00, & 0.0316436115715307D+00, & 0.9392011922216336D+00, & 0.0291551962068358D+00, & 0.9392011922216336D+00, & 0.0316436115715311D+00, & 0.0667371225764664D+00, & 0.0667371225764660D+00, & 0.8665257548470677D+00, & 0.0262093640224987D+00, & 0.0753800475153986D+00, & 0.8984105884621029D+00, & 0.0262093640224987D+00, & 0.8984105884621030D+00, & 0.0753800475153990D+00, & 0.0056981179168752D+00, & 0.0331000343360323D+00, & 0.9612018477470927D+00, & 0.0056981179168752D+00, & 0.9612018477470927D+00, & 0.0331000343360326D+00, & 0.0063401164920770D+00, & 0.0063401164920766D+00, & 0.9873197670158466D+00, & 0.0417247227421209D+00, & 0.1324861896145673D+00, & 0.8257890876433118D+00, & 0.0417247227421209D+00, & 0.8257890876433118D+00, & 0.1324861896145676D+00, & 0.1000456591065276D+00, & 0.1086871329144021D+00, & 0.7912672079790705D+00, & 0.1000456591065276D+00, & 0.7912672079790705D+00, & 0.1086871329144024D+00, & 0.0124939342072305D+00, & 0.4937530328963848D+00, & 0.4937530328963849D+00, & 0.1206144022052490D+00, & 0.2502723132905265D+00, & 0.6291132845042247D+00, & 0.1206144022052490D+00, & 0.6291132845042245D+00, & 0.2502723132905267D+00, & 0.0295379425169078D+00, & 0.3890220620427618D+00, & 0.5814399954403305D+00, & 0.0295379425169078D+00, & 0.5814399954403304D+00, & 0.3890220620427621D+00, & 0.0873784651638445D+00, & 0.3585092964276616D+00, & 0.5541122384084942D+00, & 0.0873784651638445D+00, & 0.5541122384084941D+00, & 0.3585092964276618D+00, & 0.2224250057848120D+00, & 0.3887874971075941D+00, & 0.3887874971075941D+00, & 0.0763119015129594D+00, & 0.1868691794762216D+00, & 0.7368189190108192D+00, & 0.0763119015129594D+00, & 0.7368189190108192D+00, & 0.1868691794762219D+00, & 0.2731471009290788D+00, & 0.2731471009290788D+00, & 0.4537057981418426D+00, & 0.0020575309653709D+00, & 0.4147059095903063D+00, & 0.5832365594443231D+00, & 0.0020575309653709D+00, & 0.5832365594443230D+00, & 0.4147059095903066D+00, & 0.1704787284972490D+00, & 0.3194153053834388D+00, & 0.5101059661193126D+00, & 0.1704787284972490D+00, & 0.5101059661193125D+00, & 0.3194153053834389D+00, & 0.0079996080914843D+00, & 0.1437376261997640D+00, & 0.8482627657087518D+00, & 0.0079996080914843D+00, & 0.8482627657087518D+00, & 0.1437376261997644D+00, & 0.0563428733576680D+00, & 0.4718285633211661D+00, & 0.4718285633211662D+00, & 0.1542014303645444D+00, & 0.1542014303645442D+00, & 0.6915971392709116D+00, & 0.0511658736851378D+00, & 0.2837881388594705D+00, & 0.6650459874553920D+00, & 0.0511658736851378D+00, & 0.6650459874553919D+00, & 0.2837881388594707D+00, & 0.2120431633022057D+00, & 0.2120431633022056D+00, & 0.5759136733955889D+00, & 0.1280291612312336D+00, & 0.4359854193843832D+00, & 0.4359854193843834D+00, & 0.0227845992508957D+00, & 0.2165466664734771D+00, & 0.7606687342756275D+00, & 0.0227845992508957D+00, & 0.7606687342756273D+00, & 0.2165466664734774D+00, & 0.3333333333333334D+00, & 0.0094732979122136D+00, & 0.3128985030748800D+00, & 0.6776281990129066D+00, & 0.0094732979122136D+00, & 0.6776281990129066D+00, & 0.3128985030748803D+00, & 0.0004640077321757D+00, & 0.2264347974077175D+00, & 0.7731011948601070D+00, & 0.0004640077321757D+00, & 0.7731011948601070D+00, & 0.2264347974077178D+00 /) c = (/ & 0.9151336840842468D+00, & 0.0047946609754367D+00, & 0.0800716549403163D+00, & 0.0800716549403165D+00, & 0.0047946609754365D+00, & 0.9151336840842467D+00, & 0.9392011922216335D+00, & 0.0291551962068358D+00, & 0.0316436115715305D+00, & 0.0316436115715308D+00, & 0.0291551962068356D+00, & 0.9392011922216333D+00, & 0.8665257548470676D+00, & 0.0667371225764665D+00, & 0.0667371225764658D+00, & 0.8984105884621028D+00, & 0.0262093640224987D+00, & 0.0753800475153984D+00, & 0.0753800475153987D+00, & 0.0262093640224984D+00, & 0.8984105884621026D+00, & 0.9612018477470925D+00, & 0.0056981179168753D+00, & 0.0331000343360319D+00, & 0.0331000343360323D+00, & 0.0056981179168749D+00, & 0.9612018477470925D+00, & 0.9873197670158463D+00, & 0.0063401164920770D+00, & 0.0063401164920763D+00, & 0.8257890876433118D+00, & 0.0417247227421210D+00, & 0.1324861896145672D+00, & 0.1324861896145673D+00, & 0.0417247227421208D+00, & 0.8257890876433117D+00, & 0.7912672079790704D+00, & 0.1000456591065276D+00, & 0.1086871329144019D+00, & 0.1086871329144021D+00, & 0.1000456591065274D+00, & 0.7912672079790702D+00, & 0.4937530328963847D+00, & 0.0124939342072304D+00, & 0.4937530328963846D+00, & 0.6291132845042245D+00, & 0.1206144022052490D+00, & 0.2502723132905263D+00, & 0.2502723132905264D+00, & 0.1206144022052490D+00, & 0.6291132845042244D+00, & 0.5814399954403303D+00, & 0.0295379425169078D+00, & 0.3890220620427617D+00, & 0.3890220620427617D+00, & 0.0295379425169078D+00, & 0.5814399954403302D+00, & 0.5541122384084940D+00, & 0.0873784651638444D+00, & 0.3585092964276613D+00, & 0.3585092964276615D+00, & 0.0873784651638444D+00, & 0.5541122384084938D+00, & 0.3887874971075940D+00, & 0.2224250057848119D+00, & 0.3887874971075939D+00, & 0.7368189190108190D+00, & 0.0763119015129595D+00, & 0.1868691794762213D+00, & 0.1868691794762216D+00, & 0.0763119015129592D+00, & 0.7368189190108190D+00, & 0.4537057981418425D+00, & 0.2731471009290788D+00, & 0.2731471009290786D+00, & 0.5832365594443228D+00, & 0.0020575309653708D+00, & 0.4147059095903062D+00, & 0.4147059095903062D+00, & 0.0020575309653708D+00, & 0.5832365594443227D+00, & 0.5101059661193122D+00, & 0.1704787284972489D+00, & 0.3194153053834385D+00, & 0.3194153053834387D+00, & 0.1704787284972488D+00, & 0.5101059661193122D+00, & 0.8482627657087517D+00, & 0.0079996080914843D+00, & 0.1437376261997638D+00, & 0.1437376261997640D+00, & 0.0079996080914840D+00, & 0.8482627657087516D+00, & 0.4718285633211660D+00, & 0.0563428733576679D+00, & 0.4718285633211659D+00, & 0.6915971392709115D+00, & 0.1542014303645444D+00, & 0.1542014303645439D+00, & 0.6650459874553918D+00, & 0.0511658736851378D+00, & 0.2837881388594703D+00, & 0.2837881388594704D+00, & 0.0511658736851376D+00, & 0.6650459874553916D+00, & 0.5759136733955887D+00, & 0.2120431633022057D+00, & 0.2120431633022054D+00, & 0.4359854193843832D+00, & 0.1280291612312336D+00, & 0.4359854193843831D+00, & 0.7606687342756272D+00, & 0.0227845992508957D+00, & 0.2165466664734768D+00, & 0.2165466664734771D+00, & 0.0227845992508955D+00, & 0.7606687342756271D+00, & 0.3333333333333333D+00, & 0.6776281990129065D+00, & 0.0094732979122135D+00, & 0.3128985030748798D+00, & 0.3128985030748800D+00, & 0.0094732979122133D+00, & 0.6776281990129063D+00, & 0.7731011948601068D+00, & 0.0004640077321756D+00, & 0.2264347974077173D+00, & 0.2264347974077175D+00, & 0.0004640077321755D+00, & 0.7731011948601068D+00 /) w = (/ & 0.0013985264481603D+00, & 0.0013985264481603D+00, & 0.0013985264481603D+00, & 0.0013985264481603D+00, & 0.0013985264481603D+00, & 0.0013985264481603D+00, & 0.0012055647737169D+00, & 0.0012055647737169D+00, & 0.0012055647737169D+00, & 0.0012055647737169D+00, & 0.0012055647737169D+00, & 0.0012055647737169D+00, & 0.0049138253029660D+00, & 0.0049138253029660D+00, & 0.0049138253029660D+00, & 0.0033055447129677D+00, & 0.0033055447129677D+00, & 0.0033055447129677D+00, & 0.0033055447129677D+00, & 0.0033055447129677D+00, & 0.0033055447129677D+00, & 0.0010857073429968D+00, & 0.0010857073429968D+00, & 0.0010857073429968D+00, & 0.0010857073429968D+00, & 0.0010857073429968D+00, & 0.0010857073429968D+00, & 0.0005269531166819D+00, & 0.0005269531166819D+00, & 0.0005269531166819D+00, & 0.0064035978997128D+00, & 0.0064035978997128D+00, & 0.0064035978997128D+00, & 0.0064035978997128D+00, & 0.0064035978997128D+00, & 0.0064035978997128D+00, & 0.0046142110763783D+00, & 0.0046142110763783D+00, & 0.0046142110763783D+00, & 0.0046142110763783D+00, & 0.0046142110763783D+00, & 0.0046142110763783D+00, & 0.0053021591818673D+00, & 0.0053021591818673D+00, & 0.0053021591818673D+00, & 0.0143794732275987D+00, & 0.0143794732275987D+00, & 0.0143794732275987D+00, & 0.0143794732275987D+00, & 0.0143794732275987D+00, & 0.0143794732275987D+00, & 0.0082597672170868D+00, & 0.0082597672170868D+00, & 0.0082597672170868D+00, & 0.0082597672170868D+00, & 0.0082597672170868D+00, & 0.0082597672170868D+00, & 0.0137279582160857D+00, & 0.0137279582160857D+00, & 0.0137279582160857D+00, & 0.0137279582160857D+00, & 0.0137279582160857D+00, & 0.0137279582160857D+00, & 0.0194680678371829D+00, & 0.0194680678371829D+00, & 0.0194680678371829D+00, & 0.0103976455281743D+00, & 0.0103976455281743D+00, & 0.0103976455281743D+00, & 0.0103976455281743D+00, & 0.0103976455281743D+00, & 0.0103976455281743D+00, & 0.0195356469232475D+00, & 0.0195356469232475D+00, & 0.0195356469232475D+00, & 0.0018571474709981D+00, & 0.0018571474709981D+00, & 0.0018571474709981D+00, & 0.0018571474709981D+00, & 0.0018571474709981D+00, & 0.0018571474709981D+00, & 0.0175991671806952D+00, & 0.0175991671806952D+00, & 0.0175991671806952D+00, & 0.0175991671806952D+00, & 0.0175991671806952D+00, & 0.0175991671806952D+00, & 0.0029667616626565D+00, & 0.0029667616626565D+00, & 0.0029667616626565D+00, & 0.0029667616626565D+00, & 0.0029667616626565D+00, & 0.0029667616626565D+00, & 0.0115285036346569D+00, & 0.0115285036346569D+00, & 0.0115285036346569D+00, & 0.0132552594485453D+00, & 0.0132552594485453D+00, & 0.0132552594485453D+00, & 0.0101071244320887D+00, & 0.0101071244320887D+00, & 0.0101071244320887D+00, & 0.0101071244320887D+00, & 0.0101071244320887D+00, & 0.0101071244320887D+00, & 0.0169443450785281D+00, & 0.0169443450785281D+00, & 0.0169443450785281D+00, & 0.0164124006025879D+00, & 0.0164124006025879D+00, & 0.0164124006025879D+00, & 0.0062693378460806D+00, & 0.0062693378460806D+00, & 0.0062693378460806D+00, & 0.0062693378460806D+00, & 0.0062693378460806D+00, & 0.0062693378460806D+00, & 0.0204866625892232D+00, & 0.0045915583873986D+00, & 0.0045915583873986D+00, & 0.0045915583873986D+00, & 0.0045915583873986D+00, & 0.0045915583873986D+00, & 0.0045915583873986D+00, & 0.0011395489158682D+00, & 0.0011395489158682D+00, & 0.0011395489158682D+00, & 0.0011395489158682D+00, & 0.0011395489158682D+00, & 0.0011395489158682D+00 /) return end subroutine rule27 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule27() returns the rule of precision 27. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3807140211811871D+00, & 0.3807140211811871D+00, & 0.2385719576376256D+00, & 0.4466678037038646D+00, & 0.4466678037038646D+00, & 0.1066643925922708D+00, & 0.4161413788054121D+00, & 0.4161413788054121D+00, & 0.1677172423891756D+00, & 0.0803046477884383D+00, & 0.8393907044231230D+00, & 0.0803046477884388D+00, & 0.2870421965934966D+00, & 0.6822271986792305D+00, & 0.0307306047272730D+00, & 0.6822271986792305D+00, & 0.2870421965934966D+00, & 0.0307306047272727D+00, & 0.3450878417155684D+00, & 0.5257595182209819D+00, & 0.1291526400634497D+00, & 0.5257595182209819D+00, & 0.3450878417155684D+00, & 0.1291526400634496D+00, & 0.2334004066698710D+00, & 0.5331991866602577D+00, & 0.2334004066698712D+00, & 0.3759301570486618D+00, & 0.5960363568560882D+00, & 0.0280334860952500D+00, & 0.5960363568560882D+00, & 0.3759301570486618D+00, & 0.0280334860952499D+00, & 0.3011654651665091D+00, & 0.3976690696669817D+00, & 0.3011654651665091D+00, & 0.1747799663549000D+00, & 0.6504400672901998D+00, & 0.1747799663549002D+00, & 0.3169455889331320D+00, & 0.4739234899291993D+00, & 0.2091309211376687D+00, & 0.4739234899291992D+00, & 0.3169455889331320D+00, & 0.2091309211376686D+00, & 0.4072283930427198D+00, & 0.5267326941075414D+00, & 0.0660389128497386D+00, & 0.5267326941075414D+00, & 0.4072283930427199D+00, & 0.0660389128497386D+00, & 0.2135535984578239D+00, & 0.7454158247229943D+00, & 0.0410305768191818D+00, & 0.7454158247229943D+00, & 0.2135535984578240D+00, & 0.0410305768191816D+00, & 0.3288528780688926D+00, & 0.6658474815593083D+00, & 0.0052996403717991D+00, & 0.6658474815593083D+00, & 0.3288528780688927D+00, & 0.0052996403717989D+00, & 0.4855650541851628D+00, & 0.4855650541851628D+00, & 0.0288698916296744D+00, & 0.1392953061421487D+00, & 0.7976306984429004D+00, & 0.0630739954149511D+00, & 0.7976306984429004D+00, & 0.1392953061421489D+00, & 0.0630739954149507D+00, & 0.0325715201801815D+00, & 0.9348569596396367D+00, & 0.0325715201801819D+00, & 0.2552462546969780D+00, & 0.5957908943647818D+00, & 0.1489628509382402D+00, & 0.5957908943647818D+00, & 0.2552462546969780D+00, & 0.1489628509382400D+00, & 0.2083760156003741D+00, & 0.6969269019664952D+00, & 0.0946970824331307D+00, & 0.6969269019664952D+00, & 0.2083760156003741D+00, & 0.0946970824331305D+00, & 0.4400105519462155D+00, & 0.5544087310385245D+00, & 0.0055807170152600D+00, & 0.5544087310385244D+00, & 0.4400105519462155D+00, & 0.0055807170152600D+00, & 0.1275709019046775D+00, & 0.7448581961906449D+00, & 0.1275709019046778D+00, & 0.3022209412278211D+00, & 0.6227021563389826D+00, & 0.0750769024331963D+00, & 0.6227021563389826D+00, & 0.3022209412278211D+00, & 0.0750769024331961D+00, & 0.0819468025835337D+00, & 0.9110706680920073D+00, & 0.0069825293244591D+00, & 0.9110706680920073D+00, & 0.0819468025835338D+00, & 0.0069825293244588D+00, & 0.0343649699121420D+00, & 0.9595414606840931D+00, & 0.0060935694037650D+00, & 0.9595414606840931D+00, & 0.0343649699121421D+00, & 0.0060935694037646D+00, & 0.0801120738471011D+00, & 0.8848535036252014D+00, & 0.0350344225276975D+00, & 0.8848535036252014D+00, & 0.0801120738471012D+00, & 0.0350344225276972D+00, & 0.0066392191809586D+00, & 0.9867215616380824D+00, & 0.0066392191809590D+00, & 0.1472134318989225D+00, & 0.8334345667830385D+00, & 0.0193520013180390D+00, & 0.8334345667830385D+00, & 0.1472134318989225D+00, & 0.0193520013180388D+00, & 0.2297196532578432D+00, & 0.7629478741931164D+00, & 0.0073324725490405D+00, & 0.7629478741931163D+00, & 0.2297196532578433D+00, & 0.0073324725490403D+00, & 0.1476555211198698D+00, & 0.8518541504366672D+00, & 0.0004903284434630D+00, & 0.8518541504366672D+00, & 0.1476555211198698D+00, & 0.0004903284434627D+00 /) b = (/ & 0.2385719576376257D+00, & 0.3807140211811872D+00, & 0.3807140211811873D+00, & 0.1066643925922709D+00, & 0.4466678037038647D+00, & 0.4466678037038648D+00, & 0.1677172423891757D+00, & 0.4161413788054122D+00, & 0.4161413788054124D+00, & 0.0803046477884386D+00, & 0.0803046477884383D+00, & 0.8393907044231231D+00, & 0.0307306047272729D+00, & 0.2870421965934966D+00, & 0.6822271986792307D+00, & 0.0307306047272729D+00, & 0.6822271986792307D+00, & 0.2870421965934968D+00, & 0.1291526400634497D+00, & 0.3450878417155684D+00, & 0.5257595182209820D+00, & 0.1291526400634497D+00, & 0.5257595182209820D+00, & 0.3450878417155686D+00, & 0.2334004066698712D+00, & 0.2334004066698711D+00, & 0.5331991866602579D+00, & 0.0280334860952500D+00, & 0.3759301570486618D+00, & 0.5960363568560885D+00, & 0.0280334860952500D+00, & 0.5960363568560882D+00, & 0.3759301570486621D+00, & 0.3011654651665093D+00, & 0.3011654651665092D+00, & 0.3976690696669818D+00, & 0.1747799663549002D+00, & 0.1747799663549000D+00, & 0.6504400672902000D+00, & 0.2091309211376688D+00, & 0.3169455889331320D+00, & 0.4739234899291995D+00, & 0.2091309211376688D+00, & 0.4739234899291995D+00, & 0.3169455889331322D+00, & 0.0660389128497387D+00, & 0.4072283930427200D+00, & 0.5267326941075416D+00, & 0.0660389128497387D+00, & 0.5267326941075415D+00, & 0.4072283930427201D+00, & 0.0410305768191818D+00, & 0.2135535984578240D+00, & 0.7454158247229945D+00, & 0.0410305768191818D+00, & 0.7454158247229945D+00, & 0.2135535984578242D+00, & 0.0052996403717990D+00, & 0.3288528780688927D+00, & 0.6658474815593085D+00, & 0.0052996403717990D+00, & 0.6658474815593083D+00, & 0.3288528780688930D+00, & 0.0288698916296745D+00, & 0.4855650541851628D+00, & 0.4855650541851630D+00, & 0.0630739954149509D+00, & 0.1392953061421487D+00, & 0.7976306984429004D+00, & 0.0630739954149509D+00, & 0.7976306984429004D+00, & 0.1392953061421490D+00, & 0.0325715201801818D+00, & 0.0325715201801814D+00, & 0.9348569596396370D+00, & 0.1489628509382402D+00, & 0.2552462546969780D+00, & 0.5957908943647819D+00, & 0.1489628509382402D+00, & 0.5957908943647819D+00, & 0.2552462546969783D+00, & 0.0946970824331307D+00, & 0.2083760156003741D+00, & 0.6969269019664954D+00, & 0.0946970824331307D+00, & 0.6969269019664954D+00, & 0.2083760156003744D+00, & 0.0055807170152601D+00, & 0.4400105519462155D+00, & 0.5544087310385247D+00, & 0.0055807170152601D+00, & 0.5544087310385245D+00, & 0.4400105519462157D+00, & 0.1275709019046777D+00, & 0.1275709019046775D+00, & 0.7448581961906449D+00, & 0.0750769024331962D+00, & 0.3022209412278212D+00, & 0.6227021563389828D+00, & 0.0750769024331962D+00, & 0.6227021563389828D+00, & 0.3022209412278213D+00, & 0.0069825293244590D+00, & 0.0819468025835337D+00, & 0.9110706680920074D+00, & 0.0069825293244590D+00, & 0.9110706680920074D+00, & 0.0819468025835340D+00, & 0.0060935694037648D+00, & 0.0343649699121420D+00, & 0.9595414606840932D+00, & 0.0060935694037648D+00, & 0.9595414606840934D+00, & 0.0343649699121423D+00, & 0.0350344225276974D+00, & 0.0801120738471011D+00, & 0.8848535036252017D+00, & 0.0350344225276974D+00, & 0.8848535036252017D+00, & 0.0801120738471014D+00, & 0.0066392191809589D+00, & 0.0066392191809586D+00, & 0.9867215616380827D+00, & 0.0193520013180390D+00, & 0.1472134318989225D+00, & 0.8334345667830388D+00, & 0.0193520013180390D+00, & 0.8334345667830388D+00, & 0.1472134318989227D+00, & 0.0073324725490405D+00, & 0.2297196532578432D+00, & 0.7629478741931165D+00, & 0.0073324725490405D+00, & 0.7629478741931164D+00, & 0.2297196532578435D+00, & 0.0004903284434630D+00, & 0.1476555211198698D+00, & 0.8518541504366673D+00, & 0.0004903284434630D+00, & 0.8518541504366673D+00, & 0.1476555211198702D+00 /) c = (/ & 0.3807140211811872D+00, & 0.2385719576376256D+00, & 0.3807140211811871D+00, & 0.4466678037038647D+00, & 0.1066643925922707D+00, & 0.4466678037038644D+00, & 0.4161413788054121D+00, & 0.1677172423891756D+00, & 0.4161413788054120D+00, & 0.8393907044231231D+00, & 0.0803046477884387D+00, & 0.0803046477884380D+00, & 0.6822271986792305D+00, & 0.0307306047272728D+00, & 0.2870421965934964D+00, & 0.2870421965934966D+00, & 0.0307306047272727D+00, & 0.6822271986792304D+00, & 0.5257595182209819D+00, & 0.1291526400634497D+00, & 0.3450878417155683D+00, & 0.3450878417155684D+00, & 0.1291526400634496D+00, & 0.5257595182209819D+00, & 0.5331991866602578D+00, & 0.2334004066698712D+00, & 0.2334004066698709D+00, & 0.5960363568560882D+00, & 0.0280334860952499D+00, & 0.3759301570486615D+00, & 0.3759301570486617D+00, & 0.0280334860952499D+00, & 0.5960363568560880D+00, & 0.3976690696669816D+00, & 0.3011654651665091D+00, & 0.3011654651665091D+00, & 0.6504400672901998D+00, & 0.1747799663549002D+00, & 0.1747799663548998D+00, & 0.4739234899291993D+00, & 0.2091309211376687D+00, & 0.3169455889331319D+00, & 0.3169455889331320D+00, & 0.2091309211376686D+00, & 0.4739234899291992D+00, & 0.5267326941075414D+00, & 0.0660389128497386D+00, & 0.4072283930427197D+00, & 0.4072283930427199D+00, & 0.0660389128497386D+00, & 0.5267326941075413D+00, & 0.7454158247229942D+00, & 0.0410305768191818D+00, & 0.2135535984578236D+00, & 0.2135535984578239D+00, & 0.0410305768191815D+00, & 0.7454158247229942D+00, & 0.6658474815593083D+00, & 0.0052996403717990D+00, & 0.3288528780688924D+00, & 0.3288528780688927D+00, & 0.0052996403717990D+00, & 0.6658474815593081D+00, & 0.4855650541851627D+00, & 0.0288698916296743D+00, & 0.4855650541851627D+00, & 0.7976306984429005D+00, & 0.0630739954149509D+00, & 0.1392953061421486D+00, & 0.1392953061421487D+00, & 0.0630739954149507D+00, & 0.7976306984429002D+00, & 0.9348569596396368D+00, & 0.0325715201801819D+00, & 0.0325715201801811D+00, & 0.5957908943647818D+00, & 0.1489628509382401D+00, & 0.2552462546969779D+00, & 0.2552462546969780D+00, & 0.1489628509382400D+00, & 0.5957908943647817D+00, & 0.6969269019664953D+00, & 0.0946970824331307D+00, & 0.2083760156003739D+00, & 0.2083760156003741D+00, & 0.0946970824331305D+00, & 0.6969269019664952D+00, & 0.5544087310385245D+00, & 0.0055807170152600D+00, & 0.4400105519462153D+00, & 0.4400105519462155D+00, & 0.0055807170152601D+00, & 0.5544087310385244D+00, & 0.7448581961906449D+00, & 0.1275709019046777D+00, & 0.1275709019046773D+00, & 0.6227021563389826D+00, & 0.0750769024331962D+00, & 0.3022209412278208D+00, & 0.3022209412278211D+00, & 0.0750769024331960D+00, & 0.6227021563389825D+00, & 0.9110706680920073D+00, & 0.0069825293244590D+00, & 0.0819468025835334D+00, & 0.0819468025835337D+00, & 0.0069825293244589D+00, & 0.9110706680920072D+00, & 0.9595414606840932D+00, & 0.0060935694037649D+00, & 0.0343649699121418D+00, & 0.0343649699121421D+00, & 0.0060935694037646D+00, & 0.9595414606840931D+00, & 0.8848535036252015D+00, & 0.0350344225276975D+00, & 0.0801120738471008D+00, & 0.0801120738471012D+00, & 0.0350344225276972D+00, & 0.8848535036252014D+00, & 0.9867215616380826D+00, & 0.0066392191809590D+00, & 0.0066392191809583D+00, & 0.8334345667830386D+00, & 0.0193520013180390D+00, & 0.1472134318989221D+00, & 0.1472134318989225D+00, & 0.0193520013180387D+00, & 0.8334345667830384D+00, & 0.7629478741931164D+00, & 0.0073324725490404D+00, & 0.2297196532578430D+00, & 0.2297196532578433D+00, & 0.0073324725490403D+00, & 0.7629478741931163D+00, & 0.8518541504366672D+00, & 0.0004903284434630D+00, & 0.1476555211198697D+00, & 0.1476555211198698D+00, & 0.0004903284434629D+00, & 0.8518541504366671D+00 /) w = (/ & 0.0095600849674599D+00, & 0.0095600849674599D+00, & 0.0095600849674599D+00, & 0.0094101598094542D+00, & 0.0094101598094542D+00, & 0.0094101598094542D+00, & 0.0120502270241504D+00, & 0.0120502270241504D+00, & 0.0120502270241504D+00, & 0.0052126218728019D+00, & 0.0052126218728019D+00, & 0.0052126218728019D+00, & 0.0055317948337667D+00, & 0.0055317948337667D+00, & 0.0055317948337667D+00, & 0.0055317948337667D+00, & 0.0055317948337667D+00, & 0.0055317948337667D+00, & 0.0125574362040365D+00, & 0.0125574362040365D+00, & 0.0125574362040365D+00, & 0.0125574362040365D+00, & 0.0125574362040365D+00, & 0.0125574362040365D+00, & 0.0134713153980494D+00, & 0.0134713153980494D+00, & 0.0134713153980494D+00, & 0.0063951526994544D+00, & 0.0063951526994544D+00, & 0.0063951526994544D+00, & 0.0063951526994544D+00, & 0.0063951526994544D+00, & 0.0063951526994544D+00, & 0.0157479657813627D+00, & 0.0157479657813627D+00, & 0.0157479657813627D+00, & 0.0112824425446984D+00, & 0.0112824425446984D+00, & 0.0112824425446984D+00, & 0.0137153932305508D+00, & 0.0137153932305508D+00, & 0.0137153932305508D+00, & 0.0137153932305508D+00, & 0.0137153932305508D+00, & 0.0137153932305508D+00, & 0.0098622701189896D+00, & 0.0098622701189896D+00, & 0.0098622701189896D+00, & 0.0098622701189896D+00, & 0.0098622701189896D+00, & 0.0098622701189896D+00, & 0.0064553729049297D+00, & 0.0064553729049297D+00, & 0.0064553729049297D+00, & 0.0064553729049297D+00, & 0.0064553729049297D+00, & 0.0064553729049297D+00, & 0.0029278263617991D+00, & 0.0029278263617991D+00, & 0.0029278263617991D+00, & 0.0029278263617991D+00, & 0.0029278263617991D+00, & 0.0029278263617991D+00, & 0.0071172374128746D+00, & 0.0071172374128746D+00, & 0.0071172374128746D+00, & 0.0071306353104870D+00, & 0.0071306353104870D+00, & 0.0071306353104870D+00, & 0.0071306353104870D+00, & 0.0071306353104870D+00, & 0.0071306353104870D+00, & 0.0027773395289542D+00, & 0.0027773395289542D+00, & 0.0027773395289542D+00, & 0.0123476631308614D+00, & 0.0123476631308614D+00, & 0.0123476631308614D+00, & 0.0123476631308614D+00, & 0.0123476631308614D+00, & 0.0123476631308614D+00, & 0.0106937005896163D+00, & 0.0106937005896163D+00, & 0.0106937005896163D+00, & 0.0106937005896163D+00, & 0.0106937005896163D+00, & 0.0106937005896163D+00, & 0.0032424675976393D+00, & 0.0032424675976393D+00, & 0.0032424675976393D+00, & 0.0032424675976393D+00, & 0.0032424675976393D+00, & 0.0032424675976393D+00, & 0.0097432449228177D+00, & 0.0097432449228177D+00, & 0.0097432449228177D+00, & 0.0109306110929133D+00, & 0.0109306110929133D+00, & 0.0109306110929133D+00, & 0.0109306110929133D+00, & 0.0109306110929133D+00, & 0.0109306110929133D+00, & 0.0020151231272897D+00, & 0.0020151231272897D+00, & 0.0020151231272897D+00, & 0.0020151231272897D+00, & 0.0020151231272897D+00, & 0.0020151231272897D+00, & 0.0011967736084732D+00, & 0.0011967736084732D+00, & 0.0011967736084732D+00, & 0.0011967736084732D+00, & 0.0011967736084732D+00, & 0.0011967736084732D+00, & 0.0043271580353607D+00, & 0.0043271580353607D+00, & 0.0043271580353607D+00, & 0.0043271580353607D+00, & 0.0043271580353607D+00, & 0.0043271580353607D+00, & 0.0005754424056705D+00, & 0.0005754424056705D+00, & 0.0005754424056705D+00, & 0.0046223871117811D+00, & 0.0046223871117811D+00, & 0.0046223871117811D+00, & 0.0046223871117811D+00, & 0.0046223871117811D+00, & 0.0046223871117811D+00, & 0.0033942537388070D+00, & 0.0033942537388070D+00, & 0.0033942537388070D+00, & 0.0033942537388070D+00, & 0.0033942537388070D+00, & 0.0033942537388070D+00, & 0.0008466061357639D+00, & 0.0008466061357639D+00, & 0.0008466061357639D+00, & 0.0008466061357639D+00, & 0.0008466061357639D+00, & 0.0008466061357639D+00 /) return end subroutine rule28 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule28() returns the rule of precision 28. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3039829225164841D+00, & 0.3920341549670316D+00, & 0.3039829225164841D+00, & 0.0455054005583464D+00, & 0.9329702140721974D+00, & 0.0215243853694563D+00, & 0.9329702140721974D+00, & 0.0455054005583465D+00, & 0.0215243853694558D+00, & 0.2133944547670873D+00, & 0.7375358758753532D+00, & 0.0490696693575595D+00, & 0.7375358758753532D+00, & 0.2133944547670873D+00, & 0.0490696693575593D+00, & 0.0048041261966579D+00, & 0.9903917476066839D+00, & 0.0048041261966584D+00, & 0.4582799042404119D+00, & 0.4582799042404120D+00, & 0.0834401915191761D+00, & 0.2421025119193196D+00, & 0.5802390377843101D+00, & 0.1776584502963703D+00, & 0.5802390377843101D+00, & 0.2421025119193198D+00, & 0.1776584502963702D+00, & 0.3862679735700421D+00, & 0.3862679735700420D+00, & 0.2274640528599158D+00, & 0.3271907320191700D+00, & 0.4829969116880932D+00, & 0.1898123562927368D+00, & 0.4829969116880932D+00, & 0.3271907320191700D+00, & 0.1898123562927368D+00, & 0.1419981669331742D+00, & 0.8535434510435363D+00, & 0.0044583820232894D+00, & 0.8535434510435365D+00, & 0.1419981669331742D+00, & 0.0044583820232890D+00, & 0.1753963931914617D+00, & 0.7369256303241862D+00, & 0.0876779764843521D+00, & 0.7369256303241862D+00, & 0.1753963931914618D+00, & 0.0876779764843519D+00, & 0.3921396133344145D+00, & 0.5446800590311748D+00, & 0.0631803276344107D+00, & 0.5446800590311748D+00, & 0.3921396133344145D+00, & 0.0631803276344106D+00, & 0.2582640721504621D+00, & 0.4834718556990756D+00, & 0.2582640721504622D+00, & 0.3341456150359213D+00, & 0.6617049208301551D+00, & 0.0041494641339236D+00, & 0.6617049208301550D+00, & 0.3341456150359213D+00, & 0.0041494641339235D+00, & 0.1741461960511821D+00, & 0.8030589990229017D+00, & 0.0227948049259163D+00, & 0.8030589990229016D+00, & 0.1741461960511822D+00, & 0.0227948049259160D+00, & 0.2758390080718242D+00, & 0.7014601475563789D+00, & 0.0227008443717971D+00, & 0.7014601475563788D+00, & 0.2758390080718242D+00, & 0.0227008443717968D+00, & 0.0262226671646523D+00, & 0.9676276842926838D+00, & 0.0061496485426642D+00, & 0.9676276842926838D+00, & 0.0262226671646523D+00, & 0.0061496485426637D+00, & 0.2430472023659261D+00, & 0.6449191682918028D+00, & 0.1120336293422710D+00, & 0.6449191682918028D+00, & 0.2430472023659263D+00, & 0.1120336293422708D+00, & 0.2299929840579072D+00, & 0.7652255261691058D+00, & 0.0047814897729871D+00, & 0.7652255261691057D+00, & 0.2299929840579072D+00, & 0.0047814897729869D+00, & 0.1058958441786275D+00, & 0.7882083116427446D+00, & 0.1058958441786279D+00, & 0.4295522021188993D+00, & 0.4295522021188993D+00, & 0.1408955957622013D+00, & 0.2956082808724017D+00, & 0.6419429769479655D+00, & 0.0624487421796328D+00, & 0.6419429769479654D+00, & 0.2956082808724017D+00, & 0.0624487421796327D+00, & 0.1213934507540912D+00, & 0.8283953633324806D+00, & 0.0502111859134282D+00, & 0.8283953633324806D+00, & 0.1213934507540914D+00, & 0.0502111859134279D+00, & 0.3738238003102096D+00, & 0.6004482009469115D+00, & 0.0257279987428787D+00, & 0.6004482009469116D+00, & 0.3738238003102097D+00, & 0.0257279987428786D+00, & 0.4427834065202436D+00, & 0.5515700274862902D+00, & 0.0056465659934661D+00, & 0.5515700274862904D+00, & 0.4427834065202436D+00, & 0.0056465659934661D+00, & 0.3377986632005823D+00, & 0.5441122670843226D+00, & 0.1180890697150950D+00, & 0.5441122670843226D+00, & 0.3377986632005823D+00, & 0.1180890697150949D+00, & 0.0922291891952822D+00, & 0.8895285197924230D+00, & 0.0182422910122948D+00, & 0.8895285197924231D+00, & 0.0922291891952822D+00, & 0.0182422910122945D+00, & 0.4848411325625894D+00, & 0.4848411325625895D+00, & 0.0303177348748211D+00, & 0.1586376888630596D+00, & 0.6827246222738805D+00, & 0.1586376888630599D+00, & 0.0608391923927586D+00, & 0.8783216152144825D+00, & 0.0608391923927590D+00, & 0.0702907404781327D+00, & 0.9285090039203800D+00, & 0.0012002556014873D+00, & 0.9285090039203802D+00, & 0.0702907404781328D+00, & 0.0012002556014869D+00 /) b = (/ & 0.3039829225164842D+00, & 0.3039829225164842D+00, & 0.3920341549670319D+00, & 0.0215243853694561D+00, & 0.0455054005583464D+00, & 0.9329702140721976D+00, & 0.0215243853694561D+00, & 0.9329702140721976D+00, & 0.0455054005583467D+00, & 0.0490696693575595D+00, & 0.2133944547670873D+00, & 0.7375358758753534D+00, & 0.0490696693575595D+00, & 0.7375358758753533D+00, & 0.2133944547670876D+00, & 0.0048041261966582D+00, & 0.0048041261966579D+00, & 0.9903917476066839D+00, & 0.0834401915191761D+00, & 0.4582799042404120D+00, & 0.4582799042404122D+00, & 0.1776584502963703D+00, & 0.2421025119193198D+00, & 0.5802390377843101D+00, & 0.1776584502963703D+00, & 0.5802390377843101D+00, & 0.2421025119193199D+00, & 0.2274640528599159D+00, & 0.3862679735700422D+00, & 0.3862679735700422D+00, & 0.1898123562927369D+00, & 0.3271907320191700D+00, & 0.4829969116880933D+00, & 0.1898123562927369D+00, & 0.4829969116880933D+00, & 0.3271907320191702D+00, & 0.0044583820232893D+00, & 0.1419981669331742D+00, & 0.8535434510435367D+00, & 0.0044583820232893D+00, & 0.8535434510435367D+00, & 0.1419981669331745D+00, & 0.0876779764843520D+00, & 0.1753963931914617D+00, & 0.7369256303241863D+00, & 0.0876779764843520D+00, & 0.7369256303241863D+00, & 0.1753963931914620D+00, & 0.0631803276344107D+00, & 0.3921396133344145D+00, & 0.5446800590311750D+00, & 0.0631803276344107D+00, & 0.5446800590311749D+00, & 0.3921396133344148D+00, & 0.2582640721504623D+00, & 0.2582640721504622D+00, & 0.4834718556990758D+00, & 0.0041494641339237D+00, & 0.3341456150359213D+00, & 0.6617049208301553D+00, & 0.0041494641339237D+00, & 0.6617049208301551D+00, & 0.3341456150359216D+00, & 0.0227948049259162D+00, & 0.1741461960511821D+00, & 0.8030589990229018D+00, & 0.0227948049259162D+00, & 0.8030589990229018D+00, & 0.1741461960511825D+00, & 0.0227008443717970D+00, & 0.2758390080718242D+00, & 0.7014601475563790D+00, & 0.0227008443717970D+00, & 0.7014601475563790D+00, & 0.2758390080718244D+00, & 0.0061496485426640D+00, & 0.0262226671646522D+00, & 0.9676276842926838D+00, & 0.0061496485426640D+00, & 0.9676276842926840D+00, & 0.0262226671646526D+00, & 0.1120336293422710D+00, & 0.2430472023659262D+00, & 0.6449191682918030D+00, & 0.1120336293422710D+00, & 0.6449191682918030D+00, & 0.2430472023659264D+00, & 0.0047814897729871D+00, & 0.2299929840579072D+00, & 0.7652255261691059D+00, & 0.0047814897729871D+00, & 0.7652255261691059D+00, & 0.2299929840579075D+00, & 0.1058958441786278D+00, & 0.1058958441786275D+00, & 0.7882083116427449D+00, & 0.1408955957622014D+00, & 0.4295522021188994D+00, & 0.4295522021188995D+00, & 0.0624487421796329D+00, & 0.2956082808724017D+00, & 0.6419429769479658D+00, & 0.0624487421796329D+00, & 0.6419429769479655D+00, & 0.2956082808724020D+00, & 0.0502111859134281D+00, & 0.1213934507540912D+00, & 0.8283953633324808D+00, & 0.0502111859134281D+00, & 0.8283953633324808D+00, & 0.1213934507540915D+00, & 0.0257279987428787D+00, & 0.3738238003102097D+00, & 0.6004482009469118D+00, & 0.0257279987428787D+00, & 0.6004482009469116D+00, & 0.3738238003102100D+00, & 0.0056465659934662D+00, & 0.4427834065202436D+00, & 0.5515700274862906D+00, & 0.0056465659934662D+00, & 0.5515700274862904D+00, & 0.4427834065202438D+00, & 0.1180890697150951D+00, & 0.3377986632005824D+00, & 0.5441122670843228D+00, & 0.1180890697150951D+00, & 0.5441122670843228D+00, & 0.3377986632005825D+00, & 0.0182422910122947D+00, & 0.0922291891952822D+00, & 0.8895285197924232D+00, & 0.0182422910122947D+00, & 0.8895285197924232D+00, & 0.0922291891952825D+00, & 0.0303177348748211D+00, & 0.4848411325625895D+00, & 0.4848411325625896D+00, & 0.1586376888630598D+00, & 0.1586376888630597D+00, & 0.6827246222738806D+00, & 0.0608391923927589D+00, & 0.0608391923927586D+00, & 0.8783216152144826D+00, & 0.0012002556014872D+00, & 0.0702907404781327D+00, & 0.9285090039203803D+00, & 0.0012002556014872D+00, & 0.9285090039203803D+00, & 0.0702907404781331D+00 /) c = (/ & 0.3920341549670317D+00, & 0.3039829225164841D+00, & 0.3039829225164841D+00, & 0.9329702140721975D+00, & 0.0215243853694563D+00, & 0.0455054005583461D+00, & 0.0455054005583465D+00, & 0.0215243853694559D+00, & 0.9329702140721975D+00, & 0.7375358758753532D+00, & 0.0490696693575595D+00, & 0.2133944547670871D+00, & 0.2133944547670873D+00, & 0.0490696693575593D+00, & 0.7375358758753531D+00, & 0.9903917476066840D+00, & 0.0048041261966582D+00, & 0.0048041261966577D+00, & 0.4582799042404119D+00, & 0.0834401915191760D+00, & 0.4582799042404118D+00, & 0.5802390377843101D+00, & 0.1776584502963702D+00, & 0.2421025119193196D+00, & 0.2421025119193196D+00, & 0.1776584502963702D+00, & 0.5802390377843100D+00, & 0.3862679735700420D+00, & 0.2274640528599158D+00, & 0.3862679735700420D+00, & 0.4829969116880931D+00, & 0.1898123562927367D+00, & 0.3271907320191699D+00, & 0.3271907320191699D+00, & 0.1898123562927367D+00, & 0.4829969116880931D+00, & 0.8535434510435365D+00, & 0.0044583820232895D+00, & 0.1419981669331739D+00, & 0.1419981669331742D+00, & 0.0044583820232891D+00, & 0.8535434510435363D+00, & 0.7369256303241862D+00, & 0.0876779764843520D+00, & 0.1753963931914616D+00, & 0.1753963931914617D+00, & 0.0876779764843519D+00, & 0.7369256303241862D+00, & 0.5446800590311749D+00, & 0.0631803276344107D+00, & 0.3921396133344143D+00, & 0.3921396133344145D+00, & 0.0631803276344106D+00, & 0.5446800590311747D+00, & 0.4834718556990756D+00, & 0.2582640721504622D+00, & 0.2582640721504620D+00, & 0.6617049208301550D+00, & 0.0041494641339236D+00, & 0.3341456150359210D+00, & 0.3341456150359213D+00, & 0.0041494641339236D+00, & 0.6617049208301549D+00, & 0.8030589990229017D+00, & 0.0227948049259162D+00, & 0.1741461960511819D+00, & 0.1741461960511822D+00, & 0.0227948049259160D+00, & 0.8030589990229016D+00, & 0.7014601475563788D+00, & 0.0227008443717970D+00, & 0.2758390080718239D+00, & 0.2758390080718242D+00, & 0.0227008443717968D+00, & 0.7014601475563786D+00, & 0.9676276842926838D+00, & 0.0061496485426640D+00, & 0.0262226671646520D+00, & 0.0262226671646523D+00, & 0.0061496485426636D+00, & 0.9676276842926838D+00, & 0.6449191682918028D+00, & 0.1120336293422710D+00, & 0.2430472023659260D+00, & 0.2430472023659262D+00, & 0.1120336293422708D+00, & 0.6449191682918027D+00, & 0.7652255261691058D+00, & 0.0047814897729870D+00, & 0.2299929840579069D+00, & 0.2299929840579072D+00, & 0.0047814897729869D+00, & 0.7652255261691057D+00, & 0.7882083116427447D+00, & 0.1058958441786279D+00, & 0.1058958441786272D+00, & 0.4295522021188993D+00, & 0.1408955957622013D+00, & 0.4295522021188992D+00, & 0.6419429769479654D+00, & 0.0624487421796328D+00, & 0.2956082808724014D+00, & 0.2956082808724017D+00, & 0.0624487421796328D+00, & 0.6419429769479653D+00, & 0.8283953633324806D+00, & 0.0502111859134282D+00, & 0.1213934507540910D+00, & 0.1213934507540912D+00, & 0.0502111859134279D+00, & 0.8283953633324806D+00, & 0.6004482009469115D+00, & 0.0257279987428788D+00, & 0.3738238003102096D+00, & 0.3738238003102096D+00, & 0.0257279987428787D+00, & 0.6004482009469114D+00, & 0.5515700274862902D+00, & 0.0056465659934662D+00, & 0.4427834065202433D+00, & 0.4427834065202435D+00, & 0.0056465659934660D+00, & 0.5515700274862902D+00, & 0.5441122670843227D+00, & 0.1180890697150950D+00, & 0.3377986632005822D+00, & 0.3377986632005823D+00, & 0.1180890697150949D+00, & 0.5441122670843226D+00, & 0.8895285197924231D+00, & 0.0182422910122948D+00, & 0.0922291891952820D+00, & 0.0922291891952822D+00, & 0.0182422910122946D+00, & 0.8895285197924230D+00, & 0.4848411325625894D+00, & 0.0303177348748210D+00, & 0.4848411325625892D+00, & 0.6827246222738805D+00, & 0.1586376888630598D+00, & 0.1586376888630595D+00, & 0.8783216152144825D+00, & 0.0608391923927590D+00, & 0.0608391923927584D+00, & 0.9285090039203800D+00, & 0.0012002556014872D+00, & 0.0702907404781324D+00, & 0.0702907404781327D+00, & 0.0012002556014870D+00, & 0.9285090039203799D+00 /) w = (/ & 0.0143624663006461D+00, & 0.0143624663006461D+00, & 0.0143624663006461D+00, & 0.0021175395576809D+00, & 0.0021175395576809D+00, & 0.0021175395576809D+00, & 0.0021175395576809D+00, & 0.0021175395576809D+00, & 0.0021175395576809D+00, & 0.0058956722345142D+00, & 0.0058956722345142D+00, & 0.0058956722345142D+00, & 0.0058956722345142D+00, & 0.0058956722345142D+00, & 0.0058956722345142D+00, & 0.0003111352086815D+00, & 0.0003111352086815D+00, & 0.0003111352086815D+00, & 0.0088517050108932D+00, & 0.0088517050108932D+00, & 0.0088517050108932D+00, & 0.0125572562166769D+00, & 0.0125572562166769D+00, & 0.0125572562166769D+00, & 0.0125572562166769D+00, & 0.0125572562166769D+00, & 0.0125572562166769D+00, & 0.0142105863904482D+00, & 0.0142105863904482D+00, & 0.0142105863904482D+00, & 0.0131061141240994D+00, & 0.0131061141240994D+00, & 0.0131061141240994D+00, & 0.0131061141240994D+00, & 0.0131061141240994D+00, & 0.0131061141240994D+00, & 0.0017788954192555D+00, & 0.0017788954192555D+00, & 0.0017788954192555D+00, & 0.0017788954192555D+00, & 0.0017788954192555D+00, & 0.0017788954192555D+00, & 0.0080119292866950D+00, & 0.0080119292866950D+00, & 0.0080119292866950D+00, & 0.0080119292866950D+00, & 0.0080119292866950D+00, & 0.0080119292866950D+00, & 0.0084646957342766D+00, & 0.0084646957342766D+00, & 0.0084646957342766D+00, & 0.0084646957342766D+00, & 0.0084646957342766D+00, & 0.0084646957342766D+00, & 0.0130927485890890D+00, & 0.0130927485890890D+00, & 0.0130927485890890D+00, & 0.0023767642676878D+00, & 0.0023767642676878D+00, & 0.0023767642676878D+00, & 0.0023767642676878D+00, & 0.0023767642676878D+00, & 0.0023767642676878D+00, & 0.0042769423350179D+00, & 0.0042769423350179D+00, & 0.0042769423350179D+00, & 0.0042769423350179D+00, & 0.0042769423350179D+00, & 0.0042769423350179D+00, & 0.0051312773820373D+00, & 0.0051312773820373D+00, & 0.0051312773820373D+00, & 0.0051312773820373D+00, & 0.0051312773820373D+00, & 0.0051312773820373D+00, & 0.0009485404258894D+00, & 0.0009485404258894D+00, & 0.0009485404258894D+00, & 0.0009485404258894D+00, & 0.0009485404258894D+00, & 0.0009485404258894D+00, & 0.0102459865617042D+00, & 0.0102459865617042D+00, & 0.0102459865617042D+00, & 0.0102459865617042D+00, & 0.0102459865617042D+00, & 0.0102459865617042D+00, & 0.0023245453644640D+00, & 0.0023245453644640D+00, & 0.0023245453644640D+00, & 0.0023245453644640D+00, & 0.0023245453644640D+00, & 0.0023245453644640D+00, & 0.0078099433710863D+00, & 0.0078099433710863D+00, & 0.0078099433710863D+00, & 0.0135475956033255D+00, & 0.0135475956033255D+00, & 0.0135475956033255D+00, & 0.0089251161402765D+00, & 0.0089251161402765D+00, & 0.0089251161402765D+00, & 0.0089251161402765D+00, & 0.0089251161402765D+00, & 0.0089251161402765D+00, & 0.0059178837723539D+00, & 0.0059178837723539D+00, & 0.0059178837723539D+00, & 0.0059178837723539D+00, & 0.0059178837723539D+00, & 0.0059178837723539D+00, & 0.0062605346429685D+00, & 0.0062605346429685D+00, & 0.0062605346429685D+00, & 0.0062605346429685D+00, & 0.0062605346429685D+00, & 0.0062605346429685D+00, & 0.0031401776434880D+00, & 0.0031401776434880D+00, & 0.0031401776434880D+00, & 0.0031401776434880D+00, & 0.0031401776434880D+00, & 0.0031401776434880D+00, & 0.0127871384229558D+00, & 0.0127871384229558D+00, & 0.0127871384229558D+00, & 0.0127871384229558D+00, & 0.0127871384229558D+00, & 0.0127871384229558D+00, & 0.0032049161907930D+00, & 0.0032049161907930D+00, & 0.0032049161907930D+00, & 0.0032049161907930D+00, & 0.0032049161907930D+00, & 0.0032049161907930D+00, & 0.0076821105785950D+00, & 0.0076821105785950D+00, & 0.0076821105785950D+00, & 0.0119426696402482D+00, & 0.0119426696402482D+00, & 0.0119426696402482D+00, & 0.0051282520046781D+00, & 0.0051282520046781D+00, & 0.0051282520046781D+00, & 0.0007251345949861D+00, & 0.0007251345949861D+00, & 0.0007251345949861D+00, & 0.0007251345949861D+00, & 0.0007251345949861D+00, & 0.0007251345949861D+00 /) return end subroutine rule29 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule29() returns the rule of precision 29. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0589421088402292D+00, & 0.9383291479118497D+00, & 0.0027287432479212D+00, & 0.9383291479118497D+00, & 0.0589421088402293D+00, & 0.0027287432479208D+00, & 0.3497880100093318D+00, & 0.4930342901234747D+00, & 0.1571776998671934D+00, & 0.4930342901234748D+00, & 0.3497880100093319D+00, & 0.1571776998671934D+00, & 0.3230018235435502D+00, & 0.6748972098116223D+00, & 0.0021009666448276D+00, & 0.6748972098116223D+00, & 0.3230018235435501D+00, & 0.0021009666448274D+00, & 0.4989148246376862D+00, & 0.4989148246376862D+00, & 0.0021703507246276D+00, & 0.1581458542495161D+00, & 0.7736883369367373D+00, & 0.0681658088137465D+00, & 0.7736883369367374D+00, & 0.1581458542495162D+00, & 0.0681658088137463D+00, & 0.0295494682613534D+00, & 0.9596195731350373D+00, & 0.0108309586036096D+00, & 0.9596195731350373D+00, & 0.0295494682613534D+00, & 0.0108309586036091D+00, & 0.2918191734265371D+00, & 0.4892484845932904D+00, & 0.2189323419801725D+00, & 0.4892484845932904D+00, & 0.2918191734265371D+00, & 0.2189323419801724D+00, & 0.0755221785129958D+00, & 0.9031909252462709D+00, & 0.0212868962407334D+00, & 0.9031909252462710D+00, & 0.0755221785129958D+00, & 0.0212868962407330D+00, & 0.1171166695088989D+00, & 0.8420361139149987D+00, & 0.0408472165761026D+00, & 0.8420361139149987D+00, & 0.1171166695088989D+00, & 0.0408472165761022D+00, & 0.0111662181081692D+00, & 0.9872302853957871D+00, & 0.0016034964960439D+00, & 0.9872302853957869D+00, & 0.0111662181081692D+00, & 0.0016034964960435D+00, & 0.4343804267617306D+00, & 0.4343804267617307D+00, & 0.1312391464765387D+00, & 0.0410973356271179D+00, & 0.9178053287457638D+00, & 0.0410973356271184D+00, & 0.2080456492790871D+00, & 0.6904083654940788D+00, & 0.1015459852268340D+00, & 0.6904083654940788D+00, & 0.2080456492790871D+00, & 0.1015459852268338D+00, & 0.3922101149804348D+00, & 0.5662628237507425D+00, & 0.0415270612688227D+00, & 0.5662628237507424D+00, & 0.3922101149804348D+00, & 0.0415270612688226D+00, & 0.3597112755099758D+00, & 0.5464396833448917D+00, & 0.0938490411451324D+00, & 0.5464396833448917D+00, & 0.3597112755099759D+00, & 0.0938490411451323D+00, & 0.2458746994828754D+00, & 0.7454392707127403D+00, & 0.0086860298043842D+00, & 0.7454392707127405D+00, & 0.2458746994828755D+00, & 0.0086860298043840D+00, & 0.1670027381749231D+00, & 0.8154081377810313D+00, & 0.0175891240440457D+00, & 0.8154081377810313D+00, & 0.1670027381749231D+00, & 0.0175891240440454D+00, & 0.2084053051324008D+00, & 0.5831893897351982D+00, & 0.2084053051324009D+00, & 0.1150085986319464D+00, & 0.8794678768558409D+00, & 0.0055235245122127D+00, & 0.8794678768558410D+00, & 0.1150085986319465D+00, & 0.0055235245122124D+00, & 0.1607458844319635D+00, & 0.6785082311360726D+00, & 0.1607458844319638D+00, & 0.3153953981173191D+00, & 0.6607456749400253D+00, & 0.0238589269426557D+00, & 0.6607456749400252D+00, & 0.3153953981173192D+00, & 0.0238589269426554D+00, & 0.2232226502248206D+00, & 0.7364820152304076D+00, & 0.0402953345447719D+00, & 0.7364820152304076D+00, & 0.2232226502248207D+00, & 0.0402953345447716D+00, & 0.2883958599187324D+00, & 0.6437257357698205D+00, & 0.0678784043114471D+00, & 0.6437257357698205D+00, & 0.2883958599187324D+00, & 0.0678784043114470D+00, & 0.4884016029326027D+00, & 0.4884016029326027D+00, & 0.0231967941347945D+00, & 0.2673663502727756D+00, & 0.5930980425461417D+00, & 0.1395356071810827D+00, & 0.5930980425461417D+00, & 0.2673663502727755D+00, & 0.1395356071810825D+00, & 0.3023864112151284D+00, & 0.3952271775697430D+00, & 0.3023864112151284D+00, & 0.4057653952988916D+00, & 0.5861680189969418D+00, & 0.0080665857041666D+00, & 0.5861680189969418D+00, & 0.4057653952988916D+00, & 0.0080665857041665D+00, & 0.1144268129944254D+00, & 0.7711463740111488D+00, & 0.1144268129944257D+00, & 0.4647624310807389D+00, & 0.4647624310807389D+00, & 0.0704751378385221D+00, & 0.0737218813900997D+00, & 0.8525562372198003D+00, & 0.0737218813901001D+00, & 0.3906191787832637D+00, & 0.3906191787832638D+00, & 0.2187616424334725D+00, & 0.1863207276753595D+00, & 0.8135558255123531D+00, & 0.0001234468122875D+00, & 0.8135558255123529D+00, & 0.1863207276753596D+00, & 0.0001234468122872D+00 /) b = (/ & 0.0027287432479211D+00, & 0.0589421088402292D+00, & 0.9383291479118498D+00, & 0.0027287432479211D+00, & 0.9383291479118498D+00, & 0.0589421088402295D+00, & 0.1571776998671935D+00, & 0.3497880100093319D+00, & 0.4930342901234749D+00, & 0.1571776998671935D+00, & 0.4930342901234748D+00, & 0.3497880100093320D+00, & 0.0021009666448276D+00, & 0.3230018235435502D+00, & 0.6748972098116225D+00, & 0.0021009666448276D+00, & 0.6748972098116225D+00, & 0.3230018235435504D+00, & 0.0021703507246276D+00, & 0.4989148246376863D+00, & 0.4989148246376864D+00, & 0.0681658088137464D+00, & 0.1581458542495161D+00, & 0.7736883369367377D+00, & 0.0681658088137464D+00, & 0.7736883369367376D+00, & 0.1581458542495164D+00, & 0.0108309586036094D+00, & 0.0295494682613534D+00, & 0.9596195731350372D+00, & 0.0108309586036094D+00, & 0.9596195731350375D+00, & 0.0295494682613537D+00, & 0.2189323419801726D+00, & 0.2918191734265372D+00, & 0.4892484845932905D+00, & 0.2189323419801726D+00, & 0.4892484845932905D+00, & 0.2918191734265372D+00, & 0.0212868962407333D+00, & 0.0755221785129958D+00, & 0.9031909252462711D+00, & 0.0212868962407333D+00, & 0.9031909252462711D+00, & 0.0755221785129961D+00, & 0.0408472165761025D+00, & 0.1171166695088989D+00, & 0.8420361139149987D+00, & 0.0408472165761025D+00, & 0.8420361139149989D+00, & 0.1171166695088992D+00, & 0.0016034964960438D+00, & 0.0111662181081691D+00, & 0.9872302853957873D+00, & 0.0016034964960438D+00, & 0.9872302853957873D+00, & 0.0111662181081695D+00, & 0.1312391464765388D+00, & 0.4343804267617307D+00, & 0.4343804267617308D+00, & 0.0410973356271182D+00, & 0.0410973356271179D+00, & 0.9178053287457639D+00, & 0.1015459852268340D+00, & 0.2080456492790872D+00, & 0.6904083654940790D+00, & 0.1015459852268340D+00, & 0.6904083654940790D+00, & 0.2080456492790874D+00, & 0.0415270612688227D+00, & 0.3922101149804349D+00, & 0.5662628237507427D+00, & 0.0415270612688227D+00, & 0.5662628237507425D+00, & 0.3922101149804351D+00, & 0.0938490411451324D+00, & 0.3597112755099759D+00, & 0.5464396833448918D+00, & 0.0938490411451324D+00, & 0.5464396833448918D+00, & 0.3597112755099761D+00, & 0.0086860298043841D+00, & 0.2458746994828755D+00, & 0.7454392707127405D+00, & 0.0086860298043841D+00, & 0.7454392707127405D+00, & 0.2458746994828757D+00, & 0.0175891240440456D+00, & 0.1670027381749231D+00, & 0.8154081377810315D+00, & 0.0175891240440456D+00, & 0.8154081377810315D+00, & 0.1670027381749234D+00, & 0.2084053051324010D+00, & 0.2084053051324008D+00, & 0.5831893897351984D+00, & 0.0055235245122126D+00, & 0.1150085986319464D+00, & 0.8794678768558412D+00, & 0.0055235245122126D+00, & 0.8794678768558412D+00, & 0.1150085986319467D+00, & 0.1607458844319638D+00, & 0.1607458844319636D+00, & 0.6785082311360728D+00, & 0.0238589269426556D+00, & 0.3153953981173191D+00, & 0.6607456749400253D+00, & 0.0238589269426556D+00, & 0.6607456749400253D+00, & 0.3153953981173194D+00, & 0.0402953345447718D+00, & 0.2232226502248206D+00, & 0.7364820152304077D+00, & 0.0402953345447718D+00, & 0.7364820152304077D+00, & 0.2232226502248209D+00, & 0.0678784043114471D+00, & 0.2883958599187324D+00, & 0.6437257357698207D+00, & 0.0678784043114471D+00, & 0.6437257357698207D+00, & 0.2883958599187327D+00, & 0.0231967941347945D+00, & 0.4884016029326028D+00, & 0.4884016029326029D+00, & 0.1395356071810827D+00, & 0.2673663502727756D+00, & 0.5930980425461420D+00, & 0.1395356071810827D+00, & 0.5930980425461420D+00, & 0.2673663502727758D+00, & 0.3023864112151286D+00, & 0.3023864112151285D+00, & 0.3952271775697432D+00, & 0.0080665857041666D+00, & 0.4057653952988916D+00, & 0.5861680189969420D+00, & 0.0080665857041666D+00, & 0.5861680189969419D+00, & 0.4057653952988918D+00, & 0.1144268129944257D+00, & 0.1144268129944254D+00, & 0.7711463740111490D+00, & 0.0704751378385222D+00, & 0.4647624310807390D+00, & 0.4647624310807391D+00, & 0.0737218813901000D+00, & 0.0737218813900997D+00, & 0.8525562372198006D+00, & 0.2187616424334726D+00, & 0.3906191787832639D+00, & 0.3906191787832639D+00, & 0.0001234468122874D+00, & 0.1863207276753596D+00, & 0.8135558255123532D+00, & 0.0001234468122874D+00, & 0.8135558255123531D+00, & 0.1863207276753599D+00 /) c = (/ & 0.9383291479118497D+00, & 0.0027287432479211D+00, & 0.0589421088402289D+00, & 0.0589421088402292D+00, & 0.0027287432479208D+00, & 0.9383291479118496D+00, & 0.4930342901234747D+00, & 0.1571776998671933D+00, & 0.3497880100093317D+00, & 0.3497880100093317D+00, & 0.1571776998671933D+00, & 0.4930342901234746D+00, & 0.6748972098116224D+00, & 0.0021009666448276D+00, & 0.3230018235435500D+00, & 0.3230018235435502D+00, & 0.0021009666448274D+00, & 0.6748972098116222D+00, & 0.4989148246376862D+00, & 0.0021703507246275D+00, & 0.4989148246376860D+00, & 0.7736883369367374D+00, & 0.0681658088137465D+00, & 0.1581458542495159D+00, & 0.1581458542495161D+00, & 0.0681658088137462D+00, & 0.7736883369367373D+00, & 0.9596195731350372D+00, & 0.0108309586036093D+00, & 0.0295494682613533D+00, & 0.0295494682613533D+00, & 0.0108309586036092D+00, & 0.9596195731350372D+00, & 0.4892484845932904D+00, & 0.2189323419801724D+00, & 0.2918191734265370D+00, & 0.2918191734265371D+00, & 0.2189323419801725D+00, & 0.4892484845932903D+00, & 0.9031909252462710D+00, & 0.0212868962407334D+00, & 0.0755221785129956D+00, & 0.0755221785129958D+00, & 0.0212868962407331D+00, & 0.9031909252462709D+00, & 0.8420361139149987D+00, & 0.0408472165761025D+00, & 0.1171166695088987D+00, & 0.1171166695088989D+00, & 0.0408472165761021D+00, & 0.8420361139149986D+00, & 0.9872302853957871D+00, & 0.0016034964960438D+00, & 0.0111662181081689D+00, & 0.0111662181081693D+00, & 0.0016034964960435D+00, & 0.9872302853957871D+00, & 0.4343804267617306D+00, & 0.1312391464765387D+00, & 0.4343804267617306D+00, & 0.9178053287457638D+00, & 0.0410973356271183D+00, & 0.0410973356271177D+00, & 0.6904083654940788D+00, & 0.1015459852268340D+00, & 0.2080456492790870D+00, & 0.2080456492790872D+00, & 0.1015459852268338D+00, & 0.6904083654940787D+00, & 0.5662628237507424D+00, & 0.0415270612688226D+00, & 0.3922101149804347D+00, & 0.3922101149804349D+00, & 0.0415270612688227D+00, & 0.5662628237507423D+00, & 0.5464396833448917D+00, & 0.0938490411451324D+00, & 0.3597112755099757D+00, & 0.3597112755099759D+00, & 0.0938490411451324D+00, & 0.5464396833448915D+00, & 0.7454392707127404D+00, & 0.0086860298043842D+00, & 0.2458746994828752D+00, & 0.2458746994828754D+00, & 0.0086860298043839D+00, & 0.7454392707127404D+00, & 0.8154081377810312D+00, & 0.0175891240440456D+00, & 0.1670027381749228D+00, & 0.1670027381749231D+00, & 0.0175891240440454D+00, & 0.8154081377810313D+00, & 0.5831893897351982D+00, & 0.2084053051324010D+00, & 0.2084053051324007D+00, & 0.8794678768558409D+00, & 0.0055235245122126D+00, & 0.1150085986319461D+00, & 0.1150085986319464D+00, & 0.0055235245122124D+00, & 0.8794678768558408D+00, & 0.6785082311360726D+00, & 0.1607458844319638D+00, & 0.1607458844319634D+00, & 0.6607456749400252D+00, & 0.0238589269426556D+00, & 0.3153953981173190D+00, & 0.3153953981173191D+00, & 0.0238589269426555D+00, & 0.6607456749400251D+00, & 0.7364820152304076D+00, & 0.0402953345447718D+00, & 0.2232226502248205D+00, & 0.2232226502248206D+00, & 0.0402953345447716D+00, & 0.7364820152304075D+00, & 0.6437257357698205D+00, & 0.0678784043114471D+00, & 0.2883958599187322D+00, & 0.2883958599187324D+00, & 0.0678784043114469D+00, & 0.6437257357698203D+00, & 0.4884016029326028D+00, & 0.0231967941347945D+00, & 0.4884016029326026D+00, & 0.5930980425461418D+00, & 0.1395356071810827D+00, & 0.2673663502727753D+00, & 0.2673663502727756D+00, & 0.1395356071810826D+00, & 0.5930980425461417D+00, & 0.3952271775697430D+00, & 0.3023864112151285D+00, & 0.3023864112151284D+00, & 0.5861680189969418D+00, & 0.0080665857041666D+00, & 0.4057653952988913D+00, & 0.4057653952988916D+00, & 0.0080665857041665D+00, & 0.5861680189969416D+00, & 0.7711463740111488D+00, & 0.1144268129944257D+00, & 0.1144268129944253D+00, & 0.4647624310807389D+00, & 0.0704751378385221D+00, & 0.4647624310807388D+00, & 0.8525562372198005D+00, & 0.0737218813901000D+00, & 0.0737218813900994D+00, & 0.3906191787832637D+00, & 0.2187616424334723D+00, & 0.3906191787832637D+00, & 0.8135558255123531D+00, & 0.0001234468122874D+00, & 0.1863207276753593D+00, & 0.1863207276753596D+00, & 0.0001234468122874D+00, & 0.8135558255123528D+00 /) w = (/ & 0.0007692529714762D+00, & 0.0007692529714762D+00, & 0.0007692529714762D+00, & 0.0007692529714762D+00, & 0.0007692529714762D+00, & 0.0007692529714762D+00, & 0.0104522146969224D+00, & 0.0104522146969224D+00, & 0.0104522146969224D+00, & 0.0104522146969224D+00, & 0.0104522146969224D+00, & 0.0104522146969224D+00, & 0.0013528239492524D+00, & 0.0013528239492524D+00, & 0.0013528239492524D+00, & 0.0013528239492524D+00, & 0.0013528239492524D+00, & 0.0013528239492524D+00, & 0.0015164621031569D+00, & 0.0015164621031569D+00, & 0.0015164621031569D+00, & 0.0064391367075338D+00, & 0.0064391367075338D+00, & 0.0064391367075338D+00, & 0.0064391367075338D+00, & 0.0064391367075338D+00, & 0.0064391367075338D+00, & 0.0012721944371716D+00, & 0.0012721944371716D+00, & 0.0012721944371716D+00, & 0.0012721944371716D+00, & 0.0012721944371716D+00, & 0.0012721944371716D+00, & 0.0135452465720076D+00, & 0.0135452465720076D+00, & 0.0135452465720076D+00, & 0.0135452465720076D+00, & 0.0135452465720076D+00, & 0.0135452465720076D+00, & 0.0027615307495904D+00, & 0.0027615307495904D+00, & 0.0027615307495904D+00, & 0.0027615307495904D+00, & 0.0027615307495904D+00, & 0.0027615307495904D+00, & 0.0045126868454873D+00, & 0.0045126868454873D+00, & 0.0045126868454873D+00, & 0.0045126868454873D+00, & 0.0045126868454873D+00, & 0.0045126868454873D+00, & 0.0002694922318587D+00, & 0.0002694922318587D+00, & 0.0002694922318587D+00, & 0.0002694922318587D+00, & 0.0002694922318587D+00, & 0.0002694922318587D+00, & 0.0111711002951679D+00, & 0.0111711002951679D+00, & 0.0111711002951679D+00, & 0.0028604915061569D+00, & 0.0028604915061569D+00, & 0.0028604915061569D+00, & 0.0093863306762837D+00, & 0.0093863306762837D+00, & 0.0093863306762837D+00, & 0.0093863306762837D+00, & 0.0093863306762837D+00, & 0.0093863306762837D+00, & 0.0078229184583065D+00, & 0.0078229184583065D+00, & 0.0078229184583065D+00, & 0.0078229184583065D+00, & 0.0078229184583065D+00, & 0.0078229184583065D+00, & 0.0106303963631966D+00, & 0.0106303963631966D+00, & 0.0106303963631966D+00, & 0.0106303963631966D+00, & 0.0106303963631966D+00, & 0.0106303963631966D+00, & 0.0030512388233452D+00, & 0.0030512388233452D+00, & 0.0030512388233452D+00, & 0.0030512388233452D+00, & 0.0030512388233452D+00, & 0.0030512388233452D+00, & 0.0038253666717300D+00, & 0.0038253666717300D+00, & 0.0038253666717300D+00, & 0.0038253666717300D+00, & 0.0038253666717300D+00, & 0.0038253666717300D+00, & 0.0125392034426232D+00, & 0.0125392034426232D+00, & 0.0125392034426232D+00, & 0.0017416952313017D+00, & 0.0017416952313017D+00, & 0.0017416952313017D+00, & 0.0017416952313017D+00, & 0.0017416952313017D+00, & 0.0017416952313017D+00, & 0.0105714178582276D+00, & 0.0105714178582276D+00, & 0.0105714178582276D+00, & 0.0056691534816655D+00, & 0.0056691534816655D+00, & 0.0056691534816655D+00, & 0.0056691534816655D+00, & 0.0056691534816655D+00, & 0.0056691534816655D+00, & 0.0065819977638522D+00, & 0.0065819977638522D+00, & 0.0065819977638522D+00, & 0.0065819977638522D+00, & 0.0065819977638522D+00, & 0.0065819977638522D+00, & 0.0091789241649276D+00, & 0.0091789241649276D+00, & 0.0091789241649276D+00, & 0.0091789241649276D+00, & 0.0091789241649276D+00, & 0.0091789241649276D+00, & 0.0061344011647189D+00, & 0.0061344011647189D+00, & 0.0061344011647189D+00, & 0.0125183664988344D+00, & 0.0125183664988344D+00, & 0.0125183664988344D+00, & 0.0125183664988344D+00, & 0.0125183664988344D+00, & 0.0125183664988344D+00, & 0.0163102388077432D+00, & 0.0163102388077432D+00, & 0.0163102388077432D+00, & 0.0036413404112807D+00, & 0.0036413404112807D+00, & 0.0036413404112807D+00, & 0.0036413404112807D+00, & 0.0036413404112807D+00, & 0.0036413404112807D+00, & 0.0081728784412271D+00, & 0.0081728784412271D+00, & 0.0081728784412271D+00, & 0.0103131166352585D+00, & 0.0103131166352585D+00, & 0.0103131166352585D+00, & 0.0056088471328313D+00, & 0.0056088471328313D+00, & 0.0056088471328313D+00, & 0.0159132152840889D+00, & 0.0159132152840889D+00, & 0.0159132152840889D+00, & 0.0006886726250418D+00, & 0.0006886726250418D+00, & 0.0006886726250418D+00, & 0.0006886726250418D+00, & 0.0006886726250418D+00, & 0.0006886726250418D+00 /) return end subroutine rule30 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule30() returns the rule of precision 30. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2590538845210674D+00, & 0.6931109923381602D+00, & 0.0478351231407726D+00, & 0.6931109923381601D+00, & 0.2590538845210674D+00, & 0.0478351231407724D+00, & 0.0033187249366444D+00, & 0.9933625501267108D+00, & 0.0033187249366448D+00, & 0.3915721882912563D+00, & 0.5287682847771430D+00, & 0.0796595269316006D+00, & 0.5287682847771430D+00, & 0.3915721882912564D+00, & 0.0796595269316005D+00, & 0.3561402832962335D+00, & 0.5861663154298922D+00, & 0.0576934012738742D+00, & 0.5861663154298922D+00, & 0.3561402832962335D+00, & 0.0576934012738741D+00, & 0.0723724072246778D+00, & 0.8552551855506439D+00, & 0.0723724072246782D+00, & 0.2830124973495888D+00, & 0.6397260650735270D+00, & 0.0772614375768841D+00, & 0.6397260650735271D+00, & 0.2830124973495887D+00, & 0.0772614375768839D+00, & 0.0471579102421718D+00, & 0.9056841795156562D+00, & 0.0471579102421721D+00, & 0.2416137624515244D+00, & 0.7356278532534756D+00, & 0.0227583842950001D+00, & 0.7356278532534756D+00, & 0.2416137624515244D+00, & 0.0227583842949999D+00, & 0.2527812471879329D+00, & 0.6234067740413924D+00, & 0.1238119787706746D+00, & 0.6234067740413924D+00, & 0.2527812471879329D+00, & 0.1238119787706745D+00, & 0.1849061063839171D+00, & 0.6992119263799822D+00, & 0.1158819672361006D+00, & 0.6992119263799822D+00, & 0.1849061063839172D+00, & 0.1158819672361004D+00, & 0.4680301736511254D+00, & 0.4680301736511254D+00, & 0.0639396526977491D+00, & 0.0126866046744676D+00, & 0.9746267906510645D+00, & 0.0126866046744680D+00, & 0.1937043771536401D+00, & 0.7397781780644782D+00, & 0.0665174447818817D+00, & 0.7397781780644782D+00, & 0.1937043771536401D+00, & 0.0665174447818814D+00, & 0.0764012484393875D+00, & 0.9191599701835511D+00, & 0.0044387813770616D+00, & 0.9191599701835510D+00, & 0.0764012484393877D+00, & 0.0044387813770611D+00, & 0.1215915082227279D+00, & 0.7568169835545440D+00, & 0.1215915082227282D+00, & 0.2090480874526896D+00, & 0.7862883331546218D+00, & 0.0046635793926887D+00, & 0.7862883331546218D+00, & 0.2090480874526897D+00, & 0.0046635793926884D+00, & 0.2985429940592427D+00, & 0.6967533241762803D+00, & 0.0047036817644771D+00, & 0.6967533241762803D+00, & 0.2985429940592427D+00, & 0.0047036817644769D+00, & 0.3343790400340311D+00, & 0.6404388932621004D+00, & 0.0251820667038687D+00, & 0.6404388932621002D+00, & 0.3343790400340311D+00, & 0.0251820667038686D+00, & 0.1232308023806951D+00, & 0.8109926237945619D+00, & 0.0657765738247430D+00, & 0.8109926237945619D+00, & 0.1232308023806952D+00, & 0.0657765738247426D+00, & 0.3385141624298457D+00, & 0.5353617425851648D+00, & 0.1261240949849894D+00, & 0.5353617425851648D+00, & 0.3385141624298457D+00, & 0.1261240949849893D+00, & 0.3544036021806874D+00, & 0.4507254468957941D+00, & 0.1948709509235184D+00, & 0.4507254468957941D+00, & 0.3544036021806874D+00, & 0.1948709509235184D+00, & 0.2630682977578083D+00, & 0.5459302776699086D+00, & 0.1910014245722831D+00, & 0.5459302776699086D+00, & 0.2630682977578084D+00, & 0.1910014245722829D+00, & 0.1824095615174529D+00, & 0.6351808769650940D+00, & 0.1824095615174532D+00, & 0.4345661739646696D+00, & 0.5379004199107804D+00, & 0.0275334061245499D+00, & 0.5379004199107805D+00, & 0.4345661739646697D+00, & 0.0275334061245498D+00, & 0.1640709870698783D+00, & 0.8078650909487486D+00, & 0.0280639219813731D+00, & 0.8078650909487487D+00, & 0.1640709870698785D+00, & 0.0280639219813727D+00, & 0.3622872793529498D+00, & 0.3622872793529498D+00, & 0.2754254412941003D+00, & 0.0426819997060804D+00, & 0.9414155840249848D+00, & 0.0159024162689350D+00, & 0.9414155840249848D+00, & 0.0426819997060806D+00, & 0.0159024162689344D+00, & 0.0939597946527299D+00, & 0.8787459746951742D+00, & 0.0272942306520959D+00, & 0.8787459746951743D+00, & 0.0939597946527300D+00, & 0.0272942306520955D+00, & 0.1354088535199345D+00, & 0.8588999350346495D+00, & 0.0056912114454161D+00, & 0.8588999350346495D+00, & 0.1354088535199345D+00, & 0.0056912114454159D+00, & 0.4367432485484602D+00, & 0.4367432485484602D+00, & 0.1265135029030796D+00, & 0.2724280407839282D+00, & 0.4551439184321434D+00, & 0.2724280407839283D+00, & 0.3962215147396591D+00, & 0.5986161382437196D+00, & 0.0051623470166213D+00, & 0.5986161382437196D+00, & 0.3962215147396591D+00, & 0.0051623470166212D+00, & 0.4973193390003086D+00, & 0.4973193390003087D+00, & 0.0053613219993828D+00, & 0.0294840425976739D+00, & 0.9699822487416315D+00, & 0.0005337086606946D+00, & 0.9699822487416316D+00, & 0.0294840425976741D+00, & 0.0005337086606942D+00 /) b = (/ & 0.0478351231407726D+00, & 0.2590538845210673D+00, & 0.6931109923381603D+00, & 0.0478351231407726D+00, & 0.6931109923381602D+00, & 0.2590538845210676D+00, & 0.0033187249366447D+00, & 0.0033187249366444D+00, & 0.9933625501267112D+00, & 0.0796595269316007D+00, & 0.3915721882912564D+00, & 0.5287682847771432D+00, & 0.0796595269316007D+00, & 0.5287682847771431D+00, & 0.3915721882912566D+00, & 0.0576934012738742D+00, & 0.3561402832962335D+00, & 0.5861663154298924D+00, & 0.0576934012738742D+00, & 0.5861663154298923D+00, & 0.3561402832962338D+00, & 0.0723724072246781D+00, & 0.0723724072246778D+00, & 0.8552551855506442D+00, & 0.0772614375768841D+00, & 0.2830124973495888D+00, & 0.6397260650735274D+00, & 0.0772614375768841D+00, & 0.6397260650735274D+00, & 0.2830124973495890D+00, & 0.0471579102421721D+00, & 0.0471579102421717D+00, & 0.9056841795156564D+00, & 0.0227583842950001D+00, & 0.2416137624515244D+00, & 0.7356278532534757D+00, & 0.0227583842950001D+00, & 0.7356278532534757D+00, & 0.2416137624515247D+00, & 0.1238119787706747D+00, & 0.2527812471879330D+00, & 0.6234067740413927D+00, & 0.1238119787706747D+00, & 0.6234067740413927D+00, & 0.2527812471879332D+00, & 0.1158819672361006D+00, & 0.1849061063839172D+00, & 0.6992119263799824D+00, & 0.1158819672361006D+00, & 0.6992119263799824D+00, & 0.1849061063839174D+00, & 0.0639396526977492D+00, & 0.4680301736511254D+00, & 0.4680301736511256D+00, & 0.0126866046744679D+00, & 0.0126866046744676D+00, & 0.9746267906510646D+00, & 0.0665174447818816D+00, & 0.1937043771536401D+00, & 0.7397781780644784D+00, & 0.0665174447818816D+00, & 0.7397781780644784D+00, & 0.1937043771536404D+00, & 0.0044387813770614D+00, & 0.0764012484393875D+00, & 0.9191599701835511D+00, & 0.0044387813770614D+00, & 0.9191599701835511D+00, & 0.0764012484393879D+00, & 0.1215915082227282D+00, & 0.1215915082227279D+00, & 0.7568169835545441D+00, & 0.0046635793926886D+00, & 0.2090480874526896D+00, & 0.7862883331546219D+00, & 0.0046635793926886D+00, & 0.7862883331546219D+00, & 0.2090480874526899D+00, & 0.0047036817644770D+00, & 0.2985429940592426D+00, & 0.6967533241762806D+00, & 0.0047036817644770D+00, & 0.6967533241762803D+00, & 0.2985429940592429D+00, & 0.0251820667038687D+00, & 0.3343790400340311D+00, & 0.6404388932621005D+00, & 0.0251820667038687D+00, & 0.6404388932621004D+00, & 0.3343790400340313D+00, & 0.0657765738247429D+00, & 0.1232308023806951D+00, & 0.8109926237945622D+00, & 0.0657765738247429D+00, & 0.8109926237945622D+00, & 0.1232308023806954D+00, & 0.1261240949849895D+00, & 0.3385141624298458D+00, & 0.5353617425851650D+00, & 0.1261240949849895D+00, & 0.5353617425851650D+00, & 0.3385141624298459D+00, & 0.1948709509235185D+00, & 0.3544036021806876D+00, & 0.4507254468957942D+00, & 0.1948709509235185D+00, & 0.4507254468957941D+00, & 0.3544036021806876D+00, & 0.1910014245722831D+00, & 0.2630682977578084D+00, & 0.5459302776699086D+00, & 0.1910014245722831D+00, & 0.5459302776699086D+00, & 0.2630682977578085D+00, & 0.1824095615174531D+00, & 0.1824095615174529D+00, & 0.6351808769650941D+00, & 0.0275334061245499D+00, & 0.4345661739646697D+00, & 0.5379004199107807D+00, & 0.0275334061245499D+00, & 0.5379004199107805D+00, & 0.4345661739646698D+00, & 0.0280639219813730D+00, & 0.1640709870698784D+00, & 0.8078650909487487D+00, & 0.0280639219813730D+00, & 0.8078650909487487D+00, & 0.1640709870698787D+00, & 0.2754254412941004D+00, & 0.3622872793529499D+00, & 0.3622872793529500D+00, & 0.0159024162689347D+00, & 0.0426819997060803D+00, & 0.9414155840249849D+00, & 0.0159024162689347D+00, & 0.9414155840249849D+00, & 0.0426819997060808D+00, & 0.0272942306520958D+00, & 0.0939597946527299D+00, & 0.8787459746951745D+00, & 0.0272942306520958D+00, & 0.8787459746951745D+00, & 0.0939597946527302D+00, & 0.0056912114454161D+00, & 0.1354088535199344D+00, & 0.8588999350346497D+00, & 0.0056912114454161D+00, & 0.8588999350346497D+00, & 0.1354088535199348D+00, & 0.1265135029030796D+00, & 0.4367432485484603D+00, & 0.4367432485484604D+00, & 0.2724280407839283D+00, & 0.2724280407839283D+00, & 0.4551439184321436D+00, & 0.0051623470166213D+00, & 0.3962215147396591D+00, & 0.5986161382437198D+00, & 0.0051623470166213D+00, & 0.5986161382437197D+00, & 0.3962215147396594D+00, & 0.0053613219993829D+00, & 0.4973193390003086D+00, & 0.4973193390003088D+00, & 0.0005337086606945D+00, & 0.0294840425976739D+00, & 0.9699822487416317D+00, & 0.0005337086606945D+00, & 0.9699822487416317D+00, & 0.0294840425976742D+00 /) c = (/ & 0.6931109923381601D+00, & 0.0478351231407725D+00, & 0.2590538845210671D+00, & 0.2590538845210673D+00, & 0.0478351231407724D+00, & 0.6931109923381600D+00, & 0.9933625501267110D+00, & 0.0033187249366448D+00, & 0.0033187249366441D+00, & 0.5287682847771430D+00, & 0.0796595269316006D+00, & 0.3915721882912562D+00, & 0.3915721882912563D+00, & 0.0796595269316005D+00, & 0.5287682847771429D+00, & 0.5861663154298923D+00, & 0.0576934012738743D+00, & 0.3561402832962334D+00, & 0.3561402832962336D+00, & 0.0576934012738742D+00, & 0.5861663154298921D+00, & 0.8552551855506441D+00, & 0.0723724072246782D+00, & 0.0723724072246775D+00, & 0.6397260650735271D+00, & 0.0772614375768842D+00, & 0.2830124973495886D+00, & 0.2830124973495887D+00, & 0.0772614375768840D+00, & 0.6397260650735271D+00, & 0.9056841795156562D+00, & 0.0471579102421721D+00, & 0.0471579102421714D+00, & 0.7356278532534755D+00, & 0.0227583842950000D+00, & 0.2416137624515242D+00, & 0.2416137624515244D+00, & 0.0227583842949999D+00, & 0.7356278532534755D+00, & 0.6234067740413924D+00, & 0.1238119787706746D+00, & 0.2527812471879327D+00, & 0.2527812471879329D+00, & 0.1238119787706744D+00, & 0.6234067740413923D+00, & 0.6992119263799823D+00, & 0.1158819672361006D+00, & 0.1849061063839169D+00, & 0.1849061063839172D+00, & 0.1158819672361003D+00, & 0.6992119263799823D+00, & 0.4680301736511254D+00, & 0.0639396526977491D+00, & 0.4680301736511252D+00, & 0.9746267906510645D+00, & 0.0126866046744679D+00, & 0.0126866046744674D+00, & 0.7397781780644782D+00, & 0.0665174447818817D+00, & 0.1937043771536399D+00, & 0.1937043771536402D+00, & 0.0665174447818814D+00, & 0.7397781780644782D+00, & 0.9191599701835511D+00, & 0.0044387813770613D+00, & 0.0764012484393873D+00, & 0.0764012484393876D+00, & 0.0044387813770612D+00, & 0.9191599701835510D+00, & 0.7568169835545440D+00, & 0.1215915082227281D+00, & 0.1215915082227278D+00, & 0.7862883331546218D+00, & 0.0046635793926886D+00, & 0.2090480874526894D+00, & 0.2090480874526896D+00, & 0.0046635793926885D+00, & 0.7862883331546215D+00, & 0.6967533241762803D+00, & 0.0047036817644771D+00, & 0.2985429940592425D+00, & 0.2985429940592426D+00, & 0.0047036817644769D+00, & 0.6967533241762802D+00, & 0.6404388932621002D+00, & 0.0251820667038686D+00, & 0.3343790400340308D+00, & 0.3343790400340311D+00, & 0.0251820667038686D+00, & 0.6404388932621001D+00, & 0.8109926237945619D+00, & 0.0657765738247430D+00, & 0.1232308023806948D+00, & 0.1232308023806952D+00, & 0.0657765738247427D+00, & 0.8109926237945619D+00, & 0.5353617425851648D+00, & 0.1261240949849894D+00, & 0.3385141624298456D+00, & 0.3385141624298458D+00, & 0.1261240949849892D+00, & 0.5353617425851648D+00, & 0.4507254468957941D+00, & 0.1948709509235184D+00, & 0.3544036021806874D+00, & 0.3544036021806874D+00, & 0.1948709509235184D+00, & 0.4507254468957940D+00, & 0.5459302776699086D+00, & 0.1910014245722830D+00, & 0.2630682977578083D+00, & 0.2630682977578082D+00, & 0.1910014245722830D+00, & 0.5459302776699084D+00, & 0.6351808769650941D+00, & 0.1824095615174531D+00, & 0.1824095615174527D+00, & 0.5379004199107805D+00, & 0.0275334061245499D+00, & 0.4345661739646695D+00, & 0.4345661739646696D+00, & 0.0275334061245497D+00, & 0.5379004199107804D+00, & 0.8078650909487487D+00, & 0.0280639219813731D+00, & 0.1640709870698781D+00, & 0.1640709870698783D+00, & 0.0280639219813729D+00, & 0.8078650909487486D+00, & 0.3622872793529498D+00, & 0.2754254412941003D+00, & 0.3622872793529497D+00, & 0.9414155840249848D+00, & 0.0159024162689349D+00, & 0.0426819997060801D+00, & 0.0426819997060805D+00, & 0.0159024162689345D+00, & 0.9414155840249848D+00, & 0.8787459746951743D+00, & 0.0272942306520959D+00, & 0.0939597946527296D+00, & 0.0939597946527299D+00, & 0.0272942306520956D+00, & 0.8787459746951742D+00, & 0.8588999350346495D+00, & 0.0056912114454161D+00, & 0.1354088535199341D+00, & 0.1354088535199345D+00, & 0.0056912114454158D+00, & 0.8588999350346493D+00, & 0.4367432485484603D+00, & 0.1265135029030796D+00, & 0.4367432485484601D+00, & 0.4551439184321435D+00, & 0.2724280407839283D+00, & 0.2724280407839281D+00, & 0.5986161382437196D+00, & 0.0051623470166213D+00, & 0.3962215147396588D+00, & 0.3962215147396591D+00, & 0.0051623470166212D+00, & 0.5986161382437194D+00, & 0.4973193390003086D+00, & 0.0053613219993827D+00, & 0.4973193390003083D+00, & 0.9699822487416316D+00, & 0.0005337086606946D+00, & 0.0294840425976736D+00, & 0.0294840425976739D+00, & 0.0005337086606941D+00, & 0.9699822487416315D+00 /) w = (/ & 0.0042147584639124D+00, & 0.0042147584639124D+00, & 0.0042147584639124D+00, & 0.0042147584639124D+00, & 0.0042147584639124D+00, & 0.0042147584639124D+00, & 0.0001717299013710D+00, & 0.0001717299013710D+00, & 0.0001717299013710D+00, & 0.0059249227450920D+00, & 0.0059249227450920D+00, & 0.0059249227450920D+00, & 0.0059249227450920D+00, & 0.0059249227450920D+00, & 0.0059249227450920D+00, & 0.0059442201844245D+00, & 0.0059442201844245D+00, & 0.0059442201844245D+00, & 0.0059442201844245D+00, & 0.0059442201844245D+00, & 0.0059442201844245D+00, & 0.0038019326684155D+00, & 0.0038019326684155D+00, & 0.0038019326684155D+00, & 0.0068771843875359D+00, & 0.0068771843875359D+00, & 0.0068771843875359D+00, & 0.0068771843875359D+00, & 0.0068771843875359D+00, & 0.0068771843875359D+00, & 0.0028444336676875D+00, & 0.0028444336676875D+00, & 0.0028444336676875D+00, & 0.0040924989683472D+00, & 0.0040924989683472D+00, & 0.0040924989683472D+00, & 0.0040924989683472D+00, & 0.0040924989683472D+00, & 0.0040924989683472D+00, & 0.0088726545060173D+00, & 0.0088726545060173D+00, & 0.0088726545060173D+00, & 0.0088726545060173D+00, & 0.0088726545060173D+00, & 0.0088726545060173D+00, & 0.0075343229295465D+00, & 0.0075343229295465D+00, & 0.0075343229295465D+00, & 0.0075343229295465D+00, & 0.0075343229295465D+00, & 0.0075343229295465D+00, & 0.0077841287323308D+00, & 0.0077841287323308D+00, & 0.0077841287323308D+00, & 0.0008465501453289D+00, & 0.0008465501453289D+00, & 0.0008465501453289D+00, & 0.0068040067561019D+00, & 0.0068040067561019D+00, & 0.0068040067561019D+00, & 0.0068040067561019D+00, & 0.0068040067561019D+00, & 0.0068040067561019D+00, & 0.0012066965685421D+00, & 0.0012066965685421D+00, & 0.0012066965685421D+00, & 0.0012066965685421D+00, & 0.0012066965685421D+00, & 0.0012066965685421D+00, & 0.0073869118349143D+00, & 0.0073869118349143D+00, & 0.0073869118349143D+00, & 0.0019589485778932D+00, & 0.0019589485778932D+00, & 0.0019589485778932D+00, & 0.0019589485778932D+00, & 0.0019589485778932D+00, & 0.0019589485778932D+00, & 0.0022744459009987D+00, & 0.0022744459009987D+00, & 0.0022744459009987D+00, & 0.0022744459009987D+00, & 0.0022744459009987D+00, & 0.0022744459009987D+00, & 0.0053646848461863D+00, & 0.0053646848461863D+00, & 0.0053646848461863D+00, & 0.0053646848461863D+00, & 0.0053646848461863D+00, & 0.0053646848461863D+00, & 0.0058700698030655D+00, & 0.0058700698030655D+00, & 0.0058700698030655D+00, & 0.0058700698030655D+00, & 0.0058700698030655D+00, & 0.0058700698030655D+00, & 0.0113030235429375D+00, & 0.0113030235429375D+00, & 0.0113030235429375D+00, & 0.0113030235429375D+00, & 0.0113030235429375D+00, & 0.0113030235429375D+00, & 0.0143164852696676D+00, & 0.0143164852696676D+00, & 0.0143164852696676D+00, & 0.0143164852696676D+00, & 0.0143164852696676D+00, & 0.0143164852696676D+00, & 0.0129260234501183D+00, & 0.0129260234501183D+00, & 0.0129260234501183D+00, & 0.0129260234501183D+00, & 0.0129260234501183D+00, & 0.0129260234501183D+00, & 0.0107528509654328D+00, & 0.0107528509654328D+00, & 0.0107528509654328D+00, & 0.0062815965808917D+00, & 0.0062815965808917D+00, & 0.0062815965808917D+00, & 0.0062815965808917D+00, & 0.0062815965808917D+00, & 0.0062815965808917D+00, & 0.0047019369941060D+00, & 0.0047019369941060D+00, & 0.0047019369941060D+00, & 0.0047019369941060D+00, & 0.0047019369941060D+00, & 0.0047019369941060D+00, & 0.0155960913258258D+00, & 0.0155960913258258D+00, & 0.0155960913258258D+00, & 0.0018305068761488D+00, & 0.0018305068761488D+00, & 0.0018305068761488D+00, & 0.0018305068761488D+00, & 0.0018305068761488D+00, & 0.0018305068761488D+00, & 0.0038218805470950D+00, & 0.0038218805470950D+00, & 0.0038218805470950D+00, & 0.0038218805470950D+00, & 0.0038218805470950D+00, & 0.0038218805470950D+00, & 0.0019198805574689D+00, & 0.0019198805574689D+00, & 0.0019198805574689D+00, & 0.0019198805574689D+00, & 0.0019198805574689D+00, & 0.0019198805574689D+00, & 0.0124049590281460D+00, & 0.0124049590281460D+00, & 0.0124049590281460D+00, & 0.0149145507626858D+00, & 0.0149145507626858D+00, & 0.0149145507626858D+00, & 0.0026425679231633D+00, & 0.0026425679231633D+00, & 0.0026425679231633D+00, & 0.0026425679231633D+00, & 0.0026425679231633D+00, & 0.0026425679231633D+00, & 0.0027913181197408D+00, & 0.0027913181197408D+00, & 0.0027913181197408D+00, & 0.0003356217114664D+00, & 0.0003356217114664D+00, & 0.0003356217114664D+00, & 0.0003356217114664D+00, & 0.0003356217114664D+00, & 0.0003356217114664D+00 /) return end subroutine rule31 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule31() returns the rule of precision 31. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3333333333333333D+00, & 0.4861524679130598D+00, & 0.4861524679130598D+00, & 0.0276950641738803D+00, & 0.1390906284720946D+00, & 0.7542396906638279D+00, & 0.1066696808640776D+00, & 0.7542396906638279D+00, & 0.1390906284720947D+00, & 0.1066696808640773D+00, & 0.4195880808642605D+00, & 0.4195880808642605D+00, & 0.1608238382714789D+00, & 0.1972331307896530D+00, & 0.7995057135466186D+00, & 0.0032611556637284D+00, & 0.7995057135466186D+00, & 0.1972331307896531D+00, & 0.0032611556637281D+00, & 0.2385241509843100D+00, & 0.7483360311752862D+00, & 0.0131398178404037D+00, & 0.7483360311752864D+00, & 0.2385241509843100D+00, & 0.0131398178404035D+00, & 0.0792067965066985D+00, & 0.8415864069866026D+00, & 0.0792067965066989D+00, & 0.0297507293859900D+00, & 0.9679050494853231D+00, & 0.0023442211286871D+00, & 0.9679050494853232D+00, & 0.0297507293859901D+00, & 0.0023442211286867D+00, & 0.0177313492497139D+00, & 0.9645373015005718D+00, & 0.0177313492497143D+00, & 0.3957839332968854D+00, & 0.6022546663332196D+00, & 0.0019614003698950D+00, & 0.6022546663332196D+00, & 0.3957839332968854D+00, & 0.0019614003698949D+00, & 0.3516800587760809D+00, & 0.4956833754486993D+00, & 0.1526365657752197D+00, & 0.4956833754486993D+00, & 0.3516800587760809D+00, & 0.1526365657752196D+00, & 0.2024821942617583D+00, & 0.6840925273907388D+00, & 0.1134252783475029D+00, & 0.6840925273907387D+00, & 0.2024821942617585D+00, & 0.1134252783475028D+00, & 0.4225539552222151D+00, & 0.5229246603331018D+00, & 0.0545213844446831D+00, & 0.5229246603331018D+00, & 0.4225539552222151D+00, & 0.0545213844446831D+00, & 0.1246805088474440D+00, & 0.8147145619917838D+00, & 0.0606049291607723D+00, & 0.8147145619917838D+00, & 0.1246805088474441D+00, & 0.0606049291607719D+00, & 0.2555462364028573D+00, & 0.7068648114396249D+00, & 0.0375889521575178D+00, & 0.7068648114396250D+00, & 0.2555462364028574D+00, & 0.0375889521575175D+00, & 0.0745031299353863D+00, & 0.9211105398945520D+00, & 0.0043863301700618D+00, & 0.9211105398945520D+00, & 0.0745031299353864D+00, & 0.0043863301700614D+00, & 0.4168072755236505D+00, & 0.5659193101514124D+00, & 0.0172734143249371D+00, & 0.5659193101514123D+00, & 0.4168072755236506D+00, & 0.0172734143249370D+00, & 0.1928717230061985D+00, & 0.7445502549794906D+00, & 0.0625780220143110D+00, & 0.7445502549794907D+00, & 0.1928717230061984D+00, & 0.0625780220143108D+00, & 0.0473478189395525D+00, & 0.9342442340291646D+00, & 0.0184079470312831D+00, & 0.9342442340291646D+00, & 0.0473478189395526D+00, & 0.0184079470312826D+00, & 0.2184364967909280D+00, & 0.5631270064181437D+00, & 0.2184364967909281D+00, & 0.1724507871838860D+00, & 0.6550984256322278D+00, & 0.1724507871838863D+00, & 0.0510951808223813D+00, & 0.8978096383552372D+00, & 0.0510951808223817D+00, & 0.3419050053475277D+00, & 0.6151917857097009D+00, & 0.0429032089427714D+00, & 0.6151917857097009D+00, & 0.3419050053475278D+00, & 0.0429032089427713D+00, & 0.3258139530575097D+00, & 0.6609969631634746D+00, & 0.0131890837790157D+00, & 0.6609969631634747D+00, & 0.3258139530575097D+00, & 0.0131890837790155D+00, & 0.2894259487571373D+00, & 0.7093771696121531D+00, & 0.0011968816307096D+00, & 0.7093771696121531D+00, & 0.2894259487571372D+00, & 0.0011968816307094D+00, & 0.2987897956760133D+00, & 0.4820774428938099D+00, & 0.2191327614301768D+00, & 0.4820774428938098D+00, & 0.2987897956760134D+00, & 0.2191327614301767D+00, & 0.2744757477427950D+00, & 0.6443943606878740D+00, & 0.0811298915693310D+00, & 0.6443943606878740D+00, & 0.2744757477427950D+00, & 0.0811298915693308D+00, & 0.3532298738914156D+00, & 0.5514920116265676D+00, & 0.0952781144820168D+00, & 0.5514920116265676D+00, & 0.3532298738914156D+00, & 0.0952781144820166D+00, & 0.4977486206264703D+00, & 0.4977486206264703D+00, & 0.0045027587470594D+00, & 0.2663678824750718D+00, & 0.5867434095228163D+00, & 0.1468887080021118D+00, & 0.5867434095228162D+00, & 0.2663678824750718D+00, & 0.1468887080021118D+00, & 0.3851684692456800D+00, & 0.3851684692456801D+00, & 0.2296630615086398D+00, & 0.2974914903679928D+00, & 0.4050170192640142D+00, & 0.2974914903679928D+00, & 0.0960481521010511D+00, & 0.8764212178203614D+00, & 0.0275306300785876D+00, & 0.8764212178203614D+00, & 0.0960481521010512D+00, & 0.0275306300785873D+00, & 0.0050828094627277D+00, & 0.9898343810745441D+00, & 0.0050828094627282D+00, & 0.1674078247783561D+00, & 0.8067170670017056D+00, & 0.0258751082199382D+00, & 0.8067170670017058D+00, & 0.1674078247783561D+00, & 0.0258751082199379D+00, & 0.4503409417390182D+00, & 0.4503409417390182D+00, & 0.0993181165219635D+00, & 0.1306776337702883D+00, & 0.8635250475449717D+00, & 0.0057973186847399D+00, & 0.8635250475449718D+00, & 0.1306776337702885D+00, & 0.0057973186847396D+00 /) b = (/ & 0.3333333333333334D+00, & 0.0276950641738804D+00, & 0.4861524679130599D+00, & 0.4861524679130600D+00, & 0.1066696808640776D+00, & 0.1390906284720946D+00, & 0.7542396906638279D+00, & 0.1066696808640776D+00, & 0.7542396906638279D+00, & 0.1390906284720949D+00, & 0.1608238382714791D+00, & 0.4195880808642605D+00, & 0.4195880808642607D+00, & 0.0032611556637283D+00, & 0.1972331307896530D+00, & 0.7995057135466188D+00, & 0.0032611556637283D+00, & 0.7995057135466188D+00, & 0.1972331307896533D+00, & 0.0131398178404037D+00, & 0.2385241509843100D+00, & 0.7483360311752866D+00, & 0.0131398178404037D+00, & 0.7483360311752866D+00, & 0.2385241509843103D+00, & 0.0792067965066988D+00, & 0.0792067965066985D+00, & 0.8415864069866028D+00, & 0.0023442211286869D+00, & 0.0297507293859899D+00, & 0.9679050494853232D+00, & 0.0023442211286869D+00, & 0.9679050494853232D+00, & 0.0297507293859903D+00, & 0.0177313492497142D+00, & 0.0177313492497139D+00, & 0.9645373015005720D+00, & 0.0019614003698950D+00, & 0.3957839332968854D+00, & 0.6022546663332198D+00, & 0.0019614003698950D+00, & 0.6022546663332197D+00, & 0.3957839332968856D+00, & 0.1526365657752198D+00, & 0.3516800587760810D+00, & 0.4956833754486996D+00, & 0.1526365657752198D+00, & 0.4956833754486994D+00, & 0.3516800587760812D+00, & 0.1134252783475029D+00, & 0.2024821942617584D+00, & 0.6840925273907389D+00, & 0.1134252783475029D+00, & 0.6840925273907389D+00, & 0.2024821942617586D+00, & 0.0545213844446831D+00, & 0.4225539552222151D+00, & 0.5229246603331020D+00, & 0.0545213844446831D+00, & 0.5229246603331019D+00, & 0.4225539552222153D+00, & 0.0606049291607722D+00, & 0.1246805088474439D+00, & 0.8147145619917839D+00, & 0.0606049291607722D+00, & 0.8147145619917839D+00, & 0.1246805088474443D+00, & 0.0375889521575178D+00, & 0.2555462364028573D+00, & 0.7068648114396252D+00, & 0.0375889521575178D+00, & 0.7068648114396251D+00, & 0.2555462364028576D+00, & 0.0043863301700617D+00, & 0.0745031299353863D+00, & 0.9211105398945522D+00, & 0.0043863301700617D+00, & 0.9211105398945522D+00, & 0.0745031299353866D+00, & 0.0172734143249371D+00, & 0.4168072755236506D+00, & 0.5659193101514125D+00, & 0.0172734143249371D+00, & 0.5659193101514124D+00, & 0.4168072755236508D+00, & 0.0625780220143109D+00, & 0.1928717230061985D+00, & 0.7445502549794908D+00, & 0.0625780220143109D+00, & 0.7445502549794908D+00, & 0.1928717230061987D+00, & 0.0184079470312829D+00, & 0.0473478189395524D+00, & 0.9342442340291647D+00, & 0.0184079470312829D+00, & 0.9342442340291647D+00, & 0.0473478189395528D+00, & 0.2184364967909282D+00, & 0.2184364967909281D+00, & 0.5631270064181439D+00, & 0.1724507871838862D+00, & 0.1724507871838861D+00, & 0.6550984256322279D+00, & 0.0510951808223816D+00, & 0.0510951808223813D+00, & 0.8978096383552373D+00, & 0.0429032089427714D+00, & 0.3419050053475277D+00, & 0.6151917857097011D+00, & 0.0429032089427714D+00, & 0.6151917857097009D+00, & 0.3419050053475279D+00, & 0.0131890837790157D+00, & 0.3258139530575097D+00, & 0.6609969631634748D+00, & 0.0131890837790157D+00, & 0.6609969631634748D+00, & 0.3258139530575100D+00, & 0.0011968816307096D+00, & 0.2894259487571373D+00, & 0.7093771696121534D+00, & 0.0011968816307096D+00, & 0.7093771696121534D+00, & 0.2894259487571375D+00, & 0.2191327614301768D+00, & 0.2987897956760134D+00, & 0.4820774428938099D+00, & 0.2191327614301768D+00, & 0.4820774428938099D+00, & 0.2987897956760135D+00, & 0.0811298915693310D+00, & 0.2744757477427950D+00, & 0.6443943606878743D+00, & 0.0811298915693310D+00, & 0.6443943606878741D+00, & 0.2744757477427952D+00, & 0.0952781144820168D+00, & 0.3532298738914157D+00, & 0.5514920116265677D+00, & 0.0952781144820168D+00, & 0.5514920116265677D+00, & 0.3532298738914159D+00, & 0.0045027587470595D+00, & 0.4977486206264704D+00, & 0.4977486206264705D+00, & 0.1468887080021119D+00, & 0.2663678824750718D+00, & 0.5867434095228166D+00, & 0.1468887080021119D+00, & 0.5867434095228163D+00, & 0.2663678824750720D+00, & 0.2296630615086399D+00, & 0.3851684692456802D+00, & 0.3851684692456802D+00, & 0.2974914903679930D+00, & 0.2974914903679929D+00, & 0.4050170192640143D+00, & 0.0275306300785875D+00, & 0.0960481521010511D+00, & 0.8764212178203615D+00, & 0.0275306300785875D+00, & 0.8764212178203615D+00, & 0.0960481521010514D+00, & 0.0050828094627280D+00, & 0.0050828094627277D+00, & 0.9898343810745442D+00, & 0.0258751082199382D+00, & 0.1674078247783561D+00, & 0.8067170670017060D+00, & 0.0258751082199382D+00, & 0.8067170670017060D+00, & 0.1674078247783564D+00, & 0.0993181165219637D+00, & 0.4503409417390183D+00, & 0.4503409417390184D+00, & 0.0057973186847398D+00, & 0.1306776337702883D+00, & 0.8635250475449719D+00, & 0.0057973186847398D+00, & 0.8635250475449719D+00, & 0.1306776337702887D+00 /) c = (/ & 0.3333333333333333D+00, & 0.4861524679130598D+00, & 0.0276950641738803D+00, & 0.4861524679130597D+00, & 0.7542396906638279D+00, & 0.1066696808640775D+00, & 0.1390906284720944D+00, & 0.1390906284720945D+00, & 0.1066696808640774D+00, & 0.7542396906638278D+00, & 0.4195880808642605D+00, & 0.1608238382714790D+00, & 0.4195880808642604D+00, & 0.7995057135466186D+00, & 0.0032611556637284D+00, & 0.1972331307896529D+00, & 0.1972331307896531D+00, & 0.0032611556637281D+00, & 0.7995057135466186D+00, & 0.7483360311752864D+00, & 0.0131398178404037D+00, & 0.2385241509843098D+00, & 0.2385241509843100D+00, & 0.0131398178404035D+00, & 0.7483360311752864D+00, & 0.8415864069866027D+00, & 0.0792067965066989D+00, & 0.0792067965066983D+00, & 0.9679050494853231D+00, & 0.0023442211286870D+00, & 0.0297507293859898D+00, & 0.0297507293859899D+00, & 0.0023442211286867D+00, & 0.9679050494853230D+00, & 0.9645373015005719D+00, & 0.0177313492497143D+00, & 0.0177313492497136D+00, & 0.6022546663332197D+00, & 0.0019614003698950D+00, & 0.3957839332968852D+00, & 0.3957839332968854D+00, & 0.0019614003698950D+00, & 0.6022546663332196D+00, & 0.4956833754486993D+00, & 0.1526365657752197D+00, & 0.3516800587760808D+00, & 0.3516800587760809D+00, & 0.1526365657752197D+00, & 0.4956833754486992D+00, & 0.6840925273907388D+00, & 0.1134252783475028D+00, & 0.2024821942617582D+00, & 0.2024821942617584D+00, & 0.1134252783475026D+00, & 0.6840925273907387D+00, & 0.5229246603331018D+00, & 0.0545213844446831D+00, & 0.4225539552222149D+00, & 0.4225539552222151D+00, & 0.0545213844446830D+00, & 0.5229246603331017D+00, & 0.8147145619917838D+00, & 0.0606049291607722D+00, & 0.1246805088474437D+00, & 0.1246805088474440D+00, & 0.0606049291607720D+00, & 0.8147145619917837D+00, & 0.7068648114396249D+00, & 0.0375889521575178D+00, & 0.2555462364028570D+00, & 0.2555462364028572D+00, & 0.0375889521575176D+00, & 0.7068648114396248D+00, & 0.9211105398945520D+00, & 0.0043863301700617D+00, & 0.0745031299353861D+00, & 0.0745031299353863D+00, & 0.0043863301700614D+00, & 0.9211105398945519D+00, & 0.5659193101514124D+00, & 0.0172734143249370D+00, & 0.4168072755236504D+00, & 0.4168072755236506D+00, & 0.0172734143249370D+00, & 0.5659193101514122D+00, & 0.7445502549794906D+00, & 0.0625780220143110D+00, & 0.1928717230061983D+00, & 0.1928717230061984D+00, & 0.0625780220143107D+00, & 0.7445502549794906D+00, & 0.9342442340291647D+00, & 0.0184079470312830D+00, & 0.0473478189395523D+00, & 0.0473478189395525D+00, & 0.0184079470312827D+00, & 0.9342442340291645D+00, & 0.5631270064181437D+00, & 0.2184364967909282D+00, & 0.2184364967909279D+00, & 0.6550984256322278D+00, & 0.1724507871838862D+00, & 0.1724507871838858D+00, & 0.8978096383552372D+00, & 0.0510951808223815D+00, & 0.0510951808223811D+00, & 0.6151917857097009D+00, & 0.0429032089427714D+00, & 0.3419050053475274D+00, & 0.3419050053475277D+00, & 0.0429032089427713D+00, & 0.6151917857097007D+00, & 0.6609969631634746D+00, & 0.0131890837790157D+00, & 0.3258139530575095D+00, & 0.3258139530575096D+00, & 0.0131890837790155D+00, & 0.6609969631634744D+00, & 0.7093771696121530D+00, & 0.0011968816307096D+00, & 0.2894259487571371D+00, & 0.2894259487571373D+00, & 0.0011968816307094D+00, & 0.7093771696121531D+00, & 0.4820774428938099D+00, & 0.2191327614301767D+00, & 0.2987897956760133D+00, & 0.2987897956760133D+00, & 0.2191327614301767D+00, & 0.4820774428938098D+00, & 0.6443943606878740D+00, & 0.0811298915693309D+00, & 0.2744757477427947D+00, & 0.2744757477427950D+00, & 0.0811298915693308D+00, & 0.6443943606878739D+00, & 0.5514920116265676D+00, & 0.0952781144820167D+00, & 0.3532298738914156D+00, & 0.3532298738914156D+00, & 0.0952781144820166D+00, & 0.5514920116265676D+00, & 0.4977486206264702D+00, & 0.0045027587470594D+00, & 0.4977486206264701D+00, & 0.5867434095228163D+00, & 0.1468887080021118D+00, & 0.2663678824750716D+00, & 0.2663678824750719D+00, & 0.1468887080021118D+00, & 0.5867434095228162D+00, & 0.3851684692456800D+00, & 0.2296630615086398D+00, & 0.3851684692456800D+00, & 0.4050170192640142D+00, & 0.2974914903679929D+00, & 0.2974914903679928D+00, & 0.8764212178203614D+00, & 0.0275306300785875D+00, & 0.0960481521010509D+00, & 0.0960481521010511D+00, & 0.0275306300785872D+00, & 0.8764212178203613D+00, & 0.9898343810745441D+00, & 0.0050828094627281D+00, & 0.0050828094627275D+00, & 0.8067170670017058D+00, & 0.0258751082199383D+00, & 0.1674078247783558D+00, & 0.1674078247783561D+00, & 0.0258751082199379D+00, & 0.8067170670017056D+00, & 0.4503409417390182D+00, & 0.0993181165219635D+00, & 0.4503409417390181D+00, & 0.8635250475449718D+00, & 0.0057973186847400D+00, & 0.1306776337702881D+00, & 0.1306776337702883D+00, & 0.0057973186847396D+00, & 0.8635250475449716D+00 /) w = (/ & 0.0083431208138864D+00, & 0.0040439883965194D+00, & 0.0040439883965194D+00, & 0.0040439883965194D+00, & 0.0058062932483637D+00, & 0.0058062932483637D+00, & 0.0058062932483637D+00, & 0.0058062932483637D+00, & 0.0058062932483637D+00, & 0.0058062932483637D+00, & 0.0088430826430883D+00, & 0.0088430826430883D+00, & 0.0088430826430883D+00, & 0.0012838516987697D+00, & 0.0012838516987697D+00, & 0.0012838516987697D+00, & 0.0012838516987697D+00, & 0.0012838516987697D+00, & 0.0012838516987697D+00, & 0.0028265142759277D+00, & 0.0028265142759277D+00, & 0.0028265142759277D+00, & 0.0028265142759277D+00, & 0.0028265142759277D+00, & 0.0028265142759277D+00, & 0.0042237298511032D+00, & 0.0042237298511032D+00, & 0.0042237298511032D+00, & 0.0005055090468723D+00, & 0.0005055090468723D+00, & 0.0005055090468723D+00, & 0.0005055090468723D+00, & 0.0005055090468723D+00, & 0.0005055090468723D+00, & 0.0009868661450271D+00, & 0.0009868661450271D+00, & 0.0009868661450271D+00, & 0.0013026954489735D+00, & 0.0013026954489735D+00, & 0.0013026954489735D+00, & 0.0013026954489735D+00, & 0.0013026954489735D+00, & 0.0013026954489735D+00, & 0.0101925794443413D+00, & 0.0101925794443413D+00, & 0.0101925794443413D+00, & 0.0101925794443413D+00, & 0.0101925794443413D+00, & 0.0101925794443413D+00, & 0.0078668704957381D+00, & 0.0078668704957381D+00, & 0.0078668704957381D+00, & 0.0078668704957381D+00, & 0.0078668704957381D+00, & 0.0078668704957381D+00, & 0.0071208092414188D+00, & 0.0071208092414188D+00, & 0.0071208092414188D+00, & 0.0071208092414188D+00, & 0.0071208092414188D+00, & 0.0071208092414188D+00, & 0.0049641144765077D+00, & 0.0049641144765077D+00, & 0.0049641144765077D+00, & 0.0049641144765077D+00, & 0.0049641144765077D+00, & 0.0049641144765077D+00, & 0.0054364374730136D+00, & 0.0054364374730136D+00, & 0.0054364374730136D+00, & 0.0054364374730136D+00, & 0.0054364374730136D+00, & 0.0054364374730136D+00, & 0.0011525829400843D+00, & 0.0011525829400843D+00, & 0.0011525829400843D+00, & 0.0011525829400843D+00, & 0.0011525829400843D+00, & 0.0011525829400843D+00, & 0.0041783326918215D+00, & 0.0041783326918215D+00, & 0.0041783326918215D+00, & 0.0041783326918215D+00, & 0.0041783326918215D+00, & 0.0041783326918215D+00, & 0.0063624230528669D+00, & 0.0063624230528669D+00, & 0.0063624230528669D+00, & 0.0063624230528669D+00, & 0.0063624230528669D+00, & 0.0063624230528669D+00, & 0.0018127692882839D+00, & 0.0018127692882839D+00, & 0.0018127692882839D+00, & 0.0018127692882839D+00, & 0.0018127692882839D+00, & 0.0018127692882839D+00, & 0.0112370035080132D+00, & 0.0112370035080132D+00, & 0.0112370035080132D+00, & 0.0095591959667284D+00, & 0.0095591959667284D+00, & 0.0095591959667284D+00, & 0.0032590866501858D+00, & 0.0032590866501858D+00, & 0.0032590866501858D+00, & 0.0066899592450456D+00, & 0.0066899592450456D+00, & 0.0066899592450456D+00, & 0.0066899592450456D+00, & 0.0066899592450456D+00, & 0.0066899592450456D+00, & 0.0036397134849474D+00, & 0.0036397134849474D+00, & 0.0036397134849474D+00, & 0.0036397134849474D+00, & 0.0036397134849474D+00, & 0.0036397134849474D+00, & 0.0009293703376931D+00, & 0.0009293703376931D+00, & 0.0009293703376931D+00, & 0.0009293703376931D+00, & 0.0009293703376931D+00, & 0.0009293703376931D+00, & 0.0128955867879842D+00, & 0.0128955867879842D+00, & 0.0128955867879842D+00, & 0.0128955867879842D+00, & 0.0128955867879842D+00, & 0.0128955867879842D+00, & 0.0084758977171366D+00, & 0.0084758977171366D+00, & 0.0084758977171366D+00, & 0.0084758977171366D+00, & 0.0084758977171366D+00, & 0.0084758977171366D+00, & 0.0096222755316967D+00, & 0.0096222755316967D+00, & 0.0096222755316967D+00, & 0.0096222755316967D+00, & 0.0096222755316967D+00, & 0.0096222755316967D+00, & 0.0023276606420564D+00, & 0.0023276606420564D+00, & 0.0023276606420564D+00, & 0.0115996690313856D+00, & 0.0115996690313856D+00, & 0.0115996690313856D+00, & 0.0115996690313856D+00, & 0.0115996690313856D+00, & 0.0115996690313856D+00, & 0.0137393951965683D+00, & 0.0137393951965683D+00, & 0.0137393951965683D+00, & 0.0123590405093469D+00, & 0.0123590405093469D+00, & 0.0123590405093469D+00, & 0.0036665867049268D+00, & 0.0036665867049268D+00, & 0.0036665867049268D+00, & 0.0036665867049268D+00, & 0.0036665867049268D+00, & 0.0036665867049268D+00, & 0.0003444013792726D+00, & 0.0003444013792726D+00, & 0.0003444013792726D+00, & 0.0044453379912524D+00, & 0.0044453379912524D+00, & 0.0044453379912524D+00, & 0.0044453379912524D+00, & 0.0044453379912524D+00, & 0.0044453379912524D+00, & 0.0104339772957806D+00, & 0.0104339772957806D+00, & 0.0104339772957806D+00, & 0.0018212527841225D+00, & 0.0018212527841225D+00, & 0.0018212527841225D+00, & 0.0018212527841225D+00, & 0.0018212527841225D+00, & 0.0018212527841225D+00 /) return end subroutine rule32 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule32() returns the rule of precision 32. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0014574454623699D+00, & 0.9970851090752599D+00, & 0.0014574454623703D+00, & 0.2068316863159020D+00, & 0.6343003724550512D+00, & 0.1588679412290467D+00, & 0.6343003724550512D+00, & 0.2068316863159020D+00, & 0.1588679412290465D+00, & 0.4467614265331670D+00, & 0.5384721310359784D+00, & 0.0147664424308546D+00, & 0.5384721310359784D+00, & 0.4467614265331671D+00, & 0.0147664424308546D+00, & 0.4986508935788473D+00, & 0.4986508935788473D+00, & 0.0026982128423053D+00, & 0.2324662076463787D+00, & 0.7161026651133882D+00, & 0.0514311272402331D+00, & 0.7161026651133883D+00, & 0.2324662076463787D+00, & 0.0514311272402328D+00, & 0.1168349267069579D+00, & 0.8636053329284497D+00, & 0.0195597403645925D+00, & 0.8636053329284497D+00, & 0.1168349267069580D+00, & 0.0195597403645921D+00, & 0.3282405458449340D+00, & 0.6591408874049088D+00, & 0.0126185667501573D+00, & 0.6591408874049087D+00, & 0.3282405458449340D+00, & 0.0126185667501570D+00, & 0.2593509320031201D+00, & 0.7195869113212406D+00, & 0.0210621566756393D+00, & 0.7195869113212405D+00, & 0.2593509320031203D+00, & 0.0210621566756391D+00, & 0.1654639982373495D+00, & 0.7169924925083024D+00, & 0.1175435092543480D+00, & 0.7169924925083024D+00, & 0.1654639982373496D+00, & 0.1175435092543477D+00, & 0.3824649073809372D+00, & 0.5882362420785776D+00, & 0.0292988505404852D+00, & 0.5882362420785775D+00, & 0.3824649073809373D+00, & 0.0292988505404851D+00, & 0.3978170726467208D+00, & 0.5987401057010048D+00, & 0.0034428216522743D+00, & 0.5987401057010048D+00, & 0.3978170726467208D+00, & 0.0034428216522742D+00, & 0.4811681159958368D+00, & 0.4811681159958369D+00, & 0.0376637680083264D+00, & 0.3254174696466901D+00, & 0.5842122492084456D+00, & 0.0903702811448643D+00, & 0.5842122492084456D+00, & 0.3254174696466901D+00, & 0.0903702811448641D+00, & 0.4522857565116005D+00, & 0.4522857565116005D+00, & 0.0954284869767989D+00, & 0.1133391914876031D+00, & 0.8359631725856564D+00, & 0.0506976359267406D+00, & 0.8359631725856566D+00, & 0.1133391914876031D+00, & 0.0506976359267403D+00, & 0.3110416328276417D+00, & 0.6410138882567965D+00, & 0.0479444789155618D+00, & 0.6410138882567965D+00, & 0.3110416328276417D+00, & 0.0479444789155617D+00, & 0.2988371353889130D+00, & 0.6998862072308072D+00, & 0.0012766573802799D+00, & 0.6998862072308072D+00, & 0.2988371353889130D+00, & 0.0012766573802797D+00, & 0.3763287580479190D+00, & 0.3763287580479190D+00, & 0.2473424839041620D+00, & 0.1521122809437838D+00, & 0.8436251556411046D+00, & 0.0042625634151116D+00, & 0.8436251556411045D+00, & 0.1521122809437838D+00, & 0.0042625634151113D+00, & 0.0886617050339115D+00, & 0.9074857829773694D+00, & 0.0038525119887192D+00, & 0.9074857829773694D+00, & 0.0886617050339115D+00, & 0.0038525119887188D+00, & 0.2830182798495732D+00, & 0.4339634403008535D+00, & 0.2830182798495733D+00, & 0.3191525805930605D+00, & 0.4789472707744628D+00, & 0.2019001486324766D+00, & 0.4789472707744628D+00, & 0.3191525805930605D+00, & 0.2019001486324766D+00, & 0.4136797843254134D+00, & 0.4136797843254134D+00, & 0.1726404313491732D+00, & 0.1667556935821333D+00, & 0.7655339131965976D+00, & 0.0677103932212692D+00, & 0.7655339131965975D+00, & 0.1667556935821334D+00, & 0.0677103932212689D+00, & 0.0302691910404442D+00, & 0.9394616179191112D+00, & 0.0302691910404446D+00, & 0.0128101964801118D+00, & 0.9743796070397761D+00, & 0.0128101964801123D+00, & 0.2421379240194328D+00, & 0.6622896588699126D+00, & 0.0955724171106545D+00, & 0.6622896588699126D+00, & 0.2421379240194329D+00, & 0.0955724171106544D+00, & 0.2798617479978297D+00, & 0.5697673874287119D+00, & 0.1503708645734583D+00, & 0.5697673874287120D+00, & 0.2798617479978297D+00, & 0.1503708645734581D+00, & 0.0673984002072567D+00, & 0.9082517491081563D+00, & 0.0243498506845873D+00, & 0.9082517491081562D+00, & 0.0673984002072567D+00, & 0.0243498506845868D+00, & 0.3716879666934204D+00, & 0.4989241659396562D+00, & 0.1293878673669234D+00, & 0.4989241659396562D+00, & 0.3716879666934203D+00, & 0.1293878673669233D+00, & 0.4056281490658828D+00, & 0.5311444304776159D+00, & 0.0632274204565012D+00, & 0.5311444304776159D+00, & 0.4056281490658829D+00, & 0.0632274204565011D+00, & 0.3333333333333333D+00, & 0.0620106498262642D+00, & 0.8759787003474712D+00, & 0.0620106498262646D+00, & 0.2219801657374810D+00, & 0.7727532012417533D+00, & 0.0052666330207657D+00, & 0.7727532012417532D+00, & 0.2219801657374811D+00, & 0.0052666330207656D+00, & 0.1783256820378629D+00, & 0.7955154359824860D+00, & 0.0261588819796511D+00, & 0.7955154359824860D+00, & 0.1783256820378630D+00, & 0.0261588819796509D+00, & 0.0426221905914095D+00, & 0.9518230415381582D+00, & 0.0055547678704324D+00, & 0.9518230415381583D+00, & 0.0426221905914095D+00, & 0.0055547678704320D+00, & 0.2292779969280699D+00, & 0.5414440061438599D+00, & 0.2292779969280701D+00, & 0.1019588269002696D+00, & 0.7960823461994605D+00, & 0.1019588269002699D+00, & 0.0143443003792804D+00, & 0.9850326016003745D+00, & 0.0006230980203453D+00, & 0.9850326016003746D+00, & 0.0143443003792806D+00, & 0.0006230980203448D+00 /) b = (/ & 0.0014574454623702D+00, & 0.0014574454623698D+00, & 0.9970851090752600D+00, & 0.1588679412290467D+00, & 0.2068316863159021D+00, & 0.6343003724550514D+00, & 0.1588679412290467D+00, & 0.6343003724550514D+00, & 0.2068316863159023D+00, & 0.0147664424308547D+00, & 0.4467614265331671D+00, & 0.5384721310359786D+00, & 0.0147664424308547D+00, & 0.5384721310359784D+00, & 0.4467614265331673D+00, & 0.0026982128423054D+00, & 0.4986508935788474D+00, & 0.4986508935788476D+00, & 0.0514311272402331D+00, & 0.2324662076463787D+00, & 0.7161026651133885D+00, & 0.0514311272402331D+00, & 0.7161026651133884D+00, & 0.2324662076463790D+00, & 0.0195597403645924D+00, & 0.1168349267069579D+00, & 0.8636053329284498D+00, & 0.0195597403645924D+00, & 0.8636053329284498D+00, & 0.1168349267069583D+00, & 0.0126185667501572D+00, & 0.3282405458449341D+00, & 0.6591408874049089D+00, & 0.0126185667501572D+00, & 0.6591408874049089D+00, & 0.3282405458449343D+00, & 0.0210621566756392D+00, & 0.2593509320031202D+00, & 0.7195869113212408D+00, & 0.0210621566756392D+00, & 0.7195869113212406D+00, & 0.2593509320031205D+00, & 0.1175435092543480D+00, & 0.1654639982373496D+00, & 0.7169924925083025D+00, & 0.1175435092543480D+00, & 0.7169924925083027D+00, & 0.1654639982373498D+00, & 0.0292988505404852D+00, & 0.3824649073809372D+00, & 0.5882362420785777D+00, & 0.0292988505404852D+00, & 0.5882362420785776D+00, & 0.3824649073809375D+00, & 0.0034428216522744D+00, & 0.3978170726467209D+00, & 0.5987401057010050D+00, & 0.0034428216522744D+00, & 0.5987401057010049D+00, & 0.3978170726467211D+00, & 0.0376637680083265D+00, & 0.4811681159958368D+00, & 0.4811681159958370D+00, & 0.0903702811448643D+00, & 0.3254174696466902D+00, & 0.5842122492084457D+00, & 0.0903702811448643D+00, & 0.5842122492084457D+00, & 0.3254174696466903D+00, & 0.0954284869767990D+00, & 0.4522857565116006D+00, & 0.4522857565116007D+00, & 0.0506976359267405D+00, & 0.1133391914876030D+00, & 0.8359631725856566D+00, & 0.0506976359267405D+00, & 0.8359631725856566D+00, & 0.1133391914876034D+00, & 0.0479444789155618D+00, & 0.3110416328276418D+00, & 0.6410138882567966D+00, & 0.0479444789155618D+00, & 0.6410138882567966D+00, & 0.3110416328276420D+00, & 0.0012766573802798D+00, & 0.2988371353889130D+00, & 0.6998862072308073D+00, & 0.0012766573802798D+00, & 0.6998862072308073D+00, & 0.2988371353889133D+00, & 0.2473424839041621D+00, & 0.3763287580479191D+00, & 0.3763287580479191D+00, & 0.0042625634151116D+00, & 0.1521122809437838D+00, & 0.8436251556411049D+00, & 0.0042625634151116D+00, & 0.8436251556411049D+00, & 0.1521122809437842D+00, & 0.0038525119887191D+00, & 0.0886617050339115D+00, & 0.9074857829773696D+00, & 0.0038525119887191D+00, & 0.9074857829773696D+00, & 0.0886617050339118D+00, & 0.2830182798495733D+00, & 0.2830182798495732D+00, & 0.4339634403008537D+00, & 0.2019001486324767D+00, & 0.3191525805930606D+00, & 0.4789472707744629D+00, & 0.2019001486324767D+00, & 0.4789472707744629D+00, & 0.3191525805930607D+00, & 0.1726404313491733D+00, & 0.4136797843254134D+00, & 0.4136797843254136D+00, & 0.0677103932212692D+00, & 0.1667556935821333D+00, & 0.7655339131965977D+00, & 0.0677103932212692D+00, & 0.7655339131965977D+00, & 0.1667556935821336D+00, & 0.0302691910404445D+00, & 0.0302691910404442D+00, & 0.9394616179191115D+00, & 0.0128101964801121D+00, & 0.0128101964801118D+00, & 0.9743796070397761D+00, & 0.0955724171106545D+00, & 0.2421379240194328D+00, & 0.6622896588699130D+00, & 0.0955724171106545D+00, & 0.6622896588699128D+00, & 0.2421379240194330D+00, & 0.1503708645734583D+00, & 0.2798617479978298D+00, & 0.5697673874287121D+00, & 0.1503708645734583D+00, & 0.5697673874287121D+00, & 0.2798617479978299D+00, & 0.0243498506845871D+00, & 0.0673984002072566D+00, & 0.9082517491081563D+00, & 0.0243498506845871D+00, & 0.9082517491081563D+00, & 0.0673984002072569D+00, & 0.1293878673669234D+00, & 0.3716879666934204D+00, & 0.4989241659396564D+00, & 0.1293878673669234D+00, & 0.4989241659396564D+00, & 0.3716879666934205D+00, & 0.0632274204565012D+00, & 0.4056281490658829D+00, & 0.5311444304776161D+00, & 0.0632274204565012D+00, & 0.5311444304776159D+00, & 0.4056281490658831D+00, & 0.3333333333333334D+00, & 0.0620106498262645D+00, & 0.0620106498262642D+00, & 0.8759787003474714D+00, & 0.0052666330207658D+00, & 0.2219801657374810D+00, & 0.7727532012417535D+00, & 0.0052666330207658D+00, & 0.7727532012417533D+00, & 0.2219801657374814D+00, & 0.0261588819796510D+00, & 0.1783256820378630D+00, & 0.7955154359824862D+00, & 0.0261588819796510D+00, & 0.7955154359824862D+00, & 0.1783256820378632D+00, & 0.0055547678704322D+00, & 0.0426221905914095D+00, & 0.9518230415381584D+00, & 0.0055547678704322D+00, & 0.9518230415381584D+00, & 0.0426221905914099D+00, & 0.2292779969280701D+00, & 0.2292779969280700D+00, & 0.5414440061438600D+00, & 0.1019588269002698D+00, & 0.1019588269002696D+00, & 0.7960823461994607D+00, & 0.0006230980203451D+00, & 0.0143443003792804D+00, & 0.9850326016003745D+00, & 0.0006230980203451D+00, & 0.9850326016003745D+00, & 0.0143443003792807D+00 /) c = (/ & 0.9970851090752600D+00, & 0.0014574454623702D+00, & 0.0014574454623696D+00, & 0.6343003724550513D+00, & 0.1588679412290467D+00, & 0.2068316863159019D+00, & 0.2068316863159020D+00, & 0.1588679412290465D+00, & 0.6343003724550511D+00, & 0.5384721310359784D+00, & 0.0147664424308546D+00, & 0.4467614265331668D+00, & 0.4467614265331670D+00, & 0.0147664424308546D+00, & 0.5384721310359781D+00, & 0.4986508935788472D+00, & 0.0026982128423053D+00, & 0.4986508935788471D+00, & 0.7161026651133883D+00, & 0.0514311272402331D+00, & 0.2324662076463785D+00, & 0.2324662076463787D+00, & 0.0514311272402329D+00, & 0.7161026651133883D+00, & 0.8636053329284497D+00, & 0.0195597403645924D+00, & 0.1168349267069578D+00, & 0.1168349267069580D+00, & 0.0195597403645923D+00, & 0.8636053329284495D+00, & 0.6591408874049088D+00, & 0.0126185667501571D+00, & 0.3282405458449338D+00, & 0.3282405458449341D+00, & 0.0126185667501570D+00, & 0.6591408874049086D+00, & 0.7195869113212405D+00, & 0.0210621566756392D+00, & 0.2593509320031200D+00, & 0.2593509320031203D+00, & 0.0210621566756392D+00, & 0.7195869113212403D+00, & 0.7169924925083024D+00, & 0.1175435092543480D+00, & 0.1654639982373495D+00, & 0.1654639982373496D+00, & 0.1175435092543478D+00, & 0.7169924925083024D+00, & 0.5882362420785776D+00, & 0.0292988505404851D+00, & 0.3824649073809371D+00, & 0.3824649073809373D+00, & 0.0292988505404851D+00, & 0.5882362420785774D+00, & 0.5987401057010048D+00, & 0.0034428216522743D+00, & 0.3978170726467206D+00, & 0.3978170726467209D+00, & 0.0034428216522743D+00, & 0.5987401057010047D+00, & 0.4811681159958368D+00, & 0.0376637680083263D+00, & 0.4811681159958366D+00, & 0.5842122492084457D+00, & 0.0903702811448642D+00, & 0.3254174696466899D+00, & 0.3254174696466902D+00, & 0.0903702811448642D+00, & 0.5842122492084456D+00, & 0.4522857565116005D+00, & 0.0954284869767989D+00, & 0.4522857565116003D+00, & 0.8359631725856564D+00, & 0.0506976359267405D+00, & 0.1133391914876029D+00, & 0.1133391914876030D+00, & 0.0506976359267403D+00, & 0.8359631725856563D+00, & 0.6410138882567965D+00, & 0.0479444789155617D+00, & 0.3110416328276415D+00, & 0.3110416328276417D+00, & 0.0479444789155616D+00, & 0.6410138882567964D+00, & 0.6998862072308072D+00, & 0.0012766573802798D+00, & 0.2988371353889129D+00, & 0.2988371353889130D+00, & 0.0012766573802797D+00, & 0.6998862072308070D+00, & 0.3763287580479189D+00, & 0.2473424839041619D+00, & 0.3763287580479189D+00, & 0.8436251556411046D+00, & 0.0042625634151116D+00, & 0.1521122809437835D+00, & 0.1521122809437839D+00, & 0.0042625634151113D+00, & 0.8436251556411045D+00, & 0.9074857829773694D+00, & 0.0038525119887192D+00, & 0.0886617050339112D+00, & 0.0886617050339116D+00, & 0.0038525119887188D+00, & 0.9074857829773694D+00, & 0.4339634403008535D+00, & 0.2830182798495732D+00, & 0.2830182798495731D+00, & 0.4789472707744628D+00, & 0.2019001486324766D+00, & 0.3191525805930605D+00, & 0.3191525805930606D+00, & 0.2019001486324766D+00, & 0.4789472707744628D+00, & 0.4136797843254133D+00, & 0.1726404313491732D+00, & 0.4136797843254132D+00, & 0.7655339131965976D+00, & 0.0677103932212691D+00, & 0.1667556935821330D+00, & 0.1667556935821334D+00, & 0.0677103932212689D+00, & 0.7655339131965975D+00, & 0.9394616179191114D+00, & 0.0302691910404446D+00, & 0.0302691910404439D+00, & 0.9743796070397761D+00, & 0.0128101964801121D+00, & 0.0128101964801116D+00, & 0.6622896588699126D+00, & 0.0955724171106545D+00, & 0.2421379240194326D+00, & 0.2421379240194328D+00, & 0.0955724171106543D+00, & 0.6622896588699126D+00, & 0.5697673874287120D+00, & 0.1503708645734583D+00, & 0.2798617479978296D+00, & 0.2798617479978297D+00, & 0.1503708645734582D+00, & 0.5697673874287120D+00, & 0.9082517491081562D+00, & 0.0243498506845871D+00, & 0.0673984002072564D+00, & 0.0673984002072567D+00, & 0.0243498506845869D+00, & 0.9082517491081562D+00, & 0.4989241659396563D+00, & 0.1293878673669234D+00, & 0.3716879666934201D+00, & 0.3716879666934204D+00, & 0.1293878673669233D+00, & 0.4989241659396562D+00, & 0.5311444304776159D+00, & 0.0632274204565011D+00, & 0.4056281490658827D+00, & 0.4056281490658828D+00, & 0.0632274204565012D+00, & 0.5311444304776158D+00, & 0.3333333333333333D+00, & 0.8759787003474713D+00, & 0.0620106498262646D+00, & 0.0620106498262639D+00, & 0.7727532012417532D+00, & 0.0052666330207657D+00, & 0.2219801657374807D+00, & 0.2219801657374811D+00, & 0.0052666330207656D+00, & 0.7727532012417531D+00, & 0.7955154359824861D+00, & 0.0261588819796510D+00, & 0.1783256820378627D+00, & 0.1783256820378630D+00, & 0.0261588819796509D+00, & 0.7955154359824859D+00, & 0.9518230415381583D+00, & 0.0055547678704323D+00, & 0.0426221905914091D+00, & 0.0426221905914094D+00, & 0.0055547678704321D+00, & 0.9518230415381582D+00, & 0.5414440061438600D+00, & 0.2292779969280701D+00, & 0.2292779969280699D+00, & 0.7960823461994606D+00, & 0.1019588269002699D+00, & 0.1019588269002695D+00, & 0.9850326016003745D+00, & 0.0006230980203451D+00, & 0.0143443003792801D+00, & 0.0143443003792803D+00, & 0.0006230980203449D+00, & 0.9850326016003745D+00 /) w = (/ & 0.0000533239023334D+00, & 0.0000533239023334D+00, & 0.0000533239023334D+00, & 0.0083492191295379D+00, & 0.0083492191295379D+00, & 0.0083492191295379D+00, & 0.0083492191295379D+00, & 0.0083492191295379D+00, & 0.0083492191295379D+00, & 0.0030406522577730D+00, & 0.0030406522577730D+00, & 0.0030406522577730D+00, & 0.0030406522577730D+00, & 0.0030406522577730D+00, & 0.0030406522577730D+00, & 0.0014146272476628D+00, & 0.0014146272476628D+00, & 0.0014146272476628D+00, & 0.0052860436025325D+00, & 0.0052860436025325D+00, & 0.0052860436025325D+00, & 0.0052860436025325D+00, & 0.0052860436025325D+00, & 0.0052860436025325D+00, & 0.0024932699246691D+00, & 0.0024932699246691D+00, & 0.0024932699246691D+00, & 0.0024932699246691D+00, & 0.0024932699246691D+00, & 0.0024932699246691D+00, & 0.0030205810567136D+00, & 0.0030205810567136D+00, & 0.0030205810567136D+00, & 0.0030205810567136D+00, & 0.0030205810567136D+00, & 0.0030205810567136D+00, & 0.0036441755768762D+00, & 0.0036441755768762D+00, & 0.0036441755768762D+00, & 0.0036441755768762D+00, & 0.0036441755768762D+00, & 0.0036441755768762D+00, & 0.0074810896991602D+00, & 0.0074810896991602D+00, & 0.0074810896991602D+00, & 0.0074810896991602D+00, & 0.0074810896991602D+00, & 0.0074810896991602D+00, & 0.0045681541355720D+00, & 0.0045681541355720D+00, & 0.0045681541355720D+00, & 0.0045681541355720D+00, & 0.0045681541355720D+00, & 0.0045681541355720D+00, & 0.0016852036405343D+00, & 0.0016852036405343D+00, & 0.0016852036405343D+00, & 0.0016852036405343D+00, & 0.0016852036405343D+00, & 0.0016852036405343D+00, & 0.0055800151424133D+00, & 0.0055800151424133D+00, & 0.0055800151424133D+00, & 0.0082092066464793D+00, & 0.0082092066464793D+00, & 0.0082092066464793D+00, & 0.0082092066464793D+00, & 0.0082092066464793D+00, & 0.0082092066464793D+00, & 0.0083785907041262D+00, & 0.0083785907041262D+00, & 0.0083785907041262D+00, & 0.0044656768476199D+00, & 0.0044656768476199D+00, & 0.0044656768476199D+00, & 0.0044656768476199D+00, & 0.0044656768476199D+00, & 0.0044656768476199D+00, & 0.0062028347215228D+00, & 0.0062028347215228D+00, & 0.0062028347215228D+00, & 0.0062028347215228D+00, & 0.0062028347215228D+00, & 0.0062028347215228D+00, & 0.0008888925431519D+00, & 0.0008888925431519D+00, & 0.0008888925431519D+00, & 0.0008888925431519D+00, & 0.0008888925431519D+00, & 0.0008888925431519D+00, & 0.0126612945604860D+00, & 0.0126612945604860D+00, & 0.0126612945604860D+00, & 0.0014852293291852D+00, & 0.0014852293291852D+00, & 0.0014852293291852D+00, & 0.0014852293291852D+00, & 0.0014852293291852D+00, & 0.0014852293291852D+00, & 0.0011127063455906D+00, & 0.0011127063455906D+00, & 0.0011127063455906D+00, & 0.0011127063455906D+00, & 0.0011127063455906D+00, & 0.0011127063455906D+00, & 0.0128827331771754D+00, & 0.0128827331771754D+00, & 0.0128827331771754D+00, & 0.0119733591024828D+00, & 0.0119733591024828D+00, & 0.0119733591024828D+00, & 0.0119733591024828D+00, & 0.0119733591024828D+00, & 0.0119733591024828D+00, & 0.0108804660269342D+00, & 0.0108804660269342D+00, & 0.0108804660269342D+00, & 0.0058823160628199D+00, & 0.0058823160628199D+00, & 0.0058823160628199D+00, & 0.0058823160628199D+00, & 0.0058823160628199D+00, & 0.0058823160628199D+00, & 0.0018592782531939D+00, & 0.0018592782531939D+00, & 0.0018592782531939D+00, & 0.0008017410516731D+00, & 0.0008017410516731D+00, & 0.0008017410516731D+00, & 0.0084487434719511D+00, & 0.0084487434719511D+00, & 0.0084487434719511D+00, & 0.0084487434719511D+00, & 0.0084487434719511D+00, & 0.0084487434719511D+00, & 0.0102114559163661D+00, & 0.0102114559163661D+00, & 0.0102114559163661D+00, & 0.0102114559163661D+00, & 0.0102114559163661D+00, & 0.0102114559163661D+00, & 0.0024899591532165D+00, & 0.0024899591532165D+00, & 0.0024899591532165D+00, & 0.0024899591532165D+00, & 0.0024899591532165D+00, & 0.0024899591532165D+00, & 0.0098885056550223D+00, & 0.0098885056550223D+00, & 0.0098885056550223D+00, & 0.0098885056550223D+00, & 0.0098885056550223D+00, & 0.0098885056550223D+00, & 0.0074091131429365D+00, & 0.0074091131429365D+00, & 0.0074091131429365D+00, & 0.0074091131429365D+00, & 0.0074091131429365D+00, & 0.0074091131429365D+00, & 0.0130300709957626D+00, & 0.0039763485949254D+00, & 0.0039763485949254D+00, & 0.0039763485949254D+00, & 0.0019455932409831D+00, & 0.0019455932409831D+00, & 0.0019455932409831D+00, & 0.0019455932409831D+00, & 0.0019455932409831D+00, & 0.0019455932409831D+00, & 0.0042608365965002D+00, & 0.0042608365965002D+00, & 0.0042608365965002D+00, & 0.0042608365965002D+00, & 0.0042608365965002D+00, & 0.0042608365965002D+00, & 0.0010553743696176D+00, & 0.0010553743696176D+00, & 0.0010553743696176D+00, & 0.0010553743696176D+00, & 0.0010553743696176D+00, & 0.0010553743696176D+00, & 0.0125355977256489D+00, & 0.0125355977256489D+00, & 0.0125355977256489D+00, & 0.0066293991150592D+00, & 0.0066293991150592D+00, & 0.0066293991150592D+00, & 0.0001700882477425D+00, & 0.0001700882477425D+00, & 0.0001700882477425D+00, & 0.0001700882477425D+00, & 0.0001700882477425D+00, & 0.0001700882477425D+00 /) return end subroutine rule33 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule33() returns the rule of precision 33. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0866842399345696D+00, & 0.8266315201308605D+00, & 0.0866842399345699D+00, & 0.4094279608026433D+00, & 0.4094279608026433D+00, & 0.1811440783947132D+00, & 0.2581529287895067D+00, & 0.6549184352472063D+00, & 0.0869286359632870D+00, & 0.6549184352472063D+00, & 0.2581529287895068D+00, & 0.0869286359632869D+00, & 0.2849624019720829D+00, & 0.6009455627050857D+00, & 0.1140920353228314D+00, & 0.6009455627050857D+00, & 0.2849624019720829D+00, & 0.1140920353228312D+00, & 0.3783335382962427D+00, & 0.3783335382962427D+00, & 0.2433329234075145D+00, & 0.4989797178600512D+00, & 0.4989797178600512D+00, & 0.0020405642798976D+00, & 0.1340676338419341D+00, & 0.7742670347180146D+00, & 0.0916653314400512D+00, & 0.7742670347180146D+00, & 0.1340676338419342D+00, & 0.0916653314400510D+00, & 0.3269137502096716D+00, & 0.4571468585469127D+00, & 0.2159393912434156D+00, & 0.4571468585469128D+00, & 0.3269137502096715D+00, & 0.2159393912434155D+00, & 0.2596606680087211D+00, & 0.4806786639825575D+00, & 0.2596606680087213D+00, & 0.1008457159827756D+00, & 0.8767639677306408D+00, & 0.0223903162865836D+00, & 0.8767639677306409D+00, & 0.1008457159827757D+00, & 0.0223903162865833D+00, & 0.3552328254047640D+00, & 0.5455252367072077D+00, & 0.0992419378880283D+00, & 0.5455252367072078D+00, & 0.3552328254047640D+00, & 0.0992419378880282D+00, & 0.1584027341957248D+00, & 0.8211535906601003D+00, & 0.0204436751441749D+00, & 0.8211535906601004D+00, & 0.1584027341957248D+00, & 0.0204436751441747D+00, & 0.4785119732563822D+00, & 0.4785119732563822D+00, & 0.0429760534872356D+00, & 0.4012397484580547D+00, & 0.5401481330852944D+00, & 0.0586121184566509D+00, & 0.5401481330852945D+00, & 0.4012397484580547D+00, & 0.0586121184566507D+00, & 0.2273220131649666D+00, & 0.7532530766694563D+00, & 0.0194249101655773D+00, & 0.7532530766694562D+00, & 0.2273220131649666D+00, & 0.0194249101655771D+00, & 0.1040040001314270D+00, & 0.8451258076748079D+00, & 0.0508701921937651D+00, & 0.8451258076748080D+00, & 0.1040040001314272D+00, & 0.0508701921937648D+00, & 0.2516190193630367D+00, & 0.7445747285081441D+00, & 0.0038062521288191D+00, & 0.7445747285081442D+00, & 0.2516190193630368D+00, & 0.0038062521288190D+00, & 0.1946715273720462D+00, & 0.7113747622583637D+00, & 0.0939537103695900D+00, & 0.7113747622583638D+00, & 0.1946715273720463D+00, & 0.0939537103695898D+00, & 0.1756396314580331D+00, & 0.8206933909179547D+00, & 0.0036669776240122D+00, & 0.8206933909179547D+00, & 0.1756396314580332D+00, & 0.0036669776240119D+00, & 0.1654225039506263D+00, & 0.7841517925433079D+00, & 0.0504257035060658D+00, & 0.7841517925433079D+00, & 0.1654225039506264D+00, & 0.0504257035060656D+00, & 0.0604829240909603D+00, & 0.9354049276280985D+00, & 0.0041121482809413D+00, & 0.9354049276280986D+00, & 0.0604829240909603D+00, & 0.0041121482809409D+00, & 0.3321035653575233D+00, & 0.6635597637774838D+00, & 0.0043366708649930D+00, & 0.6635597637774838D+00, & 0.3321035653575233D+00, & 0.0043366708649928D+00, & 0.3794132168456387D+00, & 0.4768226069138183D+00, & 0.1437641762405430D+00, & 0.4768226069138183D+00, & 0.3794132168456387D+00, & 0.1437641762405429D+00, & 0.0235174430579130D+00, & 0.9529651138841736D+00, & 0.0235174430579135D+00, & 0.0565688972489456D+00, & 0.9215652847226834D+00, & 0.0218658180283709D+00, & 0.9215652847226835D+00, & 0.0565688972489457D+00, & 0.0218658180283706D+00, & 0.3060238617603606D+00, & 0.3879522764792787D+00, & 0.3060238617603606D+00, & 0.1464890507166427D+00, & 0.7070218985667143D+00, & 0.1464890507166430D+00, & 0.0543792032794963D+00, & 0.8912415934410072D+00, & 0.0543792032794967D+00, & 0.2909849162693301D+00, & 0.5407077523881676D+00, & 0.1683073313425023D+00, & 0.5407077523881676D+00, & 0.2909849162693300D+00, & 0.1683073313425022D+00, & 0.2368453944831515D+00, & 0.7146406256116400D+00, & 0.0485139799052084D+00, & 0.7146406256116401D+00, & 0.2368453944831516D+00, & 0.0485139799052082D+00, & 0.4145491529764430D+00, & 0.5807136071426248D+00, & 0.0047372398809322D+00, & 0.5807136071426248D+00, & 0.4145491529764430D+00, & 0.0047372398809321D+00, & 0.3075361882409410D+00, & 0.6703285978516907D+00, & 0.0221352139073682D+00, & 0.6703285978516907D+00, & 0.3075361882409411D+00, & 0.0221352139073681D+00, & 0.1109266644334704D+00, & 0.8846799404570630D+00, & 0.0043933951094668D+00, & 0.8846799404570630D+00, & 0.1109266644334704D+00, & 0.0043933951094664D+00, & 0.2181920158632539D+00, & 0.5636159682734920D+00, & 0.2181920158632540D+00, & 0.3188631220563678D+00, & 0.6259766725873849D+00, & 0.0551602053562473D+00, & 0.6259766725873848D+00, & 0.3188631220563678D+00, & 0.0551602053562472D+00, & 0.4919913444565532D+00, & 0.4919913444565532D+00, & 0.0160173110868935D+00, & 0.3953677591013828D+00, & 0.5802323524289785D+00, & 0.0243998884696386D+00, & 0.5802323524289785D+00, & 0.3953677591013828D+00, & 0.0243998884696386D+00, & 0.4533999616178053D+00, & 0.4533999616178053D+00, & 0.0932000767643894D+00, & 0.2137578302973531D+00, & 0.6356072278734608D+00, & 0.1506349418291862D+00, & 0.6356072278734608D+00, & 0.2137578302973531D+00, & 0.1506349418291860D+00, & 0.0047266605105680D+00, & 0.9905466789788636D+00, & 0.0047266605105684D+00, & 0.0247793702175406D+00, & 0.9707182444941620D+00, & 0.0045023852882976D+00, & 0.9707182444941620D+00, & 0.0247793702175407D+00, & 0.0045023852882971D+00 /) b = (/ & 0.0866842399345699D+00, & 0.0866842399345696D+00, & 0.8266315201308606D+00, & 0.1811440783947133D+00, & 0.4094279608026434D+00, & 0.4094279608026435D+00, & 0.0869286359632870D+00, & 0.2581529287895068D+00, & 0.6549184352472064D+00, & 0.0869286359632870D+00, & 0.6549184352472064D+00, & 0.2581529287895070D+00, & 0.1140920353228314D+00, & 0.2849624019720829D+00, & 0.6009455627050859D+00, & 0.1140920353228314D+00, & 0.6009455627050859D+00, & 0.2849624019720831D+00, & 0.2433329234075146D+00, & 0.3783335382962428D+00, & 0.3783335382962429D+00, & 0.0020405642798976D+00, & 0.4989797178600513D+00, & 0.4989797178600514D+00, & 0.0916653314400512D+00, & 0.1340676338419342D+00, & 0.7742670347180148D+00, & 0.0916653314400512D+00, & 0.7742670347180148D+00, & 0.1340676338419345D+00, & 0.2159393912434157D+00, & 0.3269137502096717D+00, & 0.4571468585469129D+00, & 0.2159393912434157D+00, & 0.4571468585469129D+00, & 0.3269137502096717D+00, & 0.2596606680087213D+00, & 0.2596606680087212D+00, & 0.4806786639825577D+00, & 0.0223903162865835D+00, & 0.1008457159827756D+00, & 0.8767639677306410D+00, & 0.0223903162865835D+00, & 0.8767639677306409D+00, & 0.1008457159827759D+00, & 0.0992419378880283D+00, & 0.3552328254047640D+00, & 0.5455252367072079D+00, & 0.0992419378880283D+00, & 0.5455252367072079D+00, & 0.3552328254047642D+00, & 0.0204436751441748D+00, & 0.1584027341957248D+00, & 0.8211535906601005D+00, & 0.0204436751441748D+00, & 0.8211535906601006D+00, & 0.1584027341957251D+00, & 0.0429760534872357D+00, & 0.4785119732563822D+00, & 0.4785119732563824D+00, & 0.0586121184566509D+00, & 0.4012397484580547D+00, & 0.5401481330852946D+00, & 0.0586121184566509D+00, & 0.5401481330852945D+00, & 0.4012397484580549D+00, & 0.0194249101655772D+00, & 0.2273220131649666D+00, & 0.7532530766694563D+00, & 0.0194249101655772D+00, & 0.7532530766694563D+00, & 0.2273220131649669D+00, & 0.0508701921937650D+00, & 0.1040040001314270D+00, & 0.8451258076748080D+00, & 0.0508701921937650D+00, & 0.8451258076748080D+00, & 0.1040040001314274D+00, & 0.0038062521288191D+00, & 0.2516190193630367D+00, & 0.7445747285081444D+00, & 0.0038062521288191D+00, & 0.7445747285081442D+00, & 0.2516190193630370D+00, & 0.0939537103695900D+00, & 0.1946715273720463D+00, & 0.7113747622583638D+00, & 0.0939537103695900D+00, & 0.7113747622583639D+00, & 0.1946715273720465D+00, & 0.0036669776240121D+00, & 0.1756396314580332D+00, & 0.8206933909179549D+00, & 0.0036669776240121D+00, & 0.8206933909179549D+00, & 0.1756396314580335D+00, & 0.0504257035060658D+00, & 0.1654225039506263D+00, & 0.7841517925433081D+00, & 0.0504257035060658D+00, & 0.7841517925433080D+00, & 0.1654225039506266D+00, & 0.0041121482809412D+00, & 0.0604829240909602D+00, & 0.9354049276280987D+00, & 0.0041121482809412D+00, & 0.9354049276280987D+00, & 0.0604829240909606D+00, & 0.0043366708649929D+00, & 0.3321035653575233D+00, & 0.6635597637774840D+00, & 0.0043366708649929D+00, & 0.6635597637774838D+00, & 0.3321035653575235D+00, & 0.1437641762405430D+00, & 0.3794132168456388D+00, & 0.4768226069138184D+00, & 0.1437641762405430D+00, & 0.4768226069138183D+00, & 0.3794132168456389D+00, & 0.0235174430579133D+00, & 0.0235174430579130D+00, & 0.9529651138841736D+00, & 0.0218658180283708D+00, & 0.0565688972489457D+00, & 0.9215652847226837D+00, & 0.0218658180283708D+00, & 0.9215652847226837D+00, & 0.0565688972489460D+00, & 0.3060238617603607D+00, & 0.3060238617603607D+00, & 0.3879522764792788D+00, & 0.1464890507166429D+00, & 0.1464890507166427D+00, & 0.7070218985667144D+00, & 0.0543792032794966D+00, & 0.0543792032794963D+00, & 0.8912415934410073D+00, & 0.1683073313425024D+00, & 0.2909849162693301D+00, & 0.5407077523881677D+00, & 0.1683073313425024D+00, & 0.5407077523881677D+00, & 0.2909849162693303D+00, & 0.0485139799052084D+00, & 0.2368453944831516D+00, & 0.7146406256116403D+00, & 0.0485139799052084D+00, & 0.7146406256116402D+00, & 0.2368453944831518D+00, & 0.0047372398809322D+00, & 0.4145491529764431D+00, & 0.5807136071426250D+00, & 0.0047372398809322D+00, & 0.5807136071426249D+00, & 0.4145491529764432D+00, & 0.0221352139073682D+00, & 0.3075361882409411D+00, & 0.6703285978516910D+00, & 0.0221352139073682D+00, & 0.6703285978516909D+00, & 0.3075361882409413D+00, & 0.0043933951094667D+00, & 0.1109266644334704D+00, & 0.8846799404570631D+00, & 0.0043933951094667D+00, & 0.8846799404570631D+00, & 0.1109266644334707D+00, & 0.2181920158632541D+00, & 0.2181920158632540D+00, & 0.5636159682734921D+00, & 0.0551602053562474D+00, & 0.3188631220563678D+00, & 0.6259766725873851D+00, & 0.0551602053562474D+00, & 0.6259766725873850D+00, & 0.3188631220563680D+00, & 0.0160173110868935D+00, & 0.4919913444565533D+00, & 0.4919913444565535D+00, & 0.0243998884696387D+00, & 0.3953677591013828D+00, & 0.5802323524289787D+00, & 0.0243998884696387D+00, & 0.5802323524289786D+00, & 0.3953677591013830D+00, & 0.0932000767643895D+00, & 0.4533999616178053D+00, & 0.4533999616178054D+00, & 0.1506349418291862D+00, & 0.2137578302973531D+00, & 0.6356072278734609D+00, & 0.1506349418291862D+00, & 0.6356072278734609D+00, & 0.2137578302973533D+00, & 0.0047266605105683D+00, & 0.0047266605105680D+00, & 0.9905466789788638D+00, & 0.0045023852882974D+00, & 0.0247793702175406D+00, & 0.9707182444941621D+00, & 0.0045023852882974D+00, & 0.9707182444941621D+00, & 0.0247793702175410D+00 /) c = (/ & 0.8266315201308605D+00, & 0.0866842399345699D+00, & 0.0866842399345694D+00, & 0.4094279608026433D+00, & 0.1811440783947132D+00, & 0.4094279608026433D+00, & 0.6549184352472062D+00, & 0.0869286359632869D+00, & 0.2581529287895066D+00, & 0.2581529287895067D+00, & 0.0869286359632868D+00, & 0.6549184352472062D+00, & 0.6009455627050857D+00, & 0.1140920353228314D+00, & 0.2849624019720827D+00, & 0.2849624019720829D+00, & 0.1140920353228312D+00, & 0.6009455627050857D+00, & 0.3783335382962427D+00, & 0.2433329234075144D+00, & 0.3783335382962427D+00, & 0.4989797178600511D+00, & 0.0020405642798975D+00, & 0.4989797178600510D+00, & 0.7742670347180147D+00, & 0.0916653314400512D+00, & 0.1340676338419339D+00, & 0.1340676338419342D+00, & 0.0916653314400510D+00, & 0.7742670347180146D+00, & 0.4571468585469128D+00, & 0.2159393912434156D+00, & 0.3269137502096715D+00, & 0.3269137502096716D+00, & 0.2159393912434156D+00, & 0.4571468585469127D+00, & 0.4806786639825576D+00, & 0.2596606680087212D+00, & 0.2596606680087211D+00, & 0.8767639677306409D+00, & 0.0223903162865836D+00, & 0.1008457159827754D+00, & 0.1008457159827755D+00, & 0.0223903162865834D+00, & 0.8767639677306408D+00, & 0.5455252367072078D+00, & 0.0992419378880283D+00, & 0.3552328254047639D+00, & 0.3552328254047640D+00, & 0.0992419378880282D+00, & 0.5455252367072077D+00, & 0.8211535906601003D+00, & 0.0204436751441749D+00, & 0.1584027341957245D+00, & 0.1584027341957248D+00, & 0.0204436751441746D+00, & 0.8211535906601003D+00, & 0.4785119732563821D+00, & 0.0429760534872355D+00, & 0.4785119732563820D+00, & 0.5401481330852944D+00, & 0.0586121184566509D+00, & 0.4012397484580545D+00, & 0.4012397484580545D+00, & 0.0586121184566507D+00, & 0.5401481330852944D+00, & 0.7532530766694562D+00, & 0.0194249101655771D+00, & 0.2273220131649664D+00, & 0.2273220131649666D+00, & 0.0194249101655771D+00, & 0.7532530766694561D+00, & 0.8451258076748079D+00, & 0.0508701921937651D+00, & 0.1040040001314269D+00, & 0.1040040001314270D+00, & 0.0508701921937648D+00, & 0.8451258076748078D+00, & 0.7445747285081442D+00, & 0.0038062521288192D+00, & 0.2516190193630364D+00, & 0.2516190193630367D+00, & 0.0038062521288190D+00, & 0.7445747285081441D+00, & 0.7113747622583637D+00, & 0.0939537103695900D+00, & 0.1946715273720462D+00, & 0.1946715273720462D+00, & 0.0939537103695898D+00, & 0.7113747622583637D+00, & 0.8206933909179548D+00, & 0.0036669776240122D+00, & 0.1756396314580330D+00, & 0.1756396314580332D+00, & 0.0036669776240118D+00, & 0.8206933909179546D+00, & 0.7841517925433079D+00, & 0.0504257035060658D+00, & 0.1654225039506261D+00, & 0.1654225039506262D+00, & 0.0504257035060657D+00, & 0.7841517925433077D+00, & 0.9354049276280986D+00, & 0.0041121482809413D+00, & 0.0604829240909600D+00, & 0.0604829240909602D+00, & 0.0041121482809410D+00, & 0.9354049276280985D+00, & 0.6635597637774838D+00, & 0.0043366708649929D+00, & 0.3321035653575229D+00, & 0.3321035653575233D+00, & 0.0043366708649929D+00, & 0.6635597637774837D+00, & 0.4768226069138182D+00, & 0.1437641762405429D+00, & 0.3794132168456386D+00, & 0.3794132168456387D+00, & 0.1437641762405430D+00, & 0.4768226069138181D+00, & 0.9529651138841736D+00, & 0.0235174430579134D+00, & 0.0235174430579129D+00, & 0.9215652847226835D+00, & 0.0218658180283709D+00, & 0.0565688972489454D+00, & 0.0565688972489456D+00, & 0.0218658180283705D+00, & 0.9215652847226834D+00, & 0.3879522764792787D+00, & 0.3060238617603607D+00, & 0.3060238617603606D+00, & 0.7070218985667143D+00, & 0.1464890507166430D+00, & 0.1464890507166426D+00, & 0.8912415934410072D+00, & 0.0543792032794966D+00, & 0.0543792032794960D+00, & 0.5407077523881676D+00, & 0.1683073313425023D+00, & 0.2909849162693300D+00, & 0.2909849162693300D+00, & 0.1683073313425022D+00, & 0.5407077523881675D+00, & 0.7146406256116400D+00, & 0.0485139799052084D+00, & 0.2368453944831513D+00, & 0.2368453944831515D+00, & 0.0485139799052082D+00, & 0.7146406256116400D+00, & 0.5807136071426249D+00, & 0.0047372398809322D+00, & 0.4145491529764428D+00, & 0.4145491529764431D+00, & 0.0047372398809321D+00, & 0.5807136071426248D+00, & 0.6703285978516907D+00, & 0.0221352139073682D+00, & 0.3075361882409408D+00, & 0.3075361882409410D+00, & 0.0221352139073681D+00, & 0.6703285978516906D+00, & 0.8846799404570629D+00, & 0.0043933951094666D+00, & 0.1109266644334701D+00, & 0.1109266644334703D+00, & 0.0043933951094665D+00, & 0.8846799404570630D+00, & 0.5636159682734920D+00, & 0.2181920158632540D+00, & 0.2181920158632539D+00, & 0.6259766725873849D+00, & 0.0551602053562473D+00, & 0.3188631220563676D+00, & 0.3188631220563679D+00, & 0.0551602053562472D+00, & 0.6259766725873848D+00, & 0.4919913444565532D+00, & 0.0160173110868935D+00, & 0.4919913444565530D+00, & 0.5802323524289785D+00, & 0.0243998884696386D+00, & 0.3953677591013827D+00, & 0.3953677591013828D+00, & 0.0243998884696385D+00, & 0.5802323524289784D+00, & 0.4533999616178052D+00, & 0.0932000767643894D+00, & 0.4533999616178051D+00, & 0.6356072278734608D+00, & 0.1506349418291861D+00, & 0.2137578302973530D+00, & 0.2137578302973530D+00, & 0.1506349418291860D+00, & 0.6356072278734608D+00, & 0.9905466789788637D+00, & 0.0047266605105684D+00, & 0.0047266605105677D+00, & 0.9707182444941620D+00, & 0.0045023852882974D+00, & 0.0247793702175404D+00, & 0.0247793702175406D+00, & 0.0045023852882972D+00, & 0.9707182444941619D+00 /) w = (/ & 0.0032023640124142D+00, & 0.0032023640124142D+00, & 0.0032023640124142D+00, & 0.0068346799344681D+00, & 0.0068346799344681D+00, & 0.0068346799344681D+00, & 0.0050108234565749D+00, & 0.0050108234565749D+00, & 0.0050108234565749D+00, & 0.0050108234565749D+00, & 0.0050108234565749D+00, & 0.0050108234565749D+00, & 0.0062666715145980D+00, & 0.0062666715145980D+00, & 0.0062666715145980D+00, & 0.0062666715145980D+00, & 0.0062666715145980D+00, & 0.0062666715145980D+00, & 0.0089341618081367D+00, & 0.0089341618081367D+00, & 0.0089341618081367D+00, & 0.0010410912372864D+00, & 0.0010410912372864D+00, & 0.0010410912372864D+00, & 0.0051060923018633D+00, & 0.0051060923018633D+00, & 0.0051060923018633D+00, & 0.0051060923018633D+00, & 0.0051060923018633D+00, & 0.0051060923018633D+00, & 0.0096392468588408D+00, & 0.0096392468588408D+00, & 0.0096392468588408D+00, & 0.0096392468588408D+00, & 0.0096392468588408D+00, & 0.0096392468588408D+00, & 0.0097388572366854D+00, & 0.0097388572366854D+00, & 0.0097388572366854D+00, & 0.0024212380388685D+00, & 0.0024212380388685D+00, & 0.0024212380388685D+00, & 0.0024212380388685D+00, & 0.0024212380388685D+00, & 0.0024212380388685D+00, & 0.0076973467270549D+00, & 0.0076973467270549D+00, & 0.0076973467270549D+00, & 0.0076973467270549D+00, & 0.0076973467270549D+00, & 0.0076973467270549D+00, & 0.0029882446919490D+00, & 0.0029882446919490D+00, & 0.0029882446919490D+00, & 0.0029882446919490D+00, & 0.0029882446919490D+00, & 0.0029882446919490D+00, & 0.0054643256840460D+00, & 0.0054643256840460D+00, & 0.0054643256840460D+00, & 0.0061988540259434D+00, & 0.0061988540259434D+00, & 0.0061988540259434D+00, & 0.0061988540259434D+00, & 0.0061988540259434D+00, & 0.0061988540259434D+00, & 0.0033169972939131D+00, & 0.0033169972939131D+00, & 0.0033169972939131D+00, & 0.0033169972939131D+00, & 0.0033169972939131D+00, & 0.0033169972939131D+00, & 0.0037089296125893D+00, & 0.0037089296125893D+00, & 0.0037089296125893D+00, & 0.0037089296125893D+00, & 0.0037089296125893D+00, & 0.0037089296125893D+00, & 0.0015426465184706D+00, & 0.0015426465184706D+00, & 0.0015426465184706D+00, & 0.0015426465184706D+00, & 0.0015426465184706D+00, & 0.0015426465184706D+00, & 0.0066121724110684D+00, & 0.0066121724110684D+00, & 0.0066121724110684D+00, & 0.0066121724110684D+00, & 0.0066121724110684D+00, & 0.0066121724110684D+00, & 0.0013551781957506D+00, & 0.0013551781957506D+00, & 0.0013551781957506D+00, & 0.0013551781957506D+00, & 0.0013551781957506D+00, & 0.0013551781957506D+00, & 0.0049036283435529D+00, & 0.0049036283435529D+00, & 0.0049036283435529D+00, & 0.0049036283435529D+00, & 0.0049036283435529D+00, & 0.0049036283435529D+00, & 0.0009157661571810D+00, & 0.0009157661571810D+00, & 0.0009157661571810D+00, & 0.0009157661571810D+00, & 0.0009157661571810D+00, & 0.0009157661571810D+00, & 0.0018218162644265D+00, & 0.0018218162644265D+00, & 0.0018218162644265D+00, & 0.0018218162644265D+00, & 0.0018218162644265D+00, & 0.0018218162644265D+00, & 0.0092423799017096D+00, & 0.0092423799017096D+00, & 0.0092423799017096D+00, & 0.0092423799017096D+00, & 0.0092423799017096D+00, & 0.0092423799017096D+00, & 0.0013813690630279D+00, & 0.0013813690630279D+00, & 0.0013813690630279D+00, & 0.0019606312336932D+00, & 0.0019606312336932D+00, & 0.0019606312336932D+00, & 0.0019606312336932D+00, & 0.0019606312336932D+00, & 0.0019606312336932D+00, & 0.0120887399809166D+00, & 0.0120887399809166D+00, & 0.0120887399809166D+00, & 0.0073774464967342D+00, & 0.0073774464967342D+00, & 0.0073774464967342D+00, & 0.0032093504439416D+00, & 0.0032093504439416D+00, & 0.0032093504439416D+00, & 0.0102099177863965D+00, & 0.0102099177863965D+00, & 0.0102099177863965D+00, & 0.0102099177863965D+00, & 0.0102099177863965D+00, & 0.0102099177863965D+00, & 0.0054637704373722D+00, & 0.0054637704373722D+00, & 0.0054637704373722D+00, & 0.0054637704373722D+00, & 0.0054637704373722D+00, & 0.0054637704373722D+00, & 0.0020111020097847D+00, & 0.0020111020097847D+00, & 0.0020111020097847D+00, & 0.0020111020097847D+00, & 0.0020111020097847D+00, & 0.0020111020097847D+00, & 0.0042683347026345D+00, & 0.0042683347026345D+00, & 0.0042683347026345D+00, & 0.0042683347026345D+00, & 0.0042683347026345D+00, & 0.0042683347026345D+00, & 0.0012878764088954D+00, & 0.0012878764088954D+00, & 0.0012878764088954D+00, & 0.0012878764088954D+00, & 0.0012878764088954D+00, & 0.0012878764088954D+00, & 0.0099263761795442D+00, & 0.0099263761795442D+00, & 0.0099263761795442D+00, & 0.0065998833272568D+00, & 0.0065998833272568D+00, & 0.0065998833272568D+00, & 0.0065998833272568D+00, & 0.0065998833272568D+00, & 0.0065998833272568D+00, & 0.0038623620299660D+00, & 0.0038623620299660D+00, & 0.0038623620299660D+00, & 0.0049474328088082D+00, & 0.0049474328088082D+00, & 0.0049474328088082D+00, & 0.0049474328088082D+00, & 0.0049474328088082D+00, & 0.0049474328088082D+00, & 0.0093337977696466D+00, & 0.0093337977696466D+00, & 0.0093337977696466D+00, & 0.0091814815579271D+00, & 0.0091814815579271D+00, & 0.0091814815579271D+00, & 0.0091814815579271D+00, & 0.0091814815579271D+00, & 0.0091814815579271D+00, & 0.0002934827335780D+00, & 0.0002934827335780D+00, & 0.0002934827335780D+00, & 0.0006440017743474D+00, & 0.0006440017743474D+00, & 0.0006440017743474D+00, & 0.0006440017743474D+00, & 0.0006440017743474D+00, & 0.0006440017743474D+00 /) return end subroutine rule34 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule34() returns the rule of precision 34. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3851262518382810D+00, & 0.5937769878916170D+00, & 0.0210967602701019D+00, & 0.5937769878916170D+00, & 0.3851262518382810D+00, & 0.0210967602701018D+00, & 0.0528200673454988D+00, & 0.9437918205041110D+00, & 0.0033881121503903D+00, & 0.9437918205041111D+00, & 0.0528200673454988D+00, & 0.0033881121503898D+00, & 0.0459825951541271D+00, & 0.9080348096917454D+00, & 0.0459825951541276D+00, & 0.0508987652831316D+00, & 0.9308929059173959D+00, & 0.0182083287994725D+00, & 0.9308929059173960D+00, & 0.0508987652831318D+00, & 0.0182083287994721D+00, & 0.0208387475149684D+00, & 0.9583225049700629D+00, & 0.0208387475149688D+00, & 0.1291243720726085D+00, & 0.8103648572840793D+00, & 0.0605107706433124D+00, & 0.8103648572840793D+00, & 0.1291243720726087D+00, & 0.0605107706433121D+00, & 0.0878179027775245D+00, & 0.8762622058588977D+00, & 0.0359198913635778D+00, & 0.8762622058588977D+00, & 0.0878179027775245D+00, & 0.0359198913635776D+00, & 0.0757621741867908D+00, & 0.8484756516264180D+00, & 0.0757621741867912D+00, & 0.3766019805175457D+00, & 0.3766019805175457D+00, & 0.2467960389649085D+00, & 0.2735537380248192D+00, & 0.5623852333049681D+00, & 0.1640610286702127D+00, & 0.5623852333049681D+00, & 0.2735537380248192D+00, & 0.1640610286702125D+00, & 0.0944770656323742D+00, & 0.8948396708440374D+00, & 0.0106832635235886D+00, & 0.8948396708440374D+00, & 0.0944770656323743D+00, & 0.0106832635235882D+00, & 0.2873558398221649D+00, & 0.4252883203556701D+00, & 0.2873558398221651D+00, & 0.4111522333036005D+00, & 0.5577150863900258D+00, & 0.0311326803063737D+00, & 0.5577150863900259D+00, & 0.4111522333036006D+00, & 0.0311326803063736D+00, & 0.3594475694982553D+00, & 0.5073598072800389D+00, & 0.1331926232217058D+00, & 0.5073598072800389D+00, & 0.3594475694982553D+00, & 0.1331926232217057D+00, & 0.3884100853304371D+00, & 0.5372925954322688D+00, & 0.0742973192372942D+00, & 0.5372925954322687D+00, & 0.3884100853304370D+00, & 0.0742973192372941D+00, & 0.3253550433420577D+00, & 0.4694784588431804D+00, & 0.2051664978147619D+00, & 0.4694784588431803D+00, & 0.3253550433420578D+00, & 0.2051664978147618D+00, & 0.1747804794810684D+00, & 0.7349999143937561D+00, & 0.0902196061251755D+00, & 0.7349999143937561D+00, & 0.1747804794810685D+00, & 0.0902196061251753D+00, & 0.1941646181495633D+00, & 0.7619195089459252D+00, & 0.0439158729045115D+00, & 0.7619195089459252D+00, & 0.1941646181495633D+00, & 0.0439158729045113D+00, & 0.4744124989028456D+00, & 0.4744124989028456D+00, & 0.0511750021943088D+00, & 0.2483278734045790D+00, & 0.6827082966308193D+00, & 0.0689638299646018D+00, & 0.6827082966308193D+00, & 0.2483278734045790D+00, & 0.0689638299646015D+00, & 0.2229920412612009D+00, & 0.6518261605959125D+00, & 0.1251817981428867D+00, & 0.6518261605959125D+00, & 0.2229920412612009D+00, & 0.1251817981428865D+00, & 0.1496044235489511D+00, & 0.8457252778897656D+00, & 0.0046702985612834D+00, & 0.8457252778897657D+00, & 0.1496044235489512D+00, & 0.0046702985612830D+00, & 0.1111727012858456D+00, & 0.7776545974283084D+00, & 0.1111727012858459D+00, & 0.4918649619576897D+00, & 0.4918649619576897D+00, & 0.0162700760846206D+00, & 0.3283914136921266D+00, & 0.6226826638040091D+00, & 0.0489259225038643D+00, & 0.6226826638040089D+00, & 0.3283914136921267D+00, & 0.0489259225038643D+00, & 0.1508877227628729D+00, & 0.6982245544742539D+00, & 0.1508877227628732D+00, & 0.1423855003245428D+00, & 0.8329562498972498D+00, & 0.0246582497782074D+00, & 0.8329562498972499D+00, & 0.1423855003245429D+00, & 0.0246582497782072D+00, & 0.4238402997203689D+00, & 0.5701997570298869D+00, & 0.0059599432497442D+00, & 0.5701997570298869D+00, & 0.4238402997203689D+00, & 0.0059599432497442D+00, & 0.0041579573923189D+00, & 0.9916840852153618D+00, & 0.0041579573923194D+00, & 0.2404349104138168D+00, & 0.5191301791723664D+00, & 0.2404349104138169D+00, & 0.2676904193443056D+00, & 0.7037908578134091D+00, & 0.0285187228422855D+00, & 0.7037908578134090D+00, & 0.2676904193443056D+00, & 0.0285187228422852D+00, & 0.4155115967448372D+00, & 0.4155115967448372D+00, & 0.1689768065103256D+00, & 0.4995421826615118D+00, & 0.4995421826615117D+00, & 0.0009156346769764D+00, & 0.3454113789529011D+00, & 0.6390259777460834D+00, & 0.0155626433010154D+00, & 0.6390259777460834D+00, & 0.3454113789529011D+00, & 0.0155626433010154D+00, & 0.3534495196576637D+00, & 0.6456247621084024D+00, & 0.0009257182339338D+00, & 0.6456247621084025D+00, & 0.3534495196576638D+00, & 0.0009257182339337D+00, & 0.4485642658787082D+00, & 0.4485642658787082D+00, & 0.1028714682425834D+00, & 0.3033356394717892D+00, & 0.5973781489096254D+00, & 0.0992862116185854D+00, & 0.5973781489096254D+00, & 0.3033356394717892D+00, & 0.0992862116185853D+00, & 0.0217555603201839D+00, & 0.9742699338072974D+00, & 0.0039745058725186D+00, & 0.9742699338072975D+00, & 0.0217555603201841D+00, & 0.0039745058725182D+00, & 0.3333333333333333D+00, & 0.2075468682735205D+00, & 0.7786734923211107D+00, & 0.0137796394053689D+00, & 0.7786734923211107D+00, & 0.2075468682735205D+00, & 0.0137796394053686D+00, & 0.1943865435789661D+00, & 0.6112269128420674D+00, & 0.1943865435789664D+00, & 0.2135602395179478D+00, & 0.7856676213617251D+00, & 0.0007721391203271D+00, & 0.7856676213617252D+00, & 0.2135602395179479D+00, & 0.0007721391203269D+00, & 0.2793864317822237D+00, & 0.7151517773234828D+00, & 0.0054617908942934D+00, & 0.7151517773234828D+00, & 0.2793864317822238D+00, & 0.0054617908942933D+00, & 0.0968669225755472D+00, & 0.9031283677334342D+00, & 0.0000047096910187D+00, & 0.9031283677334343D+00, & 0.0968669225755472D+00, & 0.0000047096910183D+00 /) b = (/ & 0.0210967602701019D+00, & 0.3851262518382811D+00, & 0.5937769878916171D+00, & 0.0210967602701019D+00, & 0.5937769878916171D+00, & 0.3851262518382813D+00, & 0.0033881121503900D+00, & 0.0528200673454988D+00, & 0.9437918205041111D+00, & 0.0033881121503900D+00, & 0.9437918205041114D+00, & 0.0528200673454991D+00, & 0.0459825951541274D+00, & 0.0459825951541271D+00, & 0.9080348096917455D+00, & 0.0182083287994724D+00, & 0.0508987652831316D+00, & 0.9308929059173960D+00, & 0.0182083287994724D+00, & 0.9308929059173960D+00, & 0.0508987652831320D+00, & 0.0208387475149687D+00, & 0.0208387475149684D+00, & 0.9583225049700631D+00, & 0.0605107706433123D+00, & 0.1291243720726085D+00, & 0.8103648572840793D+00, & 0.0605107706433123D+00, & 0.8103648572840793D+00, & 0.1291243720726088D+00, & 0.0359198913635778D+00, & 0.0878179027775245D+00, & 0.8762622058588979D+00, & 0.0359198913635778D+00, & 0.8762622058588979D+00, & 0.0878179027775248D+00, & 0.0757621741867911D+00, & 0.0757621741867908D+00, & 0.8484756516264182D+00, & 0.2467960389649086D+00, & 0.3766019805175458D+00, & 0.3766019805175458D+00, & 0.1640610286702127D+00, & 0.2735537380248192D+00, & 0.5623852333049683D+00, & 0.1640610286702127D+00, & 0.5623852333049683D+00, & 0.2735537380248194D+00, & 0.0106832635235884D+00, & 0.0944770656323742D+00, & 0.8948396708440375D+00, & 0.0106832635235884D+00, & 0.8948396708440375D+00, & 0.0944770656323745D+00, & 0.2873558398221651D+00, & 0.2873558398221650D+00, & 0.4252883203556702D+00, & 0.0311326803063737D+00, & 0.4111522333036006D+00, & 0.5577150863900260D+00, & 0.0311326803063737D+00, & 0.5577150863900259D+00, & 0.4111522333036007D+00, & 0.1331926232217058D+00, & 0.3594475694982554D+00, & 0.5073598072800390D+00, & 0.1331926232217058D+00, & 0.5073598072800389D+00, & 0.3594475694982555D+00, & 0.0742973192372942D+00, & 0.3884100853304371D+00, & 0.5372925954322689D+00, & 0.0742973192372942D+00, & 0.5372925954322688D+00, & 0.3884100853304373D+00, & 0.2051664978147620D+00, & 0.3253550433420578D+00, & 0.4694784588431805D+00, & 0.2051664978147620D+00, & 0.4694784588431805D+00, & 0.3253550433420579D+00, & 0.0902196061251755D+00, & 0.1747804794810684D+00, & 0.7349999143937562D+00, & 0.0902196061251755D+00, & 0.7349999143937561D+00, & 0.1747804794810687D+00, & 0.0439158729045114D+00, & 0.1941646181495633D+00, & 0.7619195089459254D+00, & 0.0439158729045114D+00, & 0.7619195089459254D+00, & 0.1941646181495635D+00, & 0.0511750021943088D+00, & 0.4744124989028456D+00, & 0.4744124989028458D+00, & 0.0689638299646017D+00, & 0.2483278734045790D+00, & 0.6827082966308194D+00, & 0.0689638299646017D+00, & 0.6827082966308194D+00, & 0.2483278734045792D+00, & 0.1251817981428867D+00, & 0.2229920412612009D+00, & 0.6518261605959126D+00, & 0.1251817981428867D+00, & 0.6518261605959126D+00, & 0.2229920412612011D+00, & 0.0046702985612833D+00, & 0.1496044235489511D+00, & 0.8457252778897658D+00, & 0.0046702985612833D+00, & 0.8457252778897657D+00, & 0.1496044235489514D+00, & 0.1111727012858459D+00, & 0.1111727012858457D+00, & 0.7776545974283087D+00, & 0.0162700760846207D+00, & 0.4918649619576898D+00, & 0.4918649619576899D+00, & 0.0489259225038644D+00, & 0.3283914136921267D+00, & 0.6226826638040092D+00, & 0.0489259225038644D+00, & 0.6226826638040091D+00, & 0.3283914136921268D+00, & 0.1508877227628732D+00, & 0.1508877227628729D+00, & 0.6982245544742540D+00, & 0.0246582497782073D+00, & 0.1423855003245428D+00, & 0.8329562498972500D+00, & 0.0246582497782073D+00, & 0.8329562498972499D+00, & 0.1423855003245431D+00, & 0.0059599432497443D+00, & 0.4238402997203689D+00, & 0.5701997570298871D+00, & 0.0059599432497443D+00, & 0.5701997570298870D+00, & 0.4238402997203691D+00, & 0.0041579573923192D+00, & 0.0041579573923189D+00, & 0.9916840852153619D+00, & 0.2404349104138169D+00, & 0.2404349104138168D+00, & 0.5191301791723665D+00, & 0.0285187228422854D+00, & 0.2676904193443056D+00, & 0.7037908578134091D+00, & 0.0285187228422854D+00, & 0.7037908578134091D+00, & 0.2676904193443059D+00, & 0.1689768065103257D+00, & 0.4155115967448372D+00, & 0.4155115967448373D+00, & 0.0009156346769765D+00, & 0.4995421826615118D+00, & 0.4995421826615120D+00, & 0.0155626433010155D+00, & 0.3454113789529012D+00, & 0.6390259777460836D+00, & 0.0155626433010155D+00, & 0.6390259777460835D+00, & 0.3454113789529014D+00, & 0.0009257182339338D+00, & 0.3534495196576638D+00, & 0.6456247621084026D+00, & 0.0009257182339338D+00, & 0.6456247621084026D+00, & 0.3534495196576640D+00, & 0.1028714682425835D+00, & 0.4485642658787083D+00, & 0.4485642658787085D+00, & 0.0992862116185854D+00, & 0.3033356394717893D+00, & 0.5973781489096255D+00, & 0.0992862116185854D+00, & 0.5973781489096255D+00, & 0.3033356394717894D+00, & 0.0039745058725185D+00, & 0.0217555603201839D+00, & 0.9742699338072977D+00, & 0.0039745058725185D+00, & 0.9742699338072977D+00, & 0.0217555603201842D+00, & 0.3333333333333334D+00, & 0.0137796394053688D+00, & 0.2075468682735205D+00, & 0.7786734923211108D+00, & 0.0137796394053688D+00, & 0.7786734923211108D+00, & 0.2075468682735207D+00, & 0.1943865435789664D+00, & 0.1943865435789662D+00, & 0.6112269128420676D+00, & 0.0007721391203270D+00, & 0.2135602395179478D+00, & 0.7856676213617252D+00, & 0.0007721391203270D+00, & 0.7856676213617252D+00, & 0.2135602395179481D+00, & 0.0054617908942934D+00, & 0.2793864317822238D+00, & 0.7151517773234830D+00, & 0.0054617908942934D+00, & 0.7151517773234830D+00, & 0.2793864317822241D+00, & 0.0000047096910185D+00, & 0.0968669225755471D+00, & 0.9031283677334344D+00, & 0.0000047096910185D+00, & 0.9031283677334344D+00, & 0.0968669225755475D+00 /) c = (/ & 0.5937769878916170D+00, & 0.0210967602701019D+00, & 0.3851262518382809D+00, & 0.3851262518382810D+00, & 0.0210967602701019D+00, & 0.5937769878916168D+00, & 0.9437918205041113D+00, & 0.0033881121503902D+00, & 0.0528200673454986D+00, & 0.0528200673454988D+00, & 0.0033881121503898D+00, & 0.9437918205041110D+00, & 0.9080348096917454D+00, & 0.0459825951541274D+00, & 0.0459825951541269D+00, & 0.9308929059173959D+00, & 0.0182083287994725D+00, & 0.0508987652831314D+00, & 0.0508987652831316D+00, & 0.0182083287994722D+00, & 0.9308929059173959D+00, & 0.9583225049700629D+00, & 0.0208387475149687D+00, & 0.0208387475149682D+00, & 0.8103648572840793D+00, & 0.0605107706433123D+00, & 0.1291243720726084D+00, & 0.1291243720726085D+00, & 0.0605107706433120D+00, & 0.8103648572840791D+00, & 0.8762622058588978D+00, & 0.0359198913635778D+00, & 0.0878179027775242D+00, & 0.0878179027775245D+00, & 0.0359198913635775D+00, & 0.8762622058588976D+00, & 0.8484756516264181D+00, & 0.0757621741867912D+00, & 0.0757621741867905D+00, & 0.3766019805175457D+00, & 0.2467960389649085D+00, & 0.3766019805175456D+00, & 0.5623852333049681D+00, & 0.1640610286702126D+00, & 0.2735537380248191D+00, & 0.2735537380248192D+00, & 0.1640610286702125D+00, & 0.5623852333049681D+00, & 0.8948396708440375D+00, & 0.0106832635235885D+00, & 0.0944770656323740D+00, & 0.0944770656323742D+00, & 0.0106832635235882D+00, & 0.8948396708440374D+00, & 0.4252883203556700D+00, & 0.2873558398221649D+00, & 0.2873558398221648D+00, & 0.5577150863900258D+00, & 0.0311326803063737D+00, & 0.4111522333036004D+00, & 0.4111522333036004D+00, & 0.0311326803063735D+00, & 0.5577150863900256D+00, & 0.5073598072800389D+00, & 0.1331926232217057D+00, & 0.3594475694982552D+00, & 0.3594475694982552D+00, & 0.1331926232217058D+00, & 0.5073598072800387D+00, & 0.5372925954322687D+00, & 0.0742973192372940D+00, & 0.3884100853304369D+00, & 0.3884100853304371D+00, & 0.0742973192372941D+00, & 0.5372925954322686D+00, & 0.4694784588431803D+00, & 0.2051664978147618D+00, & 0.3253550433420577D+00, & 0.3253550433420577D+00, & 0.2051664978147618D+00, & 0.4694784588431803D+00, & 0.7349999143937561D+00, & 0.0902196061251755D+00, & 0.1747804794810682D+00, & 0.1747804794810684D+00, & 0.0902196061251753D+00, & 0.7349999143937560D+00, & 0.7619195089459252D+00, & 0.0439158729045115D+00, & 0.1941646181495631D+00, & 0.1941646181495634D+00, & 0.0439158729045113D+00, & 0.7619195089459252D+00, & 0.4744124989028456D+00, & 0.0511750021943088D+00, & 0.4744124989028454D+00, & 0.6827082966308193D+00, & 0.0689638299646017D+00, & 0.2483278734045787D+00, & 0.2483278734045790D+00, & 0.0689638299646015D+00, & 0.6827082966308193D+00, & 0.6518261605959125D+00, & 0.1251817981428866D+00, & 0.2229920412612008D+00, & 0.2229920412612009D+00, & 0.1251817981428865D+00, & 0.6518261605959124D+00, & 0.8457252778897656D+00, & 0.0046702985612833D+00, & 0.1496044235489508D+00, & 0.1496044235489510D+00, & 0.0046702985612831D+00, & 0.8457252778897656D+00, & 0.7776545974283084D+00, & 0.1111727012858459D+00, & 0.1111727012858454D+00, & 0.4918649619576896D+00, & 0.0162700760846206D+00, & 0.4918649619576895D+00, & 0.6226826638040089D+00, & 0.0489259225038643D+00, & 0.3283914136921265D+00, & 0.3283914136921267D+00, & 0.0489259225038643D+00, & 0.6226826638040088D+00, & 0.6982245544742540D+00, & 0.1508877227628732D+00, & 0.1508877227628728D+00, & 0.8329562498972499D+00, & 0.0246582497782074D+00, & 0.1423855003245426D+00, & 0.1423855003245427D+00, & 0.0246582497782072D+00, & 0.8329562498972497D+00, & 0.5701997570298869D+00, & 0.0059599432497442D+00, & 0.4238402997203686D+00, & 0.4238402997203689D+00, & 0.0059599432497440D+00, & 0.5701997570298867D+00, & 0.9916840852153619D+00, & 0.0041579573923193D+00, & 0.0041579573923187D+00, & 0.5191301791723663D+00, & 0.2404349104138168D+00, & 0.2404349104138167D+00, & 0.7037908578134090D+00, & 0.0285187228422853D+00, & 0.2676904193443054D+00, & 0.2676904193443056D+00, & 0.0285187228422853D+00, & 0.7037908578134089D+00, & 0.4155115967448372D+00, & 0.1689768065103256D+00, & 0.4155115967448370D+00, & 0.4995421826615117D+00, & 0.0009156346769764D+00, & 0.4995421826615116D+00, & 0.6390259777460833D+00, & 0.0155626433010154D+00, & 0.3454113789529010D+00, & 0.3454113789529011D+00, & 0.0155626433010153D+00, & 0.6390259777460832D+00, & 0.6456247621084025D+00, & 0.0009257182339338D+00, & 0.3534495196576636D+00, & 0.3534495196576637D+00, & 0.0009257182339336D+00, & 0.6456247621084023D+00, & 0.4485642658787082D+00, & 0.1028714682425834D+00, & 0.4485642658787081D+00, & 0.5973781489096254D+00, & 0.0992862116185854D+00, & 0.3033356394717891D+00, & 0.3033356394717892D+00, & 0.0992862116185853D+00, & 0.5973781489096253D+00, & 0.9742699338072977D+00, & 0.0039745058725186D+00, & 0.0217555603201837D+00, & 0.0217555603201840D+00, & 0.0039745058725184D+00, & 0.9742699338072975D+00, & 0.3333333333333333D+00, & 0.7786734923211107D+00, & 0.0137796394053688D+00, & 0.2075468682735203D+00, & 0.2075468682735205D+00, & 0.0137796394053687D+00, & 0.7786734923211107D+00, & 0.6112269128420675D+00, & 0.1943865435789664D+00, & 0.1943865435789659D+00, & 0.7856676213617251D+00, & 0.0007721391203271D+00, & 0.2135602395179477D+00, & 0.2135602395179478D+00, & 0.0007721391203269D+00, & 0.7856676213617251D+00, & 0.7151517773234829D+00, & 0.0054617908942934D+00, & 0.2793864317822236D+00, & 0.2793864317822238D+00, & 0.0054617908942932D+00, & 0.7151517773234826D+00, & 0.9031283677334343D+00, & 0.0000047096910187D+00, & 0.0968669225755469D+00, & 0.0968669225755472D+00, & 0.0000047096910184D+00, & 0.9031283677334342D+00 /) w = (/ & 0.0001016859723671D+00, & 0.0001016859723671D+00, & 0.0001016859723671D+00, & 0.0001016859723671D+00, & 0.0001016859723671D+00, & 0.0001016859723671D+00, & 0.0006540479665875D+00, & 0.0006540479665875D+00, & 0.0006540479665875D+00, & 0.0006540479665875D+00, & 0.0006540479665875D+00, & 0.0006540479665875D+00, & 0.0022989665688091D+00, & 0.0022989665688091D+00, & 0.0022989665688091D+00, & 0.0015198116582616D+00, & 0.0015198116582616D+00, & 0.0015198116582616D+00, & 0.0015198116582616D+00, & 0.0015198116582616D+00, & 0.0015198116582616D+00, & 0.0010996805664632D+00, & 0.0010996805664632D+00, & 0.0010996805664632D+00, & 0.0046696376839459D+00, & 0.0046696376839459D+00, & 0.0046696376839459D+00, & 0.0046696376839459D+00, & 0.0046696376839459D+00, & 0.0046696376839459D+00, & 0.0029521156305622D+00, & 0.0029521156305622D+00, & 0.0029521156305622D+00, & 0.0029521156305622D+00, & 0.0029521156305622D+00, & 0.0029521156305622D+00, & 0.0039973734536493D+00, & 0.0039973734536493D+00, & 0.0039973734536493D+00, & 0.0117400065912576D+00, & 0.0117400065912576D+00, & 0.0117400065912576D+00, & 0.0098609303129047D+00, & 0.0098609303129047D+00, & 0.0098609303129047D+00, & 0.0098609303129047D+00, & 0.0098609303129047D+00, & 0.0098609303129047D+00, & 0.0017262732588417D+00, & 0.0017262732588417D+00, & 0.0017262732588417D+00, & 0.0017262732588417D+00, & 0.0017262732588417D+00, & 0.0017262732588417D+00, & 0.0117612076394136D+00, & 0.0117612076394136D+00, & 0.0117612076394136D+00, & 0.0050361825013339D+00, & 0.0050361825013339D+00, & 0.0050361825013339D+00, & 0.0050361825013339D+00, & 0.0050361825013339D+00, & 0.0050361825013339D+00, & 0.0096578802294468D+00, & 0.0096578802294468D+00, & 0.0096578802294468D+00, & 0.0096578802294468D+00, & 0.0096578802294468D+00, & 0.0096578802294468D+00, & 0.0076119150208859D+00, & 0.0076119150208859D+00, & 0.0076119150208859D+00, & 0.0076119150208859D+00, & 0.0076119150208859D+00, & 0.0076119150208859D+00, & 0.0110658638875991D+00, & 0.0110658638875991D+00, & 0.0110658638875991D+00, & 0.0110658638875991D+00, & 0.0110658638875991D+00, & 0.0110658638875991D+00, & 0.0065038397126497D+00, & 0.0065038397126497D+00, & 0.0065038397126497D+00, & 0.0065038397126497D+00, & 0.0065038397126497D+00, & 0.0065038397126497D+00, & 0.0048326872534851D+00, & 0.0048326872534851D+00, & 0.0048326872534851D+00, & 0.0048326872534851D+00, & 0.0048326872534851D+00, & 0.0048326872534851D+00, & 0.0064842252138385D+00, & 0.0064842252138385D+00, & 0.0064842252138385D+00, & 0.0065935144677494D+00, & 0.0065935144677494D+00, & 0.0065935144677494D+00, & 0.0065935144677494D+00, & 0.0065935144677494D+00, & 0.0065935144677494D+00, & 0.0082852665131007D+00, & 0.0082852665131007D+00, & 0.0082852665131007D+00, & 0.0082852665131007D+00, & 0.0082852665131007D+00, & 0.0082852665131007D+00, & 0.0013994293854031D+00, & 0.0013994293854031D+00, & 0.0013994293854031D+00, & 0.0013994293854031D+00, & 0.0013994293854031D+00, & 0.0013994293854031D+00, & 0.0058334336795542D+00, & 0.0058334336795542D+00, & 0.0058334336795542D+00, & 0.0037293709434182D+00, & 0.0037293709434182D+00, & 0.0037293709434182D+00, & 0.0060952640324883D+00, & 0.0060952640324883D+00, & 0.0060952640324883D+00, & 0.0060952640324883D+00, & 0.0060952640324883D+00, & 0.0060952640324883D+00, & 0.0076873106859637D+00, & 0.0076873106859637D+00, & 0.0076873106859637D+00, & 0.0031432061481593D+00, & 0.0031432061481593D+00, & 0.0031432061481593D+00, & 0.0031432061481593D+00, & 0.0031432061481593D+00, & 0.0031432061481593D+00, & 0.0022313317933533D+00, & 0.0022313317933533D+00, & 0.0022313317933533D+00, & 0.0022313317933533D+00, & 0.0022313317933533D+00, & 0.0022313317933533D+00, & 0.0002269613567709D+00, & 0.0002269613567709D+00, & 0.0002269613567709D+00, & 0.0108136993162696D+00, & 0.0108136993162696D+00, & 0.0108136993162696D+00, & 0.0044357309734420D+00, & 0.0044357309734420D+00, & 0.0044357309734420D+00, & 0.0044357309734420D+00, & 0.0044357309734420D+00, & 0.0044357309734420D+00, & 0.0106474448424889D+00, & 0.0106474448424889D+00, & 0.0106474448424889D+00, & 0.0007609261662181D+00, & 0.0007609261662181D+00, & 0.0007609261662181D+00, & 0.0034883273457438D+00, & 0.0034883273457438D+00, & 0.0034883273457438D+00, & 0.0034883273457438D+00, & 0.0034883273457438D+00, & 0.0034883273457438D+00, & 0.0007318458736701D+00, & 0.0007318458736701D+00, & 0.0007318458736701D+00, & 0.0007318458736701D+00, & 0.0007318458736701D+00, & 0.0007318458736701D+00, & 0.0088609393001530D+00, & 0.0088609393001530D+00, & 0.0088609393001530D+00, & 0.0082507974307530D+00, & 0.0082507974307530D+00, & 0.0082507974307530D+00, & 0.0082507974307530D+00, & 0.0082507974307530D+00, & 0.0082507974307530D+00, & 0.0004979675731971D+00, & 0.0004979675731971D+00, & 0.0004979675731971D+00, & 0.0004979675731971D+00, & 0.0004979675731971D+00, & 0.0004979675731971D+00, & 0.0121009649301711D+00, & 0.0028058181373137D+00, & 0.0028058181373137D+00, & 0.0028058181373137D+00, & 0.0028058181373137D+00, & 0.0028058181373137D+00, & 0.0028058181373137D+00, & 0.0094001410371984D+00, & 0.0094001410371984D+00, & 0.0094001410371984D+00, & 0.0005776505742348D+00, & 0.0005776505742348D+00, & 0.0005776505742348D+00, & 0.0005776505742348D+00, & 0.0005776505742348D+00, & 0.0005776505742348D+00, & 0.0019626288054833D+00, & 0.0019626288054833D+00, & 0.0019626288054833D+00, & 0.0019626288054833D+00, & 0.0019626288054833D+00, & 0.0019626288054833D+00, & 0.0002873453546081D+00, & 0.0002873453546081D+00, & 0.0002873453546081D+00, & 0.0002873453546081D+00, & 0.0002873453546081D+00, & 0.0002873453546081D+00 /) return end subroutine rule35 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule35() returns the rule of precision 35. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3014351686173180D+00, & 0.3971296627653639D+00, & 0.3014351686173180D+00, & 0.4916414039828907D+00, & 0.4916414039828907D+00, & 0.0167171920342186D+00, & 0.3577931357985971D+00, & 0.3577931357985971D+00, & 0.2844137284028057D+00, & 0.0550454796915316D+00, & 0.9428863000930624D+00, & 0.0020682202154061D+00, & 0.9428863000930625D+00, & 0.0550454796915318D+00, & 0.0020682202154057D+00, & 0.4453764649152975D+00, & 0.5457185408985746D+00, & 0.0089049941861278D+00, & 0.5457185408985746D+00, & 0.4453764649152976D+00, & 0.0089049941861277D+00, & 0.1523840025243152D+00, & 0.8455000199126449D+00, & 0.0021159775630399D+00, & 0.8455000199126449D+00, & 0.1523840025243154D+00, & 0.0021159775630396D+00, & 0.2624139601093454D+00, & 0.4751720797813089D+00, & 0.2624139601093456D+00, & 0.3975166100282313D+00, & 0.5992221165426375D+00, & 0.0032612734291312D+00, & 0.5992221165426374D+00, & 0.3975166100282314D+00, & 0.0032612734291311D+00, & 0.4028164505857819D+00, & 0.4028164505857819D+00, & 0.1943670988284362D+00, & 0.1560787694034761D+00, & 0.7987533357833951D+00, & 0.0451678948131288D+00, & 0.7987533357833952D+00, & 0.1560787694034762D+00, & 0.0451678948131284D+00, & 0.4730889655006641D+00, & 0.4730889655006641D+00, & 0.0538220689986716D+00, & 0.1972956762765587D+00, & 0.7940983020176844D+00, & 0.0086060217057569D+00, & 0.7940983020176845D+00, & 0.1972956762765588D+00, & 0.0086060217057566D+00, & 0.0500938368999262D+00, & 0.9359318098485054D+00, & 0.0139743532515686D+00, & 0.9359318098485054D+00, & 0.0500938368999261D+00, & 0.0139743532515681D+00, & 0.2988590630143191D+00, & 0.5136696044857865D+00, & 0.1874713324998944D+00, & 0.5136696044857865D+00, & 0.2988590630143191D+00, & 0.1874713324998943D+00, & 0.0628680490440657D+00, & 0.8742639019118683D+00, & 0.0628680490440661D+00, & 0.4415974337549303D+00, & 0.4415974337549303D+00, & 0.1168051324901392D+00, & 0.0196271599834707D+00, & 0.9607456800330582D+00, & 0.0196271599834711D+00, & 0.3347633432653314D+00, & 0.4325143126587202D+00, & 0.2327223440759484D+00, & 0.4325143126587202D+00, & 0.3347633432653314D+00, & 0.2327223440759484D+00, & 0.2093728249763754D+00, & 0.7616252904089401D+00, & 0.0290018846146846D+00, & 0.7616252904089401D+00, & 0.2093728249763754D+00, & 0.0290018846146844D+00, & 0.1065647448613834D+00, & 0.8398677722708630D+00, & 0.0535674828677536D+00, & 0.8398677722708631D+00, & 0.1065647448613836D+00, & 0.0535674828677533D+00, & 0.3213626276695433D+00, & 0.6751411779813131D+00, & 0.0034961943491436D+00, & 0.6751411779813131D+00, & 0.3213626276695434D+00, & 0.0034961943491434D+00, & 0.2415870263479875D+00, & 0.7572369308551706D+00, & 0.0011760427968418D+00, & 0.7572369308551707D+00, & 0.2415870263479876D+00, & 0.0011760427968416D+00, & 0.3331530997207648D+00, & 0.5528929715350868D+00, & 0.1139539287441483D+00, & 0.5528929715350868D+00, & 0.3331530997207648D+00, & 0.1139539287441482D+00, & 0.1551165548133034D+00, & 0.7599448456751416D+00, & 0.0849385995115551D+00, & 0.7599448456751415D+00, & 0.1551165548133034D+00, & 0.0849385995115548D+00, & 0.3710141516774619D+00, & 0.4764206619753218D+00, & 0.1525651863472163D+00, & 0.4764206619753217D+00, & 0.3710141516774620D+00, & 0.1525651863472163D+00, & 0.0402868688301934D+00, & 0.9194262623396129D+00, & 0.0402868688301939D+00, & 0.2708836618077721D+00, & 0.7154976600831513D+00, & 0.0136186781090767D+00, & 0.7154976600831513D+00, & 0.2708836618077720D+00, & 0.0136186781090765D+00, & 0.3525067484154665D+00, & 0.5912668641409812D+00, & 0.0562263874435524D+00, & 0.5912668641409811D+00, & 0.3525067484154665D+00, & 0.0562263874435522D+00, & 0.4057201327781905D+00, & 0.5125263777821213D+00, & 0.0817534894396881D+00, & 0.5125263777821213D+00, & 0.4057201327781905D+00, & 0.0817534894396881D+00, & 0.2189496810149983D+00, & 0.7174078887952542D+00, & 0.0636424301897475D+00, & 0.7174078887952543D+00, & 0.2189496810149983D+00, & 0.0636424301897472D+00, & 0.2067092480855645D+00, & 0.6778965310783613D+00, & 0.1153942208360741D+00, & 0.6778965310783613D+00, & 0.2067092480855646D+00, & 0.1153942208360739D+00, & 0.0985261546687924D+00, & 0.8029476906624150D+00, & 0.0985261546687927D+00, & 0.2566010878790922D+00, & 0.5952117958375970D+00, & 0.1481871162833107D+00, & 0.5952117958375971D+00, & 0.2566010878790923D+00, & 0.1481871162833105D+00, & 0.1382062952112500D+00, & 0.8431958337273686D+00, & 0.0185978710613815D+00, & 0.8431958337273686D+00, & 0.1382062952112501D+00, & 0.0185978710613812D+00, & 0.1395344629893073D+00, & 0.7209310740213852D+00, & 0.1395344629893076D+00, & 0.2215360105096920D+00, & 0.5569279789806159D+00, & 0.2215360105096921D+00, & 0.4258102085854810D+00, & 0.5412187714875727D+00, & 0.0329710199269463D+00, & 0.5412187714875726D+00, & 0.4258102085854810D+00, & 0.0329710199269463D+00, & 0.1807503221352996D+00, & 0.6384993557294008D+00, & 0.1807503221352998D+00, & 0.2797259269522402D+00, & 0.6348945214748060D+00, & 0.0853795515729538D+00, & 0.6348945214748060D+00, & 0.2797259269522402D+00, & 0.0853795515729537D+00, & 0.0224666835802112D+00, & 0.9739002605768547D+00, & 0.0036330558429342D+00, & 0.9739002605768547D+00, & 0.0224666835802113D+00, & 0.0036330558429336D+00, & 0.0838622585244554D+00, & 0.8901176638131806D+00, & 0.0260200776623640D+00, & 0.8901176638131806D+00, & 0.0838622585244554D+00, & 0.0260200776623637D+00, & 0.2848003464144683D+00, & 0.6757427274290935D+00, & 0.0394569261564381D+00, & 0.6757427274290936D+00, & 0.2848003464144683D+00, & 0.0394569261564380D+00, & 0.3565941035365738D+00, & 0.6236351787590180D+00, & 0.0197707177044082D+00, & 0.6236351787590180D+00, & 0.3565941035365738D+00, & 0.0197707177044081D+00, & 0.0974242311151380D+00, & 0.8975470714692345D+00, & 0.0050286974156275D+00, & 0.8975470714692346D+00, & 0.0974242311151381D+00, & 0.0050286974156271D+00, & 0.0042772072684830D+00, & 0.9914455854630337D+00, & 0.0042772072684834D+00, & 0.4999132224862251D+00, & 0.4999132224862251D+00, & 0.0001735550275497D+00 /) b = (/ & 0.3014351686173181D+00, & 0.3014351686173181D+00, & 0.3971296627653640D+00, & 0.0167171920342186D+00, & 0.4916414039828907D+00, & 0.4916414039828909D+00, & 0.2844137284028058D+00, & 0.3577931357985972D+00, & 0.3577931357985973D+00, & 0.0020682202154059D+00, & 0.0550454796915316D+00, & 0.9428863000930624D+00, & 0.0020682202154059D+00, & 0.9428863000930624D+00, & 0.0550454796915320D+00, & 0.0089049941861278D+00, & 0.4453764649152975D+00, & 0.5457185408985749D+00, & 0.0089049941861278D+00, & 0.5457185408985747D+00, & 0.4453764649152978D+00, & 0.0021159775630399D+00, & 0.1523840025243152D+00, & 0.8455000199126450D+00, & 0.0021159775630399D+00, & 0.8455000199126450D+00, & 0.1523840025243156D+00, & 0.2624139601093456D+00, & 0.2624139601093455D+00, & 0.4751720797813091D+00, & 0.0032612734291312D+00, & 0.3975166100282314D+00, & 0.5992221165426377D+00, & 0.0032612734291312D+00, & 0.5992221165426375D+00, & 0.3975166100282316D+00, & 0.1943670988284363D+00, & 0.4028164505857819D+00, & 0.4028164505857820D+00, & 0.0451678948131287D+00, & 0.1560787694034761D+00, & 0.7987533357833954D+00, & 0.0451678948131287D+00, & 0.7987533357833954D+00, & 0.1560787694034764D+00, & 0.0538220689986717D+00, & 0.4730889655006642D+00, & 0.4730889655006644D+00, & 0.0086060217057568D+00, & 0.1972956762765587D+00, & 0.7940983020176846D+00, & 0.0086060217057568D+00, & 0.7940983020176846D+00, & 0.1972956762765590D+00, & 0.0139743532515684D+00, & 0.0500938368999262D+00, & 0.9359318098485054D+00, & 0.0139743532515684D+00, & 0.9359318098485058D+00, & 0.0500938368999265D+00, & 0.1874713324998945D+00, & 0.2988590630143192D+00, & 0.5136696044857866D+00, & 0.1874713324998945D+00, & 0.5136696044857866D+00, & 0.2988590630143193D+00, & 0.0628680490440660D+00, & 0.0628680490440657D+00, & 0.8742639019118684D+00, & 0.1168051324901393D+00, & 0.4415974337549304D+00, & 0.4415974337549305D+00, & 0.0196271599834710D+00, & 0.0196271599834707D+00, & 0.9607456800330584D+00, & 0.2327223440759485D+00, & 0.3347633432653315D+00, & 0.4325143126587203D+00, & 0.2327223440759485D+00, & 0.4325143126587202D+00, & 0.3347633432653315D+00, & 0.0290018846146845D+00, & 0.2093728249763754D+00, & 0.7616252904089403D+00, & 0.0290018846146845D+00, & 0.7616252904089402D+00, & 0.2093728249763756D+00, & 0.0535674828677535D+00, & 0.1065647448613835D+00, & 0.8398677722708632D+00, & 0.0535674828677535D+00, & 0.8398677722708632D+00, & 0.1065647448613838D+00, & 0.0034961943491435D+00, & 0.3213626276695434D+00, & 0.6751411779813132D+00, & 0.0034961943491435D+00, & 0.6751411779813132D+00, & 0.3213626276695436D+00, & 0.0011760427968418D+00, & 0.2415870263479876D+00, & 0.7572369308551709D+00, & 0.0011760427968418D+00, & 0.7572369308551709D+00, & 0.2415870263479878D+00, & 0.1139539287441484D+00, & 0.3331530997207649D+00, & 0.5528929715350870D+00, & 0.1139539287441484D+00, & 0.5528929715350869D+00, & 0.3331530997207651D+00, & 0.0849385995115550D+00, & 0.1551165548133034D+00, & 0.7599448456751416D+00, & 0.0849385995115550D+00, & 0.7599448456751416D+00, & 0.1551165548133037D+00, & 0.1525651863472164D+00, & 0.3710141516774620D+00, & 0.4764206619753220D+00, & 0.1525651863472164D+00, & 0.4764206619753218D+00, & 0.3710141516774621D+00, & 0.0402868688301937D+00, & 0.0402868688301934D+00, & 0.9194262623396129D+00, & 0.0136186781090766D+00, & 0.2708836618077721D+00, & 0.7154976600831515D+00, & 0.0136186781090766D+00, & 0.7154976600831515D+00, & 0.2708836618077723D+00, & 0.0562263874435524D+00, & 0.3525067484154665D+00, & 0.5912668641409813D+00, & 0.0562263874435524D+00, & 0.5912668641409812D+00, & 0.3525067484154668D+00, & 0.0817534894396882D+00, & 0.4057201327781905D+00, & 0.5125263777821215D+00, & 0.0817534894396882D+00, & 0.5125263777821214D+00, & 0.4057201327781906D+00, & 0.0636424301897474D+00, & 0.2189496810149984D+00, & 0.7174078887952544D+00, & 0.0636424301897474D+00, & 0.7174078887952544D+00, & 0.2189496810149986D+00, & 0.1153942208360741D+00, & 0.2067092480855645D+00, & 0.6778965310783615D+00, & 0.1153942208360741D+00, & 0.6778965310783615D+00, & 0.2067092480855648D+00, & 0.0985261546687926D+00, & 0.0985261546687924D+00, & 0.8029476906624151D+00, & 0.1481871162833107D+00, & 0.2566010878790924D+00, & 0.5952117958375971D+00, & 0.1481871162833107D+00, & 0.5952117958375971D+00, & 0.2566010878790925D+00, & 0.0185978710613814D+00, & 0.1382062952112499D+00, & 0.8431958337273687D+00, & 0.0185978710613814D+00, & 0.8431958337273687D+00, & 0.1382062952112503D+00, & 0.1395344629893075D+00, & 0.1395344629893073D+00, & 0.7209310740213853D+00, & 0.2215360105096922D+00, & 0.2215360105096921D+00, & 0.5569279789806160D+00, & 0.0329710199269464D+00, & 0.4258102085854810D+00, & 0.5412187714875728D+00, & 0.0329710199269464D+00, & 0.5412187714875727D+00, & 0.4258102085854812D+00, & 0.1807503221352998D+00, & 0.1807503221352996D+00, & 0.6384993557294009D+00, & 0.0853795515729539D+00, & 0.2797259269522402D+00, & 0.6348945214748062D+00, & 0.0853795515729539D+00, & 0.6348945214748061D+00, & 0.2797259269522404D+00, & 0.0036330558429340D+00, & 0.0224666835802112D+00, & 0.9739002605768550D+00, & 0.0036330558429340D+00, & 0.9739002605768550D+00, & 0.0224666835802115D+00, & 0.0260200776623640D+00, & 0.0838622585244554D+00, & 0.8901176638131808D+00, & 0.0260200776623640D+00, & 0.8901176638131808D+00, & 0.0838622585244558D+00, & 0.0394569261564381D+00, & 0.2848003464144683D+00, & 0.6757427274290937D+00, & 0.0394569261564381D+00, & 0.6757427274290937D+00, & 0.2848003464144686D+00, & 0.0197707177044082D+00, & 0.3565941035365738D+00, & 0.6236351787590181D+00, & 0.0197707177044082D+00, & 0.6236351787590181D+00, & 0.3565941035365741D+00, & 0.0050286974156274D+00, & 0.0974242311151380D+00, & 0.8975470714692347D+00, & 0.0050286974156274D+00, & 0.8975470714692347D+00, & 0.0974242311151384D+00, & 0.0042772072684833D+00, & 0.0042772072684829D+00, & 0.9914455854630339D+00, & 0.0001735550275498D+00, & 0.4999132224862252D+00, & 0.4999132224862253D+00 /) c = (/ & 0.3971296627653639D+00, & 0.3014351686173179D+00, & 0.3014351686173180D+00, & 0.4916414039828907D+00, & 0.0167171920342186D+00, & 0.4916414039828905D+00, & 0.3577931357985971D+00, & 0.2844137284028057D+00, & 0.3577931357985971D+00, & 0.9428863000930624D+00, & 0.0020682202154060D+00, & 0.0550454796915315D+00, & 0.0550454796915315D+00, & 0.0020682202154058D+00, & 0.9428863000930622D+00, & 0.5457185408985747D+00, & 0.0089049941861278D+00, & 0.4453764649152973D+00, & 0.4453764649152975D+00, & 0.0089049941861277D+00, & 0.5457185408985745D+00, & 0.8455000199126449D+00, & 0.0021159775630399D+00, & 0.1523840025243151D+00, & 0.1523840025243152D+00, & 0.0021159775630396D+00, & 0.8455000199126448D+00, & 0.4751720797813090D+00, & 0.2624139601093455D+00, & 0.2624139601093453D+00, & 0.5992221165426375D+00, & 0.0032612734291312D+00, & 0.3975166100282311D+00, & 0.3975166100282314D+00, & 0.0032612734291312D+00, & 0.5992221165426372D+00, & 0.4028164505857818D+00, & 0.1943670988284362D+00, & 0.4028164505857818D+00, & 0.7987533357833952D+00, & 0.0451678948131287D+00, & 0.1560787694034759D+00, & 0.1560787694034761D+00, & 0.0451678948131284D+00, & 0.7987533357833951D+00, & 0.4730889655006641D+00, & 0.0538220689986716D+00, & 0.4730889655006639D+00, & 0.7940983020176844D+00, & 0.0086060217057569D+00, & 0.1972956762765585D+00, & 0.1972956762765587D+00, & 0.0086060217057566D+00, & 0.7940983020176844D+00, & 0.9359318098485054D+00, & 0.0139743532515684D+00, & 0.0500938368999260D+00, & 0.0500938368999262D+00, & 0.0139743532515680D+00, & 0.9359318098485053D+00, & 0.5136696044857865D+00, & 0.1874713324998943D+00, & 0.2988590630143190D+00, & 0.2988590630143190D+00, & 0.1874713324998943D+00, & 0.5136696044857864D+00, & 0.8742639019118683D+00, & 0.0628680490440660D+00, & 0.0628680490440655D+00, & 0.4415974337549304D+00, & 0.1168051324901392D+00, & 0.4415974337549302D+00, & 0.9607456800330582D+00, & 0.0196271599834711D+00, & 0.0196271599834704D+00, & 0.4325143126587201D+00, & 0.2327223440759483D+00, & 0.3347633432653313D+00, & 0.3347633432653313D+00, & 0.2327223440759484D+00, & 0.4325143126587201D+00, & 0.7616252904089401D+00, & 0.0290018846146845D+00, & 0.2093728249763751D+00, & 0.2093728249763754D+00, & 0.0290018846146843D+00, & 0.7616252904089400D+00, & 0.8398677722708631D+00, & 0.0535674828677536D+00, & 0.1065647448613832D+00, & 0.1065647448613834D+00, & 0.0535674828677533D+00, & 0.8398677722708630D+00, & 0.6751411779813131D+00, & 0.0034961943491435D+00, & 0.3213626276695432D+00, & 0.3213626276695434D+00, & 0.0034961943491434D+00, & 0.6751411779813130D+00, & 0.7572369308551706D+00, & 0.0011760427968418D+00, & 0.2415870263479873D+00, & 0.2415870263479875D+00, & 0.0011760427968416D+00, & 0.7572369308551705D+00, & 0.5528929715350869D+00, & 0.1139539287441483D+00, & 0.3331530997207647D+00, & 0.3331530997207648D+00, & 0.1139539287441483D+00, & 0.5528929715350867D+00, & 0.7599448456751415D+00, & 0.0849385995115549D+00, & 0.1551165548133032D+00, & 0.1551165548133034D+00, & 0.0849385995115549D+00, & 0.7599448456751414D+00, & 0.4764206619753217D+00, & 0.1525651863472163D+00, & 0.3710141516774618D+00, & 0.3710141516774619D+00, & 0.1525651863472162D+00, & 0.4764206619753216D+00, & 0.9194262623396129D+00, & 0.0402868688301937D+00, & 0.0402868688301933D+00, & 0.7154976600831513D+00, & 0.0136186781090766D+00, & 0.2708836618077718D+00, & 0.2708836618077721D+00, & 0.0136186781090765D+00, & 0.7154976600831512D+00, & 0.5912668641409812D+00, & 0.0562263874435523D+00, & 0.3525067484154663D+00, & 0.3525067484154665D+00, & 0.0562263874435524D+00, & 0.5912668641409811D+00, & 0.5125263777821213D+00, & 0.0817534894396882D+00, & 0.4057201327781904D+00, & 0.4057201327781905D+00, & 0.0817534894396881D+00, & 0.5125263777821213D+00, & 0.7174078887952543D+00, & 0.0636424301897474D+00, & 0.2189496810149981D+00, & 0.2189496810149983D+00, & 0.0636424301897472D+00, & 0.7174078887952542D+00, & 0.6778965310783613D+00, & 0.1153942208360741D+00, & 0.2067092480855645D+00, & 0.2067092480855646D+00, & 0.1153942208360740D+00, & 0.6778965310783613D+00, & 0.8029476906624151D+00, & 0.0985261546687926D+00, & 0.0985261546687922D+00, & 0.5952117958375970D+00, & 0.1481871162833107D+00, & 0.2566010878790922D+00, & 0.2566010878790922D+00, & 0.1481871162833106D+00, & 0.5952117958375969D+00, & 0.8431958337273686D+00, & 0.0185978710613814D+00, & 0.1382062952112498D+00, & 0.1382062952112500D+00, & 0.0185978710613811D+00, & 0.8431958337273685D+00, & 0.7209310740213852D+00, & 0.1395344629893075D+00, & 0.1395344629893071D+00, & 0.5569279789806159D+00, & 0.2215360105096921D+00, & 0.2215360105096918D+00, & 0.5412187714875726D+00, & 0.0329710199269463D+00, & 0.4258102085854808D+00, & 0.4258102085854810D+00, & 0.0329710199269463D+00, & 0.5412187714875725D+00, & 0.6384993557294008D+00, & 0.1807503221352997D+00, & 0.1807503221352994D+00, & 0.6348945214748060D+00, & 0.0853795515729538D+00, & 0.2797259269522400D+00, & 0.2797259269522402D+00, & 0.0853795515729537D+00, & 0.6348945214748060D+00, & 0.9739002605768549D+00, & 0.0036330558429341D+00, & 0.0224666835802109D+00, & 0.0224666835802113D+00, & 0.0036330558429337D+00, & 0.9739002605768549D+00, & 0.8901176638131807D+00, & 0.0260200776623640D+00, & 0.0838622585244552D+00, & 0.0838622585244555D+00, & 0.0260200776623637D+00, & 0.8901176638131805D+00, & 0.6757427274290936D+00, & 0.0394569261564382D+00, & 0.2848003464144682D+00, & 0.2848003464144683D+00, & 0.0394569261564380D+00, & 0.6757427274290935D+00, & 0.6236351787590180D+00, & 0.0197707177044082D+00, & 0.3565941035365737D+00, & 0.3565941035365738D+00, & 0.0197707177044081D+00, & 0.6236351787590179D+00, & 0.8975470714692345D+00, & 0.0050286974156274D+00, & 0.0974242311151378D+00, & 0.0974242311151380D+00, & 0.0050286974156272D+00, & 0.8975470714692345D+00, & 0.9914455854630339D+00, & 0.0042772072684833D+00, & 0.0042772072684828D+00, & 0.4999132224862252D+00, & 0.0001735550275497D+00, & 0.4999132224862250D+00 /) w = (/ & 0.0057479340296702D+00, & 0.0057479340296702D+00, & 0.0057479340296702D+00, & 0.0022963680920994D+00, & 0.0022963680920994D+00, & 0.0022963680920994D+00, & 0.0079953508418643D+00, & 0.0079953508418643D+00, & 0.0079953508418643D+00, & 0.0004541993823754D+00, & 0.0004541993823754D+00, & 0.0004541993823754D+00, & 0.0004541993823754D+00, & 0.0004541993823754D+00, & 0.0004541993823754D+00, & 0.0019717493309842D+00, & 0.0019717493309842D+00, & 0.0019717493309842D+00, & 0.0019717493309842D+00, & 0.0019717493309842D+00, & 0.0019717493309842D+00, & 0.0007826663054394D+00, & 0.0007826663054394D+00, & 0.0007826663054394D+00, & 0.0007826663054394D+00, & 0.0007826663054394D+00, & 0.0007826663054394D+00, & 0.0087901858933278D+00, & 0.0087901858933278D+00, & 0.0087901858933278D+00, & 0.0012646931023972D+00, & 0.0012646931023972D+00, & 0.0012646931023972D+00, & 0.0012646931023972D+00, & 0.0012646931023972D+00, & 0.0012646931023972D+00, & 0.0083203666123256D+00, & 0.0083203666123256D+00, & 0.0083203666123256D+00, & 0.0035572562609095D+00, & 0.0035572562609095D+00, & 0.0035572562609095D+00, & 0.0035572562609095D+00, & 0.0035572562609095D+00, & 0.0035572562609095D+00, & 0.0052751882851615D+00, & 0.0052751882851615D+00, & 0.0052751882851615D+00, & 0.0018428326631755D+00, & 0.0018428326631755D+00, & 0.0018428326631755D+00, & 0.0018428326631755D+00, & 0.0018428326631755D+00, & 0.0018428326631755D+00, & 0.0013289799356542D+00, & 0.0013289799356542D+00, & 0.0013289799356542D+00, & 0.0013289799356542D+00, & 0.0013289799356542D+00, & 0.0013289799356542D+00, & 0.0090234128551062D+00, & 0.0090234128551062D+00, & 0.0090234128551062D+00, & 0.0090234128551062D+00, & 0.0090234128551062D+00, & 0.0090234128551062D+00, & 0.0029682066390516D+00, & 0.0029682066390516D+00, & 0.0029682066390516D+00, & 0.0076051825305364D+00, & 0.0076051825305364D+00, & 0.0076051825305364D+00, & 0.0010131210327381D+00, & 0.0010131210327381D+00, & 0.0010131210327381D+00, & 0.0086055044940838D+00, & 0.0086055044940838D+00, & 0.0086055044940838D+00, & 0.0086055044940838D+00, & 0.0086055044940838D+00, & 0.0086055044940838D+00, & 0.0036104679969938D+00, & 0.0036104679969938D+00, & 0.0036104679969938D+00, & 0.0036104679969938D+00, & 0.0036104679969938D+00, & 0.0036104679969938D+00, & 0.0035235607672108D+00, & 0.0035235607672108D+00, & 0.0035235607672108D+00, & 0.0035235607672108D+00, & 0.0035235607672108D+00, & 0.0035235607672108D+00, & 0.0013780765220064D+00, & 0.0013780765220064D+00, & 0.0013780765220064D+00, & 0.0013780765220064D+00, & 0.0013780765220064D+00, & 0.0013780765220064D+00, & 0.0006950295859519D+00, & 0.0006950295859519D+00, & 0.0006950295859519D+00, & 0.0006950295859519D+00, & 0.0006950295859519D+00, & 0.0006950295859519D+00, & 0.0081297205980780D+00, & 0.0081297205980780D+00, & 0.0081297205980780D+00, & 0.0081297205980780D+00, & 0.0081297205980780D+00, & 0.0081297205980780D+00, & 0.0054896563598667D+00, & 0.0054896563598667D+00, & 0.0054896563598667D+00, & 0.0054896563598667D+00, & 0.0054896563598667D+00, & 0.0054896563598667D+00, & 0.0082359873228582D+00, & 0.0082359873228582D+00, & 0.0082359873228582D+00, & 0.0082359873228582D+00, & 0.0082359873228582D+00, & 0.0082359873228582D+00, & 0.0020648356265983D+00, & 0.0020648356265983D+00, & 0.0020648356265983D+00, & 0.0027797735193626D+00, & 0.0027797735193626D+00, & 0.0027797735193626D+00, & 0.0027797735193626D+00, & 0.0027797735193626D+00, & 0.0027797735193626D+00, & 0.0063317818814834D+00, & 0.0063317818814834D+00, & 0.0063317818814834D+00, & 0.0063317818814834D+00, & 0.0063317818814834D+00, & 0.0063317818814834D+00, & 0.0069457107199416D+00, & 0.0069457107199416D+00, & 0.0069457107199416D+00, & 0.0069457107199416D+00, & 0.0069457107199416D+00, & 0.0069457107199416D+00, & 0.0055659411156861D+00, & 0.0055659411156861D+00, & 0.0055659411156861D+00, & 0.0055659411156861D+00, & 0.0055659411156861D+00, & 0.0055659411156861D+00, & 0.0073376101567627D+00, & 0.0073376101567627D+00, & 0.0073376101567627D+00, & 0.0073376101567627D+00, & 0.0073376101567627D+00, & 0.0073376101567627D+00, & 0.0050036396155573D+00, & 0.0050036396155573D+00, & 0.0050036396155573D+00, & 0.0087114266235609D+00, & 0.0087114266235609D+00, & 0.0087114266235609D+00, & 0.0087114266235609D+00, & 0.0087114266235609D+00, & 0.0087114266235609D+00, & 0.0027367494327220D+00, & 0.0027367494327220D+00, & 0.0027367494327220D+00, & 0.0027367494327220D+00, & 0.0027367494327220D+00, & 0.0027367494327220D+00, & 0.0067190798124174D+00, & 0.0067190798124174D+00, & 0.0067190798124174D+00, & 0.0091619089409373D+00, & 0.0091619089409373D+00, & 0.0091619089409373D+00, & 0.0047016575809322D+00, & 0.0047016575809322D+00, & 0.0047016575809322D+00, & 0.0047016575809322D+00, & 0.0047016575809322D+00, & 0.0047016575809322D+00, & 0.0083719066370130D+00, & 0.0083719066370130D+00, & 0.0083719066370130D+00, & 0.0071750089599327D+00, & 0.0071750089599327D+00, & 0.0071750089599327D+00, & 0.0071750089599327D+00, & 0.0071750089599327D+00, & 0.0071750089599327D+00, & 0.0004732469738005D+00, & 0.0004732469738005D+00, & 0.0004732469738005D+00, & 0.0004732469738005D+00, & 0.0004732469738005D+00, & 0.0004732469738005D+00, & 0.0025346621113678D+00, & 0.0025346621113678D+00, & 0.0025346621113678D+00, & 0.0025346621113678D+00, & 0.0025346621113678D+00, & 0.0025346621113678D+00, & 0.0050701573000114D+00, & 0.0050701573000114D+00, & 0.0050701573000114D+00, & 0.0050701573000114D+00, & 0.0050701573000114D+00, & 0.0050701573000114D+00, & 0.0040540720868840D+00, & 0.0040540720868840D+00, & 0.0040540720868840D+00, & 0.0040540720868840D+00, & 0.0040540720868840D+00, & 0.0040540720868840D+00, & 0.0012544783872410D+00, & 0.0012544783872410D+00, & 0.0012544783872410D+00, & 0.0012544783872410D+00, & 0.0012544783872410D+00, & 0.0012544783872410D+00, & 0.0002403337374048D+00, & 0.0002403337374048D+00, & 0.0002403337374048D+00, & 0.0006275843410706D+00, & 0.0006275843410706D+00, & 0.0006275843410706D+00 /) return end subroutine rule36 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule36() returns the rule of precision 36. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2550023360754195D+00, & 0.7127053999508112D+00, & 0.0322922639737694D+00, & 0.7127053999508112D+00, & 0.2550023360754196D+00, & 0.0322922639737692D+00, & 0.2711215136033400D+00, & 0.6347382765922519D+00, & 0.0941402098044082D+00, & 0.6347382765922519D+00, & 0.2711215136033400D+00, & 0.0941402098044080D+00, & 0.0926886044848755D+00, & 0.8423177234108842D+00, & 0.0649936721042403D+00, & 0.8423177234108843D+00, & 0.0926886044848757D+00, & 0.0649936721042400D+00, & 0.3294543765845505D+00, & 0.5968319589620307D+00, & 0.0737136644534188D+00, & 0.5968319589620307D+00, & 0.3294543765845505D+00, & 0.0737136644534187D+00, & 0.2883788411304420D+00, & 0.6615561707226660D+00, & 0.0500649881468920D+00, & 0.6615561707226659D+00, & 0.2883788411304421D+00, & 0.0500649881468918D+00, & 0.3921724164051739D+00, & 0.5419312451199315D+00, & 0.0658963384748946D+00, & 0.5419312451199314D+00, & 0.3921724164051738D+00, & 0.0658963384748946D+00, & 0.0076222500155876D+00, & 0.9911436314566491D+00, & 0.0012341185277635D+00, & 0.9911436314566491D+00, & 0.0076222500155876D+00, & 0.0012341185277630D+00, & 0.4123573403136303D+00, & 0.4123573403136303D+00, & 0.1752853193727393D+00, & 0.1782079366279757D+00, & 0.7160962360444145D+00, & 0.1056958273276099D+00, & 0.7160962360444145D+00, & 0.1782079366279757D+00, & 0.1056958273276097D+00, & 0.3102489314599136D+00, & 0.5658793981445355D+00, & 0.1238716703955509D+00, & 0.5658793981445355D+00, & 0.3102489314599136D+00, & 0.1238716703955508D+00, & 0.4390483832458435D+00, & 0.4390483832458435D+00, & 0.1219032335083129D+00, & 0.0829157021331252D+00, & 0.9142769002483087D+00, & 0.0028073976185662D+00, & 0.9142769002483088D+00, & 0.0829157021331253D+00, & 0.0028073976185659D+00, & 0.3796386793469431D+00, & 0.5096715423270356D+00, & 0.1106897783260212D+00, & 0.5096715423270356D+00, & 0.3796386793469431D+00, & 0.1106897783260211D+00, & 0.2350523254582137D+00, & 0.5298953490835725D+00, & 0.2350523254582138D+00, & 0.1980682921145434D+00, & 0.7991752852717510D+00, & 0.0027564226137057D+00, & 0.7991752852717511D+00, & 0.1980682921145434D+00, & 0.0027564226137055D+00, & 0.1479479453220730D+00, & 0.7800003555819109D+00, & 0.0720516990960159D+00, & 0.7800003555819111D+00, & 0.1479479453220731D+00, & 0.0720516990960157D+00, & 0.2292027665534673D+00, & 0.7563686218758484D+00, & 0.0144286115706843D+00, & 0.7563686218758484D+00, & 0.2292027665534674D+00, & 0.0144286115706841D+00, & 0.3574738503443845D+00, & 0.6397835829582036D+00, & 0.0027425666974119D+00, & 0.6397835829582036D+00, & 0.3574738503443844D+00, & 0.0027425666974117D+00, & 0.1252496722294377D+00, & 0.8357259979283462D+00, & 0.0390243298422160D+00, & 0.8357259979283463D+00, & 0.1252496722294378D+00, & 0.0390243298422157D+00, & 0.0209805646004062D+00, & 0.9715447719336604D+00, & 0.0074746634659335D+00, & 0.9715447719336604D+00, & 0.0209805646004063D+00, & 0.0074746634659331D+00, & 0.2691316117440097D+00, & 0.5552966096544709D+00, & 0.1755717786015192D+00, & 0.5552966096544710D+00, & 0.2691316117440098D+00, & 0.1755717786015191D+00, & 0.1508217347798915D+00, & 0.6983565304402166D+00, & 0.1508217347798919D+00, & 0.3462198724218936D+00, & 0.4825533687273535D+00, & 0.1712267588507529D+00, & 0.4825533687273536D+00, & 0.3462198724218935D+00, & 0.1712267588507528D+00, & 0.4423877426580685D+00, & 0.5233061138878379D+00, & 0.0343061434540937D+00, & 0.5233061138878379D+00, & 0.4423877426580686D+00, & 0.0343061434540936D+00, & 0.2746338837226588D+00, & 0.7223364807654942D+00, & 0.0030296355118472D+00, & 0.7223364807654941D+00, & 0.2746338837226588D+00, & 0.0030296355118469D+00, & 0.2237012846551441D+00, & 0.7038117568892118D+00, & 0.0724869584556441D+00, & 0.7038117568892117D+00, & 0.2237012846551442D+00, & 0.0724869584556440D+00, & 0.2264729475116298D+00, & 0.6397100291477062D+00, & 0.1338170233406640D+00, & 0.6397100291477064D+00, & 0.2264729475116297D+00, & 0.1338170233406638D+00, & 0.1633619668293704D+00, & 0.8189638129323793D+00, & 0.0176742202382503D+00, & 0.8189638129323793D+00, & 0.1633619668293705D+00, & 0.0176742202382500D+00, & 0.1907912728543789D+00, & 0.7670005101060391D+00, & 0.0422082170395822D+00, & 0.7670005101060390D+00, & 0.1907912728543789D+00, & 0.0422082170395819D+00, & 0.3581658706314307D+00, & 0.6074178089715797D+00, & 0.0344163203969896D+00, & 0.6074178089715797D+00, & 0.3581658706314307D+00, & 0.0344163203969895D+00, & 0.0993849892050522D+00, & 0.8831620205339272D+00, & 0.0174529902610207D+00, & 0.8831620205339273D+00, & 0.0993849892050523D+00, & 0.0174529902610203D+00, & 0.4502328978916524D+00, & 0.5485392672636246D+00, & 0.0012278348447230D+00, & 0.5485392672636246D+00, & 0.4502328978916525D+00, & 0.0012278348447230D+00, & 0.4642737776346700D+00, & 0.4642737776346701D+00, & 0.0714524447306599D+00, & 0.3048602929866793D+00, & 0.4588765169470121D+00, & 0.2362631900663086D+00, & 0.4588765169470121D+00, & 0.3048602929866793D+00, & 0.2362631900663085D+00, & 0.3135836062706951D+00, & 0.6708934652005731D+00, & 0.0155229285287318D+00, & 0.6708934652005731D+00, & 0.3135836062706952D+00, & 0.0155229285287316D+00, & 0.1348062882666829D+00, & 0.8613456659624720D+00, & 0.0038480457708451D+00, & 0.8613456659624721D+00, & 0.1348062882666830D+00, & 0.0038480457708449D+00, & 0.1911613618773089D+00, & 0.6176772762453819D+00, & 0.1911613618773091D+00, & 0.0658281924328199D+00, & 0.8960993382441670D+00, & 0.0380724693230132D+00, & 0.8960993382441671D+00, & 0.0658281924328200D+00, & 0.0380724693230129D+00, & 0.0293500490934269D+00, & 0.9412999018131458D+00, & 0.0293500490934273D+00, & 0.3081452189910933D+00, & 0.3837095620178134D+00, & 0.3081452189910933D+00, & 0.0531928439194577D+00, & 0.9346369019266020D+00, & 0.0121702541539404D+00, & 0.9346369019266021D+00, & 0.0531928439194579D+00, & 0.0121702541539399D+00, & 0.1111782647883809D+00, & 0.7776434704232379D+00, & 0.1111782647883812D+00, & 0.0406479626359586D+00, & 0.9584934783193574D+00, & 0.0008585590446841D+00, & 0.9584934783193575D+00, & 0.0406479626359587D+00, & 0.0008585590446836D+00, & 0.4064475672122849D+00, & 0.5812165949773879D+00, & 0.0123358378103273D+00, & 0.5812165949773879D+00, & 0.4064475672122848D+00, & 0.0123358378103271D+00, & 0.3810023496034419D+00, & 0.3810023496034418D+00, & 0.2379953007931161D+00, & 0.4944809967477004D+00, & 0.4944809967477005D+00, & 0.0110380065045990D+00 /) b = (/ & 0.0322922639737694D+00, & 0.2550023360754195D+00, & 0.7127053999508113D+00, & 0.0322922639737694D+00, & 0.7127053999508113D+00, & 0.2550023360754198D+00, & 0.0941402098044082D+00, & 0.2711215136033400D+00, & 0.6347382765922520D+00, & 0.0941402098044082D+00, & 0.6347382765922520D+00, & 0.2711215136033402D+00, & 0.0649936721042402D+00, & 0.0926886044848756D+00, & 0.8423177234108843D+00, & 0.0649936721042402D+00, & 0.8423177234108843D+00, & 0.0926886044848759D+00, & 0.0737136644534188D+00, & 0.3294543765845505D+00, & 0.5968319589620309D+00, & 0.0737136644534188D+00, & 0.5968319589620308D+00, & 0.3294543765845507D+00, & 0.0500649881468919D+00, & 0.2883788411304421D+00, & 0.6615561707226660D+00, & 0.0500649881468919D+00, & 0.6615561707226660D+00, & 0.2883788411304423D+00, & 0.0658963384748947D+00, & 0.3921724164051739D+00, & 0.5419312451199317D+00, & 0.0658963384748947D+00, & 0.5419312451199316D+00, & 0.3921724164051740D+00, & 0.0012341185277633D+00, & 0.0076222500155876D+00, & 0.9911436314566491D+00, & 0.0012341185277633D+00, & 0.9911436314566494D+00, & 0.0076222500155880D+00, & 0.1752853193727394D+00, & 0.4123573403136304D+00, & 0.4123573403136305D+00, & 0.1056958273276099D+00, & 0.1782079366279757D+00, & 0.7160962360444146D+00, & 0.1056958273276099D+00, & 0.7160962360444146D+00, & 0.1782079366279760D+00, & 0.1238716703955509D+00, & 0.3102489314599137D+00, & 0.5658793981445357D+00, & 0.1238716703955509D+00, & 0.5658793981445357D+00, & 0.3102489314599138D+00, & 0.1219032335083130D+00, & 0.4390483832458436D+00, & 0.4390483832458437D+00, & 0.0028073976185661D+00, & 0.0829157021331252D+00, & 0.9142769002483089D+00, & 0.0028073976185661D+00, & 0.9142769002483089D+00, & 0.0829157021331255D+00, & 0.1106897783260212D+00, & 0.3796386793469432D+00, & 0.5096715423270358D+00, & 0.1106897783260212D+00, & 0.5096715423270358D+00, & 0.3796386793469433D+00, & 0.2350523254582139D+00, & 0.2350523254582138D+00, & 0.5298953490835726D+00, & 0.0027564226137057D+00, & 0.1980682921145434D+00, & 0.7991752852717512D+00, & 0.0027564226137057D+00, & 0.7991752852717511D+00, & 0.1980682921145436D+00, & 0.0720516990960159D+00, & 0.1479479453220730D+00, & 0.7800003555819113D+00, & 0.0720516990960159D+00, & 0.7800003555819113D+00, & 0.1479479453220733D+00, & 0.0144286115706843D+00, & 0.2292027665534674D+00, & 0.7563686218758485D+00, & 0.0144286115706843D+00, & 0.7563686218758484D+00, & 0.2292027665534676D+00, & 0.0027425666974119D+00, & 0.3574738503443846D+00, & 0.6397835829582038D+00, & 0.0027425666974119D+00, & 0.6397835829582038D+00, & 0.3574738503443848D+00, & 0.0390243298422159D+00, & 0.1252496722294378D+00, & 0.8357259979283465D+00, & 0.0390243298422159D+00, & 0.8357259979283465D+00, & 0.1252496722294380D+00, & 0.0074746634659333D+00, & 0.0209805646004062D+00, & 0.9715447719336605D+00, & 0.0074746634659333D+00, & 0.9715447719336605D+00, & 0.0209805646004066D+00, & 0.1755717786015193D+00, & 0.2691316117440098D+00, & 0.5552966096544713D+00, & 0.1755717786015193D+00, & 0.5552966096544711D+00, & 0.2691316117440100D+00, & 0.1508217347798918D+00, & 0.1508217347798916D+00, & 0.6983565304402167D+00, & 0.1712267588507529D+00, & 0.3462198724218936D+00, & 0.4825533687273537D+00, & 0.1712267588507529D+00, & 0.4825533687273537D+00, & 0.3462198724218937D+00, & 0.0343061434540937D+00, & 0.4423877426580686D+00, & 0.5233061138878380D+00, & 0.0343061434540937D+00, & 0.5233061138878379D+00, & 0.4423877426580687D+00, & 0.0030296355118471D+00, & 0.2746338837226588D+00, & 0.7223364807654942D+00, & 0.0030296355118471D+00, & 0.7223364807654942D+00, & 0.2746338837226592D+00, & 0.0724869584556441D+00, & 0.2237012846551441D+00, & 0.7038117568892120D+00, & 0.0724869584556441D+00, & 0.7038117568892119D+00, & 0.2237012846551444D+00, & 0.1338170233406639D+00, & 0.2264729475116298D+00, & 0.6397100291477065D+00, & 0.1338170233406639D+00, & 0.6397100291477065D+00, & 0.2264729475116300D+00, & 0.0176742202382503D+00, & 0.1633619668293704D+00, & 0.8189638129323794D+00, & 0.0176742202382503D+00, & 0.8189638129323794D+00, & 0.1633619668293707D+00, & 0.0422082170395821D+00, & 0.1907912728543789D+00, & 0.7670005101060392D+00, & 0.0422082170395821D+00, & 0.7670005101060391D+00, & 0.1907912728543791D+00, & 0.0344163203969896D+00, & 0.3581658706314307D+00, & 0.6074178089715798D+00, & 0.0344163203969896D+00, & 0.6074178089715798D+00, & 0.3581658706314309D+00, & 0.0174529902610205D+00, & 0.0993849892050522D+00, & 0.8831620205339273D+00, & 0.0174529902610205D+00, & 0.8831620205339273D+00, & 0.0993849892050526D+00, & 0.0012278348447231D+00, & 0.4502328978916525D+00, & 0.5485392672636248D+00, & 0.0012278348447231D+00, & 0.5485392672636246D+00, & 0.4502328978916527D+00, & 0.0714524447306600D+00, & 0.4642737776346700D+00, & 0.4642737776346703D+00, & 0.2362631900663087D+00, & 0.3048602929866794D+00, & 0.4588765169470122D+00, & 0.2362631900663087D+00, & 0.4588765169470121D+00, & 0.3048602929866794D+00, & 0.0155229285287317D+00, & 0.3135836062706952D+00, & 0.6708934652005732D+00, & 0.0155229285287317D+00, & 0.6708934652005732D+00, & 0.3135836062706954D+00, & 0.0038480457708451D+00, & 0.1348062882666829D+00, & 0.8613456659624722D+00, & 0.0038480457708451D+00, & 0.8613456659624722D+00, & 0.1348062882666833D+00, & 0.1911613618773092D+00, & 0.1911613618773090D+00, & 0.6176772762453820D+00, & 0.0380724693230131D+00, & 0.0658281924328199D+00, & 0.8960993382441672D+00, & 0.0380724693230131D+00, & 0.8960993382441672D+00, & 0.0658281924328202D+00, & 0.0293500490934272D+00, & 0.0293500490934269D+00, & 0.9412999018131460D+00, & 0.3081452189910934D+00, & 0.3081452189910934D+00, & 0.3837095620178135D+00, & 0.0121702541539402D+00, & 0.0531928439194577D+00, & 0.9346369019266021D+00, & 0.0121702541539402D+00, & 0.9346369019266021D+00, & 0.0531928439194581D+00, & 0.1111782647883812D+00, & 0.1111782647883809D+00, & 0.7776434704232381D+00, & 0.0008585590446839D+00, & 0.0406479626359585D+00, & 0.9584934783193576D+00, & 0.0008585590446839D+00, & 0.9584934783193576D+00, & 0.0406479626359589D+00, & 0.0123358378103272D+00, & 0.4064475672122849D+00, & 0.5812165949773881D+00, & 0.0123358378103272D+00, & 0.5812165949773881D+00, & 0.4064475672122851D+00, & 0.2379953007931163D+00, & 0.3810023496034420D+00, & 0.3810023496034420D+00, & 0.0110380065045991D+00, & 0.4944809967477005D+00, & 0.4944809967477007D+00 /) c = (/ & 0.7127053999508112D+00, & 0.0322922639737693D+00, & 0.2550023360754192D+00, & 0.2550023360754194D+00, & 0.0322922639737692D+00, & 0.7127053999508109D+00, & 0.6347382765922518D+00, & 0.0941402098044081D+00, & 0.2711215136033398D+00, & 0.2711215136033399D+00, & 0.0941402098044080D+00, & 0.6347382765922518D+00, & 0.8423177234108842D+00, & 0.0649936721042403D+00, & 0.0926886044848754D+00, & 0.0926886044848755D+00, & 0.0649936721042400D+00, & 0.8423177234108841D+00, & 0.5968319589620307D+00, & 0.0737136644534188D+00, & 0.3294543765845502D+00, & 0.3294543765845506D+00, & 0.0737136644534188D+00, & 0.5968319589620306D+00, & 0.6615561707226660D+00, & 0.0500649881468919D+00, & 0.2883788411304420D+00, & 0.2883788411304422D+00, & 0.0500649881468919D+00, & 0.6615561707226659D+00, & 0.5419312451199314D+00, & 0.0658963384748946D+00, & 0.3921724164051736D+00, & 0.3921724164051739D+00, & 0.0658963384748946D+00, & 0.5419312451199314D+00, & 0.9911436314566492D+00, & 0.0012341185277633D+00, & 0.0076222500155874D+00, & 0.0076222500155877D+00, & 0.0012341185277630D+00, & 0.9911436314566491D+00, & 0.4123573403136304D+00, & 0.1752853193727394D+00, & 0.4123573403136302D+00, & 0.7160962360444145D+00, & 0.1056958273276098D+00, & 0.1782079366279755D+00, & 0.1782079366279756D+00, & 0.1056958273276097D+00, & 0.7160962360444144D+00, & 0.5658793981445355D+00, & 0.1238716703955509D+00, & 0.3102489314599134D+00, & 0.3102489314599136D+00, & 0.1238716703955508D+00, & 0.5658793981445354D+00, & 0.4390483832458435D+00, & 0.1219032335083129D+00, & 0.4390483832458434D+00, & 0.9142769002483087D+00, & 0.0028073976185661D+00, & 0.0829157021331249D+00, & 0.0829157021331251D+00, & 0.0028073976185659D+00, & 0.9142769002483084D+00, & 0.5096715423270357D+00, & 0.1106897783260212D+00, & 0.3796386793469430D+00, & 0.3796386793469432D+00, & 0.1106897783260211D+00, & 0.5096715423270355D+00, & 0.5298953490835724D+00, & 0.2350523254582137D+00, & 0.2350523254582136D+00, & 0.7991752852717510D+00, & 0.0027564226137057D+00, & 0.1980682921145430D+00, & 0.1980682921145433D+00, & 0.0027564226137056D+00, & 0.7991752852717509D+00, & 0.7800003555819111D+00, & 0.0720516990960160D+00, & 0.1479479453220728D+00, & 0.1479479453220731D+00, & 0.0720516990960156D+00, & 0.7800003555819111D+00, & 0.7563686218758484D+00, & 0.0144286115706842D+00, & 0.2292027665534672D+00, & 0.2292027665534673D+00, & 0.0144286115706841D+00, & 0.7563686218758482D+00, & 0.6397835829582036D+00, & 0.0027425666974119D+00, & 0.3574738503443843D+00, & 0.3574738503443846D+00, & 0.0027425666974118D+00, & 0.6397835829582035D+00, & 0.8357259979283463D+00, & 0.0390243298422160D+00, & 0.1252496722294375D+00, & 0.1252496722294377D+00, & 0.0390243298422157D+00, & 0.8357259979283462D+00, & 0.9715447719336605D+00, & 0.0074746634659334D+00, & 0.0209805646004060D+00, & 0.0209805646004063D+00, & 0.0074746634659332D+00, & 0.9715447719336603D+00, & 0.5552966096544710D+00, & 0.1755717786015193D+00, & 0.2691316117440096D+00, & 0.2691316117440097D+00, & 0.1755717786015191D+00, & 0.5552966096544709D+00, & 0.6983565304402167D+00, & 0.1508217347798918D+00, & 0.1508217347798914D+00, & 0.4825533687273535D+00, & 0.1712267588507528D+00, & 0.3462198724218934D+00, & 0.3462198724218936D+00, & 0.1712267588507529D+00, & 0.4825533687273535D+00, & 0.5233061138878379D+00, & 0.0343061434540936D+00, & 0.4423877426580684D+00, & 0.4423877426580685D+00, & 0.0343061434540936D+00, & 0.5233061138878377D+00, & 0.7223364807654941D+00, & 0.0030296355118470D+00, & 0.2746338837226586D+00, & 0.2746338837226588D+00, & 0.0030296355118470D+00, & 0.7223364807654939D+00, & 0.7038117568892118D+00, & 0.0724869584556440D+00, & 0.2237012846551438D+00, & 0.2237012846551442D+00, & 0.0724869584556439D+00, & 0.7038117568892116D+00, & 0.6397100291477062D+00, & 0.1338170233406640D+00, & 0.2264729475116296D+00, & 0.2264729475116297D+00, & 0.1338170233406638D+00, & 0.6397100291477062D+00, & 0.8189638129323793D+00, & 0.0176742202382503D+00, & 0.1633619668293703D+00, & 0.1633619668293704D+00, & 0.0176742202382502D+00, & 0.8189638129323793D+00, & 0.7670005101060391D+00, & 0.0422082170395821D+00, & 0.1907912728543787D+00, & 0.1907912728543789D+00, & 0.0422082170395820D+00, & 0.7670005101060390D+00, & 0.6074178089715797D+00, & 0.0344163203969896D+00, & 0.3581658706314306D+00, & 0.3581658706314307D+00, & 0.0344163203969895D+00, & 0.6074178089715796D+00, & 0.8831620205339272D+00, & 0.0174529902610206D+00, & 0.0993849892050520D+00, & 0.0993849892050521D+00, & 0.0174529902610204D+00, & 0.8831620205339271D+00, & 0.5485392672636246D+00, & 0.0012278348447229D+00, & 0.4502328978916522D+00, & 0.4502328978916524D+00, & 0.0012278348447229D+00, & 0.5485392672636243D+00, & 0.4642737776346700D+00, & 0.0714524447306598D+00, & 0.4642737776346698D+00, & 0.4588765169470120D+00, & 0.2362631900663085D+00, & 0.3048602929866792D+00, & 0.3048602929866792D+00, & 0.2362631900663086D+00, & 0.4588765169470121D+00, & 0.6708934652005731D+00, & 0.0155229285287317D+00, & 0.3135836062706950D+00, & 0.3135836062706951D+00, & 0.0155229285287316D+00, & 0.6708934652005729D+00, & 0.8613456659624720D+00, & 0.0038480457708451D+00, & 0.1348062882666826D+00, & 0.1348062882666829D+00, & 0.0038480457708449D+00, & 0.8613456659624719D+00, & 0.6176772762453819D+00, & 0.1911613618773091D+00, & 0.1911613618773088D+00, & 0.8960993382441670D+00, & 0.0380724693230132D+00, & 0.0658281924328196D+00, & 0.0658281924328198D+00, & 0.0380724693230129D+00, & 0.8960993382441669D+00, & 0.9412999018131459D+00, & 0.0293500490934273D+00, & 0.0293500490934266D+00, & 0.3837095620178134D+00, & 0.3081452189910933D+00, & 0.3081452189910932D+00, & 0.9346369019266020D+00, & 0.0121702541539403D+00, & 0.0531928439194576D+00, & 0.0531928439194577D+00, & 0.0121702541539400D+00, & 0.9346369019266020D+00, & 0.7776434704232380D+00, & 0.1111782647883812D+00, & 0.1111782647883807D+00, & 0.9584934783193575D+00, & 0.0008585590446841D+00, & 0.0406479626359583D+00, & 0.0406479626359586D+00, & 0.0008585590446838D+00, & 0.9584934783193574D+00, & 0.5812165949773879D+00, & 0.0123358378103273D+00, & 0.4064475672122846D+00, & 0.4064475672122849D+00, & 0.0123358378103272D+00, & 0.5812165949773878D+00, & 0.3810023496034419D+00, & 0.2379953007931162D+00, & 0.3810023496034418D+00, & 0.4944809967477005D+00, & 0.0110380065045990D+00, & 0.4944809967477002D+00 /) w = (/ & 0.0030616831670682D+00, & 0.0030616831670682D+00, & 0.0030616831670682D+00, & 0.0030616831670682D+00, & 0.0030616831670682D+00, & 0.0030616831670682D+00, & 0.0049232719752900D+00, & 0.0049232719752900D+00, & 0.0049232719752900D+00, & 0.0049232719752900D+00, & 0.0049232719752900D+00, & 0.0049232719752900D+00, & 0.0033237208433952D+00, & 0.0033237208433952D+00, & 0.0033237208433952D+00, & 0.0033237208433952D+00, & 0.0033237208433952D+00, & 0.0033237208433952D+00, & 0.0047427364930338D+00, & 0.0047427364930338D+00, & 0.0047427364930338D+00, & 0.0047427364930338D+00, & 0.0047427364930338D+00, & 0.0047427364930338D+00, & 0.0041138012926497D+00, & 0.0041138012926497D+00, & 0.0041138012926497D+00, & 0.0041138012926497D+00, & 0.0041138012926497D+00, & 0.0041138012926497D+00, & 0.0052353425228938D+00, & 0.0052353425228938D+00, & 0.0052353425228938D+00, & 0.0052353425228938D+00, & 0.0052353425228938D+00, & 0.0052353425228938D+00, & 0.0001303399284527D+00, & 0.0001303399284527D+00, & 0.0001303399284527D+00, & 0.0001303399284527D+00, & 0.0001303399284527D+00, & 0.0001303399284527D+00, & 0.0076704945179086D+00, & 0.0076704945179086D+00, & 0.0076704945179086D+00, & 0.0052277042839384D+00, & 0.0052277042839384D+00, & 0.0052277042839384D+00, & 0.0052277042839384D+00, & 0.0052277042839384D+00, & 0.0052277042839384D+00, & 0.0066311375415485D+00, & 0.0066311375415485D+00, & 0.0066311375415485D+00, & 0.0066311375415485D+00, & 0.0066311375415485D+00, & 0.0066311375415485D+00, & 0.0068762957093961D+00, & 0.0068762957093961D+00, & 0.0068762957093961D+00, & 0.0006952346397171D+00, & 0.0006952346397171D+00, & 0.0006952346397171D+00, & 0.0006952346397171D+00, & 0.0006952346397171D+00, & 0.0006952346397171D+00, & 0.0069183724873925D+00, & 0.0069183724873925D+00, & 0.0069183724873925D+00, & 0.0069183724873925D+00, & 0.0069183724873925D+00, & 0.0069183724873925D+00, & 0.0080679977166382D+00, & 0.0080679977166382D+00, & 0.0080679977166382D+00, & 0.0010177068493549D+00, & 0.0010177068493549D+00, & 0.0010177068493549D+00, & 0.0010177068493549D+00, & 0.0010177068493549D+00, & 0.0010177068493549D+00, & 0.0045309912970645D+00, & 0.0045309912970645D+00, & 0.0045309912970645D+00, & 0.0045309912970645D+00, & 0.0045309912970645D+00, & 0.0045309912970645D+00, & 0.0023792804956386D+00, & 0.0023792804956386D+00, & 0.0023792804956386D+00, & 0.0023792804956386D+00, & 0.0023792804956386D+00, & 0.0023792804956386D+00, & 0.0012168791097054D+00, & 0.0012168791097054D+00, & 0.0012168791097054D+00, & 0.0012168791097054D+00, & 0.0012168791097054D+00, & 0.0012168791097054D+00, & 0.0031130272403783D+00, & 0.0031130272403783D+00, & 0.0031130272403783D+00, & 0.0031130272403783D+00, & 0.0031130272403783D+00, & 0.0031130272403783D+00, & 0.0006481853328131D+00, & 0.0006481853328131D+00, & 0.0006481853328131D+00, & 0.0006481853328131D+00, & 0.0006481853328131D+00, & 0.0006481853328131D+00, & 0.0083451647460546D+00, & 0.0083451647460546D+00, & 0.0083451647460546D+00, & 0.0083451647460546D+00, & 0.0083451647460546D+00, & 0.0083451647460546D+00, & 0.0061710606814515D+00, & 0.0061710606814515D+00, & 0.0061710606814515D+00, & 0.0089038028492518D+00, & 0.0089038028492518D+00, & 0.0089038028492518D+00, & 0.0089038028492518D+00, & 0.0089038028492518D+00, & 0.0089038028492518D+00, & 0.0047638139693883D+00, & 0.0047638139693883D+00, & 0.0047638139693883D+00, & 0.0047638139693883D+00, & 0.0047638139693883D+00, & 0.0047638139693883D+00, & 0.0012331434914374D+00, & 0.0012331434914374D+00, & 0.0012331434914374D+00, & 0.0012331434914374D+00, & 0.0012331434914374D+00, & 0.0012331434914374D+00, & 0.0052810362353661D+00, & 0.0052810362353661D+00, & 0.0052810362353661D+00, & 0.0052810362353661D+00, & 0.0052810362353661D+00, & 0.0052810362353661D+00, & 0.0072039581630510D+00, & 0.0072039581630510D+00, & 0.0072039581630510D+00, & 0.0072039581630510D+00, & 0.0072039581630510D+00, & 0.0072039581630510D+00, & 0.0025500464663513D+00, & 0.0025500464663513D+00, & 0.0025500464663513D+00, & 0.0025500464663513D+00, & 0.0025500464663513D+00, & 0.0025500464663513D+00, & 0.0040931211574027D+00, & 0.0040931211574027D+00, & 0.0040931211574027D+00, & 0.0040931211574027D+00, & 0.0040931211574027D+00, & 0.0040931211574027D+00, & 0.0044693917436126D+00, & 0.0044693917436126D+00, & 0.0044693917436126D+00, & 0.0044693917436126D+00, & 0.0044693917436126D+00, & 0.0044693917436126D+00, & 0.0021012224230352D+00, & 0.0021012224230352D+00, & 0.0021012224230352D+00, & 0.0021012224230352D+00, & 0.0021012224230352D+00, & 0.0021012224230352D+00, & 0.0008220891073142D+00, & 0.0008220891073142D+00, & 0.0008220891073142D+00, & 0.0008220891073142D+00, & 0.0008220891073142D+00, & 0.0008220891073142D+00, & 0.0066612336212475D+00, & 0.0066612336212475D+00, & 0.0066612336212475D+00, & 0.0102133456155291D+00, & 0.0102133456155291D+00, & 0.0102133456155291D+00, & 0.0102133456155291D+00, & 0.0102133456155291D+00, & 0.0102133456155291D+00, & 0.0030402213548301D+00, & 0.0030402213548301D+00, & 0.0030402213548301D+00, & 0.0030402213548301D+00, & 0.0030402213548301D+00, & 0.0030402213548301D+00, & 0.0011096101536171D+00, & 0.0011096101536171D+00, & 0.0011096101536171D+00, & 0.0011096101536171D+00, & 0.0011096101536171D+00, & 0.0011096101536171D+00, & 0.0080932250756891D+00, & 0.0080932250756891D+00, & 0.0080932250756891D+00, & 0.0026669011660035D+00, & 0.0026669011660035D+00, & 0.0026669011660035D+00, & 0.0026669011660035D+00, & 0.0026669011660035D+00, & 0.0026669011660035D+00, & 0.0015674237111509D+00, & 0.0015674237111509D+00, & 0.0015674237111509D+00, & 0.0110082761617136D+00, & 0.0110082761617136D+00, & 0.0110082761617136D+00, & 0.0013356087640650D+00, & 0.0013356087640650D+00, & 0.0013356087640650D+00, & 0.0013356087640650D+00, & 0.0013356087640650D+00, & 0.0013356087640650D+00, & 0.0054235489241326D+00, & 0.0054235489241326D+00, & 0.0054235489241326D+00, & 0.0002661778238934D+00, & 0.0002661778238934D+00, & 0.0002661778238934D+00, & 0.0002661778238934D+00, & 0.0002661778238934D+00, & 0.0002661778238934D+00, & 0.0028876869913215D+00, & 0.0028876869913215D+00, & 0.0028876869913215D+00, & 0.0028876869913215D+00, & 0.0028876869913215D+00, & 0.0028876869913215D+00, & 0.0105063460068171D+00, & 0.0105063460068171D+00, & 0.0105063460068171D+00, & 0.0028959157634686D+00, & 0.0028959157634686D+00, & 0.0028959157634686D+00 /) return end subroutine rule37 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule37() returns the rule of precision 37. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1023039321577603D+00, & 0.7953921356844791D+00, & 0.1023039321577607D+00, & 0.3160240964966399D+00, & 0.6501468128206388D+00, & 0.0338290906827213D+00, & 0.6501468128206388D+00, & 0.3160240964966400D+00, & 0.0338290906827212D+00, & 0.0350202358754684D+00, & 0.9299595282490629D+00, & 0.0350202358754688D+00, & 0.1053594119602819D+00, & 0.8614945984835296D+00, & 0.0331459895561886D+00, & 0.8614945984835296D+00, & 0.1053594119602819D+00, & 0.0331459895561881D+00, & 0.0749810217841138D+00, & 0.9229855021397688D+00, & 0.0020334760761175D+00, & 0.9229855021397688D+00, & 0.0749810217841139D+00, & 0.0020334760761171D+00, & 0.1194865933803552D+00, & 0.8250030034571860D+00, & 0.0555104031624590D+00, & 0.8250030034571859D+00, & 0.1194865933803553D+00, & 0.0555104031624586D+00, & 0.3192351650459891D+00, & 0.4427039878369861D+00, & 0.2380608471170247D+00, & 0.4427039878369861D+00, & 0.3192351650459891D+00, & 0.2380608471170247D+00, & 0.3917882577236701D+00, & 0.5329411933388201D+00, & 0.0752705489375098D+00, & 0.5329411933388201D+00, & 0.3917882577236701D+00, & 0.0752705489375098D+00, & 0.2592434904565495D+00, & 0.4815130190869007D+00, & 0.2592434904565497D+00, & 0.3175434072141983D+00, & 0.6288357611566886D+00, & 0.0536208316291132D+00, & 0.6288357611566886D+00, & 0.3175434072141983D+00, & 0.0536208316291130D+00, & 0.3267645245927318D+00, & 0.5819407083122254D+00, & 0.0912947670950428D+00, & 0.5819407083122254D+00, & 0.3267645245927318D+00, & 0.0912947670950427D+00, & 0.3187496668271801D+00, & 0.5461345841025351D+00, & 0.1351157490702847D+00, & 0.5461345841025351D+00, & 0.3187496668271802D+00, & 0.1351157490702846D+00, & 0.0674578790813868D+00, & 0.8917719971619344D+00, & 0.0407701237566788D+00, & 0.8917719971619346D+00, & 0.0674578790813870D+00, & 0.0407701237566784D+00, & 0.0183794409210812D+00, & 0.9786302812023548D+00, & 0.0029902778765640D+00, & 0.9786302812023550D+00, & 0.0183794409210812D+00, & 0.0029902778765637D+00, & 0.0476569358622159D+00, & 0.9350921036839764D+00, & 0.0172509604538077D+00, & 0.9350921036839764D+00, & 0.0476569358622161D+00, & 0.0172509604538073D+00, & 0.3357227870380101D+00, & 0.4831608037664580D+00, & 0.1811164091955319D+00, & 0.4831608037664580D+00, & 0.3357227870380101D+00, & 0.1811164091955318D+00, & 0.1394412358722927D+00, & 0.7211175282554143D+00, & 0.1394412358722930D+00, & 0.4611684588908100D+00, & 0.4611684588908100D+00, & 0.0776630822183799D+00, & 0.1356716079161176D+00, & 0.7741981202355922D+00, & 0.0901302718482901D+00, & 0.7741981202355922D+00, & 0.1356716079161178D+00, & 0.0901302718482899D+00, & 0.0417693614359698D+00, & 0.9542135414767989D+00, & 0.0040170970872315D+00, & 0.9542135414767989D+00, & 0.0417693614359699D+00, & 0.0040170970872310D+00, & 0.3791537179550378D+00, & 0.3791537179550378D+00, & 0.2416925640899243D+00, & 0.1912637374380762D+00, & 0.7277709423326696D+00, & 0.0809653202292542D+00, & 0.7277709423326697D+00, & 0.1912637374380762D+00, & 0.0809653202292539D+00, & 0.4489203299566428D+00, & 0.5341982115332263D+00, & 0.0168814585101307D+00, & 0.5341982115332264D+00, & 0.4489203299566429D+00, & 0.0168814585101307D+00, & 0.3970833791349885D+00, & 0.5614399423313745D+00, & 0.0414766785336368D+00, & 0.5614399423313746D+00, & 0.3970833791349885D+00, & 0.0414766785336368D+00, & 0.0862263440628872D+00, & 0.9000390697749006D+00, & 0.0137345861622123D+00, & 0.9000390697749007D+00, & 0.0862263440628872D+00, & 0.0137345861622120D+00, & 0.0173411753639024D+00, & 0.9653176492721949D+00, & 0.0173411753639029D+00, & 0.2814879599422820D+00, & 0.7005934357274263D+00, & 0.0179186043302919D+00, & 0.7005934357274262D+00, & 0.2814879599422819D+00, & 0.0179186043302916D+00, & 0.1923768347442593D+00, & 0.6791517751989478D+00, & 0.1284713900567929D+00, & 0.6791517751989478D+00, & 0.1923768347442593D+00, & 0.1284713900567927D+00, & 0.2517942475174331D+00, & 0.6108845927509712D+00, & 0.1373211597315956D+00, & 0.6108845927509713D+00, & 0.2517942475174332D+00, & 0.1373211597315955D+00, & 0.0779889301806426D+00, & 0.8440221396387144D+00, & 0.0779889301806430D+00, & 0.3650347949363280D+00, & 0.6175233785692882D+00, & 0.0174418264943838D+00, & 0.6175233785692882D+00, & 0.3650347949363280D+00, & 0.0174418264943837D+00, & 0.4792449355569203D+00, & 0.4792449355569204D+00, & 0.0415101288861593D+00, & 0.4120614054796895D+00, & 0.4120614054796895D+00, & 0.1758771890406210D+00, & 0.2571566355502535D+00, & 0.6566451941716462D+00, & 0.0861981702781003D+00, & 0.6566451941716462D+00, & 0.2571566355502535D+00, & 0.0861981702781001D+00, & 0.4984105744139570D+00, & 0.4984105744139570D+00, & 0.0031788511720860D+00, & 0.3091259486853505D+00, & 0.3817481026292989D+00, & 0.3091259486853505D+00, & 0.1241816119341110D+00, & 0.8724071202650543D+00, & 0.0034112678008348D+00, & 0.8724071202650543D+00, & 0.1241816119341111D+00, & 0.0034112678008344D+00, & 0.1716507278093692D+00, & 0.7837937554788413D+00, & 0.0445555167117896D+00, & 0.7837937554788413D+00, & 0.1716507278093692D+00, & 0.0445555167117893D+00, & 0.3977231091982856D+00, & 0.4801793419171518D+00, & 0.1220975488845627D+00, & 0.4801793419171518D+00, & 0.3977231091982856D+00, & 0.1220975488845626D+00, & 0.0036715668219831D+00, & 0.9926568663560335D+00, & 0.0036715668219836D+00, & 0.2578966456698565D+00, & 0.5463929830937153D+00, & 0.1957103712364281D+00, & 0.5463929830937154D+00, & 0.2578966456698565D+00, & 0.1957103712364280D+00, & 0.1441500744811936D+00, & 0.8375385335389723D+00, & 0.0183113919798341D+00, & 0.8375385335389725D+00, & 0.1441500744811937D+00, & 0.0183113919798338D+00, & 0.4122595610017910D+00, & 0.5844781809630051D+00, & 0.0032622580352039D+00, & 0.5844781809630052D+00, & 0.4122595610017911D+00, & 0.0032622580352037D+00, & 0.2524284647914363D+00, & 0.7440960937012480D+00, & 0.0034754415073158D+00, & 0.7440960937012480D+00, & 0.2524284647914364D+00, & 0.0034754415073155D+00, & 0.3293669274857745D+00, & 0.6670942824316437D+00, & 0.0035387900825819D+00, & 0.6670942824316437D+00, & 0.3293669274857746D+00, & 0.0035387900825817D+00, & 0.2095814817005154D+00, & 0.7715735792437323D+00, & 0.0188449390557522D+00, & 0.7715735792437323D+00, & 0.2095814817005155D+00, & 0.0188449390557521D+00, & 0.1836401694462322D+00, & 0.8127217284450714D+00, & 0.0036381021086965D+00, & 0.8127217284450714D+00, & 0.1836401694462323D+00, & 0.0036381021086962D+00, & 0.2416962324693375D+00, & 0.7125504805693451D+00, & 0.0457532869613175D+00, & 0.7125504805693450D+00, & 0.2416962324693376D+00, & 0.0457532869613173D+00, & 0.1893642612001962D+00, & 0.6212714775996074D+00, & 0.1893642612001963D+00 /) b = (/ & 0.1023039321577605D+00, & 0.1023039321577603D+00, & 0.7953921356844793D+00, & 0.0338290906827213D+00, & 0.3160240964966399D+00, & 0.6501468128206390D+00, & 0.0338290906827213D+00, & 0.6501468128206389D+00, & 0.3160240964966402D+00, & 0.0350202358754687D+00, & 0.0350202358754684D+00, & 0.9299595282490630D+00, & 0.0331459895561884D+00, & 0.1053594119602819D+00, & 0.8614945984835296D+00, & 0.0331459895561884D+00, & 0.8614945984835299D+00, & 0.1053594119602822D+00, & 0.0020334760761173D+00, & 0.0749810217841138D+00, & 0.9229855021397689D+00, & 0.0020334760761173D+00, & 0.9229855021397689D+00, & 0.0749810217841142D+00, & 0.0555104031624589D+00, & 0.1194865933803552D+00, & 0.8250030034571860D+00, & 0.0555104031624589D+00, & 0.8250030034571860D+00, & 0.1194865933803555D+00, & 0.2380608471170249D+00, & 0.3192351650459893D+00, & 0.4427039878369862D+00, & 0.2380608471170249D+00, & 0.4427039878369862D+00, & 0.3192351650459893D+00, & 0.0752705489375098D+00, & 0.3917882577236702D+00, & 0.5329411933388202D+00, & 0.0752705489375098D+00, & 0.5329411933388202D+00, & 0.3917882577236704D+00, & 0.2592434904565497D+00, & 0.2592434904565497D+00, & 0.4815130190869009D+00, & 0.0536208316291131D+00, & 0.3175434072141983D+00, & 0.6288357611566887D+00, & 0.0536208316291131D+00, & 0.6288357611566887D+00, & 0.3175434072141985D+00, & 0.0912947670950428D+00, & 0.3267645245927318D+00, & 0.5819407083122257D+00, & 0.0912947670950428D+00, & 0.5819407083122256D+00, & 0.3267645245927320D+00, & 0.1351157490702847D+00, & 0.3187496668271802D+00, & 0.5461345841025353D+00, & 0.1351157490702847D+00, & 0.5461345841025353D+00, & 0.3187496668271803D+00, & 0.0407701237566787D+00, & 0.0674578790813868D+00, & 0.8917719971619346D+00, & 0.0407701237566787D+00, & 0.8917719971619346D+00, & 0.0674578790813871D+00, & 0.0029902778765639D+00, & 0.0183794409210811D+00, & 0.9786302812023551D+00, & 0.0029902778765639D+00, & 0.9786302812023551D+00, & 0.0183794409210815D+00, & 0.0172509604538075D+00, & 0.0476569358622160D+00, & 0.9350921036839765D+00, & 0.0172509604538075D+00, & 0.9350921036839765D+00, & 0.0476569358622163D+00, & 0.1811164091955320D+00, & 0.3357227870380101D+00, & 0.4831608037664581D+00, & 0.1811164091955320D+00, & 0.4831608037664581D+00, & 0.3357227870380102D+00, & 0.1394412358722930D+00, & 0.1394412358722927D+00, & 0.7211175282554145D+00, & 0.0776630822183800D+00, & 0.4611684588908101D+00, & 0.4611684588908102D+00, & 0.0901302718482901D+00, & 0.1356716079161177D+00, & 0.7741981202355923D+00, & 0.0901302718482901D+00, & 0.7741981202355923D+00, & 0.1356716079161179D+00, & 0.0040170970872313D+00, & 0.0417693614359697D+00, & 0.9542135414767990D+00, & 0.0040170970872313D+00, & 0.9542135414767990D+00, & 0.0417693614359701D+00, & 0.2416925640899244D+00, & 0.3791537179550379D+00, & 0.3791537179550379D+00, & 0.0809653202292541D+00, & 0.1912637374380763D+00, & 0.7277709423326698D+00, & 0.0809653202292541D+00, & 0.7277709423326699D+00, & 0.1912637374380765D+00, & 0.0168814585101308D+00, & 0.4489203299566429D+00, & 0.5341982115332266D+00, & 0.0168814585101308D+00, & 0.5341982115332264D+00, & 0.4489203299566431D+00, & 0.0414766785336369D+00, & 0.3970833791349886D+00, & 0.5614399423313748D+00, & 0.0414766785336369D+00, & 0.5614399423313746D+00, & 0.3970833791349888D+00, & 0.0137345861622122D+00, & 0.0862263440628872D+00, & 0.9000390697749008D+00, & 0.0137345861622122D+00, & 0.9000390697749008D+00, & 0.0862263440628875D+00, & 0.0173411753639027D+00, & 0.0173411753639024D+00, & 0.9653176492721949D+00, & 0.0179186043302918D+00, & 0.2814879599422820D+00, & 0.7005934357274264D+00, & 0.0179186043302918D+00, & 0.7005934357274264D+00, & 0.2814879599422823D+00, & 0.1284713900567929D+00, & 0.1923768347442593D+00, & 0.6791517751989480D+00, & 0.1284713900567929D+00, & 0.6791517751989480D+00, & 0.1923768347442595D+00, & 0.1373211597315956D+00, & 0.2517942475174332D+00, & 0.6108845927509714D+00, & 0.1373211597315956D+00, & 0.6108845927509713D+00, & 0.2517942475174334D+00, & 0.0779889301806429D+00, & 0.0779889301806426D+00, & 0.8440221396387146D+00, & 0.0174418264943838D+00, & 0.3650347949363281D+00, & 0.6175233785692883D+00, & 0.0174418264943838D+00, & 0.6175233785692883D+00, & 0.3650347949363282D+00, & 0.0415101288861593D+00, & 0.4792449355569204D+00, & 0.4792449355569205D+00, & 0.1758771890406211D+00, & 0.4120614054796896D+00, & 0.4120614054796897D+00, & 0.0861981702781003D+00, & 0.2571566355502535D+00, & 0.6566451941716464D+00, & 0.0861981702781003D+00, & 0.6566451941716464D+00, & 0.2571566355502538D+00, & 0.0031788511720861D+00, & 0.4984105744139570D+00, & 0.4984105744139572D+00, & 0.3091259486853506D+00, & 0.3091259486853506D+00, & 0.3817481026292990D+00, & 0.0034112678008347D+00, & 0.1241816119341110D+00, & 0.8724071202650543D+00, & 0.0034112678008347D+00, & 0.8724071202650543D+00, & 0.1241816119341114D+00, & 0.0445555167117895D+00, & 0.1716507278093692D+00, & 0.7837937554788414D+00, & 0.0445555167117895D+00, & 0.7837937554788414D+00, & 0.1716507278093694D+00, & 0.1220975488845627D+00, & 0.3977231091982856D+00, & 0.4801793419171519D+00, & 0.1220975488845627D+00, & 0.4801793419171518D+00, & 0.3977231091982857D+00, & 0.0036715668219834D+00, & 0.0036715668219831D+00, & 0.9926568663560336D+00, & 0.1957103712364281D+00, & 0.2578966456698565D+00, & 0.5463929830937155D+00, & 0.1957103712364281D+00, & 0.5463929830937155D+00, & 0.2578966456698567D+00, & 0.0183113919798340D+00, & 0.1441500744811936D+00, & 0.8375385335389725D+00, & 0.0183113919798340D+00, & 0.8375385335389725D+00, & 0.1441500744811939D+00, & 0.0032622580352038D+00, & 0.4122595610017911D+00, & 0.5844781809630053D+00, & 0.0032622580352038D+00, & 0.5844781809630052D+00, & 0.4122595610017913D+00, & 0.0034754415073157D+00, & 0.2524284647914364D+00, & 0.7440960937012481D+00, & 0.0034754415073157D+00, & 0.7440960937012481D+00, & 0.2524284647914367D+00, & 0.0035387900825818D+00, & 0.3293669274857746D+00, & 0.6670942824316438D+00, & 0.0035387900825818D+00, & 0.6670942824316437D+00, & 0.3293669274857748D+00, & 0.0188449390557523D+00, & 0.2095814817005154D+00, & 0.7715735792437326D+00, & 0.0188449390557523D+00, & 0.7715735792437324D+00, & 0.2095814817005157D+00, & 0.0036381021086963D+00, & 0.1836401694462322D+00, & 0.8127217284450715D+00, & 0.0036381021086963D+00, & 0.8127217284450715D+00, & 0.1836401694462325D+00, & 0.0457532869613174D+00, & 0.2416962324693375D+00, & 0.7125504805693452D+00, & 0.0457532869613174D+00, & 0.7125504805693452D+00, & 0.2416962324693378D+00, & 0.1893642612001964D+00, & 0.1893642612001962D+00, & 0.6212714775996077D+00 /) c = (/ & 0.7953921356844791D+00, & 0.1023039321577606D+00, & 0.1023039321577600D+00, & 0.6501468128206388D+00, & 0.0338290906827213D+00, & 0.3160240964966398D+00, & 0.3160240964966399D+00, & 0.0338290906827211D+00, & 0.6501468128206387D+00, & 0.9299595282490629D+00, & 0.0350202358754687D+00, & 0.0350202358754682D+00, & 0.8614945984835297D+00, & 0.0331459895561885D+00, & 0.1053594119602818D+00, & 0.1053594119602820D+00, & 0.0331459895561882D+00, & 0.8614945984835297D+00, & 0.9229855021397688D+00, & 0.0020334760761174D+00, & 0.0749810217841136D+00, & 0.0749810217841139D+00, & 0.0020334760761173D+00, & 0.9229855021397688D+00, & 0.8250030034571860D+00, & 0.0555104031624588D+00, & 0.1194865933803551D+00, & 0.1194865933803552D+00, & 0.0555104031624587D+00, & 0.8250030034571859D+00, & 0.4427039878369860D+00, & 0.2380608471170247D+00, & 0.3192351650459891D+00, & 0.3192351650459891D+00, & 0.2380608471170248D+00, & 0.4427039878369860D+00, & 0.5329411933388201D+00, & 0.0752705489375098D+00, & 0.3917882577236700D+00, & 0.3917882577236701D+00, & 0.0752705489375097D+00, & 0.5329411933388200D+00, & 0.4815130190869008D+00, & 0.2592434904565497D+00, & 0.2592434904565494D+00, & 0.6288357611566886D+00, & 0.0536208316291131D+00, & 0.3175434072141982D+00, & 0.3175434072141983D+00, & 0.0536208316291130D+00, & 0.6288357611566884D+00, & 0.5819407083122254D+00, & 0.0912947670950428D+00, & 0.3267645245927315D+00, & 0.3267645245927318D+00, & 0.0912947670950427D+00, & 0.5819407083122253D+00, & 0.5461345841025352D+00, & 0.1351157490702847D+00, & 0.3187496668271800D+00, & 0.3187496668271802D+00, & 0.1351157490702845D+00, & 0.5461345841025351D+00, & 0.8917719971619346D+00, & 0.0407701237566787D+00, & 0.0674578790813867D+00, & 0.0674578790813868D+00, & 0.0407701237566785D+00, & 0.8917719971619344D+00, & 0.9786302812023550D+00, & 0.0029902778765640D+00, & 0.0183794409210809D+00, & 0.0183794409210811D+00, & 0.0029902778765637D+00, & 0.9786302812023547D+00, & 0.9350921036839765D+00, & 0.0172509604538076D+00, & 0.0476569358622158D+00, & 0.0476569358622160D+00, & 0.0172509604538074D+00, & 0.9350921036839764D+00, & 0.4831608037664580D+00, & 0.1811164091955319D+00, & 0.3357227870380099D+00, & 0.3357227870380101D+00, & 0.1811164091955318D+00, & 0.4831608037664579D+00, & 0.7211175282554143D+00, & 0.1394412358722930D+00, & 0.1394412358722925D+00, & 0.4611684588908100D+00, & 0.0776630822183799D+00, & 0.4611684588908099D+00, & 0.7741981202355923D+00, & 0.0901302718482901D+00, & 0.1356716079161175D+00, & 0.1356716079161177D+00, & 0.0901302718482899D+00, & 0.7741981202355923D+00, & 0.9542135414767989D+00, & 0.0040170970872313D+00, & 0.0417693614359694D+00, & 0.0417693614359698D+00, & 0.0040170970872310D+00, & 0.9542135414767989D+00, & 0.3791537179550378D+00, & 0.2416925640899242D+00, & 0.3791537179550377D+00, & 0.7277709423326697D+00, & 0.0809653202292542D+00, & 0.1912637374380760D+00, & 0.1912637374380762D+00, & 0.0809653202292538D+00, & 0.7277709423326697D+00, & 0.5341982115332263D+00, & 0.0168814585101308D+00, & 0.4489203299566428D+00, & 0.4489203299566428D+00, & 0.0168814585101307D+00, & 0.5341982115332262D+00, & 0.5614399423313746D+00, & 0.0414766785336369D+00, & 0.3970833791349883D+00, & 0.3970833791349885D+00, & 0.0414766785336368D+00, & 0.5614399423313745D+00, & 0.9000390697749007D+00, & 0.0137345861622123D+00, & 0.0862263440628869D+00, & 0.0862263440628872D+00, & 0.0137345861622120D+00, & 0.9000390697749004D+00, & 0.9653176492721949D+00, & 0.0173411753639027D+00, & 0.0173411753639022D+00, & 0.7005934357274263D+00, & 0.0179186043302917D+00, & 0.2814879599422817D+00, & 0.2814879599422820D+00, & 0.0179186043302917D+00, & 0.7005934357274261D+00, & 0.6791517751989478D+00, & 0.1284713900567929D+00, & 0.1923768347442592D+00, & 0.1923768347442593D+00, & 0.1284713900567928D+00, & 0.6791517751989478D+00, & 0.6108845927509713D+00, & 0.1373211597315956D+00, & 0.2517942475174331D+00, & 0.2517942475174331D+00, & 0.1373211597315954D+00, & 0.6108845927509711D+00, & 0.8440221396387144D+00, & 0.0779889301806430D+00, & 0.0779889301806423D+00, & 0.6175233785692882D+00, & 0.0174418264943837D+00, & 0.3650347949363278D+00, & 0.3650347949363280D+00, & 0.0174418264943837D+00, & 0.6175233785692880D+00, & 0.4792449355569203D+00, & 0.0415101288861592D+00, & 0.4792449355569202D+00, & 0.4120614054796894D+00, & 0.1758771890406209D+00, & 0.4120614054796893D+00, & 0.6566451941716462D+00, & 0.0861981702781002D+00, & 0.2571566355502534D+00, & 0.2571566355502534D+00, & 0.0861981702781002D+00, & 0.6566451941716460D+00, & 0.4984105744139569D+00, & 0.0031788511720860D+00, & 0.4984105744139568D+00, & 0.3817481026292989D+00, & 0.3091259486853504D+00, & 0.3091259486853505D+00, & 0.8724071202650543D+00, & 0.0034112678008347D+00, & 0.1241816119341108D+00, & 0.1241816119341110D+00, & 0.0034112678008346D+00, & 0.8724071202650542D+00, & 0.7837937554788413D+00, & 0.0445555167117895D+00, & 0.1716507278093690D+00, & 0.1716507278093692D+00, & 0.0445555167117894D+00, & 0.7837937554788413D+00, & 0.4801793419171517D+00, & 0.1220975488845625D+00, & 0.3977231091982854D+00, & 0.3977231091982855D+00, & 0.1220975488845626D+00, & 0.4801793419171517D+00, & 0.9926568663560335D+00, & 0.0036715668219834D+00, & 0.0036715668219829D+00, & 0.5463929830937153D+00, & 0.1957103712364281D+00, & 0.2578966456698564D+00, & 0.2578966456698564D+00, & 0.1957103712364280D+00, & 0.5463929830937153D+00, & 0.8375385335389723D+00, & 0.0183113919798340D+00, & 0.1441500744811934D+00, & 0.1441500744811935D+00, & 0.0183113919798339D+00, & 0.8375385335389723D+00, & 0.5844781809630052D+00, & 0.0032622580352038D+00, & 0.4122595610017908D+00, & 0.4122595610017910D+00, & 0.0032622580352036D+00, & 0.5844781809630050D+00, & 0.7440960937012480D+00, & 0.0034754415073157D+00, & 0.2524284647914362D+00, & 0.2524284647914363D+00, & 0.0034754415073156D+00, & 0.7440960937012479D+00, & 0.6670942824316437D+00, & 0.0035387900825817D+00, & 0.3293669274857743D+00, & 0.3293669274857745D+00, & 0.0035387900825817D+00, & 0.6670942824316435D+00, & 0.7715735792437323D+00, & 0.0188449390557523D+00, & 0.2095814817005152D+00, & 0.2095814817005154D+00, & 0.0188449390557521D+00, & 0.7715735792437322D+00, & 0.8127217284450715D+00, & 0.0036381021086964D+00, & 0.1836401694462321D+00, & 0.1836401694462323D+00, & 0.0036381021086961D+00, & 0.8127217284450713D+00, & 0.7125504805693451D+00, & 0.0457532869613174D+00, & 0.2416962324693372D+00, & 0.2416962324693376D+00, & 0.0457532869613172D+00, & 0.7125504805693449D+00, & 0.6212714775996074D+00, & 0.1893642612001964D+00, & 0.1893642612001961D+00 /) w = (/ & 0.0015139897718580D+00, & 0.0015139897718580D+00, & 0.0015139897718580D+00, & 0.0020991920973495D+00, & 0.0020991920973495D+00, & 0.0020991920973495D+00, & 0.0020991920973495D+00, & 0.0020991920973495D+00, & 0.0020991920973495D+00, & 0.0011046836690446D+00, & 0.0011046836690446D+00, & 0.0011046836690446D+00, & 0.0019226251721821D+00, & 0.0019226251721821D+00, & 0.0019226251721821D+00, & 0.0019226251721821D+00, & 0.0019226251721821D+00, & 0.0019226251721821D+00, & 0.0004804430100019D+00, & 0.0004804430100019D+00, & 0.0004804430100019D+00, & 0.0004804430100019D+00, & 0.0004804430100019D+00, & 0.0004804430100019D+00, & 0.0030325474600895D+00, & 0.0030325474600895D+00, & 0.0030325474600895D+00, & 0.0030325474600895D+00, & 0.0030325474600895D+00, & 0.0030325474600895D+00, & 0.0073189063292417D+00, & 0.0073189063292417D+00, & 0.0073189063292417D+00, & 0.0073189063292417D+00, & 0.0073189063292417D+00, & 0.0073189063292417D+00, & 0.0053883188429810D+00, & 0.0053883188429810D+00, & 0.0053883188429810D+00, & 0.0053883188429810D+00, & 0.0053883188429810D+00, & 0.0053883188429810D+00, & 0.0075850923563705D+00, & 0.0075850923563705D+00, & 0.0075850923563705D+00, & 0.0045692159189815D+00, & 0.0045692159189815D+00, & 0.0045692159189815D+00, & 0.0045692159189815D+00, & 0.0045692159189815D+00, & 0.0045692159189815D+00, & 0.0057203599064585D+00, & 0.0057203599064585D+00, & 0.0057203599064585D+00, & 0.0057203599064585D+00, & 0.0057203599064585D+00, & 0.0057203599064585D+00, & 0.0067120048490857D+00, & 0.0067120048490857D+00, & 0.0067120048490857D+00, & 0.0067120048490857D+00, & 0.0067120048490857D+00, & 0.0067120048490857D+00, & 0.0023170775093131D+00, & 0.0023170775093131D+00, & 0.0023170775093131D+00, & 0.0023170775093131D+00, & 0.0023170775093131D+00, & 0.0023170775093131D+00, & 0.0003086692619705D+00, & 0.0003086692619705D+00, & 0.0003086692619705D+00, & 0.0003086692619705D+00, & 0.0003086692619705D+00, & 0.0003086692619705D+00, & 0.0012047027694411D+00, & 0.0012047027694411D+00, & 0.0012047027694411D+00, & 0.0012047027694411D+00, & 0.0012047027694411D+00, & 0.0012047027694411D+00, & 0.0081637462521436D+00, & 0.0081637462521436D+00, & 0.0081637462521436D+00, & 0.0081637462521436D+00, & 0.0081637462521436D+00, & 0.0081637462521436D+00, & 0.0052500601543288D+00, & 0.0052500601543288D+00, & 0.0052500601543288D+00, & 0.0058808346792778D+00, & 0.0058808346792778D+00, & 0.0058808346792778D+00, & 0.0043645240281899D+00, & 0.0043645240281899D+00, & 0.0043645240281899D+00, & 0.0043645240281899D+00, & 0.0043645240281899D+00, & 0.0043645240281899D+00, & 0.0005497965506473D+00, & 0.0005497965506473D+00, & 0.0005497965506473D+00, & 0.0005497965506473D+00, & 0.0005497965506473D+00, & 0.0005497965506473D+00, & 0.0086445565740853D+00, & 0.0086445565740853D+00, & 0.0086445565740853D+00, & 0.0052464381586922D+00, & 0.0052464381586922D+00, & 0.0052464381586922D+00, & 0.0052464381586922D+00, & 0.0052464381586922D+00, & 0.0052464381586922D+00, & 0.0032584894563913D+00, & 0.0032584894563913D+00, & 0.0032584894563913D+00, & 0.0032584894563913D+00, & 0.0032584894563913D+00, & 0.0032584894563913D+00, & 0.0047812349883804D+00, & 0.0047812349883804D+00, & 0.0047812349883804D+00, & 0.0047812349883804D+00, & 0.0047812349883804D+00, & 0.0047812349883804D+00, & 0.0016087719028869D+00, & 0.0016087719028869D+00, & 0.0016087719028869D+00, & 0.0016087719028869D+00, & 0.0016087719028869D+00, & 0.0016087719028869D+00, & 0.0008775872521508D+00, & 0.0008775872521508D+00, & 0.0008775872521508D+00, & 0.0029825665052993D+00, & 0.0029825665052993D+00, & 0.0029825665052993D+00, & 0.0029825665052993D+00, & 0.0029825665052993D+00, & 0.0029825665052993D+00, & 0.0060939488435529D+00, & 0.0060939488435529D+00, & 0.0060939488435529D+00, & 0.0060939488435529D+00, & 0.0060939488435529D+00, & 0.0060939488435529D+00, & 0.0070873407460566D+00, & 0.0070873407460566D+00, & 0.0070873407460566D+00, & 0.0070873407460566D+00, & 0.0070873407460566D+00, & 0.0070873407460566D+00, & 0.0035862336027497D+00, & 0.0035862336027497D+00, & 0.0035862336027497D+00, & 0.0031497526280812D+00, & 0.0031497526280812D+00, & 0.0031497526280812D+00, & 0.0031497526280812D+00, & 0.0031497526280812D+00, & 0.0031497526280812D+00, & 0.0049992428284758D+00, & 0.0049992428284758D+00, & 0.0049992428284758D+00, & 0.0090788425055397D+00, & 0.0090788425055397D+00, & 0.0090788425055397D+00, & 0.0062518699531210D+00, & 0.0062518699531210D+00, & 0.0062518699531210D+00, & 0.0062518699531210D+00, & 0.0062518699531210D+00, & 0.0062518699531210D+00, & 0.0014156781091945D+00, & 0.0014156781091945D+00, & 0.0014156781091945D+00, & 0.0102066366491736D+00, & 0.0102066366491736D+00, & 0.0102066366491736D+00, & 0.0009493053225472D+00, & 0.0009493053225472D+00, & 0.0009493053225472D+00, & 0.0009493053225472D+00, & 0.0009493053225472D+00, & 0.0009493053225472D+00, & 0.0040312520842928D+00, & 0.0040312520842928D+00, & 0.0040312520842928D+00, & 0.0040312520842928D+00, & 0.0040312520842928D+00, & 0.0040312520842928D+00, & 0.0081722175482304D+00, & 0.0081722175482304D+00, & 0.0081722175482304D+00, & 0.0081722175482304D+00, & 0.0081722175482304D+00, & 0.0081722175482304D+00, & 0.0001732953357809D+00, & 0.0001732953357809D+00, & 0.0001732953357809D+00, & 0.0089586590287218D+00, & 0.0089586590287218D+00, & 0.0089586590287218D+00, & 0.0089586590287218D+00, & 0.0089586590287218D+00, & 0.0089586590287218D+00, & 0.0024620987414923D+00, & 0.0024620987414923D+00, & 0.0024620987414923D+00, & 0.0024620987414923D+00, & 0.0024620987414923D+00, & 0.0024620987414923D+00, & 0.0014212929213219D+00, & 0.0014212929213219D+00, & 0.0014212929213219D+00, & 0.0014212929213219D+00, & 0.0014212929213219D+00, & 0.0014212929213219D+00, & 0.0013051564959187D+00, & 0.0013051564959187D+00, & 0.0013051564959187D+00, & 0.0013051564959187D+00, & 0.0013051564959187D+00, & 0.0013051564959187D+00, & 0.0014459095277887D+00, & 0.0014459095277887D+00, & 0.0014459095277887D+00, & 0.0014459095277887D+00, & 0.0014459095277887D+00, & 0.0014459095277887D+00, & 0.0029345950580795D+00, & 0.0029345950580795D+00, & 0.0029345950580795D+00, & 0.0029345950580795D+00, & 0.0029345950580795D+00, & 0.0029345950580795D+00, & 0.0011964590052698D+00, & 0.0011964590052698D+00, & 0.0011964590052698D+00, & 0.0011964590052698D+00, & 0.0011964590052698D+00, & 0.0011964590052698D+00, & 0.0048735044199229D+00, & 0.0048735044199229D+00, & 0.0048735044199229D+00, & 0.0048735044199229D+00, & 0.0048735044199229D+00, & 0.0048735044199229D+00, & 0.0082906132570537D+00, & 0.0082906132570537D+00, & 0.0082906132570537D+00 /) return end subroutine rule38 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule38() returns the rule of precision 38. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4590721360317646D+00, & 0.4590721360317646D+00, & 0.0818557279364708D+00, & 0.2837655147017407D+00, & 0.6639373713962480D+00, & 0.0522971139020114D+00, & 0.6639373713962479D+00, & 0.2837655147017407D+00, & 0.0522971139020114D+00, & 0.3932680062553601D+00, & 0.3932680062553601D+00, & 0.2134639874892798D+00, & 0.1285165649696939D+00, & 0.7724036723284647D+00, & 0.0990797627018414D+00, & 0.7724036723284647D+00, & 0.1285165649696941D+00, & 0.0990797627018411D+00, & 0.4681825892069357D+00, & 0.4681825892069357D+00, & 0.0636348215861285D+00, & 0.0413075041428614D+00, & 0.9566280907078333D+00, & 0.0020644051493054D+00, & 0.9566280907078334D+00, & 0.0413075041428616D+00, & 0.0020644051493049D+00, & 0.0892719800534145D+00, & 0.8739978442972371D+00, & 0.0367301756493484D+00, & 0.8739978442972371D+00, & 0.0892719800534145D+00, & 0.0367301756493481D+00, & 0.3372052923179872D+00, & 0.4368488831942271D+00, & 0.2259458244877856D+00, & 0.4368488831942271D+00, & 0.3372052923179872D+00, & 0.2259458244877856D+00, & 0.2738513741241787D+00, & 0.6934474438857674D+00, & 0.0327011819900538D+00, & 0.6934474438857675D+00, & 0.2738513741241788D+00, & 0.0327011819900536D+00, & 0.0399162626294194D+00, & 0.9470142283262505D+00, & 0.0130695090443302D+00, & 0.9470142283262506D+00, & 0.0399162626294196D+00, & 0.0130695090443297D+00, & 0.0175045040462673D+00, & 0.9649909919074650D+00, & 0.0175045040462677D+00, & 0.3081068327593843D+00, & 0.6181755526695998D+00, & 0.0737176145710159D+00, & 0.6181755526695998D+00, & 0.3081068327593843D+00, & 0.0737176145710158D+00, & 0.1454801146528607D+00, & 0.7090397706942783D+00, & 0.1454801146528609D+00, & 0.2196247131384356D+00, & 0.7776714046470208D+00, & 0.0027038822145437D+00, & 0.7776714046470208D+00, & 0.2196247131384357D+00, & 0.0027038822145434D+00, & 0.2734646071142814D+00, & 0.5073771294396898D+00, & 0.2191582634460287D+00, & 0.5073771294396898D+00, & 0.2734646071142814D+00, & 0.2191582634460286D+00, & 0.0686830028555527D+00, & 0.9105941852629332D+00, & 0.0207228118815142D+00, & 0.9105941852629332D+00, & 0.0686830028555528D+00, & 0.0207228118815138D+00, & 0.1830135998401795D+00, & 0.7163646792677445D+00, & 0.1006217208920760D+00, & 0.7163646792677445D+00, & 0.1830135998401795D+00, & 0.1006217208920759D+00, & 0.0030471742663605D+00, & 0.9939056514672787D+00, & 0.0030471742663609D+00, & 0.2287994832299253D+00, & 0.7017106989365653D+00, & 0.0694898178335093D+00, & 0.7017106989365655D+00, & 0.2287994832299252D+00, & 0.0694898178335091D+00, & 0.0587361601120220D+00, & 0.8825276797759557D+00, & 0.0587361601120223D+00, & 0.1018827114869391D+00, & 0.8297399330905469D+00, & 0.0683773554225139D+00, & 0.8297399330905471D+00, & 0.1018827114869392D+00, & 0.0683773554225136D+00, & 0.2435636733958171D+00, & 0.7421158852408665D+00, & 0.0143204413633164D+00, & 0.7421158852408665D+00, & 0.2435636733958172D+00, & 0.0143204413633164D+00, & 0.2058877165179012D+00, & 0.7551444267398045D+00, & 0.0389678567422944D+00, & 0.7551444267398045D+00, & 0.2058877165179013D+00, & 0.0389678567422941D+00, & 0.2018695088876031D+00, & 0.6487340291944527D+00, & 0.1493964619179441D+00, & 0.6487340291944528D+00, & 0.2018695088876032D+00, & 0.1493964619179440D+00, & 0.1591160210105452D+00, & 0.7786557671705014D+00, & 0.0622282118189533D+00, & 0.7786557671705016D+00, & 0.1591160210105452D+00, & 0.0622282118189531D+00, & 0.1779476358555918D+00, & 0.8044331226739222D+00, & 0.0176192414704860D+00, & 0.8044331226739222D+00, & 0.1779476358555919D+00, & 0.0176192414704858D+00, & 0.1620367479496921D+00, & 0.8340155243850955D+00, & 0.0039477276652125D+00, & 0.8340155243850954D+00, & 0.1620367479496921D+00, & 0.0039477276652123D+00, & 0.2918549838585246D+00, & 0.7052138362553024D+00, & 0.0029311798861729D+00, & 0.7052138362553025D+00, & 0.2918549838585245D+00, & 0.0029311798861727D+00, & 0.3718786917495892D+00, & 0.6253433272679723D+00, & 0.0027779809824385D+00, & 0.6253433272679723D+00, & 0.3718786917495892D+00, & 0.0027779809824384D+00, & 0.1349693726524653D+00, & 0.8307084415116845D+00, & 0.0343221858358503D+00, & 0.8307084415116845D+00, & 0.1349693726524654D+00, & 0.0343221858358500D+00, & 0.0373835575017465D+00, & 0.9252328849965067D+00, & 0.0373835575017469D+00, & 0.2855047782912640D+00, & 0.4289904434174718D+00, & 0.2855047782912640D+00, & 0.2524534299064219D+00, & 0.6388225307516531D+00, & 0.1087240393419249D+00, & 0.6388225307516532D+00, & 0.2524534299064219D+00, & 0.1087240393419247D+00, & 0.4203335017700142D+00, & 0.4203335017700143D+00, & 0.1593329964599715D+00, & 0.3242351641083045D+00, & 0.6608157279836501D+00, & 0.0149491079080454D+00, & 0.6608157279836501D+00, & 0.3242351641083045D+00, & 0.0149491079080453D+00, & 0.2076894216538629D+00, & 0.5846211566922740D+00, & 0.2076894216538630D+00, & 0.4921962729553108D+00, & 0.4921962729553108D+00, & 0.0156074540893784D+00, & 0.4374161906466257D+00, & 0.5252597321941108D+00, & 0.0373240771592634D+00, & 0.5252597321941108D+00, & 0.4374161906466257D+00, & 0.0373240771592634D+00, & 0.4559988036612093D+00, & 0.5410379244071537D+00, & 0.0029632719316369D+00, & 0.5410379244071537D+00, & 0.4559988036612093D+00, & 0.0029632719316369D+00, & 0.0754872857005683D+00, & 0.9203097361386582D+00, & 0.0042029781607736D+00, & 0.9203097361386582D+00, & 0.0754872857005683D+00, & 0.0042029781607733D+00, & 0.3260541266529466D+00, & 0.5596716859665990D+00, & 0.1142741873804544D+00, & 0.5596716859665990D+00, & 0.3260541266529467D+00, & 0.1142741873804543D+00, & 0.4011995885054882D+00, & 0.4859123261815903D+00, & 0.1128880853129214D+00, & 0.4859123261815903D+00, & 0.4011995885054881D+00, & 0.1128880853129214D+00, & 0.2687606603412640D+00, & 0.5710426617589802D+00, & 0.1601966778997558D+00, & 0.5710426617589801D+00, & 0.2687606603412641D+00, & 0.1601966778997558D+00, & 0.4060147025738772D+00, & 0.5788301687858335D+00, & 0.0151551286402894D+00, & 0.5788301687858335D+00, & 0.4060147025738773D+00, & 0.0151551286402893D+00, & 0.3565655939830261D+00, & 0.3565655939830261D+00, & 0.2868688120339477D+00, & 0.3835103468343402D+00, & 0.5464474716652220D+00, & 0.0700421815004378D+00, & 0.5464474716652219D+00, & 0.3835103468343402D+00, & 0.0700421815004378D+00, & 0.0164470646369432D+00, & 0.9801099468614760D+00, & 0.0034429885015809D+00, & 0.9801099468614760D+00, & 0.0164470646369433D+00, & 0.0034429885015805D+00, & 0.3542977861626948D+00, & 0.6080345993586279D+00, & 0.0376676144786774D+00, & 0.6080345993586279D+00, & 0.3542977861626948D+00, & 0.0376676144786772D+00, & 0.3419951757983160D+00, & 0.4920063975249682D+00, & 0.1659984266767156D+00, & 0.4920063975249683D+00, & 0.3419951757983161D+00, & 0.1659984266767155D+00, & 0.1152888910792784D+00, & 0.8726785778095564D+00, & 0.0120325311111653D+00, & 0.8726785778095565D+00, & 0.1152888910792785D+00, & 0.0120325311111650D+00, & 0.1165281018124025D+00, & 0.8831736765060774D+00, & 0.0002982216815202D+00, & 0.8831736765060774D+00, & 0.1165281018124027D+00, & 0.0002982216815200D+00 /) b = (/ & 0.0818557279364709D+00, & 0.4590721360317646D+00, & 0.4590721360317648D+00, & 0.0522971139020114D+00, & 0.2837655147017407D+00, & 0.6639373713962481D+00, & 0.0522971139020114D+00, & 0.6639373713962480D+00, & 0.2837655147017409D+00, & 0.2134639874892799D+00, & 0.3932680062553601D+00, & 0.3932680062553602D+00, & 0.0990797627018413D+00, & 0.1285165649696940D+00, & 0.7724036723284649D+00, & 0.0990797627018413D+00, & 0.7724036723284649D+00, & 0.1285165649696943D+00, & 0.0636348215861286D+00, & 0.4681825892069358D+00, & 0.4681825892069360D+00, & 0.0020644051493052D+00, & 0.0413075041428614D+00, & 0.9566280907078335D+00, & 0.0020644051493052D+00, & 0.9566280907078335D+00, & 0.0413075041428617D+00, & 0.0367301756493483D+00, & 0.0892719800534144D+00, & 0.8739978442972374D+00, & 0.0367301756493483D+00, & 0.8739978442972374D+00, & 0.0892719800534148D+00, & 0.2259458244877857D+00, & 0.3372052923179873D+00, & 0.4368488831942272D+00, & 0.2259458244877857D+00, & 0.4368488831942272D+00, & 0.3372052923179874D+00, & 0.0327011819900538D+00, & 0.2738513741241788D+00, & 0.6934474438857677D+00, & 0.0327011819900538D+00, & 0.6934474438857677D+00, & 0.2738513741241790D+00, & 0.0130695090443300D+00, & 0.0399162626294194D+00, & 0.9470142283262506D+00, & 0.0130695090443300D+00, & 0.9470142283262506D+00, & 0.0399162626294198D+00, & 0.0175045040462676D+00, & 0.0175045040462673D+00, & 0.9649909919074653D+00, & 0.0737176145710159D+00, & 0.3081068327593843D+00, & 0.6181755526695999D+00, & 0.0737176145710159D+00, & 0.6181755526695998D+00, & 0.3081068327593845D+00, & 0.1454801146528609D+00, & 0.1454801146528608D+00, & 0.7090397706942786D+00, & 0.0027038822145435D+00, & 0.2196247131384356D+00, & 0.7776714046470209D+00, & 0.0027038822145435D+00, & 0.7776714046470209D+00, & 0.2196247131384359D+00, & 0.2191582634460288D+00, & 0.2734646071142815D+00, & 0.5073771294396899D+00, & 0.2191582634460288D+00, & 0.5073771294396899D+00, & 0.2734646071142816D+00, & 0.0207228118815140D+00, & 0.0686830028555526D+00, & 0.9105941852629333D+00, & 0.0207228118815140D+00, & 0.9105941852629333D+00, & 0.0686830028555530D+00, & 0.1006217208920761D+00, & 0.1830135998401795D+00, & 0.7163646792677447D+00, & 0.1006217208920761D+00, & 0.7163646792677446D+00, & 0.1830135998401798D+00, & 0.0030471742663608D+00, & 0.0030471742663604D+00, & 0.9939056514672788D+00, & 0.0694898178335093D+00, & 0.2287994832299253D+00, & 0.7017106989365657D+00, & 0.0694898178335093D+00, & 0.7017106989365657D+00, & 0.2287994832299255D+00, & 0.0587361601120223D+00, & 0.0587361601120220D+00, & 0.8825276797759559D+00, & 0.0683773554225139D+00, & 0.1018827114869391D+00, & 0.8297399330905472D+00, & 0.0683773554225139D+00, & 0.8297399330905472D+00, & 0.1018827114869394D+00, & 0.0143204413633165D+00, & 0.2435636733958171D+00, & 0.7421158852408667D+00, & 0.0143204413633165D+00, & 0.7421158852408665D+00, & 0.2435636733958174D+00, & 0.0389678567422943D+00, & 0.2058877165179012D+00, & 0.7551444267398046D+00, & 0.0389678567422943D+00, & 0.7551444267398046D+00, & 0.2058877165179015D+00, & 0.1493964619179442D+00, & 0.2018695088876032D+00, & 0.6487340291944529D+00, & 0.1493964619179442D+00, & 0.6487340291944529D+00, & 0.2018695088876034D+00, & 0.0622282118189533D+00, & 0.1591160210105452D+00, & 0.7786557671705017D+00, & 0.0622282118189533D+00, & 0.7786557671705017D+00, & 0.1591160210105455D+00, & 0.0176192414704860D+00, & 0.1779476358555918D+00, & 0.8044331226739224D+00, & 0.0176192414704860D+00, & 0.8044331226739224D+00, & 0.1779476358555921D+00, & 0.0039477276652125D+00, & 0.1620367479496921D+00, & 0.8340155243850956D+00, & 0.0039477276652125D+00, & 0.8340155243850956D+00, & 0.1620367479496924D+00, & 0.0029311798861729D+00, & 0.2918549838585247D+00, & 0.7052138362553028D+00, & 0.0029311798861729D+00, & 0.7052138362553028D+00, & 0.2918549838585249D+00, & 0.0027779809824386D+00, & 0.3718786917495892D+00, & 0.6253433272679726D+00, & 0.0027779809824386D+00, & 0.6253433272679724D+00, & 0.3718786917495893D+00, & 0.0343221858358502D+00, & 0.1349693726524653D+00, & 0.8307084415116845D+00, & 0.0343221858358502D+00, & 0.8307084415116845D+00, & 0.1349693726524656D+00, & 0.0373835575017468D+00, & 0.0373835575017464D+00, & 0.9252328849965068D+00, & 0.2855047782912642D+00, & 0.2855047782912641D+00, & 0.4289904434174719D+00, & 0.1087240393419249D+00, & 0.2524534299064219D+00, & 0.6388225307516533D+00, & 0.1087240393419249D+00, & 0.6388225307516533D+00, & 0.2524534299064221D+00, & 0.1593329964599716D+00, & 0.4203335017700143D+00, & 0.4203335017700144D+00, & 0.0149491079080454D+00, & 0.3242351641083045D+00, & 0.6608157279836503D+00, & 0.0149491079080454D+00, & 0.6608157279836503D+00, & 0.3242351641083048D+00, & 0.2076894216538631D+00, & 0.2076894216538630D+00, & 0.5846211566922742D+00, & 0.0156074540893784D+00, & 0.4921962729553109D+00, & 0.4921962729553110D+00, & 0.0373240771592635D+00, & 0.4374161906466258D+00, & 0.5252597321941110D+00, & 0.0373240771592635D+00, & 0.5252597321941109D+00, & 0.4374161906466259D+00, & 0.0029632719316370D+00, & 0.4559988036612094D+00, & 0.5410379244071539D+00, & 0.0029632719316370D+00, & 0.5410379244071538D+00, & 0.4559988036612095D+00, & 0.0042029781607735D+00, & 0.0754872857005682D+00, & 0.9203097361386584D+00, & 0.0042029781607735D+00, & 0.9203097361386584D+00, & 0.0754872857005686D+00, & 0.1142741873804544D+00, & 0.3260541266529467D+00, & 0.5596716859665991D+00, & 0.1142741873804544D+00, & 0.5596716859665990D+00, & 0.3260541266529468D+00, & 0.1128880853129215D+00, & 0.4011995885054883D+00, & 0.4859123261815905D+00, & 0.1128880853129215D+00, & 0.4859123261815904D+00, & 0.4011995885054884D+00, & 0.1601966778997559D+00, & 0.2687606603412641D+00, & 0.5710426617589803D+00, & 0.1601966778997559D+00, & 0.5710426617589802D+00, & 0.2687606603412642D+00, & 0.0151551286402894D+00, & 0.4060147025738772D+00, & 0.5788301687858336D+00, & 0.0151551286402894D+00, & 0.5788301687858335D+00, & 0.4060147025738775D+00, & 0.2868688120339477D+00, & 0.3565655939830263D+00, & 0.3565655939830263D+00, & 0.0700421815004379D+00, & 0.3835103468343402D+00, & 0.5464474716652222D+00, & 0.0700421815004379D+00, & 0.5464474716652220D+00, & 0.3835103468343404D+00, & 0.0034429885015808D+00, & 0.0164470646369432D+00, & 0.9801099468614761D+00, & 0.0034429885015808D+00, & 0.9801099468614761D+00, & 0.0164470646369435D+00, & 0.0376676144786773D+00, & 0.3542977861626948D+00, & 0.6080345993586280D+00, & 0.0376676144786773D+00, & 0.6080345993586280D+00, & 0.3542977861626950D+00, & 0.1659984266767157D+00, & 0.3419951757983162D+00, & 0.4920063975249684D+00, & 0.1659984266767157D+00, & 0.4920063975249684D+00, & 0.3419951757983163D+00, & 0.0120325311111652D+00, & 0.1152888910792784D+00, & 0.8726785778095566D+00, & 0.0120325311111652D+00, & 0.8726785778095566D+00, & 0.1152888910792787D+00, & 0.0002982216815201D+00, & 0.1165281018124025D+00, & 0.8831736765060775D+00, & 0.0002982216815201D+00, & 0.8831736765060774D+00, & 0.1165281018124029D+00 /) c = (/ & 0.4590721360317646D+00, & 0.0818557279364708D+00, & 0.4590721360317643D+00, & 0.6639373713962479D+00, & 0.0522971139020113D+00, & 0.2837655147017405D+00, & 0.2837655147017407D+00, & 0.0522971139020113D+00, & 0.6639373713962476D+00, & 0.3932680062553600D+00, & 0.2134639874892798D+00, & 0.3932680062553600D+00, & 0.7724036723284647D+00, & 0.0990797627018413D+00, & 0.1285165649696938D+00, & 0.1285165649696940D+00, & 0.0990797627018410D+00, & 0.7724036723284646D+00, & 0.4681825892069357D+00, & 0.0636348215861285D+00, & 0.4681825892069355D+00, & 0.9566280907078334D+00, & 0.0020644051493053D+00, & 0.0413075041428611D+00, & 0.0413075041428614D+00, & 0.0020644051493049D+00, & 0.9566280907078334D+00, & 0.8739978442972371D+00, & 0.0367301756493484D+00, & 0.0892719800534142D+00, & 0.0892719800534145D+00, & 0.0367301756493481D+00, & 0.8739978442972371D+00, & 0.4368488831942270D+00, & 0.2259458244877856D+00, & 0.3372052923179872D+00, & 0.3372052923179872D+00, & 0.2259458244877856D+00, & 0.4368488831942270D+00, & 0.6934474438857675D+00, & 0.0327011819900538D+00, & 0.2738513741241785D+00, & 0.2738513741241787D+00, & 0.0327011819900535D+00, & 0.6934474438857674D+00, & 0.9470142283262506D+00, & 0.0130695090443301D+00, & 0.0399162626294192D+00, & 0.0399162626294194D+00, & 0.0130695090443298D+00, & 0.9470142283262505D+00, & 0.9649909919074652D+00, & 0.0175045040462678D+00, & 0.0175045040462670D+00, & 0.6181755526695998D+00, & 0.0737176145710159D+00, & 0.3081068327593842D+00, & 0.3081068327593843D+00, & 0.0737176145710159D+00, & 0.6181755526695998D+00, & 0.7090397706942784D+00, & 0.1454801146528610D+00, & 0.1454801146528605D+00, & 0.7776714046470208D+00, & 0.0027038822145436D+00, & 0.2196247131384355D+00, & 0.2196247131384357D+00, & 0.0027038822145434D+00, & 0.7776714046470208D+00, & 0.5073771294396898D+00, & 0.2191582634460287D+00, & 0.2734646071142813D+00, & 0.2734646071142814D+00, & 0.2191582634460286D+00, & 0.5073771294396898D+00, & 0.9105941852629332D+00, & 0.0207228118815141D+00, & 0.0686830028555525D+00, & 0.0686830028555527D+00, & 0.0207228118815138D+00, & 0.9105941852629332D+00, & 0.7163646792677445D+00, & 0.1006217208920760D+00, & 0.1830135998401792D+00, & 0.1830135998401794D+00, & 0.1006217208920760D+00, & 0.7163646792677443D+00, & 0.9939056514672787D+00, & 0.0030471742663608D+00, & 0.0030471742663603D+00, & 0.7017106989365655D+00, & 0.0694898178335094D+00, & 0.2287994832299250D+00, & 0.2287994832299253D+00, & 0.0694898178335092D+00, & 0.7017106989365653D+00, & 0.8825276797759557D+00, & 0.0587361601120223D+00, & 0.0587361601120219D+00, & 0.8297399330905469D+00, & 0.0683773554225139D+00, & 0.1018827114869388D+00, & 0.1018827114869391D+00, & 0.0683773554225137D+00, & 0.8297399330905468D+00, & 0.7421158852408665D+00, & 0.0143204413633164D+00, & 0.2435636733958169D+00, & 0.2435636733958171D+00, & 0.0143204413633163D+00, & 0.7421158852408662D+00, & 0.7551444267398045D+00, & 0.0389678567422943D+00, & 0.2058877165179009D+00, & 0.2058877165179012D+00, & 0.0389678567422941D+00, & 0.7551444267398044D+00, & 0.6487340291944528D+00, & 0.1493964619179442D+00, & 0.2018695088876029D+00, & 0.2018695088876030D+00, & 0.1493964619179439D+00, & 0.6487340291944527D+00, & 0.7786557671705016D+00, & 0.0622282118189533D+00, & 0.1591160210105450D+00, & 0.1591160210105451D+00, & 0.0622282118189531D+00, & 0.7786557671705014D+00, & 0.8044331226739222D+00, & 0.0176192414704860D+00, & 0.1779476358555916D+00, & 0.1779476358555918D+00, & 0.0176192414704858D+00, & 0.8044331226739220D+00, & 0.8340155243850955D+00, & 0.0039477276652124D+00, & 0.1620367479496919D+00, & 0.1620367479496921D+00, & 0.0039477276652123D+00, & 0.8340155243850953D+00, & 0.7052138362553025D+00, & 0.0029311798861729D+00, & 0.2918549838585244D+00, & 0.2918549838585245D+00, & 0.0029311798861728D+00, & 0.7052138362553024D+00, & 0.6253433272679724D+00, & 0.0027779809824385D+00, & 0.3718786917495890D+00, & 0.3718786917495892D+00, & 0.0027779809824385D+00, & 0.6253433272679723D+00, & 0.8307084415116845D+00, & 0.0343221858358502D+00, & 0.1349693726524651D+00, & 0.1349693726524652D+00, & 0.0343221858358500D+00, & 0.8307084415116844D+00, & 0.9252328849965067D+00, & 0.0373835575017469D+00, & 0.0373835575017463D+00, & 0.4289904434174717D+00, & 0.2855047782912640D+00, & 0.2855047782912640D+00, & 0.6388225307516532D+00, & 0.1087240393419250D+00, & 0.2524534299064218D+00, & 0.2524534299064219D+00, & 0.1087240393419248D+00, & 0.6388225307516531D+00, & 0.4203335017700142D+00, & 0.1593329964599714D+00, & 0.4203335017700142D+00, & 0.6608157279836501D+00, & 0.0149491079080454D+00, & 0.3242351641083042D+00, & 0.3242351641083045D+00, & 0.0149491079080452D+00, & 0.6608157279836500D+00, & 0.5846211566922739D+00, & 0.2076894216538630D+00, & 0.2076894216538628D+00, & 0.4921962729553108D+00, & 0.0156074540893784D+00, & 0.4921962729553107D+00, & 0.5252597321941109D+00, & 0.0373240771592634D+00, & 0.4374161906466255D+00, & 0.4374161906466257D+00, & 0.0373240771592634D+00, & 0.5252597321941106D+00, & 0.5410379244071538D+00, & 0.0029632719316369D+00, & 0.4559988036612092D+00, & 0.4559988036612093D+00, & 0.0029632719316369D+00, & 0.5410379244071535D+00, & 0.9203097361386582D+00, & 0.0042029781607736D+00, & 0.0754872857005680D+00, & 0.0754872857005683D+00, & 0.0042029781607732D+00, & 0.9203097361386581D+00, & 0.5596716859665989D+00, & 0.1142741873804543D+00, & 0.3260541266529464D+00, & 0.3260541266529466D+00, & 0.1142741873804544D+00, & 0.5596716859665989D+00, & 0.4859123261815903D+00, & 0.1128880853129214D+00, & 0.4011995885054880D+00, & 0.4011995885054882D+00, & 0.1128880853129214D+00, & 0.4859123261815902D+00, & 0.5710426617589801D+00, & 0.1601966778997557D+00, & 0.2687606603412638D+00, & 0.2687606603412640D+00, & 0.1601966778997558D+00, & 0.5710426617589801D+00, & 0.5788301687858334D+00, & 0.0151551286402893D+00, & 0.4060147025738771D+00, & 0.4060147025738771D+00, & 0.0151551286402892D+00, & 0.5788301687858333D+00, & 0.3565655939830262D+00, & 0.2868688120339476D+00, & 0.3565655939830261D+00, & 0.5464474716652219D+00, & 0.0700421815004378D+00, & 0.3835103468343400D+00, & 0.3835103468343402D+00, & 0.0700421815004378D+00, & 0.5464474716652218D+00, & 0.9801099468614761D+00, & 0.0034429885015808D+00, & 0.0164470646369429D+00, & 0.0164470646369432D+00, & 0.0034429885015806D+00, & 0.9801099468614759D+00, & 0.6080345993586279D+00, & 0.0376676144786773D+00, & 0.3542977861626946D+00, & 0.3542977861626948D+00, & 0.0376676144786772D+00, & 0.6080345993586278D+00, & 0.4920063975249683D+00, & 0.1659984266767156D+00, & 0.3419951757983160D+00, & 0.3419951757983161D+00, & 0.1659984266767155D+00, & 0.4920063975249681D+00, & 0.8726785778095564D+00, & 0.0120325311111653D+00, & 0.1152888910792781D+00, & 0.1152888910792783D+00, & 0.0120325311111650D+00, & 0.8726785778095563D+00, & 0.8831736765060773D+00, & 0.0002982216815201D+00, & 0.1165281018124024D+00, & 0.1165281018124025D+00, & 0.0002982216815199D+00, & 0.8831736765060771D+00 /) w = (/ & 0.0031639644402839D+00, & 0.0031639644402839D+00, & 0.0031639644402839D+00, & 0.0024850052311427D+00, & 0.0024850052311427D+00, & 0.0024850052311427D+00, & 0.0024850052311427D+00, & 0.0024850052311427D+00, & 0.0024850052311427D+00, & 0.0058616582191086D+00, & 0.0058616582191086D+00, & 0.0058616582191086D+00, & 0.0036964891607068D+00, & 0.0036964891607068D+00, & 0.0036964891607068D+00, & 0.0036964891607068D+00, & 0.0036964891607068D+00, & 0.0036964891607068D+00, & 0.0039302169037011D+00, & 0.0039302169037011D+00, & 0.0039302169037011D+00, & 0.0003477043989937D+00, & 0.0003477043989937D+00, & 0.0003477043989937D+00, & 0.0003477043989937D+00, & 0.0003477043989937D+00, & 0.0003477043989937D+00, & 0.0020738268739408D+00, & 0.0020738268739408D+00, & 0.0020738268739408D+00, & 0.0020738268739408D+00, & 0.0020738268739408D+00, & 0.0020738268739408D+00, & 0.0073710410900113D+00, & 0.0073710410900113D+00, & 0.0073710410900113D+00, & 0.0073710410900113D+00, & 0.0073710410900113D+00, & 0.0073710410900113D+00, & 0.0031253981144399D+00, & 0.0031253981144399D+00, & 0.0031253981144399D+00, & 0.0031253981144399D+00, & 0.0031253981144399D+00, & 0.0031253981144399D+00, & 0.0009061762144521D+00, & 0.0009061762144521D+00, & 0.0009061762144521D+00, & 0.0009061762144521D+00, & 0.0009061762144521D+00, & 0.0009061762144521D+00, & 0.0006994697673296D+00, & 0.0006994697673296D+00, & 0.0006994697673296D+00, & 0.0049956277697467D+00, & 0.0049956277697467D+00, & 0.0049956277697467D+00, & 0.0049956277697467D+00, & 0.0049956277697467D+00, & 0.0049956277697467D+00, & 0.0052024225110439D+00, & 0.0052024225110439D+00, & 0.0052024225110439D+00, & 0.0009256681988499D+00, & 0.0009256681988499D+00, & 0.0009256681988499D+00, & 0.0009256681988499D+00, & 0.0009256681988499D+00, & 0.0009256681988499D+00, & 0.0082821664626930D+00, & 0.0082821664626930D+00, & 0.0082821664626930D+00, & 0.0082821664626930D+00, & 0.0082821664626930D+00, & 0.0082821664626930D+00, & 0.0015368424658073D+00, & 0.0015368424658073D+00, & 0.0015368424658073D+00, & 0.0015368424658073D+00, & 0.0015368424658073D+00, & 0.0015368424658073D+00, & 0.0052227407388144D+00, & 0.0052227407388144D+00, & 0.0052227407388144D+00, & 0.0052227407388144D+00, & 0.0052227407388144D+00, & 0.0052227407388144D+00, & 0.0001240466626531D+00, & 0.0001240466626531D+00, & 0.0001240466626531D+00, & 0.0047183927884199D+00, & 0.0047183927884199D+00, & 0.0047183927884199D+00, & 0.0047183927884199D+00, & 0.0047183927884199D+00, & 0.0047183927884199D+00, & 0.0025063822165145D+00, & 0.0025063822165145D+00, & 0.0025063822165145D+00, & 0.0036021170049529D+00, & 0.0036021170049529D+00, & 0.0036021170049529D+00, & 0.0036021170049529D+00, & 0.0036021170049529D+00, & 0.0036021170049529D+00, & 0.0023702904673934D+00, & 0.0023702904673934D+00, & 0.0023702904673934D+00, & 0.0023702904673934D+00, & 0.0023702904673934D+00, & 0.0023702904673934D+00, & 0.0036104898333758D+00, & 0.0036104898333758D+00, & 0.0036104898333758D+00, & 0.0036104898333758D+00, & 0.0036104898333758D+00, & 0.0036104898333758D+00, & 0.0065404545307455D+00, & 0.0065404545307455D+00, & 0.0065404545307455D+00, & 0.0065404545307455D+00, & 0.0065404545307455D+00, & 0.0065404545307455D+00, & 0.0040792214803126D+00, & 0.0040792214803126D+00, & 0.0040792214803126D+00, & 0.0040792214803126D+00, & 0.0040792214803126D+00, & 0.0040792214803126D+00, & 0.0023256389181058D+00, & 0.0023256389181058D+00, & 0.0023256389181058D+00, & 0.0023256389181058D+00, & 0.0023256389181058D+00, & 0.0023256389181058D+00, & 0.0010057440220833D+00, & 0.0010057440220833D+00, & 0.0010057440220833D+00, & 0.0010057440220833D+00, & 0.0010057440220833D+00, & 0.0010057440220833D+00, & 0.0011431617714117D+00, & 0.0011431617714117D+00, & 0.0011431617714117D+00, & 0.0011431617714117D+00, & 0.0011431617714117D+00, & 0.0011431617714117D+00, & 0.0011884613225083D+00, & 0.0011884613225083D+00, & 0.0011884613225083D+00, & 0.0011884613225083D+00, & 0.0011884613225083D+00, & 0.0011884613225083D+00, & 0.0029052189452109D+00, & 0.0029052189452109D+00, & 0.0029052189452109D+00, & 0.0029052189452109D+00, & 0.0029052189452109D+00, & 0.0029052189452109D+00, & 0.0017075502039157D+00, & 0.0017075502039157D+00, & 0.0017075502039157D+00, & 0.0089856095188050D+00, & 0.0089856095188050D+00, & 0.0089856095188050D+00, & 0.0063267151975866D+00, & 0.0063267151975866D+00, & 0.0063267151975866D+00, & 0.0063267151975866D+00, & 0.0063267151975866D+00, & 0.0063267151975866D+00, & 0.0079377042751205D+00, & 0.0079377042751205D+00, & 0.0079377042751205D+00, & 0.0027256862207201D+00, & 0.0027256862207201D+00, & 0.0027256862207201D+00, & 0.0027256862207201D+00, & 0.0027256862207201D+00, & 0.0027256862207201D+00, & 0.0077485531926675D+00, & 0.0077485531926675D+00, & 0.0077485531926675D+00, & 0.0030358975545344D+00, & 0.0030358975545344D+00, & 0.0030358975545344D+00, & 0.0045215915998052D+00, & 0.0045215915998052D+00, & 0.0045215915998052D+00, & 0.0045215915998052D+00, & 0.0045215915998052D+00, & 0.0045215915998052D+00, & 0.0012891742774294D+00, & 0.0012891742774294D+00, & 0.0012891742774294D+00, & 0.0012891742774294D+00, & 0.0012891742774294D+00, & 0.0012891742774294D+00, & 0.0008166839181728D+00, & 0.0008166839181728D+00, & 0.0008166839181728D+00, & 0.0008166839181728D+00, & 0.0008166839181728D+00, & 0.0008166839181728D+00, & 0.0069477793235522D+00, & 0.0069477793235522D+00, & 0.0069477793235522D+00, & 0.0069477793235522D+00, & 0.0069477793235522D+00, & 0.0069477793235522D+00, & 0.0070986179394903D+00, & 0.0070986179394903D+00, & 0.0070986179394903D+00, & 0.0070986179394903D+00, & 0.0070986179394903D+00, & 0.0070986179394903D+00, & 0.0076919203485779D+00, & 0.0076919203485779D+00, & 0.0076919203485779D+00, & 0.0076919203485779D+00, & 0.0076919203485779D+00, & 0.0076919203485779D+00, & 0.0029252190187241D+00, & 0.0029252190187241D+00, & 0.0029252190187241D+00, & 0.0029252190187241D+00, & 0.0029252190187241D+00, & 0.0029252190187241D+00, & 0.0099759936103826D+00, & 0.0099759936103826D+00, & 0.0099759936103826D+00, & 0.0060566969964858D+00, & 0.0060566969964858D+00, & 0.0060566969964858D+00, & 0.0060566969964858D+00, & 0.0060566969964858D+00, & 0.0060566969964858D+00, & 0.0003337056331188D+00, & 0.0003337056331188D+00, & 0.0003337056331188D+00, & 0.0003337056331188D+00, & 0.0003337056331188D+00, & 0.0003337056331188D+00, & 0.0045294689209488D+00, & 0.0045294689209488D+00, & 0.0045294689209488D+00, & 0.0045294689209488D+00, & 0.0045294689209488D+00, & 0.0045294689209488D+00, & 0.0084025374143198D+00, & 0.0084025374143198D+00, & 0.0084025374143198D+00, & 0.0084025374143198D+00, & 0.0084025374143198D+00, & 0.0084025374143198D+00, & 0.0018109718524034D+00, & 0.0018109718524034D+00, & 0.0018109718524034D+00, & 0.0018109718524034D+00, & 0.0018109718524034D+00, & 0.0018109718524034D+00, & 0.0002922856631828D+00, & 0.0002922856631828D+00, & 0.0002922856631828D+00, & 0.0002922856631828D+00, & 0.0002922856631828D+00, & 0.0002922856631828D+00 /) return end subroutine rule39 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule39() returns the rule of precision 39. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2382752085845570D+00, & 0.7573503089771818D+00, & 0.0043744824382613D+00, & 0.7573503089771818D+00, & 0.2382752085845571D+00, & 0.0043744824382611D+00, & 0.5022902013149184D+00, & 0.2662727227960811D+00, & 0.2314370758890004D+00, & 0.2662727227960811D+00, & 0.5022902013149184D+00, & 0.2314370758890005D+00, & 0.3506827341571583D+00, & 0.4132178184063219D+00, & 0.2360994474365198D+00, & 0.4132178184063219D+00, & 0.3506827341571582D+00, & 0.2360994474365199D+00, & 0.2778089177192840D+00, & 0.7195287425328243D+00, & 0.0026623397478918D+00, & 0.7195287425328242D+00, & 0.2778089177192840D+00, & 0.0026623397478915D+00, & 0.4724094821505567D+00, & 0.4724094821505566D+00, & 0.0551810356988866D+00, & 0.3212034826826168D+00, & 0.4713569053824377D+00, & 0.2074396119349455D+00, & 0.4713569053824377D+00, & 0.3212034826826168D+00, & 0.2074396119349454D+00, & 0.4575079686738243D+00, & 0.4575079686738243D+00, & 0.0849840626523514D+00, & 0.4574242168529821D+00, & 0.5306666306702293D+00, & 0.0119091524767885D+00, & 0.5306666306702292D+00, & 0.4574242168529821D+00, & 0.0119091524767886D+00, & 0.1910383428521846D+00, & 0.8068046948089155D+00, & 0.0021569623388999D+00, & 0.8068046948089155D+00, & 0.1910383428521847D+00, & 0.0021569623388998D+00, & 0.3538472919168833D+00, & 0.3538472919168833D+00, & 0.2923054161662332D+00, & 0.4991061498602990D+00, & 0.4991061498602990D+00, & 0.0017877002794020D+00, & 0.2063519407328363D+00, & 0.6863905655155179D+00, & 0.1072574937516458D+00, & 0.6863905655155178D+00, & 0.2063519407328364D+00, & 0.1072574937516456D+00, & 0.2612383827874719D+00, & 0.6263232239210454D+00, & 0.1124383932914825D+00, & 0.6263232239210456D+00, & 0.2612383827874720D+00, & 0.1124383932914823D+00, & 0.1133316581963653D+00, & 0.7733366836072691D+00, & 0.1133316581963656D+00, & 0.1593888996231203D+00, & 0.7265207753801600D+00, & 0.1140903249967197D+00, & 0.7265207753801599D+00, & 0.1593888996231204D+00, & 0.1140903249967195D+00, & 0.3988695132240669D+00, & 0.5391856448598707D+00, & 0.0619448419160624D+00, & 0.5391856448598707D+00, & 0.3988695132240669D+00, & 0.0619448419160624D+00, & 0.3122725792733609D+00, & 0.5657645375013545D+00, & 0.1219628832252846D+00, & 0.5657645375013546D+00, & 0.3122725792733608D+00, & 0.1219628832252845D+00, & 0.3644362623584764D+00, & 0.5969189412939834D+00, & 0.0386447963475403D+00, & 0.5969189412939834D+00, & 0.3644362623584764D+00, & 0.0386447963475401D+00, & 0.2305648342404432D+00, & 0.7522011939909903D+00, & 0.0172339717685666D+00, & 0.7522011939909903D+00, & 0.2305648342404432D+00, & 0.0172339717685664D+00, & 0.0157787047228343D+00, & 0.9684425905543310D+00, & 0.0157787047228348D+00, & 0.0392682833818940D+00, & 0.9461693463150468D+00, & 0.0145623703030595D+00, & 0.9461693463150468D+00, & 0.0392682833818942D+00, & 0.0145623703030590D+00, & 0.3582577335477227D+00, & 0.4875811564549278D+00, & 0.1541611099973494D+00, & 0.4875811564549278D+00, & 0.3582577335477227D+00, & 0.1541611099973493D+00, & 0.3805078825483125D+00, & 0.5183519867727387D+00, & 0.1011401306789488D+00, & 0.5183519867727387D+00, & 0.3805078825483125D+00, & 0.1011401306789487D+00, & 0.1318865755866089D+00, & 0.7948276077652688D+00, & 0.0732858166481222D+00, & 0.7948276077652688D+00, & 0.1318865755866089D+00, & 0.0732858166481220D+00, & 0.1726302550688860D+00, & 0.8138522815338993D+00, & 0.0135174633972147D+00, & 0.8138522815338993D+00, & 0.1726302550688861D+00, & 0.0135174633972144D+00, & 0.0707756358900086D+00, & 0.8860757177287693D+00, & 0.0431486463812223D+00, & 0.8860757177287693D+00, & 0.0707756358900087D+00, & 0.0431486463812219D+00, & 0.0473824731204699D+00, & 0.9497691880411768D+00, & 0.0028483388383533D+00, & 0.9497691880411769D+00, & 0.0473824731204700D+00, & 0.0028483388383529D+00, & 0.1640091847666056D+00, & 0.6719816304667885D+00, & 0.1640091847666059D+00, & 0.4084715607291340D+00, & 0.4084715607291340D+00, & 0.1830568785417320D+00, & 0.2971932482957449D+00, & 0.6624092975072737D+00, & 0.0403974541969814D+00, & 0.6624092975072737D+00, & 0.2971932482957449D+00, & 0.0403974541969812D+00, & 0.4437652399535983D+00, & 0.5252322117028740D+00, & 0.0310025483435276D+00, & 0.5252322117028740D+00, & 0.4437652399535983D+00, & 0.0310025483435276D+00, & 0.2298548902498229D+00, & 0.7308596458500963D+00, & 0.0392854639000808D+00, & 0.7308596458500963D+00, & 0.2298548902498229D+00, & 0.0392854639000805D+00, & 0.4365416551079566D+00, & 0.4365416551079566D+00, & 0.1269166897840867D+00, & 0.2515254271389071D+00, & 0.6769104408114252D+00, & 0.0715641320496676D+00, & 0.6769104408114253D+00, & 0.2515254271389073D+00, & 0.0715641320496676D+00, & 0.2206287919327525D+00, & 0.6249766162864728D+00, & 0.1543945917807746D+00, & 0.6249766162864728D+00, & 0.2206287919327525D+00, & 0.1543945917807745D+00, & 0.0370326513393936D+00, & 0.9259346973212126D+00, & 0.0370326513393939D+00, & 0.4164031820468178D+00, & 0.5808233445804072D+00, & 0.0027734733727750D+00, & 0.5808233445804072D+00, & 0.4164031820468178D+00, & 0.0027734733727749D+00, & 0.2780372435840275D+00, & 0.5501168873807294D+00, & 0.1718458690352431D+00, & 0.5501168873807294D+00, & 0.2780372435840275D+00, & 0.1718458690352429D+00, & 0.3420758322145085D+00, & 0.6546717575274422D+00, & 0.0032524102580493D+00, & 0.6546717575274422D+00, & 0.3420758322145085D+00, & 0.0032524102580491D+00, & 0.2117317495651855D+00, & 0.5765365008696287D+00, & 0.2117317495651856D+00, & 0.3766515227420243D+00, & 0.6072672777807482D+00, & 0.0160811994772276D+00, & 0.6072672777807481D+00, & 0.3766515227420243D+00, & 0.0160811994772275D+00, & 0.1122979167412356D+00, & 0.8440428845538768D+00, & 0.0436591987048877D+00, & 0.8440428845538769D+00, & 0.1122979167412357D+00, & 0.0436591987048873D+00, & 0.1861411558417737D+00, & 0.7455631517971735D+00, & 0.0682956923610529D+00, & 0.7455631517971736D+00, & 0.1861411558417738D+00, & 0.0682956923610526D+00, & 0.3217033982751871D+00, & 0.6035740986139331D+00, & 0.0747225031108797D+00, & 0.6035740986139331D+00, & 0.3217033982751872D+00, & 0.0747225031108797D+00, & 0.1660126851788667D+00, & 0.7978319404567993D+00, & 0.0361553743643340D+00, & 0.7978319404567994D+00, & 0.1660126851788668D+00, & 0.0361553743643337D+00, & 0.0193576952354285D+00, & 0.9778092140653304D+00, & 0.0028330906992414D+00, & 0.9778092140653304D+00, & 0.0193576952354286D+00, & 0.0028330906992409D+00, & 0.0719904092251254D+00, & 0.9100597072441559D+00, & 0.0179498835307189D+00, & 0.9100597072441557D+00, & 0.0719904092251255D+00, & 0.0179498835307185D+00, & 0.2869572884590686D+00, & 0.4260854230818626D+00, & 0.2869572884590688D+00, & 0.1333327168798979D+00, & 0.8634747432495302D+00, & 0.0031925398705718D+00, & 0.8634747432495303D+00, & 0.1333327168798978D+00, & 0.0031925398705716D+00, & 0.2994455291729939D+00, & 0.6842620134079914D+00, & 0.0162924574190148D+00, & 0.6842620134079914D+00, & 0.2994455291729938D+00, & 0.0162924574190146D+00, & 0.1171078851891533D+00, & 0.8649767156294978D+00, & 0.0179153991813488D+00, & 0.8649767156294980D+00, & 0.1171078851891534D+00, & 0.0179153991813485D+00, & 0.0806765828829425D+00, & 0.8386468342341147D+00, & 0.0806765828829429D+00, & 0.0853676016562655D+00, & 0.9110651490396003D+00, & 0.0035672493041343D+00, & 0.9110651490396005D+00, & 0.0853676016562656D+00, & 0.0035672493041339D+00, & 0.0036432199207299D+00, & 0.9927135601585398D+00, & 0.0036432199207303D+00 /) b = (/ & 0.0043744824382613D+00, & 0.2382752085845570D+00, & 0.7573503089771819D+00, & 0.0043744824382613D+00, & 0.7573503089771818D+00, & 0.2382752085845573D+00, & 0.2314370758890006D+00, & 0.5022902013149185D+00, & 0.2662727227960813D+00, & 0.2314370758890006D+00, & 0.2662727227960812D+00, & 0.5022902013149185D+00, & 0.2360994474365199D+00, & 0.3506827341571583D+00, & 0.4132178184063220D+00, & 0.2360994474365199D+00, & 0.4132178184063219D+00, & 0.3506827341571584D+00, & 0.0026623397478917D+00, & 0.2778089177192841D+00, & 0.7195287425328244D+00, & 0.0026623397478917D+00, & 0.7195287425328244D+00, & 0.2778089177192843D+00, & 0.0551810356988867D+00, & 0.4724094821505568D+00, & 0.4724094821505569D+00, & 0.2074396119349455D+00, & 0.3212034826826168D+00, & 0.4713569053824378D+00, & 0.2074396119349455D+00, & 0.4713569053824377D+00, & 0.3212034826826170D+00, & 0.0849840626523515D+00, & 0.4575079686738243D+00, & 0.4575079686738245D+00, & 0.0119091524767886D+00, & 0.4574242168529821D+00, & 0.5306666306702296D+00, & 0.0119091524767886D+00, & 0.5306666306702293D+00, & 0.4574242168529823D+00, & 0.0021569623388999D+00, & 0.1910383428521846D+00, & 0.8068046948089157D+00, & 0.0021569623388999D+00, & 0.8068046948089155D+00, & 0.1910383428521849D+00, & 0.2923054161662334D+00, & 0.3538472919168835D+00, & 0.3538472919168835D+00, & 0.0017877002794021D+00, & 0.4991061498602991D+00, & 0.4991061498602992D+00, & 0.1072574937516458D+00, & 0.2063519407328363D+00, & 0.6863905655155180D+00, & 0.1072574937516458D+00, & 0.6863905655155180D+00, & 0.2063519407328365D+00, & 0.1124383932914825D+00, & 0.2612383827874720D+00, & 0.6263232239210457D+00, & 0.1124383932914825D+00, & 0.6263232239210456D+00, & 0.2612383827874722D+00, & 0.1133316581963656D+00, & 0.1133316581963653D+00, & 0.7733366836072691D+00, & 0.1140903249967197D+00, & 0.1593888996231203D+00, & 0.7265207753801601D+00, & 0.1140903249967197D+00, & 0.7265207753801601D+00, & 0.1593888996231206D+00, & 0.0619448419160625D+00, & 0.3988695132240669D+00, & 0.5391856448598709D+00, & 0.0619448419160625D+00, & 0.5391856448598707D+00, & 0.3988695132240671D+00, & 0.1219628832252846D+00, & 0.3122725792733609D+00, & 0.5657645375013547D+00, & 0.1219628832252846D+00, & 0.5657645375013547D+00, & 0.3122725792733611D+00, & 0.0386447963475402D+00, & 0.3644362623584764D+00, & 0.5969189412939835D+00, & 0.0386447963475402D+00, & 0.5969189412939835D+00, & 0.3644362623584766D+00, & 0.0172339717685666D+00, & 0.2305648342404432D+00, & 0.7522011939909904D+00, & 0.0172339717685666D+00, & 0.7522011939909904D+00, & 0.2305648342404434D+00, & 0.0157787047228346D+00, & 0.0157787047228343D+00, & 0.9684425905543311D+00, & 0.0145623703030592D+00, & 0.0392682833818940D+00, & 0.9461693463150468D+00, & 0.0145623703030592D+00, & 0.9461693463150468D+00, & 0.0392682833818944D+00, & 0.1541611099973495D+00, & 0.3582577335477228D+00, & 0.4875811564549280D+00, & 0.1541611099973495D+00, & 0.4875811564549279D+00, & 0.3582577335477229D+00, & 0.1011401306789488D+00, & 0.3805078825483126D+00, & 0.5183519867727389D+00, & 0.1011401306789488D+00, & 0.5183519867727387D+00, & 0.3805078825483127D+00, & 0.0732858166481222D+00, & 0.1318865755866089D+00, & 0.7948276077652691D+00, & 0.0732858166481222D+00, & 0.7948276077652691D+00, & 0.1318865755866092D+00, & 0.0135174633972146D+00, & 0.1726302550688860D+00, & 0.8138522815338995D+00, & 0.0135174633972146D+00, & 0.8138522815338995D+00, & 0.1726302550688863D+00, & 0.0431486463812222D+00, & 0.0707756358900086D+00, & 0.8860757177287693D+00, & 0.0431486463812222D+00, & 0.8860757177287693D+00, & 0.0707756358900089D+00, & 0.0028483388383532D+00, & 0.0473824731204699D+00, & 0.9497691880411770D+00, & 0.0028483388383532D+00, & 0.9497691880411770D+00, & 0.0473824731204703D+00, & 0.1640091847666058D+00, & 0.1640091847666057D+00, & 0.6719816304667886D+00, & 0.1830568785417320D+00, & 0.4084715607291341D+00, & 0.4084715607291342D+00, & 0.0403974541969814D+00, & 0.2971932482957449D+00, & 0.6624092975072738D+00, & 0.0403974541969814D+00, & 0.6624092975072738D+00, & 0.2971932482957452D+00, & 0.0310025483435277D+00, & 0.4437652399535983D+00, & 0.5252322117028743D+00, & 0.0310025483435277D+00, & 0.5252322117028742D+00, & 0.4437652399535986D+00, & 0.0392854639000807D+00, & 0.2298548902498229D+00, & 0.7308596458500966D+00, & 0.0392854639000807D+00, & 0.7308596458500966D+00, & 0.2298548902498232D+00, & 0.1269166897840868D+00, & 0.4365416551079567D+00, & 0.4365416551079568D+00, & 0.0715641320496677D+00, & 0.2515254271389071D+00, & 0.6769104408114255D+00, & 0.0715641320496677D+00, & 0.6769104408114252D+00, & 0.2515254271389074D+00, & 0.1543945917807747D+00, & 0.2206287919327525D+00, & 0.6249766162864731D+00, & 0.1543945917807747D+00, & 0.6249766162864731D+00, & 0.2206287919327527D+00, & 0.0370326513393939D+00, & 0.0370326513393935D+00, & 0.9259346973212128D+00, & 0.0027734733727750D+00, & 0.4164031820468178D+00, & 0.5808233445804074D+00, & 0.0027734733727750D+00, & 0.5808233445804073D+00, & 0.4164031820468180D+00, & 0.1718458690352430D+00, & 0.2780372435840276D+00, & 0.5501168873807295D+00, & 0.1718458690352430D+00, & 0.5501168873807295D+00, & 0.2780372435840278D+00, & 0.0032524102580493D+00, & 0.3420758322145085D+00, & 0.6546717575274423D+00, & 0.0032524102580493D+00, & 0.6546717575274423D+00, & 0.3420758322145088D+00, & 0.2117317495651857D+00, & 0.2117317495651856D+00, & 0.5765365008696289D+00, & 0.0160811994772277D+00, & 0.3766515227420243D+00, & 0.6072672777807483D+00, & 0.0160811994772277D+00, & 0.6072672777807482D+00, & 0.3766515227420245D+00, & 0.0436591987048876D+00, & 0.1122979167412356D+00, & 0.8440428845538770D+00, & 0.0436591987048876D+00, & 0.8440428845538770D+00, & 0.1122979167412359D+00, & 0.0682956923610528D+00, & 0.1861411558417737D+00, & 0.7455631517971736D+00, & 0.0682956923610528D+00, & 0.7455631517971735D+00, & 0.1861411558417740D+00, & 0.0747225031108798D+00, & 0.3217033982751872D+00, & 0.6035740986139333D+00, & 0.0747225031108798D+00, & 0.6035740986139331D+00, & 0.3217033982751874D+00, & 0.0361553743643339D+00, & 0.1660126851788667D+00, & 0.7978319404567995D+00, & 0.0361553743643339D+00, & 0.7978319404567995D+00, & 0.1660126851788670D+00, & 0.0028330906992412D+00, & 0.0193576952354285D+00, & 0.9778092140653304D+00, & 0.0028330906992412D+00, & 0.9778092140653306D+00, & 0.0193576952354288D+00, & 0.0179498835307188D+00, & 0.0719904092251254D+00, & 0.9100597072441560D+00, & 0.0179498835307188D+00, & 0.9100597072441560D+00, & 0.0719904092251257D+00, & 0.2869572884590688D+00, & 0.2869572884590687D+00, & 0.4260854230818627D+00, & 0.0031925398705718D+00, & 0.1333327168798978D+00, & 0.8634747432495306D+00, & 0.0031925398705718D+00, & 0.8634747432495306D+00, & 0.1333327168798982D+00, & 0.0162924574190147D+00, & 0.2994455291729939D+00, & 0.6842620134079915D+00, & 0.0162924574190147D+00, & 0.6842620134079915D+00, & 0.2994455291729942D+00, & 0.0179153991813487D+00, & 0.1171078851891533D+00, & 0.8649767156294981D+00, & 0.0179153991813487D+00, & 0.8649767156294981D+00, & 0.1171078851891536D+00, & 0.0806765828829428D+00, & 0.0806765828829425D+00, & 0.8386468342341149D+00, & 0.0035672493041342D+00, & 0.0853676016562654D+00, & 0.9110651490396005D+00, & 0.0035672493041342D+00, & 0.9110651490396005D+00, & 0.0853676016562658D+00, & 0.0036432199207302D+00, & 0.0036432199207299D+00, & 0.9927135601585401D+00 /) c = (/ & 0.7573503089771818D+00, & 0.0043744824382612D+00, & 0.2382752085845569D+00, & 0.2382752085845569D+00, & 0.0043744824382611D+00, & 0.7573503089771817D+00, & 0.2662727227960810D+00, & 0.2314370758890004D+00, & 0.5022902013149183D+00, & 0.5022902013149184D+00, & 0.2314370758890004D+00, & 0.2662727227960809D+00, & 0.4132178184063218D+00, & 0.2360994474365198D+00, & 0.3506827341571581D+00, & 0.3506827341571582D+00, & 0.2360994474365198D+00, & 0.4132178184063217D+00, & 0.7195287425328243D+00, & 0.0026623397478917D+00, & 0.2778089177192838D+00, & 0.2778089177192841D+00, & 0.0026623397478917D+00, & 0.7195287425328241D+00, & 0.4724094821505567D+00, & 0.0551810356988865D+00, & 0.4724094821505564D+00, & 0.4713569053824377D+00, & 0.2074396119349455D+00, & 0.3212034826826167D+00, & 0.3212034826826168D+00, & 0.2074396119349455D+00, & 0.4713569053824377D+00, & 0.4575079686738243D+00, & 0.0849840626523514D+00, & 0.4575079686738240D+00, & 0.5306666306702292D+00, & 0.0119091524767885D+00, & 0.4574242168529820D+00, & 0.4574242168529821D+00, & 0.0119091524767886D+00, & 0.5306666306702290D+00, & 0.8068046948089155D+00, & 0.0021569623388999D+00, & 0.1910383428521844D+00, & 0.1910383428521846D+00, & 0.0021569623388998D+00, & 0.8068046948089154D+00, & 0.3538472919168832D+00, & 0.2923054161662332D+00, & 0.3538472919168832D+00, & 0.4991061498602989D+00, & 0.0017877002794019D+00, & 0.4991061498602988D+00, & 0.6863905655155179D+00, & 0.1072574937516458D+00, & 0.2063519407328361D+00, & 0.2063519407328364D+00, & 0.1072574937516456D+00, & 0.6863905655155178D+00, & 0.6263232239210456D+00, & 0.1124383932914826D+00, & 0.2612383827874718D+00, & 0.2612383827874719D+00, & 0.1124383932914824D+00, & 0.6263232239210454D+00, & 0.7733366836072691D+00, & 0.1133316581963655D+00, & 0.1133316581963651D+00, & 0.7265207753801600D+00, & 0.1140903249967197D+00, & 0.1593888996231201D+00, & 0.1593888996231204D+00, & 0.1140903249967194D+00, & 0.7265207753801600D+00, & 0.5391856448598706D+00, & 0.0619448419160623D+00, & 0.3988695132240667D+00, & 0.3988695132240668D+00, & 0.0619448419160623D+00, & 0.5391856448598705D+00, & 0.5657645375013545D+00, & 0.1219628832252846D+00, & 0.3122725792733607D+00, & 0.3122725792733608D+00, & 0.1219628832252845D+00, & 0.5657645375013545D+00, & 0.5969189412939834D+00, & 0.0386447963475402D+00, & 0.3644362623584763D+00, & 0.3644362623584764D+00, & 0.0386447963475401D+00, & 0.5969189412939833D+00, & 0.7522011939909903D+00, & 0.0172339717685665D+00, & 0.2305648342404431D+00, & 0.2305648342404432D+00, & 0.0172339717685664D+00, & 0.7522011939909903D+00, & 0.9684425905543311D+00, & 0.0157787047228347D+00, & 0.0157787047228340D+00, & 0.9461693463150469D+00, & 0.0145623703030592D+00, & 0.0392682833818937D+00, & 0.0392682833818940D+00, & 0.0145623703030590D+00, & 0.9461693463150466D+00, & 0.4875811564549278D+00, & 0.1541611099973494D+00, & 0.3582577335477226D+00, & 0.3582577335477227D+00, & 0.1541611099973494D+00, & 0.4875811564549277D+00, & 0.5183519867727386D+00, & 0.1011401306789487D+00, & 0.3805078825483124D+00, & 0.3805078825483125D+00, & 0.1011401306789487D+00, & 0.5183519867727385D+00, & 0.7948276077652688D+00, & 0.0732858166481222D+00, & 0.1318865755866087D+00, & 0.1318865755866090D+00, & 0.0732858166481219D+00, & 0.7948276077652687D+00, & 0.8138522815338993D+00, & 0.0135174633972147D+00, & 0.1726302550688857D+00, & 0.1726302550688860D+00, & 0.0135174633972144D+00, & 0.8138522815338993D+00, & 0.8860757177287693D+00, & 0.0431486463812222D+00, & 0.0707756358900085D+00, & 0.0707756358900086D+00, & 0.0431486463812221D+00, & 0.8860757177287691D+00, & 0.9497691880411768D+00, & 0.0028483388383533D+00, & 0.0473824731204696D+00, & 0.0473824731204699D+00, & 0.0028483388383530D+00, & 0.9497691880411768D+00, & 0.6719816304667885D+00, & 0.1640091847666058D+00, & 0.1640091847666055D+00, & 0.4084715607291339D+00, & 0.1830568785417319D+00, & 0.4084715607291339D+00, & 0.6624092975072737D+00, & 0.0403974541969814D+00, & 0.2971932482957448D+00, & 0.2971932482957449D+00, & 0.0403974541969813D+00, & 0.6624092975072735D+00, & 0.5252322117028740D+00, & 0.0310025483435276D+00, & 0.4437652399535981D+00, & 0.4437652399535983D+00, & 0.0310025483435276D+00, & 0.5252322117028738D+00, & 0.7308596458500963D+00, & 0.0392854639000808D+00, & 0.2298548902498226D+00, & 0.2298548902498230D+00, & 0.0392854639000805D+00, & 0.7308596458500963D+00, & 0.4365416551079566D+00, & 0.1269166897840867D+00, & 0.4365416551079564D+00, & 0.6769104408114252D+00, & 0.0715641320496677D+00, & 0.2515254271389069D+00, & 0.2515254271389070D+00, & 0.0715641320496675D+00, & 0.6769104408114250D+00, & 0.6249766162864728D+00, & 0.1543945917807746D+00, & 0.2206287919327523D+00, & 0.2206287919327525D+00, & 0.1543945917807744D+00, & 0.6249766162864727D+00, & 0.9259346973212126D+00, & 0.0370326513393939D+00, & 0.0370326513393933D+00, & 0.5808233445804073D+00, & 0.0027734733727750D+00, & 0.4164031820468176D+00, & 0.4164031820468178D+00, & 0.0027734733727750D+00, & 0.5808233445804071D+00, & 0.5501168873807295D+00, & 0.1718458690352430D+00, & 0.2780372435840274D+00, & 0.2780372435840276D+00, & 0.1718458690352430D+00, & 0.5501168873807294D+00, & 0.6546717575274421D+00, & 0.0032524102580492D+00, & 0.3420758322145083D+00, & 0.3420758322145085D+00, & 0.0032524102580491D+00, & 0.6546717575274421D+00, & 0.5765365008696287D+00, & 0.2117317495651857D+00, & 0.2117317495651855D+00, & 0.6072672777807481D+00, & 0.0160811994772275D+00, & 0.3766515227420241D+00, & 0.3766515227420243D+00, & 0.0160811994772275D+00, & 0.6072672777807480D+00, & 0.8440428845538769D+00, & 0.0436591987048877D+00, & 0.1122979167412353D+00, & 0.1122979167412356D+00, & 0.0436591987048873D+00, & 0.8440428845538768D+00, & 0.7455631517971735D+00, & 0.0682956923610528D+00, & 0.1861411558417735D+00, & 0.1861411558417736D+00, & 0.0682956923610527D+00, & 0.7455631517971734D+00, & 0.6035740986139331D+00, & 0.0747225031108797D+00, & 0.3217033982751869D+00, & 0.3217033982751871D+00, & 0.0747225031108797D+00, & 0.6035740986139329D+00, & 0.7978319404567993D+00, & 0.0361553743643340D+00, & 0.1660126851788665D+00, & 0.1660126851788667D+00, & 0.0361553743643337D+00, & 0.7978319404567993D+00, & 0.9778092140653303D+00, & 0.0028330906992411D+00, & 0.0193576952354283D+00, & 0.0193576952354284D+00, & 0.0028330906992408D+00, & 0.9778092140653303D+00, & 0.9100597072441557D+00, & 0.0179498835307187D+00, & 0.0719904092251252D+00, & 0.0719904092251255D+00, & 0.0179498835307185D+00, & 0.9100597072441557D+00, & 0.4260854230818627D+00, & 0.2869572884590687D+00, & 0.2869572884590685D+00, & 0.8634747432495303D+00, & 0.0031925398705719D+00, & 0.1333327168798976D+00, & 0.1333327168798979D+00, & 0.0031925398705716D+00, & 0.8634747432495302D+00, & 0.6842620134079914D+00, & 0.0162924574190147D+00, & 0.2994455291729936D+00, & 0.2994455291729938D+00, & 0.0162924574190146D+00, & 0.6842620134079912D+00, & 0.8649767156294980D+00, & 0.0179153991813489D+00, & 0.1171078851891532D+00, & 0.1171078851891533D+00, & 0.0179153991813485D+00, & 0.8649767156294980D+00, & 0.8386468342341147D+00, & 0.0806765828829429D+00, & 0.0806765828829422D+00, & 0.9110651490396003D+00, & 0.0035672493041342D+00, & 0.0853676016562652D+00, & 0.0853676016562654D+00, & 0.0035672493041340D+00, & 0.9110651490396003D+00, & 0.9927135601585400D+00, & 0.0036432199207303D+00, & 0.0036432199207296D+00 /) w = (/ & 0.0007824030328396D+00, & 0.0007824030328396D+00, & 0.0007824030328396D+00, & 0.0007824030328396D+00, & 0.0007824030328396D+00, & 0.0007824030328396D+00, & 0.0054259258789525D+00, & 0.0054259258789525D+00, & 0.0054259258789525D+00, & 0.0054259258789525D+00, & 0.0054259258789525D+00, & 0.0054259258789525D+00, & 0.0064335649832209D+00, & 0.0064335649832209D+00, & 0.0064335649832209D+00, & 0.0064335649832209D+00, & 0.0064335649832209D+00, & 0.0064335649832209D+00, & 0.0007645106376317D+00, & 0.0007645106376317D+00, & 0.0007645106376317D+00, & 0.0007645106376317D+00, & 0.0007645106376317D+00, & 0.0007645106376317D+00, & 0.0038004729776007D+00, & 0.0038004729776007D+00, & 0.0038004729776007D+00, & 0.0062594886810264D+00, & 0.0062594886810264D+00, & 0.0062594886810264D+00, & 0.0062594886810264D+00, & 0.0062594886810264D+00, & 0.0062594886810264D+00, & 0.0048090357401686D+00, & 0.0048090357401686D+00, & 0.0048090357401686D+00, & 0.0021620874068945D+00, & 0.0021620874068945D+00, & 0.0021620874068945D+00, & 0.0021620874068945D+00, & 0.0021620874068945D+00, & 0.0021620874068945D+00, & 0.0006908539783223D+00, & 0.0006908539783223D+00, & 0.0006908539783223D+00, & 0.0006908539783223D+00, & 0.0006908539783223D+00, & 0.0006908539783223D+00, & 0.0080789945453473D+00, & 0.0080789945453473D+00, & 0.0080789945453473D+00, & 0.0008384766818292D+00, & 0.0008384766818292D+00, & 0.0008384766818292D+00, & 0.0043810960857082D+00, & 0.0043810960857082D+00, & 0.0043810960857082D+00, & 0.0043810960857082D+00, & 0.0043810960857082D+00, & 0.0043810960857082D+00, & 0.0048977390707915D+00, & 0.0048977390707915D+00, & 0.0048977390707915D+00, & 0.0048977390707915D+00, & 0.0048977390707915D+00, & 0.0048977390707915D+00, & 0.0037089356213762D+00, & 0.0037089356213762D+00, & 0.0037089356213762D+00, & 0.0044309896508941D+00, & 0.0044309896508941D+00, & 0.0044309896508941D+00, & 0.0044309896508941D+00, & 0.0044309896508941D+00, & 0.0044309896508941D+00, & 0.0046998784286279D+00, & 0.0046998784286279D+00, & 0.0046998784286279D+00, & 0.0046998784286279D+00, & 0.0046998784286279D+00, & 0.0046998784286279D+00, & 0.0056949471589669D+00, & 0.0056949471589669D+00, & 0.0056949471589669D+00, & 0.0056949471589669D+00, & 0.0056949471589669D+00, & 0.0056949471589669D+00, & 0.0037232299887488D+00, & 0.0037232299887488D+00, & 0.0037232299887488D+00, & 0.0037232299887488D+00, & 0.0037232299887488D+00, & 0.0037232299887488D+00, & 0.0022711066220262D+00, & 0.0022711066220262D+00, & 0.0022711066220262D+00, & 0.0022711066220262D+00, & 0.0022711066220262D+00, & 0.0022711066220262D+00, & 0.0006686069116893D+00, & 0.0006686069116893D+00, & 0.0006686069116893D+00, & 0.0009501856551478D+00, & 0.0009501856551478D+00, & 0.0009501856551478D+00, & 0.0009501856551478D+00, & 0.0009501856551478D+00, & 0.0009501856551478D+00, & 0.0074331006305706D+00, & 0.0074331006305706D+00, & 0.0074331006305706D+00, & 0.0074331006305706D+00, & 0.0074331006305706D+00, & 0.0074331006305706D+00, & 0.0061864305337419D+00, & 0.0061864305337419D+00, & 0.0061864305337419D+00, & 0.0061864305337419D+00, & 0.0061864305337419D+00, & 0.0061864305337419D+00, & 0.0038374222817439D+00, & 0.0038374222817439D+00, & 0.0038374222817439D+00, & 0.0038374222817439D+00, & 0.0038374222817439D+00, & 0.0038374222817439D+00, & 0.0018958729657531D+00, & 0.0018958729657531D+00, & 0.0018958729657531D+00, & 0.0018958729657531D+00, & 0.0018958729657531D+00, & 0.0018958729657531D+00, & 0.0023158771686324D+00, & 0.0023158771686324D+00, & 0.0023158771686324D+00, & 0.0023158771686324D+00, & 0.0023158771686324D+00, & 0.0023158771686324D+00, & 0.0004882707622038D+00, & 0.0004882707622038D+00, & 0.0004882707622038D+00, & 0.0004882707622038D+00, & 0.0004882707622038D+00, & 0.0004882707622038D+00, & 0.0058035379196036D+00, & 0.0058035379196036D+00, & 0.0058035379196036D+00, & 0.0076992066322763D+00, & 0.0076992066322763D+00, & 0.0076992066322763D+00, & 0.0039332470075349D+00, & 0.0039332470075349D+00, & 0.0039332470075349D+00, & 0.0039332470075349D+00, & 0.0039332470075349D+00, & 0.0039332470075349D+00, & 0.0037369831874343D+00, & 0.0037369831874343D+00, & 0.0037369831874343D+00, & 0.0037369831874343D+00, & 0.0037369831874343D+00, & 0.0037369831874343D+00, & 0.0035306268703356D+00, & 0.0035306268703356D+00, & 0.0035306268703356D+00, & 0.0035306268703356D+00, & 0.0035306268703356D+00, & 0.0035306268703356D+00, & 0.0067765032180855D+00, & 0.0067765032180855D+00, & 0.0067765032180855D+00, & 0.0048733014906139D+00, & 0.0048733014906139D+00, & 0.0048733014906139D+00, & 0.0048733014906139D+00, & 0.0048733014906139D+00, & 0.0048733014906139D+00, & 0.0060696924219261D+00, & 0.0060696924219261D+00, & 0.0060696924219261D+00, & 0.0060696924219261D+00, & 0.0060696924219261D+00, & 0.0060696924219261D+00, & 0.0015920496320693D+00, & 0.0015920496320693D+00, & 0.0015920496320693D+00, & 0.0011017635807508D+00, & 0.0011017635807508D+00, & 0.0011017635807508D+00, & 0.0011017635807508D+00, & 0.0011017635807508D+00, & 0.0011017635807508D+00, & 0.0073091828155223D+00, & 0.0073091828155223D+00, & 0.0073091828155223D+00, & 0.0073091828155223D+00, & 0.0073091828155223D+00, & 0.0073091828155223D+00, & 0.0011736195277390D+00, & 0.0011736195277390D+00, & 0.0011736195277390D+00, & 0.0011736195277390D+00, & 0.0011736195277390D+00, & 0.0011736195277390D+00, & 0.0071255638341493D+00, & 0.0071255638341493D+00, & 0.0071255638341493D+00, & 0.0028277464204102D+00, & 0.0028277464204102D+00, & 0.0028277464204102D+00, & 0.0028277464204102D+00, & 0.0028277464204102D+00, & 0.0028277464204102D+00, & 0.0028118195580629D+00, & 0.0028118195580629D+00, & 0.0028118195580629D+00, & 0.0028118195580629D+00, & 0.0028118195580629D+00, & 0.0028118195580629D+00, & 0.0043776217728844D+00, & 0.0043776217728844D+00, & 0.0043776217728844D+00, & 0.0043776217728844D+00, & 0.0043776217728844D+00, & 0.0043776217728844D+00, & 0.0057797851749689D+00, & 0.0057797851749689D+00, & 0.0057797851749689D+00, & 0.0057797851749689D+00, & 0.0057797851749689D+00, & 0.0057797851749689D+00, & 0.0033216883150331D+00, & 0.0033216883150331D+00, & 0.0033216883150331D+00, & 0.0033216883150331D+00, & 0.0033216883150331D+00, & 0.0033216883150331D+00, & 0.0003234214385767D+00, & 0.0003234214385767D+00, & 0.0003234214385767D+00, & 0.0003234214385767D+00, & 0.0003234214385767D+00, & 0.0003234214385767D+00, & 0.0015599585117589D+00, & 0.0015599585117589D+00, & 0.0015599585117589D+00, & 0.0015599585117589D+00, & 0.0015599585117589D+00, & 0.0015599585117589D+00, & 0.0087287285098108D+00, & 0.0087287285098108D+00, & 0.0087287285098108D+00, & 0.0008684596573017D+00, & 0.0008684596573017D+00, & 0.0008684596573017D+00, & 0.0008684596573017D+00, & 0.0008684596573017D+00, & 0.0008684596573017D+00, & 0.0027516782565965D+00, & 0.0027516782565965D+00, & 0.0027516782565965D+00, & 0.0027516782565965D+00, & 0.0027516782565965D+00, & 0.0027516782565965D+00, & 0.0020505862443132D+00, & 0.0020505862443132D+00, & 0.0020505862443132D+00, & 0.0020505862443132D+00, & 0.0020505862443132D+00, & 0.0020505862443132D+00, & 0.0037076853680653D+00, & 0.0037076853680653D+00, & 0.0037076853680653D+00, & 0.0007841501256460D+00, & 0.0007841501256460D+00, & 0.0007841501256460D+00, & 0.0007841501256460D+00, & 0.0007841501256460D+00, & 0.0007841501256460D+00, & 0.0001749077815533D+00, & 0.0001749077815533D+00, & 0.0001749077815533D+00 /) return end subroutine rule40 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule40() returns the rule of precision 40. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1671778383557105D+00, & 0.8312942125952762D+00, & 0.0015279490490133D+00, & 0.8312942125952764D+00, & 0.1671778383557105D+00, & 0.0015279490490130D+00, & 0.3714780994452375D+00, & 0.6135500780826215D+00, & 0.0149718224721411D+00, & 0.6135500780826214D+00, & 0.3714780994452375D+00, & 0.0149718224721410D+00, & 0.1590238847123736D+00, & 0.8341718564884986D+00, & 0.0068042587991279D+00, & 0.8341718564884986D+00, & 0.1590238847123738D+00, & 0.0068042587991276D+00, & 0.0462179329282665D+00, & 0.9184680923701788D+00, & 0.0353139747015547D+00, & 0.9184680923701789D+00, & 0.0462179329282665D+00, & 0.0353139747015544D+00, & 0.1148651673800807D+00, & 0.8835508461723146D+00, & 0.0015839864476049D+00, & 0.8835508461723147D+00, & 0.1148651673800808D+00, & 0.0015839864476045D+00, & 0.3342460081847144D+00, & 0.6442373197308038D+00, & 0.0215166720844818D+00, & 0.6442373197308038D+00, & 0.3342460081847144D+00, & 0.0215166720844817D+00, & 0.0723711649483900D+00, & 0.9256035733590469D+00, & 0.0020252616925632D+00, & 0.9256035733590469D+00, & 0.0723711649483901D+00, & 0.0020252616925628D+00, & 0.2236842466647887D+00, & 0.7609545495861244D+00, & 0.0153612037490869D+00, & 0.7609545495861244D+00, & 0.2236842466647888D+00, & 0.0153612037490867D+00, & 0.1111290169905849D+00, & 0.8787050390615000D+00, & 0.0101659439479151D+00, & 0.8787050390615001D+00, & 0.1111290169905850D+00, & 0.0101659439479147D+00, & 0.2764445418077909D+00, & 0.6935416044083799D+00, & 0.0300138537838293D+00, & 0.6935416044083799D+00, & 0.2764445418077908D+00, & 0.0300138537838291D+00, & 0.1692633554656758D+00, & 0.8117666018943027D+00, & 0.0189700426400217D+00, & 0.8117666018943026D+00, & 0.1692633554656758D+00, & 0.0189700426400213D+00, & 0.1196509552487583D+00, & 0.8536082605291146D+00, & 0.0267407842221271D+00, & 0.8536082605291146D+00, & 0.1196509552487584D+00, & 0.0267407842221267D+00, & 0.2830190971292686D+00, & 0.7161270841771937D+00, & 0.0008538186935376D+00, & 0.7161270841771938D+00, & 0.2830190971292687D+00, & 0.0008538186935374D+00, & 0.0704045501511468D+00, & 0.9173369798048715D+00, & 0.0122584700439818D+00, & 0.9173369798048715D+00, & 0.0704045501511468D+00, & 0.0122584700439815D+00, & 0.2164720987514121D+00, & 0.7463578541350908D+00, & 0.0371700471134971D+00, & 0.7463578541350909D+00, & 0.2164720987514122D+00, & 0.0371700471134968D+00, & 0.0769268815632591D+00, & 0.8908789177732704D+00, & 0.0321942006634706D+00, & 0.8908789177732706D+00, & 0.0769268815632591D+00, & 0.0321942006634703D+00, & 0.4292227320385513D+00, & 0.5618451152501334D+00, & 0.0089321527113154D+00, & 0.5618451152501333D+00, & 0.4292227320385513D+00, & 0.0089321527113153D+00, & 0.0157037453637930D+00, & 0.9685925092724137D+00, & 0.0157037453637935D+00, & 0.2938899628974431D+00, & 0.4122200742051138D+00, & 0.2938899628974431D+00, & 0.3701028684237416D+00, & 0.3701028684237416D+00, & 0.2597942631525166D+00, & 0.3251479248852048D+00, & 0.4508068598872954D+00, & 0.2240452152274997D+00, & 0.4508068598872955D+00, & 0.3251479248852048D+00, & 0.2240452152274996D+00, & 0.2782727102869363D+00, & 0.5341010727223879D+00, & 0.1876262169906756D+00, & 0.5341010727223879D+00, & 0.2782727102869363D+00, & 0.1876262169906754D+00, & 0.2852102535187100D+00, & 0.7050312251574219D+00, & 0.0097585213238682D+00, & 0.7050312251574219D+00, & 0.2852102535187100D+00, & 0.0097585213238680D+00, & 0.2727256318298310D+00, & 0.6685680775484955D+00, & 0.0587062906216736D+00, & 0.6685680775484953D+00, & 0.2727256318298311D+00, & 0.0587062906216735D+00, & 0.4154695947712394D+00, & 0.5537884055426003D+00, & 0.0307419996861603D+00, & 0.5537884055426003D+00, & 0.4154695947712395D+00, & 0.0307419996861602D+00, & 0.2205774465337091D+00, & 0.7761657998291807D+00, & 0.0032567536371101D+00, & 0.7761657998291808D+00, & 0.2205774465337091D+00, & 0.0032567536371099D+00, & 0.3428856203943587D+00, & 0.6119267566451521D+00, & 0.0451876229604891D+00, & 0.6119267566451522D+00, & 0.3428856203943588D+00, & 0.0451876229604890D+00, & 0.2315038606116803D+00, & 0.6176776291642629D+00, & 0.1508185102240567D+00, & 0.6176776291642631D+00, & 0.2315038606116803D+00, & 0.1508185102240566D+00, & 0.0381017129649182D+00, & 0.9452246129976019D+00, & 0.0166736740374801D+00, & 0.9452246129976020D+00, & 0.0381017129649182D+00, & 0.0166736740374796D+00, & 0.3528911085101677D+00, & 0.4850036493442883D+00, & 0.1621052421455439D+00, & 0.4850036493442883D+00, & 0.3528911085101677D+00, & 0.1621052421455439D+00, & 0.4000760699195811D+00, & 0.5353980699804886D+00, & 0.0645258600999303D+00, & 0.5353980699804887D+00, & 0.4000760699195811D+00, & 0.0645258600999302D+00, & 0.1877843415465376D+00, & 0.6978359629848933D+00, & 0.1143796954685691D+00, & 0.6978359629848933D+00, & 0.1877843415465377D+00, & 0.1143796954685689D+00, & 0.2073769376903412D+00, & 0.7230510664568768D+00, & 0.0695719958527821D+00, & 0.7230510664568768D+00, & 0.2073769376903412D+00, & 0.0695719958527819D+00, & 0.1078038302263755D+00, & 0.8361618100730819D+00, & 0.0560343597005427D+00, & 0.8361618100730819D+00, & 0.1078038302263756D+00, & 0.0560343597005424D+00, & 0.1479014660731261D+00, & 0.7705088681427068D+00, & 0.0815896657841672D+00, & 0.7705088681427068D+00, & 0.1479014660731260D+00, & 0.0815896657841669D+00, & 0.1600426684113588D+00, & 0.7953280578174164D+00, & 0.0446292737712248D+00, & 0.7953280578174164D+00, & 0.1600426684113588D+00, & 0.0446292737712245D+00, & 0.3778766696887720D+00, & 0.5133314537120106D+00, & 0.1087918765992173D+00, & 0.5133314537120106D+00, & 0.3778766696887720D+00, & 0.1087918765992173D+00, & 0.2526963148522067D+00, & 0.4946073702955864D+00, & 0.2526963148522068D+00, & 0.0392233696648084D+00, & 0.9575704817506674D+00, & 0.0032061485845244D+00, & 0.9575704817506674D+00, & 0.0392233696648085D+00, & 0.0032061485845240D+00, & 0.3243044450771381D+00, & 0.5927190068639427D+00, & 0.0829765480589191D+00, & 0.5927190068639427D+00, & 0.3243044450771381D+00, & 0.0829765480589190D+00, & 0.2105771295148042D+00, & 0.5788457409703914D+00, & 0.2105771295148043D+00, & 0.0030575106285418D+00, & 0.9938849787429160D+00, & 0.0030575106285423D+00, & 0.4032922222742628D+00, & 0.4032922222742628D+00, & 0.1934155554514743D+00, & 0.4767516468002929D+00, & 0.4767516468002928D+00, & 0.0464967063994142D+00, & 0.3509848476225047D+00, & 0.6454944173675070D+00, & 0.0035207350099882D+00, & 0.6454944173675071D+00, & 0.3509848476225048D+00, & 0.0035207350099881D+00, & 0.0648562451597025D+00, & 0.8702875096805947D+00, & 0.0648562451597030D+00, & 0.1688963797829617D+00, & 0.6622072404340762D+00, & 0.1688963797829621D+00, & 0.3333333333333333D+00, & 0.4208708276256937D+00, & 0.5785308776456697D+00, & 0.0005982947286367D+00, & 0.5785308776456696D+00, & 0.4208708276256937D+00, & 0.0005982947286367D+00, & 0.0962980341591576D+00, & 0.8074039316816845D+00, & 0.0962980341591579D+00, & 0.2526560385602647D+00, & 0.6476602419795359D+00, & 0.0996837194601995D+00, & 0.6476602419795359D+00, & 0.2526560385602647D+00, & 0.0996837194601994D+00, & 0.4907015691302040D+00, & 0.4907015691302040D+00, & 0.0185968617395920D+00, & 0.4984645792365976D+00, & 0.4984645792365976D+00, & 0.0030708415268047D+00, & 0.3016703335605275D+00, & 0.5675057520644238D+00, & 0.1308239143750486D+00, & 0.5675057520644238D+00, & 0.3016703335605276D+00, & 0.1308239143750485D+00, & 0.4322719776068064D+00, & 0.4322719776068064D+00, & 0.1354560447863873D+00, & 0.1302416069902091D+00, & 0.7395167860195814D+00, & 0.1302416069902094D+00, & 0.4568717371543228D+00, & 0.4568717371543228D+00, & 0.0862565256913544D+00, & 0.0160613879667907D+00, & 0.9809430242931965D+00, & 0.0029955877400129D+00, & 0.9809430242931966D+00, & 0.0160613879667909D+00, & 0.0029955877400125D+00 /) b = (/ & 0.0015279490490132D+00, & 0.1671778383557105D+00, & 0.8312942125952765D+00, & 0.0015279490490132D+00, & 0.8312942125952765D+00, & 0.1671778383557108D+00, & 0.0149718224721411D+00, & 0.3714780994452375D+00, & 0.6135500780826216D+00, & 0.0149718224721411D+00, & 0.6135500780826215D+00, & 0.3714780994452377D+00, & 0.0068042587991278D+00, & 0.1590238847123736D+00, & 0.8341718564884987D+00, & 0.0068042587991278D+00, & 0.8341718564884987D+00, & 0.1590238847123739D+00, & 0.0353139747015546D+00, & 0.0462179329282665D+00, & 0.9184680923701790D+00, & 0.0353139747015546D+00, & 0.9184680923701790D+00, & 0.0462179329282669D+00, & 0.0015839864476047D+00, & 0.1148651673800806D+00, & 0.8835508461723147D+00, & 0.0015839864476047D+00, & 0.8835508461723147D+00, & 0.1148651673800810D+00, & 0.0215166720844818D+00, & 0.3342460081847145D+00, & 0.6442373197308039D+00, & 0.0215166720844818D+00, & 0.6442373197308039D+00, & 0.3342460081847147D+00, & 0.0020252616925631D+00, & 0.0723711649483900D+00, & 0.9256035733590470D+00, & 0.0020252616925631D+00, & 0.9256035733590470D+00, & 0.0723711649483903D+00, & 0.0153612037490869D+00, & 0.2236842466647887D+00, & 0.7609545495861246D+00, & 0.0153612037490869D+00, & 0.7609545495861246D+00, & 0.2236842466647890D+00, & 0.0101659439479150D+00, & 0.1111290169905849D+00, & 0.8787050390615002D+00, & 0.0101659439479150D+00, & 0.8787050390615003D+00, & 0.1111290169905853D+00, & 0.0300138537838293D+00, & 0.2764445418077909D+00, & 0.6935416044083801D+00, & 0.0300138537838293D+00, & 0.6935416044083801D+00, & 0.2764445418077912D+00, & 0.0189700426400216D+00, & 0.1692633554656758D+00, & 0.8117666018943028D+00, & 0.0189700426400216D+00, & 0.8117666018943028D+00, & 0.1692633554656761D+00, & 0.0267407842221270D+00, & 0.1196509552487583D+00, & 0.8536082605291148D+00, & 0.0267407842221270D+00, & 0.8536082605291149D+00, & 0.1196509552487586D+00, & 0.0008538186935375D+00, & 0.2830190971292687D+00, & 0.7161270841771940D+00, & 0.0008538186935375D+00, & 0.7161270841771940D+00, & 0.2830190971292690D+00, & 0.0122584700439817D+00, & 0.0704045501511468D+00, & 0.9173369798048717D+00, & 0.0122584700439817D+00, & 0.9173369798048717D+00, & 0.0704045501511471D+00, & 0.0371700471134970D+00, & 0.2164720987514121D+00, & 0.7463578541350910D+00, & 0.0371700471134970D+00, & 0.7463578541350910D+00, & 0.2164720987514124D+00, & 0.0321942006634705D+00, & 0.0769268815632591D+00, & 0.8908789177732706D+00, & 0.0321942006634705D+00, & 0.8908789177732707D+00, & 0.0769268815632594D+00, & 0.0089321527113154D+00, & 0.4292227320385513D+00, & 0.5618451152501336D+00, & 0.0089321527113154D+00, & 0.5618451152501334D+00, & 0.4292227320385515D+00, & 0.0157037453637933D+00, & 0.0157037453637930D+00, & 0.9685925092724137D+00, & 0.2938899628974431D+00, & 0.2938899628974431D+00, & 0.4122200742051139D+00, & 0.2597942631525167D+00, & 0.3701028684237417D+00, & 0.3701028684237418D+00, & 0.2240452152274997D+00, & 0.3251479248852049D+00, & 0.4508068598872956D+00, & 0.2240452152274997D+00, & 0.4508068598872956D+00, & 0.3251479248852050D+00, & 0.1876262169906757D+00, & 0.2782727102869364D+00, & 0.5341010727223882D+00, & 0.1876262169906757D+00, & 0.5341010727223882D+00, & 0.2782727102869366D+00, & 0.0097585213238681D+00, & 0.2852102535187100D+00, & 0.7050312251574220D+00, & 0.0097585213238681D+00, & 0.7050312251574220D+00, & 0.2852102535187103D+00, & 0.0587062906216736D+00, & 0.2727256318298311D+00, & 0.6685680775484956D+00, & 0.0587062906216736D+00, & 0.6685680775484956D+00, & 0.2727256318298313D+00, & 0.0307419996861603D+00, & 0.4154695947712395D+00, & 0.5537884055426004D+00, & 0.0307419996861603D+00, & 0.5537884055426003D+00, & 0.4154695947712397D+00, & 0.0032567536371102D+00, & 0.2205774465337091D+00, & 0.7761657998291810D+00, & 0.0032567536371102D+00, & 0.7761657998291810D+00, & 0.2205774465337094D+00, & 0.0451876229604891D+00, & 0.3428856203943588D+00, & 0.6119267566451523D+00, & 0.0451876229604891D+00, & 0.6119267566451522D+00, & 0.3428856203943590D+00, & 0.1508185102240568D+00, & 0.2315038606116803D+00, & 0.6176776291642632D+00, & 0.1508185102240568D+00, & 0.6176776291642631D+00, & 0.2315038606116805D+00, & 0.0166736740374799D+00, & 0.0381017129649183D+00, & 0.9452246129976019D+00, & 0.0166736740374799D+00, & 0.9452246129976022D+00, & 0.0381017129649186D+00, & 0.1621052421455440D+00, & 0.3528911085101678D+00, & 0.4850036493442885D+00, & 0.1621052421455440D+00, & 0.4850036493442884D+00, & 0.3528911085101679D+00, & 0.0645258600999304D+00, & 0.4000760699195811D+00, & 0.5353980699804888D+00, & 0.0645258600999304D+00, & 0.5353980699804887D+00, & 0.4000760699195813D+00, & 0.1143796954685691D+00, & 0.1877843415465376D+00, & 0.6978359629848935D+00, & 0.1143796954685691D+00, & 0.6978359629848934D+00, & 0.1877843415465379D+00, & 0.0695719958527821D+00, & 0.2073769376903412D+00, & 0.7230510664568770D+00, & 0.0695719958527821D+00, & 0.7230510664568770D+00, & 0.2073769376903414D+00, & 0.0560343597005426D+00, & 0.1078038302263755D+00, & 0.8361618100730821D+00, & 0.0560343597005426D+00, & 0.8361618100730820D+00, & 0.1078038302263758D+00, & 0.0815896657841671D+00, & 0.1479014660731261D+00, & 0.7705088681427070D+00, & 0.0815896657841671D+00, & 0.7705088681427070D+00, & 0.1479014660731263D+00, & 0.0446292737712247D+00, & 0.1600426684113588D+00, & 0.7953280578174167D+00, & 0.0446292737712247D+00, & 0.7953280578174167D+00, & 0.1600426684113591D+00, & 0.1087918765992174D+00, & 0.3778766696887721D+00, & 0.5133314537120108D+00, & 0.1087918765992174D+00, & 0.5133314537120107D+00, & 0.3778766696887723D+00, & 0.2526963148522068D+00, & 0.2526963148522067D+00, & 0.4946073702955866D+00, & 0.0032061485845242D+00, & 0.0392233696648084D+00, & 0.9575704817506674D+00, & 0.0032061485845242D+00, & 0.9575704817506674D+00, & 0.0392233696648088D+00, & 0.0829765480589191D+00, & 0.3243044450771382D+00, & 0.5927190068639430D+00, & 0.0829765480589191D+00, & 0.5927190068639429D+00, & 0.3243044450771383D+00, & 0.2105771295148044D+00, & 0.2105771295148043D+00, & 0.5788457409703917D+00, & 0.0030575106285422D+00, & 0.0030575106285418D+00, & 0.9938849787429160D+00, & 0.1934155554514744D+00, & 0.4032922222742629D+00, & 0.4032922222742630D+00, & 0.0464967063994142D+00, & 0.4767516468002930D+00, & 0.4767516468002931D+00, & 0.0035207350099882D+00, & 0.3509848476225048D+00, & 0.6454944173675073D+00, & 0.0035207350099882D+00, & 0.6454944173675070D+00, & 0.3509848476225050D+00, & 0.0648562451597028D+00, & 0.0648562451597025D+00, & 0.8702875096805948D+00, & 0.1688963797829620D+00, & 0.1688963797829618D+00, & 0.6622072404340763D+00, & 0.3333333333333334D+00, & 0.0005982947286368D+00, & 0.4208708276256937D+00, & 0.5785308776456698D+00, & 0.0005982947286368D+00, & 0.5785308776456696D+00, & 0.4208708276256939D+00, & 0.0962980341591579D+00, & 0.0962980341591576D+00, & 0.8074039316816847D+00, & 0.0996837194601995D+00, & 0.2526560385602647D+00, & 0.6476602419795360D+00, & 0.0996837194601995D+00, & 0.6476602419795360D+00, & 0.2526560385602649D+00, & 0.0185968617395921D+00, & 0.4907015691302040D+00, & 0.4907015691302042D+00, & 0.0030708415268048D+00, & 0.4984645792365977D+00, & 0.4984645792365979D+00, & 0.1308239143750487D+00, & 0.3016703335605276D+00, & 0.5675057520644240D+00, & 0.1308239143750487D+00, & 0.5675057520644239D+00, & 0.3016703335605278D+00, & 0.1354560447863873D+00, & 0.4322719776068065D+00, & 0.4322719776068065D+00, & 0.1302416069902094D+00, & 0.1302416069902092D+00, & 0.7395167860195816D+00, & 0.0862565256913544D+00, & 0.4568717371543228D+00, & 0.4568717371543230D+00, & 0.0029955877400127D+00, & 0.0160613879667907D+00, & 0.9809430242931966D+00, & 0.0029955877400127D+00, & 0.9809430242931966D+00, & 0.0160613879667911D+00 /) c = (/ & 0.8312942125952764D+00, & 0.0015279490490133D+00, & 0.1671778383557102D+00, & 0.1671778383557104D+00, & 0.0015279490490130D+00, & 0.8312942125952762D+00, & 0.6135500780826214D+00, & 0.0149718224721410D+00, & 0.3714780994452372D+00, & 0.3714780994452375D+00, & 0.0149718224721410D+00, & 0.6135500780826213D+00, & 0.8341718564884986D+00, & 0.0068042587991278D+00, & 0.1590238847123734D+00, & 0.1590238847123737D+00, & 0.0068042587991276D+00, & 0.8341718564884986D+00, & 0.9184680923701788D+00, & 0.0353139747015547D+00, & 0.0462179329282663D+00, & 0.0462179329282665D+00, & 0.0353139747015544D+00, & 0.9184680923701787D+00, & 0.8835508461723147D+00, & 0.0015839864476048D+00, & 0.1148651673800805D+00, & 0.1148651673800806D+00, & 0.0015839864476045D+00, & 0.8835508461723145D+00, & 0.6442373197308037D+00, & 0.0215166720844817D+00, & 0.3342460081847143D+00, & 0.3342460081847144D+00, & 0.0215166720844816D+00, & 0.6442373197308036D+00, & 0.9256035733590469D+00, & 0.0020252616925631D+00, & 0.0723711649483898D+00, & 0.0723711649483900D+00, & 0.0020252616925630D+00, & 0.9256035733590467D+00, & 0.7609545495861244D+00, & 0.0153612037490869D+00, & 0.2236842466647885D+00, & 0.2236842466647887D+00, & 0.0153612037490866D+00, & 0.7609545495861243D+00, & 0.8787050390615000D+00, & 0.0101659439479151D+00, & 0.1111290169905846D+00, & 0.1111290169905849D+00, & 0.0101659439479147D+00, & 0.8787050390615000D+00, & 0.6935416044083799D+00, & 0.0300138537838292D+00, & 0.2764445418077907D+00, & 0.2764445418077909D+00, & 0.0300138537838291D+00, & 0.6935416044083798D+00, & 0.8117666018943027D+00, & 0.0189700426400215D+00, & 0.1692633554656755D+00, & 0.1692633554656758D+00, & 0.0189700426400213D+00, & 0.8117666018943026D+00, & 0.8536082605291146D+00, & 0.0267407842221270D+00, & 0.1196509552487581D+00, & 0.1196509552487584D+00, & 0.0267407842221268D+00, & 0.8536082605291145D+00, & 0.7161270841771938D+00, & 0.0008538186935376D+00, & 0.2830190971292684D+00, & 0.2830190971292686D+00, & 0.0008538186935373D+00, & 0.7161270841771936D+00, & 0.9173369798048715D+00, & 0.0122584700439817D+00, & 0.0704045501511464D+00, & 0.0704045501511468D+00, & 0.0122584700439815D+00, & 0.9173369798048714D+00, & 0.7463578541350908D+00, & 0.0371700471134971D+00, & 0.2164720987514119D+00, & 0.2164720987514120D+00, & 0.0371700471134968D+00, & 0.7463578541350908D+00, & 0.8908789177732704D+00, & 0.0321942006634705D+00, & 0.0769268815632589D+00, & 0.0769268815632590D+00, & 0.0321942006634702D+00, & 0.8908789177732704D+00, & 0.5618451152501333D+00, & 0.0089321527113153D+00, & 0.4292227320385511D+00, & 0.4292227320385513D+00, & 0.0089321527113153D+00, & 0.5618451152501331D+00, & 0.9685925092724137D+00, & 0.0157037453637933D+00, & 0.0157037453637928D+00, & 0.4122200742051138D+00, & 0.2938899628974431D+00, & 0.2938899628974430D+00, & 0.3701028684237416D+00, & 0.2597942631525166D+00, & 0.3701028684237416D+00, & 0.4508068598872954D+00, & 0.2240452152274997D+00, & 0.3251479248852048D+00, & 0.3251479248852048D+00, & 0.2240452152274996D+00, & 0.4508068598872954D+00, & 0.5341010727223880D+00, & 0.1876262169906757D+00, & 0.2782727102869362D+00, & 0.2782727102869364D+00, & 0.1876262169906756D+00, & 0.5341010727223879D+00, & 0.7050312251574219D+00, & 0.0097585213238681D+00, & 0.2852102535187098D+00, & 0.2852102535187100D+00, & 0.0097585213238680D+00, & 0.7050312251574217D+00, & 0.6685680775484953D+00, & 0.0587062906216735D+00, & 0.2727256318298309D+00, & 0.2727256318298311D+00, & 0.0587062906216734D+00, & 0.6685680775484952D+00, & 0.5537884055426002D+00, & 0.0307419996861601D+00, & 0.4154695947712393D+00, & 0.4154695947712394D+00, & 0.0307419996861602D+00, & 0.5537884055426001D+00, & 0.7761657998291807D+00, & 0.0032567536371102D+00, & 0.2205774465337088D+00, & 0.2205774465337091D+00, & 0.0032567536371099D+00, & 0.7761657998291808D+00, & 0.6119267566451522D+00, & 0.0451876229604891D+00, & 0.3428856203943587D+00, & 0.3428856203943587D+00, & 0.0451876229604889D+00, & 0.6119267566451519D+00, & 0.6176776291642629D+00, & 0.1508185102240568D+00, & 0.2315038606116802D+00, & 0.2315038606116802D+00, & 0.1508185102240566D+00, & 0.6176776291642629D+00, & 0.9452246129976020D+00, & 0.0166736740374799D+00, & 0.0381017129649180D+00, & 0.0381017129649182D+00, & 0.0166736740374797D+00, & 0.9452246129976017D+00, & 0.4850036493442883D+00, & 0.1621052421455439D+00, & 0.3528911085101676D+00, & 0.3528911085101677D+00, & 0.1621052421455439D+00, & 0.4850036493442882D+00, & 0.5353980699804886D+00, & 0.0645258600999303D+00, & 0.4000760699195809D+00, & 0.4000760699195810D+00, & 0.0645258600999302D+00, & 0.5353980699804886D+00, & 0.6978359629848934D+00, & 0.1143796954685691D+00, & 0.1877843415465373D+00, & 0.1877843415465376D+00, & 0.1143796954685690D+00, & 0.6978359629848931D+00, & 0.7230510664568768D+00, & 0.0695719958527820D+00, & 0.2073769376903409D+00, & 0.2073769376903412D+00, & 0.0695719958527818D+00, & 0.7230510664568766D+00, & 0.8361618100730819D+00, & 0.0560343597005426D+00, & 0.1078038302263753D+00, & 0.1078038302263755D+00, & 0.0560343597005425D+00, & 0.8361618100730819D+00, & 0.7705088681427068D+00, & 0.0815896657841671D+00, & 0.1479014660731258D+00, & 0.1479014660731261D+00, & 0.0815896657841669D+00, & 0.7705088681427068D+00, & 0.7953280578174166D+00, & 0.0446292737712247D+00, & 0.1600426684113585D+00, & 0.1600426684113588D+00, & 0.0446292737712245D+00, & 0.7953280578174164D+00, & 0.5133314537120105D+00, & 0.1087918765992172D+00, & 0.3778766696887719D+00, & 0.3778766696887720D+00, & 0.1087918765992172D+00, & 0.5133314537120104D+00, & 0.4946073702955865D+00, & 0.2526963148522068D+00, & 0.2526963148522066D+00, & 0.9575704817506674D+00, & 0.0032061485845242D+00, & 0.0392233696648082D+00, & 0.0392233696648084D+00, & 0.0032061485845241D+00, & 0.9575704817506673D+00, & 0.5927190068639426D+00, & 0.0829765480589191D+00, & 0.3243044450771380D+00, & 0.3243044450771381D+00, & 0.0829765480589190D+00, & 0.5927190068639427D+00, & 0.5788457409703913D+00, & 0.2105771295148043D+00, & 0.2105771295148041D+00, & 0.9938849787429159D+00, & 0.0030575106285421D+00, & 0.0030575106285416D+00, & 0.4032922222742629D+00, & 0.1934155554514743D+00, & 0.4032922222742628D+00, & 0.4767516468002930D+00, & 0.0464967063994142D+00, & 0.4767516468002927D+00, & 0.6454944173675070D+00, & 0.0035207350099882D+00, & 0.3509848476225045D+00, & 0.3509848476225046D+00, & 0.0035207350099882D+00, & 0.6454944173675068D+00, & 0.8702875096805947D+00, & 0.0648562451597028D+00, & 0.0648562451597022D+00, & 0.6622072404340763D+00, & 0.1688963797829620D+00, & 0.1688963797829616D+00, & 0.3333333333333333D+00, & 0.5785308776456696D+00, & 0.0005982947286366D+00, & 0.4208708276256935D+00, & 0.4208708276256937D+00, & 0.0005982947286368D+00, & 0.5785308776456694D+00, & 0.8074039316816846D+00, & 0.0962980341591579D+00, & 0.0962980341591574D+00, & 0.6476602419795358D+00, & 0.0996837194601994D+00, & 0.2526560385602645D+00, & 0.2526560385602646D+00, & 0.0996837194601993D+00, & 0.6476602419795356D+00, & 0.4907015691302040D+00, & 0.0185968617395921D+00, & 0.4907015691302037D+00, & 0.4984645792365976D+00, & 0.0030708415268047D+00, & 0.4984645792365974D+00, & 0.5675057520644238D+00, & 0.1308239143750486D+00, & 0.3016703335605274D+00, & 0.3016703335605275D+00, & 0.1308239143750486D+00, & 0.5675057520644238D+00, & 0.4322719776068064D+00, & 0.1354560447863872D+00, & 0.4322719776068062D+00, & 0.7395167860195815D+00, & 0.1302416069902095D+00, & 0.1302416069902089D+00, & 0.4568717371543228D+00, & 0.0862565256913544D+00, & 0.4568717371543227D+00, & 0.9809430242931965D+00, & 0.0029955877400128D+00, & 0.0160613879667905D+00, & 0.0160613879667907D+00, & 0.0029955877400126D+00, & 0.9809430242931964D+00 /) w = (/ & 0.0003775523678536D+00, & 0.0003775523678536D+00, & 0.0003775523678536D+00, & 0.0003775523678536D+00, & 0.0003775523678536D+00, & 0.0003775523678536D+00, & 0.0015516849698550D+00, & 0.0015516849698550D+00, & 0.0015516849698550D+00, & 0.0015516849698550D+00, & 0.0015516849698550D+00, & 0.0015516849698550D+00, & 0.0008644145607466D+00, & 0.0008644145607466D+00, & 0.0008644145607466D+00, & 0.0008644145607466D+00, & 0.0008644145607466D+00, & 0.0008644145607466D+00, & 0.0009971849318732D+00, & 0.0009971849318732D+00, & 0.0009971849318732D+00, & 0.0009971849318732D+00, & 0.0009971849318732D+00, & 0.0009971849318732D+00, & 0.0004090770312980D+00, & 0.0004090770312980D+00, & 0.0004090770312980D+00, & 0.0004090770312980D+00, & 0.0004090770312980D+00, & 0.0004090770312980D+00, & 0.0020436671600844D+00, & 0.0020436671600844D+00, & 0.0020436671600844D+00, & 0.0020436671600844D+00, & 0.0020436671600844D+00, & 0.0020436671600844D+00, & 0.0004126443326276D+00, & 0.0004126443326276D+00, & 0.0004126443326276D+00, & 0.0004126443326276D+00, & 0.0004126443326276D+00, & 0.0004126443326276D+00, & 0.0019146967543968D+00, & 0.0019146967543968D+00, & 0.0019146967543968D+00, & 0.0019146967543968D+00, & 0.0019146967543968D+00, & 0.0019146967543968D+00, & 0.0011640031359899D+00, & 0.0011640031359899D+00, & 0.0011640031359899D+00, & 0.0011640031359899D+00, & 0.0011640031359899D+00, & 0.0011640031359899D+00, & 0.0029186737106524D+00, & 0.0029186737106524D+00, & 0.0029186737106524D+00, & 0.0029186737106524D+00, & 0.0029186737106524D+00, & 0.0029186737106524D+00, & 0.0019423381723224D+00, & 0.0019423381723224D+00, & 0.0019423381723224D+00, & 0.0019423381723224D+00, & 0.0019423381723224D+00, & 0.0019423381723224D+00, & 0.0020437160642330D+00, & 0.0020437160642330D+00, & 0.0020437160642330D+00, & 0.0020437160642330D+00, & 0.0020437160642330D+00, & 0.0020437160642330D+00, & 0.0004561788584349D+00, & 0.0004561788584349D+00, & 0.0004561788584349D+00, & 0.0004561788584349D+00, & 0.0004561788584349D+00, & 0.0004561788584349D+00, & 0.0011181526506985D+00, & 0.0011181526506985D+00, & 0.0011181526506985D+00, & 0.0011181526506985D+00, & 0.0011181526506985D+00, & 0.0011181526506985D+00, & 0.0030364724116124D+00, & 0.0030364724116124D+00, & 0.0030364724116124D+00, & 0.0030364724116124D+00, & 0.0030364724116124D+00, & 0.0030364724116124D+00, & 0.0019401856791114D+00, & 0.0019401856791114D+00, & 0.0019401856791114D+00, & 0.0019401856791114D+00, & 0.0019401856791114D+00, & 0.0019401856791114D+00, & 0.0019149234843930D+00, & 0.0019149234843930D+00, & 0.0019149234843930D+00, & 0.0019149234843930D+00, & 0.0019149234843930D+00, & 0.0019149234843930D+00, & 0.0006256066196749D+00, & 0.0006256066196749D+00, & 0.0006256066196749D+00, & 0.0085945289589868D+00, & 0.0085945289589868D+00, & 0.0085945289589868D+00, & 0.0085993323415620D+00, & 0.0085993323415620D+00, & 0.0085993323415620D+00, & 0.0082321340562276D+00, & 0.0082321340562276D+00, & 0.0082321340562276D+00, & 0.0082321340562276D+00, & 0.0082321340562276D+00, & 0.0082321340562276D+00, & 0.0075395204858702D+00, & 0.0075395204858702D+00, & 0.0075395204858702D+00, & 0.0075395204858702D+00, & 0.0075395204858702D+00, & 0.0075395204858702D+00, & 0.0018551746248727D+00, & 0.0018551746248727D+00, & 0.0018551746248727D+00, & 0.0018551746248727D+00, & 0.0018551746248727D+00, & 0.0018551746248727D+00, & 0.0044048213741681D+00, & 0.0044048213741681D+00, & 0.0044048213741681D+00, & 0.0044048213741681D+00, & 0.0044048213741681D+00, & 0.0044048213741681D+00, & 0.0038072050061859D+00, & 0.0038072050061859D+00, & 0.0038072050061859D+00, & 0.0038072050061859D+00, & 0.0038072050061859D+00, & 0.0038072050061859D+00, & 0.0009694445790545D+00, & 0.0009694445790545D+00, & 0.0009694445790545D+00, & 0.0009694445790545D+00, & 0.0009694445790545D+00, & 0.0009694445790545D+00, & 0.0042240803334808D+00, & 0.0042240803334808D+00, & 0.0042240803334808D+00, & 0.0042240803334808D+00, & 0.0042240803334808D+00, & 0.0042240803334808D+00, & 0.0066193255529404D+00, & 0.0066193255529404D+00, & 0.0066193255529404D+00, & 0.0066193255529404D+00, & 0.0066193255529404D+00, & 0.0066193255529404D+00, & 0.0010014072888268D+00, & 0.0010014072888268D+00, & 0.0010014072888268D+00, & 0.0010014072888268D+00, & 0.0010014072888268D+00, & 0.0010014072888268D+00, & 0.0075563110745215D+00, & 0.0075563110745215D+00, & 0.0075563110745215D+00, & 0.0075563110745215D+00, & 0.0075563110745215D+00, & 0.0075563110745215D+00, & 0.0052987050439936D+00, & 0.0052987050439936D+00, & 0.0052987050439936D+00, & 0.0052987050439936D+00, & 0.0052987050439936D+00, & 0.0052987050439936D+00, & 0.0055546897961284D+00, & 0.0055546897961284D+00, & 0.0055546897961284D+00, & 0.0055546897961284D+00, & 0.0055546897961284D+00, & 0.0055546897961284D+00, & 0.0045059845609494D+00, & 0.0045059845609494D+00, & 0.0045059845609494D+00, & 0.0045059845609494D+00, & 0.0045059845609494D+00, & 0.0045059845609494D+00, & 0.0031131351389203D+00, & 0.0031131351389203D+00, & 0.0031131351389203D+00, & 0.0031131351389203D+00, & 0.0031131351389203D+00, & 0.0031131351389203D+00, & 0.0043898382162027D+00, & 0.0043898382162027D+00, & 0.0043898382162027D+00, & 0.0043898382162027D+00, & 0.0043898382162027D+00, & 0.0043898382162027D+00, & 0.0032385523720829D+00, & 0.0032385523720829D+00, & 0.0032385523720829D+00, & 0.0032385523720829D+00, & 0.0032385523720829D+00, & 0.0032385523720829D+00, & 0.0065742981116095D+00, & 0.0065742981116095D+00, & 0.0065742981116095D+00, & 0.0065742981116095D+00, & 0.0065742981116095D+00, & 0.0065742981116095D+00, & 0.0080391355993214D+00, & 0.0080391355993214D+00, & 0.0080391355993214D+00, & 0.0004619375803747D+00, & 0.0004619375803747D+00, & 0.0004619375803747D+00, & 0.0004619375803747D+00, & 0.0004619375803747D+00, & 0.0004619375803747D+00, & 0.0056203298622696D+00, & 0.0056203298622696D+00, & 0.0056203298622696D+00, & 0.0056203298622696D+00, & 0.0056203298622696D+00, & 0.0056203298622696D+00, & 0.0072118235949089D+00, & 0.0072118235949089D+00, & 0.0072118235949089D+00, & 0.0001229638851333D+00, & 0.0001229638851333D+00, & 0.0001229638851333D+00, & 0.0080668049674519D+00, & 0.0080668049674519D+00, & 0.0080668049674519D+00, & 0.0046789762284529D+00, & 0.0046789762284529D+00, & 0.0046789762284529D+00, & 0.0012327695569297D+00, & 0.0012327695569297D+00, & 0.0012327695569297D+00, & 0.0012327695569297D+00, & 0.0012327695569297D+00, & 0.0012327695569297D+00, & 0.0027172985719248D+00, & 0.0027172985719248D+00, & 0.0027172985719248D+00, & 0.0062399420305303D+00, & 0.0062399420305303D+00, & 0.0062399420305303D+00, & 0.0087854844528631D+00, & 0.0004490102381961D+00, & 0.0004490102381961D+00, & 0.0004490102381961D+00, & 0.0004490102381961D+00, & 0.0004490102381961D+00, & 0.0004490102381961D+00, & 0.0038909093796050D+00, & 0.0038909093796050D+00, & 0.0038909093796050D+00, & 0.0056881832653567D+00, & 0.0056881832653567D+00, & 0.0056881832653567D+00, & 0.0056881832653567D+00, & 0.0056881832653567D+00, & 0.0056881832653567D+00, & 0.0030289691062773D+00, & 0.0030289691062773D+00, & 0.0030289691062773D+00, & 0.0012050280622555D+00, & 0.0012050280622555D+00, & 0.0012050280622555D+00, & 0.0067479088961223D+00, & 0.0067479088961223D+00, & 0.0067479088961223D+00, & 0.0067479088961223D+00, & 0.0067479088961223D+00, & 0.0067479088961223D+00, & 0.0072248857349589D+00, & 0.0072248857349589D+00, & 0.0072248857349589D+00, & 0.0051363917261404D+00, & 0.0051363917261404D+00, & 0.0051363917261404D+00, & 0.0060844538754953D+00, & 0.0060844538754953D+00, & 0.0060844538754953D+00, & 0.0002785606250486D+00, & 0.0002785606250486D+00, & 0.0002785606250486D+00, & 0.0002785606250486D+00, & 0.0002785606250486D+00, & 0.0002785606250486D+00 /) return end subroutine rule41 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule41() returns the rule of precision 41. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0018100550930815D+00, & 0.9963798898138365D+00, & 0.0018100550930819D+00, & 0.3146077513838778D+00, & 0.3707844972322443D+00, & 0.3146077513838778D+00, & 0.3718324578394357D+00, & 0.3718324578394359D+00, & 0.2563350843211283D+00, & 0.9338478958692606D+00, & 0.0393793019220240D+00, & 0.0267728022087153D+00, & 0.0393793019220239D+00, & 0.9338478958692605D+00, & 0.0267728022087157D+00, & 0.0708749727266859D+00, & 0.9076576411610010D+00, & 0.0214673861123131D+00, & 0.9076576411610010D+00, & 0.0708749727266859D+00, & 0.0214673861123128D+00, & 0.0227676589099524D+00, & 0.9652472298472927D+00, & 0.0119851112427549D+00, & 0.9652472298472928D+00, & 0.0227676589099525D+00, & 0.0119851112427545D+00, & 0.2127026585190979D+00, & 0.6908861388566330D+00, & 0.0964112026242691D+00, & 0.6908861388566331D+00, & 0.2127026585190979D+00, & 0.0964112026242688D+00, & 0.1970799949415202D+00, & 0.6749417822120469D+00, & 0.1279782228464328D+00, & 0.6749417822120470D+00, & 0.1970799949415203D+00, & 0.1279782228464326D+00, & 0.4818489601758344D+00, & 0.4818489601758343D+00, & 0.0363020796483312D+00, & 0.0639130414360007D+00, & 0.8936878519528431D+00, & 0.0423991066111563D+00, & 0.8936878519528432D+00, & 0.0639130414360007D+00, & 0.0423991066111560D+00, & 0.0916254632757577D+00, & 0.8966875393230677D+00, & 0.0116869974011748D+00, & 0.8966875393230677D+00, & 0.0916254632757578D+00, & 0.0116869974011745D+00, & 0.0889175403557380D+00, & 0.8478409267056788D+00, & 0.0632415329385833D+00, & 0.8478409267056788D+00, & 0.0889175403557381D+00, & 0.0632415329385829D+00, & 0.4592305589036990D+00, & 0.5259284962555215D+00, & 0.0148409448407795D+00, & 0.5259284962555214D+00, & 0.4592305589036990D+00, & 0.0148409448407795D+00, & 0.0338843822348439D+00, & 0.9642755781495430D+00, & 0.0018400396156133D+00, & 0.9642755781495431D+00, & 0.0338843822348439D+00, & 0.0018400396156128D+00, & 0.3200752104066154D+00, & 0.4218676758535129D+00, & 0.2580571137398716D+00, & 0.4218676758535129D+00, & 0.3200752104066154D+00, & 0.2580571137398715D+00, & 0.1422819983084207D+00, & 0.7154360033831583D+00, & 0.1422819983084210D+00, & 0.4220684925318889D+00, & 0.5417122820340925D+00, & 0.0362192254340186D+00, & 0.5417122820340925D+00, & 0.4220684925318889D+00, & 0.0362192254340186D+00, & 0.0478764410729284D+00, & 0.9415795928827051D+00, & 0.0105439660443666D+00, & 0.9415795928827051D+00, & 0.0478764410729285D+00, & 0.0105439660443662D+00, & 0.1746336148663416D+00, & 0.6507327702673166D+00, & 0.1746336148663419D+00, & 0.4251980784151399D+00, & 0.4251980784151399D+00, & 0.1496038431697200D+00, & 0.3617990227060762D+00, & 0.4871740897943582D+00, & 0.1510268874995655D+00, & 0.4871740897943583D+00, & 0.3617990227060763D+00, & 0.1510268874995655D+00, & 0.2099773723379177D+00, & 0.5800452553241643D+00, & 0.2099773723379179D+00, & 0.0684569430922210D+00, & 0.9290609960060465D+00, & 0.0024820609017325D+00, & 0.9290609960060466D+00, & 0.0684569430922210D+00, & 0.0024820609017321D+00, & 0.2362884725964560D+00, & 0.6087537603815811D+00, & 0.1549577670219628D+00, & 0.6087537603815811D+00, & 0.2362884725964560D+00, & 0.1549577670219627D+00, & 0.2978954189850496D+00, & 0.5501430273498515D+00, & 0.1519615536650988D+00, & 0.5501430273498515D+00, & 0.2978954189850496D+00, & 0.1519615536650987D+00, & 0.1125572515239218D+00, & 0.8850652027457061D+00, & 0.0023775457303723D+00, & 0.8850652027457061D+00, & 0.1125572515239218D+00, & 0.0023775457303719D+00, & 0.0120658629713076D+00, & 0.9848848989428542D+00, & 0.0030492380858384D+00, & 0.9848848989428541D+00, & 0.0120658629713077D+00, & 0.0030492380858379D+00, & 0.3906530970863169D+00, & 0.5942714371631589D+00, & 0.0150754657505243D+00, & 0.5942714371631588D+00, & 0.3906530970863170D+00, & 0.0150754657505242D+00, & 0.4274107273739702D+00, & 0.5697047185184613D+00, & 0.0028845541075684D+00, & 0.5697047185184614D+00, & 0.4274107273739702D+00, & 0.0028845541075684D+00, & 0.2627399736253427D+00, & 0.4745200527493144D+00, & 0.2627399736253428D+00, & 0.4118455220977197D+00, & 0.4833893401764346D+00, & 0.1047651377258456D+00, & 0.4833893401764346D+00, & 0.4118455220977197D+00, & 0.1047651377258456D+00, & 0.4986036392311143D+00, & 0.4986036392311143D+00, & 0.0027927215377713D+00, & 0.3222211945168437D+00, & 0.6629470379075842D+00, & 0.0148317675755723D+00, & 0.6629470379075841D+00, & 0.3222211945168438D+00, & 0.0148317675755720D+00, & 0.3545249016308813D+00, & 0.6087299048044915D+00, & 0.0367451935646271D+00, & 0.6087299048044915D+00, & 0.3545249016308814D+00, & 0.0367451935646270D+00, & 0.3320276172987797D+00, & 0.4651394056449660D+00, & 0.2028329770562542D+00, & 0.4651394056449660D+00, & 0.3320276172987797D+00, & 0.2028329770562542D+00, & 0.2530297390847723D+00, & 0.6813809432255311D+00, & 0.0655893176896967D+00, & 0.6813809432255310D+00, & 0.2530297390847723D+00, & 0.0655893176896965D+00, & 0.3570399048945097D+00, & 0.6401266872236777D+00, & 0.0028334078818126D+00, & 0.6401266872236777D+00, & 0.3570399048945097D+00, & 0.0028334078818124D+00, & 0.2870606892116554D+00, & 0.6768867950216703D+00, & 0.0360525157666745D+00, & 0.6768867950216702D+00, & 0.2870606892116554D+00, & 0.0360525157666742D+00, & 0.1361313516311361D+00, & 0.8497124512417364D+00, & 0.0141561971271276D+00, & 0.8497124512417363D+00, & 0.1361313516311361D+00, & 0.0141561971271272D+00, & 0.1322241256617750D+00, & 0.8040030646660921D+00, & 0.0637728096721329D+00, & 0.8040030646660922D+00, & 0.1322241256617751D+00, & 0.0637728096721326D+00, & 0.1079242198395523D+00, & 0.8585223406145746D+00, & 0.0335534395458731D+00, & 0.8585223406145744D+00, & 0.1079242198395524D+00, & 0.0335534395458729D+00, & 0.1528869021413866D+00, & 0.7475340532550706D+00, & 0.0995790446035428D+00, & 0.7475340532550706D+00, & 0.1528869021413866D+00, & 0.0995790446035426D+00, & 0.1881017719296066D+00, & 0.7472490760453540D+00, & 0.0646491520250393D+00, & 0.7472490760453540D+00, & 0.1881017719296067D+00, & 0.0646491520250392D+00, & 0.2549824291508879D+00, & 0.7301188439783041D+00, & 0.0148987268708080D+00, & 0.7301188439783041D+00, & 0.2549824291508879D+00, & 0.0148987268708078D+00, & 0.2230780804812777D+00, & 0.7740674722407084D+00, & 0.0028544472780139D+00, & 0.7740674722407084D+00, & 0.2230780804812778D+00, & 0.0028544472780137D+00, & 0.3995665255269703D+00, & 0.3995665255269703D+00, & 0.2008669489460594D+00, & 0.1640507360210325D+00, & 0.8331184921577857D+00, & 0.0028307718211819D+00, & 0.8331184921577858D+00, & 0.1640507360210327D+00, & 0.0028307718211816D+00, & 0.2881511174189886D+00, & 0.7090129357844225D+00, & 0.0028359467965890D+00, & 0.7090129357844225D+00, & 0.2881511174189885D+00, & 0.0028359467965888D+00, & 0.3409577888740615D+00, & 0.5534095248477606D+00, & 0.1056326862781778D+00, & 0.5534095248477606D+00, & 0.3409577888740616D+00, & 0.1056326862781778D+00, & 0.2682934480692839D+00, & 0.5262976561479694D+00, & 0.2054088957827467D+00, & 0.5262976561479694D+00, & 0.2682934480692839D+00, & 0.2054088957827466D+00, & 0.3194090035283247D+00, & 0.6131123654037490D+00, & 0.0674786310679263D+00, & 0.6131123654037490D+00, & 0.3194090035283247D+00, & 0.0674786310679262D+00, & 0.1922954651859523D+00, & 0.7927714274510961D+00, & 0.0149331073629516D+00, & 0.7927714274510962D+00, & 0.1922954651859524D+00, & 0.0149331073629514D+00, & 0.1604140534029236D+00, & 0.8042006531916337D+00, & 0.0353852934054428D+00, & 0.8042006531916338D+00, & 0.1604140534029238D+00, & 0.0353852934054425D+00, & 0.2212534989804217D+00, & 0.7424945051857205D+00, & 0.0362519958338579D+00, & 0.7424945051857206D+00, & 0.2212534989804218D+00, & 0.0362519958338575D+00, & 0.2711942240688135D+00, & 0.6222060789581492D+00, & 0.1065996969730373D+00, & 0.6222060789581491D+00, & 0.2711942240688137D+00, & 0.1065996969730372D+00, & 0.3923234112997704D+00, & 0.5411068810465550D+00, & 0.0665697076536745D+00, & 0.5411068810465550D+00, & 0.3923234112997703D+00, & 0.0665697076536745D+00, & 0.4667610577855150D+00, & 0.4667610577855150D+00, & 0.0664778844289700D+00, & 0.1030954855760305D+00, & 0.7938090288479388D+00, & 0.1030954855760309D+00 /) b = (/ & 0.0018100550930818D+00, & 0.0018100550930815D+00, & 0.9963798898138368D+00, & 0.3146077513838779D+00, & 0.3146077513838779D+00, & 0.3707844972322444D+00, & 0.2563350843211284D+00, & 0.3718324578394359D+00, & 0.3718324578394359D+00, & 0.0267728022087155D+00, & 0.9338478958692606D+00, & 0.0393793019220242D+00, & 0.0267728022087155D+00, & 0.0393793019220238D+00, & 0.9338478958692606D+00, & 0.0214673861123130D+00, & 0.0708749727266859D+00, & 0.9076576411610012D+00, & 0.0214673861123130D+00, & 0.9076576411610013D+00, & 0.0708749727266862D+00, & 0.0119851112427548D+00, & 0.0227676589099523D+00, & 0.9652472298472929D+00, & 0.0119851112427548D+00, & 0.9652472298472929D+00, & 0.0227676589099527D+00, & 0.0964112026242690D+00, & 0.2127026585190980D+00, & 0.6908861388566332D+00, & 0.0964112026242690D+00, & 0.6908861388566333D+00, & 0.2127026585190982D+00, & 0.1279782228464328D+00, & 0.1970799949415202D+00, & 0.6749417822120471D+00, & 0.1279782228464328D+00, & 0.6749417822120471D+00, & 0.1970799949415204D+00, & 0.0363020796483313D+00, & 0.4818489601758345D+00, & 0.4818489601758346D+00, & 0.0423991066111562D+00, & 0.0639130414360007D+00, & 0.8936878519528434D+00, & 0.0423991066111562D+00, & 0.8936878519528434D+00, & 0.0639130414360010D+00, & 0.0116869974011747D+00, & 0.0916254632757577D+00, & 0.8966875393230677D+00, & 0.0116869974011747D+00, & 0.8966875393230677D+00, & 0.0916254632757580D+00, & 0.0632415329385832D+00, & 0.0889175403557380D+00, & 0.8478409267056790D+00, & 0.0632415329385832D+00, & 0.8478409267056790D+00, & 0.0889175403557383D+00, & 0.0148409448407795D+00, & 0.4592305589036991D+00, & 0.5259284962555217D+00, & 0.0148409448407795D+00, & 0.5259284962555215D+00, & 0.4592305589036992D+00, & 0.0018400396156131D+00, & 0.0338843822348439D+00, & 0.9642755781495430D+00, & 0.0018400396156131D+00, & 0.9642755781495433D+00, & 0.0338843822348442D+00, & 0.2580571137398717D+00, & 0.3200752104066155D+00, & 0.4218676758535131D+00, & 0.2580571137398717D+00, & 0.4218676758535130D+00, & 0.3200752104066156D+00, & 0.1422819983084210D+00, & 0.1422819983084208D+00, & 0.7154360033831585D+00, & 0.0362192254340186D+00, & 0.4220684925318890D+00, & 0.5417122820340926D+00, & 0.0362192254340186D+00, & 0.5417122820340925D+00, & 0.4220684925318892D+00, & 0.0105439660443664D+00, & 0.0478764410729283D+00, & 0.9415795928827053D+00, & 0.0105439660443664D+00, & 0.9415795928827053D+00, & 0.0478764410729287D+00, & 0.1746336148663418D+00, & 0.1746336148663417D+00, & 0.6507327702673166D+00, & 0.1496038431697201D+00, & 0.4251980784151401D+00, & 0.4251980784151402D+00, & 0.1510268874995656D+00, & 0.3617990227060763D+00, & 0.4871740897943584D+00, & 0.1510268874995656D+00, & 0.4871740897943583D+00, & 0.3617990227060764D+00, & 0.2099773723379179D+00, & 0.2099773723379178D+00, & 0.5800452553241644D+00, & 0.0024820609017324D+00, & 0.0684569430922209D+00, & 0.9290609960060469D+00, & 0.0024820609017324D+00, & 0.9290609960060469D+00, & 0.0684569430922213D+00, & 0.1549577670219629D+00, & 0.2362884725964561D+00, & 0.6087537603815814D+00, & 0.1549577670219629D+00, & 0.6087537603815814D+00, & 0.2362884725964562D+00, & 0.1519615536650989D+00, & 0.2978954189850497D+00, & 0.5501430273498518D+00, & 0.1519615536650989D+00, & 0.5501430273498517D+00, & 0.2978954189850498D+00, & 0.0023775457303722D+00, & 0.1125572515239218D+00, & 0.8850652027457062D+00, & 0.0023775457303722D+00, & 0.8850652027457062D+00, & 0.1125572515239221D+00, & 0.0030492380858382D+00, & 0.0120658629713075D+00, & 0.9848848989428544D+00, & 0.0030492380858382D+00, & 0.9848848989428544D+00, & 0.0120658629713080D+00, & 0.0150754657505243D+00, & 0.3906530970863170D+00, & 0.5942714371631590D+00, & 0.0150754657505243D+00, & 0.5942714371631588D+00, & 0.3906530970863172D+00, & 0.0028845541075685D+00, & 0.4274107273739702D+00, & 0.5697047185184615D+00, & 0.0028845541075685D+00, & 0.5697047185184614D+00, & 0.4274107273739705D+00, & 0.2627399736253429D+00, & 0.2627399736253428D+00, & 0.4745200527493146D+00, & 0.1047651377258457D+00, & 0.4118455220977198D+00, & 0.4833893401764348D+00, & 0.1047651377258457D+00, & 0.4833893401764347D+00, & 0.4118455220977200D+00, & 0.0027927215377714D+00, & 0.4986036392311144D+00, & 0.4986036392311146D+00, & 0.0148317675755722D+00, & 0.3222211945168437D+00, & 0.6629470379075844D+00, & 0.0148317675755722D+00, & 0.6629470379075841D+00, & 0.3222211945168439D+00, & 0.0367451935646272D+00, & 0.3545249016308813D+00, & 0.6087299048044917D+00, & 0.0367451935646272D+00, & 0.6087299048044916D+00, & 0.3545249016308816D+00, & 0.2028329770562543D+00, & 0.3320276172987798D+00, & 0.4651394056449663D+00, & 0.2028329770562543D+00, & 0.4651394056449661D+00, & 0.3320276172987799D+00, & 0.0655893176896967D+00, & 0.2530297390847723D+00, & 0.6813809432255312D+00, & 0.0655893176896967D+00, & 0.6813809432255311D+00, & 0.2530297390847726D+00, & 0.0028334078818125D+00, & 0.3570399048945098D+00, & 0.6401266872236778D+00, & 0.0028334078818125D+00, & 0.6401266872236778D+00, & 0.3570399048945100D+00, & 0.0360525157666744D+00, & 0.2870606892116554D+00, & 0.6768867950216704D+00, & 0.0360525157666744D+00, & 0.6768867950216704D+00, & 0.2870606892116557D+00, & 0.0141561971271275D+00, & 0.1361313516311361D+00, & 0.8497124512417367D+00, & 0.0141561971271275D+00, & 0.8497124512417367D+00, & 0.1361313516311364D+00, & 0.0637728096721328D+00, & 0.1322241256617750D+00, & 0.8040030646660923D+00, & 0.0637728096721328D+00, & 0.8040030646660923D+00, & 0.1322241256617753D+00, & 0.0335534395458731D+00, & 0.1079242198395524D+00, & 0.8585223406145748D+00, & 0.0335534395458731D+00, & 0.8585223406145748D+00, & 0.1079242198395527D+00, & 0.0995790446035428D+00, & 0.1528869021413866D+00, & 0.7475340532550708D+00, & 0.0995790446035428D+00, & 0.7475340532550708D+00, & 0.1528869021413868D+00, & 0.0646491520250394D+00, & 0.1881017719296067D+00, & 0.7472490760453542D+00, & 0.0646491520250394D+00, & 0.7472490760453542D+00, & 0.1881017719296069D+00, & 0.0148987268708080D+00, & 0.2549824291508879D+00, & 0.7301188439783043D+00, & 0.0148987268708080D+00, & 0.7301188439783043D+00, & 0.2549824291508882D+00, & 0.0028544472780139D+00, & 0.2230780804812777D+00, & 0.7740674722407086D+00, & 0.0028544472780139D+00, & 0.7740674722407086D+00, & 0.2230780804812780D+00, & 0.2008669489460595D+00, & 0.3995665255269704D+00, & 0.3995665255269705D+00, & 0.0028307718211818D+00, & 0.1640507360210326D+00, & 0.8331184921577858D+00, & 0.0028307718211818D+00, & 0.8331184921577858D+00, & 0.1640507360210328D+00, & 0.0028359467965890D+00, & 0.2881511174189886D+00, & 0.7090129357844227D+00, & 0.0028359467965890D+00, & 0.7090129357844227D+00, & 0.2881511174189888D+00, & 0.1056326862781779D+00, & 0.3409577888740616D+00, & 0.5534095248477607D+00, & 0.1056326862781779D+00, & 0.5534095248477606D+00, & 0.3409577888740618D+00, & 0.2054088957827467D+00, & 0.2682934480692840D+00, & 0.5262976561479695D+00, & 0.2054088957827467D+00, & 0.5262976561479695D+00, & 0.2682934480692841D+00, & 0.0674786310679263D+00, & 0.3194090035283247D+00, & 0.6131123654037492D+00, & 0.0674786310679263D+00, & 0.6131123654037491D+00, & 0.3194090035283249D+00, & 0.0149331073629516D+00, & 0.1922954651859523D+00, & 0.7927714274510964D+00, & 0.0149331073629516D+00, & 0.7927714274510963D+00, & 0.1922954651859526D+00, & 0.0353852934054427D+00, & 0.1604140534029236D+00, & 0.8042006531916338D+00, & 0.0353852934054427D+00, & 0.8042006531916338D+00, & 0.1604140534029239D+00, & 0.0362519958338577D+00, & 0.2212534989804218D+00, & 0.7424945051857206D+00, & 0.0362519958338577D+00, & 0.7424945051857206D+00, & 0.2212534989804221D+00, & 0.1065996969730374D+00, & 0.2711942240688135D+00, & 0.6222060789581494D+00, & 0.1065996969730374D+00, & 0.6222060789581492D+00, & 0.2711942240688138D+00, & 0.0665697076536746D+00, & 0.3923234112997704D+00, & 0.5411068810465552D+00, & 0.0665697076536746D+00, & 0.5411068810465551D+00, & 0.3923234112997706D+00, & 0.0664778844289701D+00, & 0.4667610577855150D+00, & 0.4667610577855152D+00, & 0.1030954855760308D+00, & 0.1030954855760305D+00, & 0.7938090288479389D+00 /) c = (/ & 0.9963798898138366D+00, & 0.0018100550930820D+00, & 0.0018100550930812D+00, & 0.3707844972322443D+00, & 0.3146077513838778D+00, & 0.3146077513838778D+00, & 0.3718324578394358D+00, & 0.2563350843211282D+00, & 0.3718324578394358D+00, & 0.0393793019220238D+00, & 0.0267728022087154D+00, & 0.9338478958692605D+00, & 0.9338478958692605D+00, & 0.0267728022087156D+00, & 0.0393793019220237D+00, & 0.9076576411610010D+00, & 0.0214673861123131D+00, & 0.0708749727266856D+00, & 0.0708749727266860D+00, & 0.0214673861123128D+00, & 0.9076576411610010D+00, & 0.9652472298472928D+00, & 0.0119851112427549D+00, & 0.0227676589099521D+00, & 0.0227676589099524D+00, & 0.0119851112427546D+00, & 0.9652472298472928D+00, & 0.6908861388566330D+00, & 0.0964112026242691D+00, & 0.2127026585190978D+00, & 0.2127026585190979D+00, & 0.0964112026242688D+00, & 0.6908861388566330D+00, & 0.6749417822120470D+00, & 0.1279782228464328D+00, & 0.1970799949415201D+00, & 0.1970799949415202D+00, & 0.1279782228464326D+00, & 0.6749417822120470D+00, & 0.4818489601758343D+00, & 0.0363020796483312D+00, & 0.4818489601758342D+00, & 0.8936878519528431D+00, & 0.0423991066111563D+00, & 0.0639130414360004D+00, & 0.0639130414360007D+00, & 0.0423991066111559D+00, & 0.8936878519528431D+00, & 0.8966875393230676D+00, & 0.0116869974011747D+00, & 0.0916254632757575D+00, & 0.0916254632757577D+00, & 0.0116869974011745D+00, & 0.8966875393230674D+00, & 0.8478409267056789D+00, & 0.0632415329385832D+00, & 0.0889175403557377D+00, & 0.0889175403557380D+00, & 0.0632415329385829D+00, & 0.8478409267056788D+00, & 0.5259284962555214D+00, & 0.0148409448407794D+00, & 0.4592305589036988D+00, & 0.4592305589036991D+00, & 0.0148409448407795D+00, & 0.5259284962555213D+00, & 0.9642755781495431D+00, & 0.0018400396156131D+00, & 0.0338843822348437D+00, & 0.0338843822348438D+00, & 0.0018400396156127D+00, & 0.9642755781495430D+00, & 0.4218676758535130D+00, & 0.2580571137398716D+00, & 0.3200752104066153D+00, & 0.3200752104066154D+00, & 0.2580571137398716D+00, & 0.4218676758535129D+00, & 0.7154360033831584D+00, & 0.1422819983084209D+00, & 0.1422819983084206D+00, & 0.5417122820340924D+00, & 0.0362192254340185D+00, & 0.4220684925318888D+00, & 0.4220684925318889D+00, & 0.0362192254340186D+00, & 0.5417122820340923D+00, & 0.9415795928827051D+00, & 0.0105439660443666D+00, & 0.0478764410729281D+00, & 0.0478764410729285D+00, & 0.0105439660443661D+00, & 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0.0028307718211818D+00, & 0.1640507360210324D+00, & 0.1640507360210325D+00, & 0.0028307718211816D+00, & 0.8331184921577856D+00, & 0.7090129357844225D+00, & 0.0028359467965889D+00, & 0.2881511174189882D+00, & 0.2881511174189886D+00, & 0.0028359467965887D+00, & 0.7090129357844224D+00, & 0.5534095248477605D+00, & 0.1056326862781777D+00, & 0.3409577888740615D+00, & 0.3409577888740615D+00, & 0.1056326862781778D+00, & 0.5534095248477604D+00, & 0.5262976561479693D+00, & 0.2054088957827466D+00, & 0.2682934480692838D+00, & 0.2682934480692838D+00, & 0.2054088957827466D+00, & 0.5262976561479693D+00, & 0.6131123654037490D+00, & 0.0674786310679262D+00, & 0.3194090035283245D+00, & 0.3194090035283246D+00, & 0.0674786310679262D+00, & 0.6131123654037488D+00, & 0.7927714274510961D+00, & 0.0149331073629516D+00, & 0.1922954651859521D+00, & 0.1922954651859523D+00, & 0.0149331073629514D+00, & 0.7927714274510961D+00, & 0.8042006531916337D+00, & 0.0353852934054427D+00, & 0.1604140534029234D+00, & 0.1604140534029235D+00, & 0.0353852934054425D+00, & 0.8042006531916336D+00, & 0.7424945051857205D+00, & 0.0362519958338578D+00, & 0.2212534989804216D+00, & 0.2212534989804217D+00, & 0.0362519958338576D+00, & 0.7424945051857204D+00, & 0.6222060789581491D+00, & 0.1065996969730373D+00, & 0.2711942240688133D+00, & 0.2711942240688135D+00, & 0.1065996969730372D+00, & 0.6222060789581491D+00, & 0.5411068810465549D+00, & 0.0665697076536745D+00, & 0.3923234112997702D+00, & 0.3923234112997703D+00, & 0.0665697076536745D+00, & 0.5411068810465549D+00, & 0.4667610577855149D+00, & 0.0664778844289700D+00, & 0.4667610577855147D+00, & 0.7938090288479388D+00, & 0.1030954855760307D+00, & 0.1030954855760302D+00 /) w = (/ & 0.0000522093231255D+00, & 0.0000522093231255D+00, & 0.0000522093231255D+00, & 0.0064432696708827D+00, & 0.0064432696708827D+00, & 0.0064432696708827D+00, & 0.0056462037725046D+00, & 0.0056462037725046D+00, & 0.0056462037725046D+00, & 0.0009466339964529D+00, & 0.0009466339964529D+00, & 0.0009466339964529D+00, & 0.0009466339964529D+00, & 0.0009466339964529D+00, & 0.0009466339964529D+00, & 0.0010778383293871D+00, & 0.0010778383293871D+00, & 0.0010778383293871D+00, & 0.0010778383293871D+00, & 0.0010778383293871D+00, & 0.0010778383293871D+00, & 0.0005535514063046D+00, & 0.0005535514063046D+00, & 0.0005535514063046D+00, & 0.0005535514063046D+00, & 0.0005535514063046D+00, & 0.0005535514063046D+00, & 0.0037447209152800D+00, & 0.0037447209152800D+00, & 0.0037447209152800D+00, & 0.0037447209152800D+00, & 0.0037447209152800D+00, & 0.0037447209152800D+00, & 0.0040737392096224D+00, & 0.0040737392096224D+00, & 0.0040737392096224D+00, & 0.0040737392096224D+00, & 0.0040737392096224D+00, & 0.0040737392096224D+00, & 0.0029751068247424D+00, & 0.0029751068247424D+00, & 0.0029751068247424D+00, & 0.0017887545706646D+00, & 0.0017887545706646D+00, & 0.0017887545706646D+00, & 0.0017887545706646D+00, & 0.0017887545706646D+00, & 0.0017887545706646D+00, & 0.0010314247381435D+00, & 0.0010314247381435D+00, & 0.0010314247381435D+00, & 0.0010314247381435D+00, & 0.0010314247381435D+00, & 0.0010314247381435D+00, & 0.0025322072683271D+00, & 0.0025322072683271D+00, & 0.0025322072683271D+00, & 0.0025322072683271D+00, & 0.0025322072683271D+00, & 0.0025322072683271D+00, & 0.0022524785579246D+00, & 0.0022524785579246D+00, & 0.0022524785579246D+00, & 0.0022524785579246D+00, & 0.0022524785579246D+00, & 0.0022524785579246D+00, & 0.0002818375084659D+00, & 0.0002818375084659D+00, & 0.0002818375084659D+00, & 0.0002818375084659D+00, & 0.0002818375084659D+00, & 0.0002818375084659D+00, & 0.0061093730696482D+00, & 0.0061093730696482D+00, & 0.0061093730696482D+00, & 0.0061093730696482D+00, & 0.0061093730696482D+00, & 0.0061093730696482D+00, & 0.0042449557771112D+00, & 0.0042449557771112D+00, & 0.0042449557771112D+00, & 0.0033089712153024D+00, & 0.0033089712153024D+00, & 0.0033089712153024D+00, & 0.0033089712153024D+00, & 0.0033089712153024D+00, & 0.0033089712153024D+00, & 0.0007503403741006D+00, & 0.0007503403741006D+00, & 0.0007503403741006D+00, & 0.0007503403741006D+00, & 0.0007503403741006D+00, & 0.0007503403741006D+00, & 0.0050362517089764D+00, & 0.0050362517089764D+00, & 0.0050362517089764D+00, & 0.0060101004771622D+00, & 0.0060101004771622D+00, & 0.0060101004771622D+00, & 0.0062236592332096D+00, & 0.0062236592332096D+00, & 0.0062236592332096D+00, & 0.0062236592332096D+00, & 0.0062236592332096D+00, & 0.0062236592332096D+00, & 0.0060772289969774D+00, & 0.0060772289969774D+00, & 0.0060772289969774D+00, & 0.0004904208710143D+00, & 0.0004904208710143D+00, & 0.0004904208710143D+00, & 0.0004904208710143D+00, & 0.0004904208710143D+00, & 0.0004904208710143D+00, & 0.0058906442657042D+00, & 0.0058906442657042D+00, & 0.0058906442657042D+00, & 0.0058906442657042D+00, & 0.0058906442657042D+00, & 0.0058906442657042D+00, & 0.0062381201191140D+00, & 0.0062381201191140D+00, & 0.0062381201191140D+00, & 0.0062381201191140D+00, & 0.0062381201191140D+00, & 0.0062381201191140D+00, & 0.0005889181881281D+00, & 0.0005889181881281D+00, & 0.0005889181881281D+00, & 0.0005889181881281D+00, & 0.0005889181881281D+00, & 0.0005889181881281D+00, & 0.0002390515618048D+00, & 0.0002390515618048D+00, & 0.0002390515618048D+00, & 0.0002390515618048D+00, & 0.0002390515618048D+00, & 0.0002390515618048D+00, & 0.0023381337598691D+00, & 0.0023381337598691D+00, & 0.0023381337598691D+00, & 0.0023381337598691D+00, & 0.0023381337598691D+00, & 0.0023381337598691D+00, & 0.0010454329707756D+00, & 0.0010454329707756D+00, & 0.0010454329707756D+00, & 0.0010454329707756D+00, & 0.0010454329707756D+00, & 0.0010454329707756D+00, & 0.0067671402084225D+00, & 0.0067671402084225D+00, & 0.0067671402084225D+00, & 0.0059901891203096D+00, & 0.0059901891203096D+00, & 0.0059901891203096D+00, & 0.0059901891203096D+00, & 0.0059901891203096D+00, & 0.0059901891203096D+00, & 0.0010236399703004D+00, & 0.0010236399703004D+00, & 0.0010236399703004D+00, & 0.0022882495872613D+00, & 0.0022882495872613D+00, & 0.0022882495872613D+00, & 0.0022882495872613D+00, & 0.0022882495872613D+00, & 0.0022882495872613D+00, & 0.0036104870565558D+00, & 0.0036104870565558D+00, & 0.0036104870565558D+00, & 0.0036104870565558D+00, & 0.0036104870565558D+00, & 0.0036104870565558D+00, & 0.0070586578085502D+00, & 0.0070586578085502D+00, & 0.0070586578085502D+00, & 0.0070586578085502D+00, & 0.0070586578085502D+00, & 0.0070586578085502D+00, & 0.0043785525737028D+00, & 0.0043785525737028D+00, & 0.0043785525737028D+00, & 0.0043785525737028D+00, & 0.0043785525737028D+00, & 0.0043785525737028D+00, & 0.0010171383589503D+00, & 0.0010171383589503D+00, & 0.0010171383589503D+00, & 0.0010171383589503D+00, & 0.0010171383589503D+00, & 0.0010171383589503D+00, & 0.0034554845247205D+00, & 0.0034554845247205D+00, & 0.0034554845247205D+00, & 0.0034554845247205D+00, & 0.0034554845247205D+00, & 0.0034554845247205D+00, & 0.0016626192415772D+00, & 0.0016626192415772D+00, & 0.0016626192415772D+00, & 0.0016626192415772D+00, & 0.0016626192415772D+00, & 0.0016626192415772D+00, & 0.0033511706532687D+00, & 0.0033511706532687D+00, & 0.0033511706532687D+00, & 0.0033511706532687D+00, & 0.0033511706532687D+00, & 0.0033511706532687D+00, & 0.0023865646505329D+00, & 0.0023865646505329D+00, & 0.0023865646505329D+00, & 0.0023865646505329D+00, & 0.0023865646505329D+00, & 0.0023865646505329D+00, & 0.0041753789931688D+00, & 0.0041753789931688D+00, & 0.0041753789931688D+00, & 0.0041753789931688D+00, & 0.0041753789931688D+00, & 0.0041753789931688D+00, & 0.0038711214885426D+00, & 0.0038711214885426D+00, & 0.0038711214885426D+00, & 0.0038711214885426D+00, & 0.0038711214885426D+00, & 0.0038711214885426D+00, & 0.0021923391960439D+00, & 0.0021923391960439D+00, & 0.0021923391960439D+00, & 0.0021923391960439D+00, & 0.0021923391960439D+00, & 0.0021923391960439D+00, & 0.0009127323365215D+00, & 0.0009127323365215D+00, & 0.0009127323365215D+00, & 0.0009127323365215D+00, & 0.0009127323365215D+00, & 0.0009127323365215D+00, & 0.0072301097329517D+00, & 0.0072301097329517D+00, & 0.0072301097329517D+00, & 0.0008028346526154D+00, & 0.0008028346526154D+00, & 0.0008028346526154D+00, & 0.0008028346526154D+00, & 0.0008028346526154D+00, & 0.0008028346526154D+00, & 0.0009793596015786D+00, & 0.0009793596015786D+00, & 0.0009793596015786D+00, & 0.0009793596015786D+00, & 0.0009793596015786D+00, & 0.0009793596015786D+00, & 0.0059550867608881D+00, & 0.0059550867608881D+00, & 0.0059550867608881D+00, & 0.0059550867608881D+00, & 0.0059550867608881D+00, & 0.0059550867608881D+00, & 0.0067525153387175D+00, & 0.0067525153387175D+00, & 0.0067525153387175D+00, & 0.0067525153387175D+00, & 0.0067525153387175D+00, & 0.0067525153387175D+00, & 0.0049326746082459D+00, & 0.0049326746082459D+00, & 0.0049326746082459D+00, & 0.0049326746082459D+00, & 0.0049326746082459D+00, & 0.0049326746082459D+00, & 0.0019995171236440D+00, & 0.0019995171236440D+00, & 0.0019995171236440D+00, & 0.0019995171236440D+00, & 0.0019995171236440D+00, & 0.0019995171236440D+00, & 0.0028581698928275D+00, & 0.0028581698928275D+00, & 0.0028581698928275D+00, & 0.0028581698928275D+00, & 0.0028581698928275D+00, & 0.0028581698928275D+00, & 0.0032573829494494D+00, & 0.0032573829494494D+00, & 0.0032573829494494D+00, & 0.0032573829494494D+00, & 0.0032573829494494D+00, & 0.0032573829494494D+00, & 0.0058722816583725D+00, & 0.0058722816583725D+00, & 0.0058722816583725D+00, & 0.0058722816583725D+00, & 0.0058722816583725D+00, & 0.0058722816583725D+00, & 0.0050950784475005D+00, & 0.0050950784475005D+00, & 0.0050950784475005D+00, & 0.0050950784475005D+00, & 0.0050950784475005D+00, & 0.0050950784475005D+00, & 0.0051338703252384D+00, & 0.0051338703252384D+00, & 0.0051338703252384D+00, & 0.0039695690393596D+00, & 0.0039695690393596D+00, & 0.0039695690393596D+00 /) return end subroutine rule42 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule42() returns the rule of precision 42. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4023719251097932D+00, & 0.4023719251097932D+00, & 0.1952561497804134D+00, & 0.0013653925759540D+00, & 0.9972692148480916D+00, & 0.0013653925759544D+00, & 0.3305538536843531D+00, & 0.6678757207141839D+00, & 0.0015704256014629D+00, & 0.6678757207141840D+00, & 0.3305538536843532D+00, & 0.0015704256014628D+00, & 0.4975317296252054D+00, & 0.4975317296252054D+00, & 0.0049365407495892D+00, & 0.9699539651466832D+00, & 0.0204313657326067D+00, & 0.0096146691207099D+00, & 0.0204313657326067D+00, & 0.9699539651466832D+00, & 0.0096146691207102D+00, & 0.0571983061939757D+00, & 0.9208981351903950D+00, & 0.0219035586156294D+00, & 0.9208981351903950D+00, & 0.0571983061939758D+00, & 0.0219035586156291D+00, & 0.4799002957544191D+00, & 0.4799002957544192D+00, & 0.0401994084911617D+00, & 0.0664663290557836D+00, & 0.8670673418884325D+00, & 0.0664663290557839D+00, & 0.4532709716379456D+00, & 0.5452354770717635D+00, & 0.0014935512902909D+00, & 0.5452354770717635D+00, & 0.4532709716379456D+00, & 0.0014935512902909D+00, & 0.1407324739067203D+00, & 0.8038260264189151D+00, & 0.0554414996743646D+00, & 0.8038260264189151D+00, & 0.1407324739067203D+00, & 0.0554414996743643D+00, & 0.1837886303019410D+00, & 0.6975178002766640D+00, & 0.1186935694213951D+00, & 0.6975178002766639D+00, & 0.1837886303019411D+00, & 0.1186935694213948D+00, & 0.0432363893877460D+00, & 0.9135272212245076D+00, & 0.0432363893877464D+00, & 0.0321121524868778D+00, & 0.9664947902959359D+00, & 0.0013930572171864D+00, & 0.9664947902959361D+00, & 0.0321121524868780D+00, & 0.0013930572171859D+00, & 0.4903050142016467D+00, & 0.4903050142016467D+00, & 0.0193899715967066D+00, & 0.0429640722006761D+00, & 0.9467364526174824D+00, & 0.0102994751818416D+00, & 0.9467364526174824D+00, & 0.0429640722006762D+00, & 0.0102994751818411D+00, & 0.0105248427300749D+00, & 0.9868904472776370D+00, & 0.0025847099922883D+00, & 0.9868904472776370D+00, & 0.0105248427300750D+00, & 0.0025847099922879D+00, & 0.0753790285629703D+00, & 0.8851466587208721D+00, & 0.0394743127161577D+00, & 0.8851466587208721D+00, & 0.0753790285629704D+00, & 0.0394743127161574D+00, & 0.4363333620899560D+00, & 0.5513727993854914D+00, & 0.0122938385245525D+00, & 0.5513727993854914D+00, & 0.4363333620899560D+00, & 0.0122938385245524D+00, & 0.2704907465149770D+00, & 0.7269194442371774D+00, & 0.0025898092478457D+00, & 0.7269194442371772D+00, & 0.2704907465149770D+00, & 0.0025898092478455D+00, & 0.3508136433810974D+00, & 0.6116299677466058D+00, & 0.0375563888722968D+00, & 0.6116299677466057D+00, & 0.3508136433810974D+00, & 0.0375563888722968D+00, & 0.3727655119742921D+00, & 0.6101399413050006D+00, & 0.0170945467207073D+00, & 0.6101399413050006D+00, & 0.3727655119742921D+00, & 0.0170945467207072D+00, & 0.2171073522633415D+00, & 0.6971343314423426D+00, & 0.0857583162943159D+00, & 0.6971343314423426D+00, & 0.2171073522633415D+00, & 0.0857583162943157D+00, & 0.1927563650090058D+00, & 0.7492579900268798D+00, & 0.0579856449641145D+00, & 0.7492579900268798D+00, & 0.1927563650090059D+00, & 0.0579856449641142D+00, & 0.4206850306864163D+00, & 0.5454667964305935D+00, & 0.0338481728829903D+00, & 0.5454667964305935D+00, & 0.4206850306864162D+00, & 0.0338481728829902D+00, & 0.0269988226283730D+00, & 0.9460023547432537D+00, & 0.0269988226283734D+00, & 0.2124851854370911D+00, & 0.7849881231777003D+00, & 0.0025266913852087D+00, & 0.7849881231777003D+00, & 0.2124851854370911D+00, & 0.0025266913852085D+00, & 0.3192572087291873D+00, & 0.6700862491552849D+00, & 0.0106565421155276D+00, & 0.6700862491552850D+00, & 0.3192572087291874D+00, & 0.0106565421155275D+00, & 0.1385048069103228D+00, & 0.7229903861793542D+00, & 0.1385048069103231D+00, & 0.4670132073557640D+00, & 0.4670132073557640D+00, & 0.0659735852884720D+00, & 0.2516382355125726D+00, & 0.7349320912451689D+00, & 0.0134296732422586D+00, & 0.7349320912451689D+00, & 0.2516382355125727D+00, & 0.0134296732422583D+00, & 0.1522119814568094D+00, & 0.7594462402499256D+00, & 0.0883417782932651D+00, & 0.7594462402499256D+00, & 0.1522119814568094D+00, & 0.0883417782932648D+00, & 0.1111420947940333D+00, & 0.8559357869948059D+00, & 0.0329221182111609D+00, & 0.8559357869948060D+00, & 0.1111420947940334D+00, & 0.0329221182111606D+00, & 0.3581500588512503D+00, & 0.4470491803714221D+00, & 0.1948007607773276D+00, & 0.4470491803714221D+00, & 0.3581500588512503D+00, & 0.1948007607773276D+00, & 0.1637998569561501D+00, & 0.8047391270819582D+00, & 0.0314610159618919D+00, & 0.8047391270819582D+00, & 0.1637998569561501D+00, & 0.0314610159618916D+00, & 0.1021127733366743D+00, & 0.8305189164987998D+00, & 0.0673683101645260D+00, & 0.8305189164987997D+00, & 0.1021127733366744D+00, & 0.0673683101645256D+00, & 0.2335557030193516D+00, & 0.5798790527806756D+00, & 0.1865652441999727D+00, & 0.5798790527806756D+00, & 0.2335557030193516D+00, & 0.1865652441999726D+00, & 0.3214164628317113D+00, & 0.6147000537558933D+00, & 0.0638834834123954D+00, & 0.6147000537558933D+00, & 0.3214164628317114D+00, & 0.0638834834123952D+00, & 0.2233361848957126D+00, & 0.7440925933093376D+00, & 0.0325712217949499D+00, & 0.7440925933093376D+00, & 0.2233361848957126D+00, & 0.0325712217949497D+00, & 0.1905881189463203D+00, & 0.7961383982975219D+00, & 0.0132734827561579D+00, & 0.7961383982975220D+00, & 0.1905881189463203D+00, & 0.0132734827561576D+00, & 0.2273558402454795D+00, & 0.6364103842453923D+00, & 0.1362337755091281D+00, & 0.6364103842453924D+00, & 0.2273558402454797D+00, & 0.1362337755091279D+00, & 0.1065804258588588D+00, & 0.7868391482822822D+00, & 0.1065804258588591D+00, & 0.1567679227871600D+00, & 0.8406166996789507D+00, & 0.0026153775338892D+00, & 0.8406166996789507D+00, & 0.1567679227871602D+00, & 0.0026153775338890D+00, & 0.1340333349867785D+00, & 0.8524854538080647D+00, & 0.0134812112051569D+00, & 0.8524854538080647D+00, & 0.1340333349867785D+00, & 0.0134812112051566D+00, & 0.2957211757454536D+00, & 0.5123947199023402D+00, & 0.1918841043522062D+00, & 0.5123947199023402D+00, & 0.2957211757454536D+00, & 0.1918841043522061D+00, & 0.1067192718130004D+00, & 0.8907334465548298D+00, & 0.0025472816321699D+00, & 0.8907334465548298D+00, & 0.1067192718130003D+00, & 0.0025472816321696D+00, & 0.4125664194839165D+00, & 0.4863962861603238D+00, & 0.1010372943557596D+00, & 0.4863962861603238D+00, & 0.4125664194839165D+00, & 0.1010372943557596D+00, & 0.3078519829928861D+00, & 0.4423972758418252D+00, & 0.2497507411652887D+00, & 0.4423972758418251D+00, & 0.3078519829928861D+00, & 0.2497507411652886D+00, & 0.0870205486996966D+00, & 0.8992668260117453D+00, & 0.0137126252885581D+00, & 0.8992668260117453D+00, & 0.0870205486996967D+00, & 0.0137126252885578D+00, & 0.3894283316812197D+00, & 0.6072270728853777D+00, & 0.0033445954334026D+00, & 0.6072270728853777D+00, & 0.3894283316812197D+00, & 0.0033445954334026D+00, & 0.3117353910725873D+00, & 0.3765292178548252D+00, & 0.3117353910725873D+00, & 0.2612939703141770D+00, & 0.6830313992552178D+00, & 0.0556746304306052D+00, & 0.6830313992552177D+00, & 0.2612939703141770D+00, & 0.0556746304306051D+00, & 0.0649755331098119D+00, & 0.9322207082966478D+00, & 0.0028037585935404D+00, & 0.9322207082966478D+00, & 0.0649755331098119D+00, & 0.0028037585935401D+00, & 0.2719500060981310D+00, & 0.6316994938246291D+00, & 0.0963505000772399D+00, & 0.6316994938246292D+00, & 0.2719500060981311D+00, & 0.0963505000772396D+00, & 0.2930903642725462D+00, & 0.6777105291270178D+00, & 0.0291991066004360D+00, & 0.6777105291270178D+00, & 0.2930903642725463D+00, & 0.0291991066004358D+00, & 0.3946648265878192D+00, & 0.5417606227500117D+00, & 0.0635745506621692D+00, & 0.5417606227500116D+00, & 0.3946648265878193D+00, & 0.0635745506621691D+00, & 0.3568522181929828D+00, & 0.4992192017414733D+00, & 0.1439285800655438D+00, & 0.4992192017414734D+00, & 0.3568522181929829D+00, & 0.1439285800655437D+00, & 0.2448605758688817D+00, & 0.5102788482622364D+00, & 0.2448605758688818D+00, & 0.3413613516388763D+00, & 0.5594299486078240D+00, & 0.0992086997532998D+00, & 0.5594299486078240D+00, & 0.3413613516388763D+00, & 0.0992086997532997D+00, & 0.2895129410795146D+00, & 0.5700981374990226D+00, & 0.1403889214214628D+00, & 0.5700981374990226D+00, & 0.2895129410795146D+00, & 0.1403889214214627D+00, & 0.1748351458111906D+00, & 0.6503297083776184D+00, & 0.1748351458111909D+00, & 0.4275693341501904D+00, & 0.4275693341501904D+00, & 0.1448613316996191D+00, & 0.3742701566784477D+00, & 0.3742701566784477D+00, & 0.2514596866431046D+00 /) b = (/ & 0.1952561497804135D+00, & 0.4023719251097934D+00, & 0.4023719251097935D+00, & 0.0013653925759543D+00, & 0.0013653925759540D+00, & 0.9972692148480918D+00, & 0.0015704256014629D+00, & 0.3305538536843532D+00, & 0.6678757207141842D+00, & 0.0015704256014629D+00, & 0.6678757207141840D+00, & 0.3305538536843535D+00, & 0.0049365407495893D+00, & 0.4975317296252054D+00, & 0.4975317296252056D+00, & 0.0096146691207101D+00, & 0.9699539651466834D+00, & 0.0204313657326070D+00, & 0.0096146691207101D+00, & 0.0204313657326066D+00, & 0.9699539651466834D+00, & 0.0219035586156294D+00, & 0.0571983061939757D+00, & 0.9208981351903952D+00, & 0.0219035586156294D+00, & 0.9208981351903952D+00, & 0.0571983061939760D+00, & 0.0401994084911617D+00, & 0.4799002957544192D+00, & 0.4799002957544193D+00, & 0.0664663290557839D+00, & 0.0664663290557836D+00, & 0.8670673418884327D+00, & 0.0014935512902910D+00, & 0.4532709716379457D+00, & 0.5452354770717637D+00, & 0.0014935512902910D+00, & 0.5452354770717636D+00, & 0.4532709716379458D+00, & 0.0554414996743645D+00, & 0.1407324739067203D+00, & 0.8038260264189153D+00, & 0.0554414996743645D+00, & 0.8038260264189153D+00, & 0.1407324739067206D+00, & 0.1186935694213950D+00, & 0.1837886303019410D+00, & 0.6975178002766641D+00, & 0.1186935694213950D+00, & 0.6975178002766641D+00, & 0.1837886303019413D+00, & 0.0432363893877463D+00, & 0.0432363893877460D+00, & 0.9135272212245078D+00, & 0.0013930572171862D+00, & 0.0321121524868778D+00, & 0.9664947902959360D+00, & 0.0013930572171862D+00, & 0.9664947902959360D+00, & 0.0321121524868782D+00, & 0.0193899715967067D+00, & 0.4903050142016467D+00, & 0.4903050142016469D+00, & 0.0102994751818414D+00, & 0.0429640722006761D+00, & 0.9467364526174826D+00, & 0.0102994751818414D+00, & 0.9467364526174826D+00, & 0.0429640722006765D+00, & 0.0025847099922882D+00, & 0.0105248427300749D+00, & 0.9868904472776371D+00, & 0.0025847099922882D+00, & 0.9868904472776371D+00, & 0.0105248427300752D+00, & 0.0394743127161577D+00, & 0.0753790285629703D+00, & 0.8851466587208722D+00, & 0.0394743127161577D+00, & 0.8851466587208722D+00, & 0.0753790285629706D+00, & 0.0122938385245525D+00, & 0.4363333620899560D+00, & 0.5513727993854917D+00, & 0.0122938385245525D+00, & 0.5513727993854916D+00, & 0.4363333620899563D+00, & 0.0025898092478457D+00, & 0.2704907465149770D+00, & 0.7269194442371776D+00, & 0.0025898092478457D+00, & 0.7269194442371776D+00, & 0.2704907465149773D+00, & 0.0375563888722969D+00, & 0.3508136433810974D+00, & 0.6116299677466061D+00, & 0.0375563888722969D+00, & 0.6116299677466058D+00, & 0.3508136433810976D+00, & 0.0170945467207073D+00, & 0.3727655119742921D+00, & 0.6101399413050007D+00, & 0.0170945467207073D+00, & 0.6101399413050007D+00, & 0.3727655119742924D+00, & 0.0857583162943159D+00, & 0.2171073522633416D+00, & 0.6971343314423428D+00, & 0.0857583162943159D+00, & 0.6971343314423428D+00, & 0.2171073522633418D+00, & 0.0579856449641144D+00, & 0.1927563650090059D+00, & 0.7492579900268799D+00, & 0.0579856449641144D+00, & 0.7492579900268799D+00, & 0.1927563650090061D+00, & 0.0338481728829903D+00, & 0.4206850306864163D+00, & 0.5454667964305936D+00, & 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0.0026153775338892D+00, & 0.1567679227871598D+00, & 0.1567679227871601D+00, & 0.0026153775338892D+00, & 0.8406166996789505D+00, & 0.8524854538080647D+00, & 0.0134812112051568D+00, & 0.1340333349867783D+00, & 0.1340333349867785D+00, & 0.0134812112051567D+00, & 0.8524854538080646D+00, & 0.5123947199023401D+00, & 0.1918841043522061D+00, & 0.2957211757454535D+00, & 0.2957211757454535D+00, & 0.1918841043522062D+00, & 0.5123947199023400D+00, & 0.8907334465548298D+00, & 0.0025472816321699D+00, & 0.1067192718130000D+00, & 0.1067192718130004D+00, & 0.0025472816321696D+00, & 0.8907334465548297D+00, & 0.4863962861603238D+00, & 0.1010372943557597D+00, & 0.4125664194839165D+00, & 0.4125664194839166D+00, & 0.1010372943557597D+00, & 0.4863962861603237D+00, & 0.4423972758418251D+00, & 0.2497507411652887D+00, & 0.3078519829928861D+00, & 0.3078519829928861D+00, & 0.2497507411652886D+00, & 0.4423972758418251D+00, & 0.8992668260117453D+00, & 0.0137126252885580D+00, & 0.0870205486996963D+00, & 0.0870205486996966D+00, & 0.0137126252885578D+00, & 0.8992668260117452D+00, & 0.6072270728853777D+00, & 0.0033445954334025D+00, & 0.3894283316812195D+00, & 0.3894283316812197D+00, & 0.0033445954334025D+00, & 0.6072270728853775D+00, & 0.3765292178548252D+00, & 0.3117353910725874D+00, & 0.3117353910725874D+00, & 0.6830313992552178D+00, & 0.0556746304306052D+00, & 0.2612939703141767D+00, & 0.2612939703141771D+00, & 0.0556746304306051D+00, & 0.6830313992552177D+00, & 0.9322207082966478D+00, & 0.0028037585935403D+00, & 0.0649755331098116D+00, & 0.0649755331098119D+00, & 0.0028037585935402D+00, & 0.9322207082966477D+00, & 0.6316994938246291D+00, & 0.0963505000772398D+00, & 0.2719500060981309D+00, & 0.2719500060981310D+00, & 0.0963505000772397D+00, & 0.6316994938246290D+00, & 0.6777105291270178D+00, & 0.0291991066004360D+00, & 0.2930903642725460D+00, & 0.2930903642725462D+00, & 0.0291991066004359D+00, & 0.6777105291270177D+00, & 0.5417606227500116D+00, & 0.0635745506621690D+00, & 0.3946648265878190D+00, & 0.3946648265878193D+00, & 0.0635745506621691D+00, & 0.5417606227500115D+00, & 0.4992192017414734D+00, & 0.1439285800655438D+00, & 0.3568522181929827D+00, & 0.3568522181929827D+00, & 0.1439285800655437D+00, & 0.4992192017414732D+00, & 0.5102788482622364D+00, & 0.2448605758688819D+00, & 0.2448605758688817D+00, & 0.5594299486078239D+00, & 0.0992086997532996D+00, & 0.3413613516388762D+00, & 0.3413613516388762D+00, & 0.0992086997532997D+00, & 0.5594299486078238D+00, & 0.5700981374990226D+00, & 0.1403889214214628D+00, & 0.2895129410795144D+00, & 0.2895129410795145D+00, & 0.1403889214214628D+00, & 0.5700981374990224D+00, & 0.6503297083776185D+00, & 0.1748351458111909D+00, & 0.1748351458111904D+00, & 0.4275693341501904D+00, & 0.1448613316996192D+00, & 0.4275693341501903D+00, & 0.3742701566784477D+00, & 0.2514596866431046D+00, & 0.3742701566784476D+00 /) w = (/ & 0.0035464400159772D+00, & 0.0035464400159772D+00, & 0.0035464400159772D+00, & 0.0000347195354366D+00, & 0.0000347195354366D+00, & 0.0000347195354366D+00, & 0.0005327316943405D+00, & 0.0005327316943405D+00, & 0.0005327316943405D+00, & 0.0005327316943405D+00, & 0.0005327316943405D+00, & 0.0005327316943405D+00, & 0.0010141696428327D+00, & 0.0010141696428327D+00, & 0.0010141696428327D+00, & 0.0004390770271698D+00, & 0.0004390770271698D+00, & 0.0004390770271698D+00, & 0.0004390770271698D+00, & 0.0004390770271698D+00, & 0.0004390770271698D+00, & 0.0010370250465354D+00, & 0.0010370250465354D+00, & 0.0010370250465354D+00, & 0.0010370250465354D+00, & 0.0010370250465354D+00, & 0.0010370250465354D+00, & 0.0028441859570122D+00, & 0.0028441859570122D+00, & 0.0028441859570122D+00, & 0.0018709815380229D+00, & 0.0018709815380229D+00, & 0.0018709815380229D+00, & 0.0005595519502280D+00, & 0.0005595519502280D+00, & 0.0005595519502280D+00, & 0.0005595519502280D+00, & 0.0005595519502280D+00, & 0.0005595519502280D+00, & 0.0025379205064648D+00, & 0.0025379205064648D+00, & 0.0025379205064648D+00, & 0.0025379205064648D+00, & 0.0025379205064648D+00, & 0.0025379205064648D+00, & 0.0040581577981140D+00, & 0.0040581577981140D+00, & 0.0040581577981140D+00, & 0.0040581577981140D+00, & 0.0040581577981140D+00, & 0.0040581577981140D+00, & 0.0013326250004080D+00, & 0.0013326250004080D+00, & 0.0013326250004080D+00, & 0.0002266425752075D+00, & 0.0002266425752075D+00, & 0.0002266425752075D+00, & 0.0002266425752075D+00, & 0.0002266425752075D+00, & 0.0002266425752075D+00, & 0.0021926816815859D+00, & 0.0021926816815859D+00, & 0.0021926816815859D+00, & 0.0006818533431415D+00, & 0.0006818533431415D+00, & 0.0006818533431415D+00, & 0.0006818533431415D+00, & 0.0006818533431415D+00, & 0.0006818533431415D+00, & 0.0001870930686156D+00, & 0.0001870930686156D+00, & 0.0001870930686156D+00, & 0.0001870930686156D+00, & 0.0001870930686156D+00, & 0.0001870930686156D+00, & 0.0016866296698237D+00, & 0.0016866296698237D+00, & 0.0016866296698237D+00, & 0.0016866296698237D+00, & 0.0016866296698237D+00, & 0.0016866296698237D+00, & 0.0019025497964579D+00, & 0.0019025497964579D+00, & 0.0019025497964579D+00, & 0.0019025497964579D+00, & 0.0019025497964579D+00, & 0.0019025497964579D+00, & 0.0007733670252998D+00, & 0.0007733670252998D+00, & 0.0007733670252998D+00, & 0.0007733670252998D+00, & 0.0007733670252998D+00, & 0.0007733670252998D+00, & 0.0031723878909002D+00, & 0.0031723878909002D+00, & 0.0031723878909002D+00, & 0.0031723878909002D+00, & 0.0031723878909002D+00, & 0.0031723878909002D+00, & 0.0021685247098617D+00, & 0.0021685247098617D+00, & 0.0021685247098617D+00, & 0.0021685247098617D+00, & 0.0021685247098617D+00, & 0.0021685247098617D+00, & 0.0040741174736407D+00, & 0.0040741174736407D+00, & 0.0040741174736407D+00, & 0.0040741174736407D+00, & 0.0040741174736407D+00, & 0.0040741174736407D+00, & 0.0033720890143962D+00, & 0.0033720890143962D+00, & 0.0033720890143962D+00, & 0.0033720890143962D+00, & 0.0033720890143962D+00, & 0.0033720890143962D+00, & 0.0033374654153493D+00, & 0.0033374654153493D+00, & 0.0033374654153493D+00, & 0.0033374654153493D+00, & 0.0033374654153493D+00, & 0.0033374654153493D+00, & 0.0009524059556547D+00, & 0.0009524059556547D+00, & 0.0009524059556547D+00, & 0.0007443004607122D+00, & 0.0007443004607122D+00, & 0.0007443004607122D+00, & 0.0007443004607122D+00, & 0.0007443004607122D+00, & 0.0007443004607122D+00, & 0.0017490056575093D+00, & 0.0017490056575093D+00, & 0.0017490056575093D+00, & 0.0017490056575093D+00, & 0.0017490056575093D+00, & 0.0017490056575093D+00, & 0.0043598500418925D+00, & 0.0043598500418925D+00, & 0.0043598500418925D+00, & 0.0045325322550328D+00, & 0.0045325322550328D+00, & 0.0045325322550328D+00, & 0.0019031683954380D+00, & 0.0019031683954380D+00, & 0.0019031683954380D+00, & 0.0019031683954380D+00, & 0.0019031683954380D+00, & 0.0019031683954380D+00, & 0.0039581444907566D+00, & 0.0039581444907566D+00, & 0.0039581444907566D+00, & 0.0039581444907566D+00, & 0.0039581444907566D+00, & 0.0039581444907566D+00, & 0.0021633300119175D+00, & 0.0021633300119175D+00, & 0.0021633300119175D+00, & 0.0021633300119175D+00, & 0.0021633300119175D+00, & 0.0021633300119175D+00, & 0.0062667413965418D+00, & 0.0062667413965418D+00, & 0.0062667413965418D+00, & 0.0062667413965418D+00, & 0.0062667413965418D+00, & 0.0062667413965418D+00, & 0.0024314709447528D+00, & 0.0024314709447528D+00, & 0.0024314709447528D+00, & 0.0024314709447528D+00, & 0.0024314709447528D+00, & 0.0024314709447528D+00, & 0.0028265780976025D+00, & 0.0028265780976025D+00, & 0.0028265780976025D+00, & 0.0028265780976025D+00, & 0.0028265780976025D+00, & 0.0028265780976025D+00, & 0.0064753562254833D+00, & 0.0064753562254833D+00, & 0.0064753562254833D+00, & 0.0064753562254833D+00, & 0.0064753562254833D+00, & 0.0064753562254833D+00, & 0.0042484824512542D+00, & 0.0042484824512542D+00, & 0.0042484824512542D+00, & 0.0042484824512542D+00, & 0.0042484824512542D+00, & 0.0042484824512542D+00, & 0.0029100859090623D+00, & 0.0029100859090623D+00, & 0.0029100859090623D+00, & 0.0029100859090623D+00, & 0.0029100859090623D+00, & 0.0029100859090623D+00, & 0.0017543943309314D+00, & 0.0017543943309314D+00, & 0.0017543943309314D+00, & 0.0017543943309314D+00, & 0.0017543943309314D+00, & 0.0017543943309314D+00, & 0.0053278143635326D+00, & 0.0053278143635326D+00, & 0.0053278143635326D+00, & 0.0053278143635326D+00, & 0.0053278143635326D+00, & 0.0053278143635326D+00, & 0.0036960706615539D+00, & 0.0036960706615539D+00, & 0.0036960706615539D+00, & 0.0007117355150534D+00, & 0.0007117355150534D+00, & 0.0007117355150534D+00, & 0.0007117355150534D+00, & 0.0007117355150534D+00, & 0.0007117355150534D+00, & 0.0015685196181434D+00, & 0.0015685196181434D+00, & 0.0015685196181434D+00, & 0.0015685196181434D+00, & 0.0015685196181434D+00, & 0.0015685196181434D+00, & 0.0069096837033853D+00, & 0.0069096837033853D+00, & 0.0069096837033853D+00, & 0.0069096837033853D+00, & 0.0069096837033853D+00, & 0.0069096837033853D+00, & 0.0006077668893384D+00, & 0.0006077668893384D+00, & 0.0006077668893384D+00, & 0.0006077668893384D+00, & 0.0006077668893384D+00, & 0.0006077668893384D+00, & 0.0058599060505518D+00, & 0.0058599060505518D+00, & 0.0058599060505518D+00, & 0.0058599060505518D+00, & 0.0058599060505518D+00, & 0.0058599060505518D+00, & 0.0077651860406297D+00, & 0.0077651860406297D+00, & 0.0077651860406297D+00, & 0.0077651860406297D+00, & 0.0077651860406297D+00, & 0.0077651860406297D+00, & 0.0013100408329861D+00, & 0.0013100408329861D+00, & 0.0013100408329861D+00, & 0.0013100408329861D+00, & 0.0013100408329861D+00, & 0.0013100408329861D+00, & 0.0010570972491723D+00, & 0.0010570972491723D+00, & 0.0010570972491723D+00, & 0.0010570972491723D+00, & 0.0010570972491723D+00, & 0.0010570972491723D+00, & 0.0080973376090284D+00, & 0.0080973376090284D+00, & 0.0080973376090284D+00, & 0.0040411976507506D+00, & 0.0040411976507506D+00, & 0.0040411976507506D+00, & 0.0040411976507506D+00, & 0.0040411976507506D+00, & 0.0040411976507506D+00, & 0.0005242478913459D+00, & 0.0005242478913459D+00, & 0.0005242478913459D+00, & 0.0005242478913459D+00, & 0.0005242478913459D+00, & 0.0005242478913459D+00, & 0.0052048680063201D+00, & 0.0052048680063201D+00, & 0.0052048680063201D+00, & 0.0052048680063201D+00, & 0.0052048680063201D+00, & 0.0052048680063201D+00, & 0.0030333113262699D+00, & 0.0030333113262699D+00, & 0.0030333113262699D+00, & 0.0030333113262699D+00, & 0.0030333113262699D+00, & 0.0030333113262699D+00, & 0.0048685523603979D+00, & 0.0048685523603979D+00, & 0.0048685523603979D+00, & 0.0048685523603979D+00, & 0.0048685523603979D+00, & 0.0048685523603979D+00, & 0.0066028726180890D+00, & 0.0066028726180890D+00, & 0.0066028726180890D+00, & 0.0066028726180890D+00, & 0.0066028726180890D+00, & 0.0066028726180890D+00, & 0.0072906010527868D+00, & 0.0072906010527868D+00, & 0.0072906010527868D+00, & 0.0056531366883124D+00, & 0.0056531366883124D+00, & 0.0056531366883124D+00, & 0.0056531366883124D+00, & 0.0056531366883124D+00, & 0.0056531366883124D+00, & 0.0061919290123439D+00, & 0.0061919290123439D+00, & 0.0061919290123439D+00, & 0.0061919290123439D+00, & 0.0061919290123439D+00, & 0.0061919290123439D+00, & 0.0060555267820254D+00, & 0.0060555267820254D+00, & 0.0060555267820254D+00, & 0.0067589446392298D+00, & 0.0067589446392298D+00, & 0.0067589446392298D+00, & 0.0079220445765913D+00, & 0.0079220445765913D+00, & 0.0079220445765913D+00 /) return end subroutine rule43 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule43() returns the rule of precision 43. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4117801708599338D+00, & 0.4117801708599338D+00, & 0.1764396582801323D+00, & 0.4755758670991315D+00, & 0.4755758670991315D+00, & 0.0488482658017370D+00, & 0.2297394365272492D+00, & 0.6248067680849181D+00, & 0.1454537953878327D+00, & 0.6248067680849182D+00, & 0.2297394365272493D+00, & 0.1454537953878325D+00, & 0.4991798367344780D+00, & 0.4991798367344780D+00, & 0.0016403265310439D+00, & 0.2962479881688698D+00, & 0.4075040236622601D+00, & 0.2962479881688698D+00, & 0.3605580760887838D+00, & 0.6070264490694377D+00, & 0.0324154748417785D+00, & 0.6070264490694376D+00, & 0.3605580760887839D+00, & 0.0324154748417784D+00, & 0.0959172276669437D+00, & 0.8916698641086179D+00, & 0.0124129082244385D+00, & 0.8916698641086179D+00, & 0.0959172276669437D+00, & 0.0124129082244381D+00, & 0.1898015101110885D+00, & 0.6723403719974184D+00, & 0.1378581178914931D+00, & 0.6723403719974185D+00, & 0.1898015101110885D+00, & 0.1378581178914929D+00, & 0.4010584512926051D+00, & 0.4636054175537986D+00, & 0.1353361311535962D+00, & 0.4636054175537986D+00, & 0.4010584512926052D+00, & 0.1353361311535961D+00, & 0.2775825322761021D+00, & 0.5788906758314212D+00, & 0.1435267918924767D+00, & 0.5788906758314212D+00, & 0.2775825322761021D+00, & 0.1435267918924765D+00, & 0.3531888048870007D+00, & 0.3531888048870007D+00, & 0.2936223902259985D+00, & 0.3061183766903350D+00, & 0.6584300317131508D+00, & 0.0354515915965141D+00, & 0.6584300317131508D+00, & 0.3061183766903349D+00, & 0.0354515915965140D+00, & 0.4951059808027699D+00, & 0.4951059808027699D+00, & 0.0097880383944601D+00, & 0.4182891701734248D+00, & 0.5462922966952530D+00, & 0.0354185331313221D+00, & 0.5462922966952531D+00, & 0.4182891701734248D+00, & 0.0354185331313221D+00, & 0.0329098159605346D+00, & 0.9341803680789306D+00, & 0.0329098159605350D+00, & 0.0965099243357524D+00, & 0.8476962075384494D+00, & 0.0557938681257983D+00, & 0.8476962075384494D+00, & 0.0965099243357524D+00, & 0.0557938681257979D+00, & 0.1328397411105292D+00, & 0.8031840240996622D+00, & 0.0639762347898087D+00, & 0.8031840240996622D+00, & 0.1328397411105293D+00, & 0.0639762347898084D+00, & 0.0969643297980663D+00, & 0.8727730904601626D+00, & 0.0302625797417711D+00, & 0.8727730904601626D+00, & 0.0969643297980663D+00, & 0.0302625797417709D+00, & 0.4865637511306883D+00, & 0.4865637511306884D+00, & 0.0268724977386232D+00, & 0.4287537536910129D+00, & 0.5566086299500186D+00, & 0.0146376163589685D+00, & 0.5566086299500185D+00, & 0.4287537536910130D+00, & 0.0146376163589684D+00, & 0.0627150483897617D+00, & 0.8745699032204765D+00, & 0.0627150483897621D+00, & 0.1368534453260830D+00, & 0.8495413037445184D+00, & 0.0136052509293986D+00, & 0.8495413037445184D+00, & 0.1368534453260831D+00, & 0.0136052509293983D+00, & 0.3635619090992528D+00, & 0.6339620502785548D+00, & 0.0024760406221923D+00, & 0.6339620502785549D+00, & 0.3635619090992528D+00, & 0.0024760406221921D+00, & 0.1447435597702214D+00, & 0.7105128804595570D+00, & 0.1447435597702216D+00, & 0.3361435723276197D+00, & 0.5209304542944508D+00, & 0.1429259733779294D+00, & 0.5209304542944510D+00, & 0.3361435723276198D+00, & 0.1429259733779293D+00, & 0.0133646206082616D+00, & 0.9732707587834765D+00, & 0.0133646206082620D+00, & 0.0940988534499003D+00, & 0.9034803688043024D+00, & 0.0024207777457974D+00, & 0.9034803688043024D+00, & 0.0940988534499004D+00, & 0.0024207777457970D+00, & 0.2427105866699005D+00, & 0.5621390733405861D+00, & 0.1951503399895134D+00, & 0.5621390733405861D+00, & 0.2427105866699005D+00, & 0.1951503399895132D+00, & 0.4252384428310576D+00, & 0.5107064553472853D+00, & 0.0640551018216570D+00, & 0.5107064553472853D+00, & 0.4252384428310577D+00, & 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0.0341431958895440D+00, & 0.7713906073293496D+00, & 0.1944661967811067D+00, & 0.0138046252946413D+00, & 0.2394826350852046D+00, & 0.7467127396201543D+00, & 0.0138046252946413D+00, & 0.7467127396201543D+00, & 0.2394826350852048D+00, & 0.1864972142995551D+00, & 0.3645542277763408D+00, & 0.4489485579241043D+00, & 0.1864972142995551D+00, & 0.4489485579241042D+00, & 0.3645542277763409D+00, & 0.0025417593646838D+00, & 0.1373564023661998D+00, & 0.8601018382691167D+00, & 0.0025417593646838D+00, & 0.8601018382691167D+00, & 0.1373564023662001D+00, & 0.0630349337046810D+00, & 0.2322320373188904D+00, & 0.7047330289764286D+00, & 0.0630349337046810D+00, & 0.7047330289764286D+00, & 0.2322320373188907D+00, & 0.0638769125793660D+00, & 0.2926613950722469D+00, & 0.6434616923483873D+00, & 0.0638769125793660D+00, & 0.6434616923483871D+00, & 0.2926613950722471D+00, & 0.2419528451754752D+00, & 0.3176481163981568D+00, & 0.4403990384263682D+00, & 0.2419528451754752D+00, & 0.4403990384263682D+00, & 0.3176481163981569D+00, & 0.0145992712589763D+00, & 0.3003015966157783D+00, & 0.6850991321252455D+00, & 0.0145992712589763D+00, & 0.6850991321252453D+00, & 0.3003015966157786D+00, & 0.0028181145969261D+00, & 0.3005613537168110D+00, & 0.6966205316862633D+00, & 0.0028181145969261D+00, & 0.6966205316862629D+00, & 0.3005613537168113D+00, & 0.0341344995593797D+00, & 0.0605239793987312D+00, & 0.9053415210418891D+00, & 0.0341344995593797D+00, & 0.9053415210418891D+00, & 0.0605239793987315D+00, & 0.1933554772764183D+00, & 0.3007859192338894D+00, & 0.5058586034896925D+00, & 0.1933554772764183D+00, & 0.5058586034896925D+00, & 0.3007859192338895D+00, & 0.0973629697501509D+00, & 0.1895507039776853D+00, & 0.7130863262721642D+00, & 0.0973629697501509D+00, & 0.7130863262721641D+00, & 0.1895507039776855D+00, & 0.0027883024051114D+00, & 0.4301399033621490D+00, & 0.5670717942327399D+00, & 0.0027883024051114D+00, & 0.5670717942327398D+00, & 0.4301399033621491D+00, & 0.0027559624464837D+00, & 0.1870185722176647D+00, & 0.8102254653358518D+00, & 0.0027559624464837D+00, & 0.8102254653358517D+00, & 0.1870185722176650D+00, & 0.0978271071588678D+00, & 0.3791895225090076D+00, & 0.5229833703321249D+00, & 0.0978271071588678D+00, & 0.5229833703321249D+00, & 0.3791895225090077D+00, & 0.0995736856368710D+00, & 0.3129669769821593D+00, & 0.5874593373809700D+00, & 0.0995736856368710D+00, & 0.5874593373809698D+00, & 0.3129669769821595D+00, & 0.0341143516662649D+00, & 0.1418044870172890D+00, & 0.8240811613164464D+00, & 0.0341143516662649D+00, & 0.8240811613164463D+00, & 0.1418044870172893D+00, & 0.0942154783080980D+00, & 0.4528922608459511D+00, & 0.4528922608459512D+00, & 0.1004974432729284D+00, & 0.2481814600155886D+00, & 0.6513210967114832D+00, & 0.1004974432729284D+00, & 0.6513210967114832D+00, & 0.2481814600155887D+00, & 0.0616738036965517D+00, & 0.3587978354079987D+00, & 0.5795283608954498D+00, & 0.0616738036965517D+00, & 0.5795283608954497D+00, & 0.3587978354079990D+00, & 0.0928670462140481D+00, & 0.0928670462140479D+00, & 0.8142659075719042D+00, & 0.2524849326490909D+00, & 0.2524849326490908D+00, & 0.4950301347018185D+00 /) c = (/ & 0.4117801708599338D+00, & 0.1764396582801323D+00, & 0.4117801708599337D+00, & 0.4755758670991314D+00, & 0.0488482658017370D+00, & 0.4755758670991312D+00, & 0.6248067680849181D+00, & 0.1454537953878327D+00, & 0.2297394365272490D+00, & 0.2297394365272492D+00, & 0.1454537953878324D+00, & 0.6248067680849181D+00, & 0.4991798367344780D+00, & 0.0016403265310440D+00, & 0.4991798367344778D+00, & 0.4075040236622602D+00, & 0.2962479881688699D+00, & 0.2962479881688699D+00, & 0.6070264490694376D+00, & 0.0324154748417784D+00, & 0.3605580760887837D+00, & 0.3605580760887839D+00, & 0.0324154748417784D+00, & 0.6070264490694375D+00, & 0.8916698641086179D+00, & 0.0124129082244384D+00, & 0.0959172276669434D+00, & 0.0959172276669437D+00, & 0.0124129082244381D+00, & 0.8916698641086179D+00, & 0.6723403719974185D+00, & 0.1378581178914932D+00, & 0.1898015101110884D+00, & 0.1898015101110885D+00, & 0.1378581178914929D+00, & 0.6723403719974185D+00, & 0.4636054175537986D+00, & 0.1353361311535962D+00, & 0.4010584512926051D+00, & 0.4010584512926051D+00, & 0.1353361311535961D+00, & 0.4636054175537985D+00, & 0.5788906758314213D+00, & 0.1435267918924766D+00, & 0.2775825322761020D+00, & 0.2775825322761022D+00, & 0.1435267918924766D+00, & 0.5788906758314212D+00, & 0.3531888048870007D+00, & 0.2936223902259986D+00, & 0.3531888048870007D+00, & 0.6584300317131508D+00, & 0.0354515915965142D+00, & 0.3061183766903348D+00, & 0.3061183766903350D+00, & 0.0354515915965140D+00, & 0.6584300317131507D+00, & 0.4951059808027699D+00, & 0.0097880383944601D+00, & 0.4951059808027697D+00, & 0.5462922966952530D+00, & 0.0354185331313221D+00, & 0.4182891701734245D+00, & 0.4182891701734247D+00, & 0.0354185331313220D+00, & 0.5462922966952530D+00, & 0.9341803680789306D+00, & 0.0329098159605349D+00, & 0.0329098159605343D+00, & 0.8476962075384495D+00, & 0.0557938681257982D+00, & 0.0965099243357521D+00, & 0.0965099243357524D+00, & 0.0557938681257980D+00, & 0.8476962075384494D+00, & 0.8031840240996622D+00, & 0.0639762347898086D+00, & 0.1328397411105290D+00, & 0.1328397411105292D+00, & 0.0639762347898084D+00, & 0.8031840240996621D+00, & 0.8727730904601625D+00, & 0.0302625797417711D+00, & 0.0969643297980661D+00, & 0.0969643297980663D+00, & 0.0302625797417709D+00, & 0.8727730904601624D+00, & 0.4865637511306883D+00, & 0.0268724977386232D+00, & 0.4865637511306882D+00, & 0.5566086299500186D+00, & 0.0146376163589684D+00, & 0.4287537536910128D+00, & 0.4287537536910130D+00, & 0.0146376163589684D+00, & 0.5566086299500184D+00, & 0.8745699032204765D+00, & 0.0627150483897619D+00, & 0.0627150483897614D+00, & 0.8495413037445185D+00, & 0.0136052509293985D+00, & 0.1368534453260828D+00, & 0.1368534453260831D+00, & 0.0136052509293983D+00, & 0.8495413037445183D+00, & 0.6339620502785549D+00, & 0.0024760406221923D+00, & 0.3635619090992527D+00, & 0.3635619090992528D+00, & 0.0024760406221922D+00, & 0.6339620502785547D+00, & 0.7105128804595570D+00, & 0.1447435597702217D+00, & 0.1447435597702212D+00, & 0.5209304542944508D+00, & 0.1429259733779293D+00, & 0.3361435723276197D+00, & 0.3361435723276196D+00, & 0.1429259733779292D+00, & 0.5209304542944507D+00, & 0.9732707587834766D+00, & 0.0133646206082620D+00, & 0.0133646206082614D+00, & 0.9034803688043024D+00, & 0.0024207777457973D+00, & 0.0940988534499001D+00, & 0.0940988534499004D+00, & 0.0024207777457971D+00, & 0.9034803688043024D+00, & 0.5621390733405861D+00, & 0.1951503399895133D+00, & 0.2427105866699004D+00, & 0.2427105866699005D+00, & 0.1951503399895133D+00, & 0.5621390733405861D+00, & 0.5107064553472853D+00, & 0.0640551018216570D+00, & 0.4252384428310575D+00, & 0.4252384428310577D+00, & 0.0640551018216570D+00, & 0.5107064553472852D+00, & 0.6225342617933295D+00, & 0.0131876112324832D+00, & 0.3642781269741872D+00, & 0.3642781269741873D+00, & 0.0131876112324831D+00, & 0.6225342617933294D+00, & 0.7604631914033508D+00, & 0.0618730821070127D+00, & 0.1776637264896362D+00, & 0.1776637264896365D+00, & 0.0618730821070125D+00, & 0.7604631914033507D+00, & 0.9385418797080261D+00, & 0.0026124723427689D+00, & 0.0588456479492049D+00, & 0.0588456479492050D+00, & 0.0026124723427686D+00, & 0.9385418797080262D+00, & 0.7157099945300758D+00, & 0.0341904035600950D+00, & 0.2500996019098289D+00, & 0.2500996019098294D+00, & 0.0341904035600947D+00, & 0.7157099945300756D+00, & 0.9653765821329180D+00, & 0.0026508313305475D+00, & 0.0319725865365343D+00, & 0.0319725865365347D+00, & 0.0026508313305472D+00, & 0.9653765821329180D+00, & 0.7556844695525969D+00, & 0.0025915690897241D+00, & 0.2417239613576789D+00, & 0.2417239613576791D+00, & 0.0025915690897239D+00, & 0.7556844695525968D+00, & 0.8013219460698174D+00, & 0.0142733464909807D+00, & 0.1844047074392015D+00, & 0.1844047074392018D+00, & 0.0142733464909806D+00, & 0.8013219460698173D+00, & 0.9248872032992935D+00, & 0.0138564076854345D+00, & 0.0612563890152718D+00, & 0.0612563890152719D+00, & 0.0138564076854343D+00, & 0.9248872032992934D+00, & 0.9842490320417303D+00, & 0.0024938262659978D+00, & 0.0132571416922715D+00, & 0.0132571416922719D+00, & 0.0024938262659976D+00, & 0.9842490320417302D+00, & 0.9948701172599593D+00, & 0.0025649413700205D+00, & 0.0025649413700199D+00, & 0.6244555144428430D+00, & 0.1877722427785785D+00, & 0.1877722427785783D+00, & 0.7615859288601728D+00, & 0.1004409310583719D+00, & 0.1379731400814550D+00, & 0.1379731400814553D+00, & 0.1004409310583718D+00, & 0.7615859288601728D+00, & 0.9530968777199651D+00, & 0.0136974423527237D+00, & 0.0332056799273112D+00, & 0.0332056799273113D+00, & 0.0136974423527233D+00, & 0.9530968777199650D+00, & 0.3825643087869355D+00, & 0.2348713824261289D+00, & 0.3825643087869354D+00, & 0.7713906073293495D+00, & 0.0341431958895440D+00, & 0.1944661967811062D+00, & 0.1944661967811065D+00, & 0.0341431958895438D+00, & 0.7713906073293494D+00, & 0.7467127396201543D+00, & 0.0138046252946413D+00, & 0.2394826350852044D+00, & 0.2394826350852046D+00, & 0.0138046252946411D+00, & 0.7467127396201541D+00, & 0.4489485579241042D+00, & 0.1864972142995550D+00, & 0.3645542277763407D+00, & 0.3645542277763407D+00, & 0.1864972142995550D+00, & 0.4489485579241040D+00, & 0.8601018382691163D+00, & 0.0025417593646838D+00, & 0.1373564023661995D+00, & 0.1373564023661998D+00, & 0.0025417593646836D+00, & 0.8601018382691163D+00, & 0.7047330289764286D+00, & 0.0630349337046809D+00, & 0.2322320373188903D+00, & 0.2322320373188904D+00, & 0.0630349337046808D+00, & 0.7047330289764285D+00, & 0.6434616923483871D+00, & 0.0638769125793661D+00, & 0.2926613950722466D+00, & 0.2926613950722469D+00, & 0.0638769125793659D+00, & 0.6434616923483869D+00, & 0.4403990384263681D+00, & 0.2419528451754751D+00, & 0.3176481163981567D+00, & 0.3176481163981567D+00, & 0.2419528451754751D+00, & 0.4403990384263681D+00, & 0.6850991321252454D+00, & 0.0145992712589764D+00, & 0.3003015966157780D+00, & 0.3003015966157783D+00, & 0.0145992712589763D+00, & 0.6850991321252452D+00, & 0.6966205316862629D+00, & 0.0028181145969260D+00, & 0.3005613537168107D+00, & 0.3005613537168110D+00, & 0.0028181145969260D+00, & 0.6966205316862628D+00, & 0.9053415210418890D+00, & 0.0341344995593799D+00, & 0.0605239793987310D+00, & 0.0605239793987312D+00, & 0.0341344995593795D+00, & 0.9053415210418889D+00, & 0.5058586034896924D+00, & 0.1933554772764182D+00, & 0.3007859192338892D+00, & 0.3007859192338893D+00, & 0.1933554772764182D+00, & 0.5058586034896922D+00, & 0.7130863262721640D+00, & 0.0973629697501509D+00, & 0.1895507039776850D+00, & 0.1895507039776852D+00, & 0.0973629697501507D+00, & 0.7130863262721638D+00, & 0.5670717942327397D+00, & 0.0027883024051114D+00, & 0.4301399033621487D+00, & 0.4301399033621489D+00, & 0.0027883024051113D+00, & 0.5670717942327396D+00, & 0.8102254653358516D+00, & 0.0027559624464837D+00, & 0.1870185722176645D+00, & 0.1870185722176647D+00, & 0.0027559624464836D+00, & 0.8102254653358514D+00, & 0.5229833703321248D+00, & 0.0978271071588677D+00, & 0.3791895225090074D+00, & 0.3791895225090074D+00, & 0.0978271071588676D+00, & 0.5229833703321246D+00, & 0.5874593373809698D+00, & 0.0995736856368709D+00, & 0.3129669769821590D+00, & 0.3129669769821593D+00, & 0.0995736856368709D+00, & 0.5874593373809696D+00, & 0.8240811613164462D+00, & 0.0341143516662649D+00, & 0.1418044870172886D+00, & 0.1418044870172890D+00, & 0.0341143516662646D+00, & 0.8240811613164462D+00, & 0.4528922608459510D+00, & 0.0942154783080978D+00, & 0.4528922608459508D+00, & 0.6513210967114831D+00, & 0.1004974432729284D+00, & 0.2481814600155884D+00, & 0.2481814600155885D+00, & 0.1004974432729283D+00, & 0.6513210967114831D+00, & 0.5795283608954496D+00, & 0.0616738036965517D+00, & 0.3587978354079986D+00, & 0.3587978354079986D+00, & 0.0616738036965515D+00, & 0.5795283608954496D+00, & 0.8142659075719041D+00, & 0.0928670462140481D+00, & 0.0928670462140476D+00, & 0.4950301347018183D+00, & 0.2524849326490907D+00, & 0.2524849326490906D+00 /) w = (/ & 0.0030799655691816D+00, & 0.0030799655691816D+00, & 0.0030799655691816D+00, & 0.0024873482202465D+00, & 0.0024873482202465D+00, & 0.0024873482202465D+00, & 0.0039126383408176D+00, & 0.0039126383408176D+00, & 0.0039126383408176D+00, & 0.0039126383408176D+00, & 0.0039126383408176D+00, & 0.0039126383408176D+00, & 0.0006086157221808D+00, & 0.0006086157221808D+00, & 0.0006086157221808D+00, & 0.0058780823337592D+00, & 0.0058780823337592D+00, & 0.0058780823337592D+00, & 0.0026575597720771D+00, & 0.0026575597720771D+00, & 0.0026575597720771D+00, & 0.0026575597720771D+00, & 0.0026575597720771D+00, & 0.0026575597720771D+00, & 0.0010403858576164D+00, & 0.0010403858576164D+00, & 0.0010403858576164D+00, & 0.0010403858576164D+00, & 0.0010403858576164D+00, & 0.0010403858576164D+00, & 0.0038688222455242D+00, & 0.0038688222455242D+00, & 0.0038688222455242D+00, & 0.0038688222455242D+00, & 0.0038688222455242D+00, & 0.0038688222455242D+00, & 0.0054360079215851D+00, & 0.0054360079215851D+00, & 0.0054360079215851D+00, & 0.0054360079215851D+00, & 0.0054360079215851D+00, & 0.0054360079215851D+00, & 0.0051330210770134D+00, & 0.0051330210770134D+00, & 0.0051330210770134D+00, & 0.0051330210770134D+00, & 0.0051330210770134D+00, & 0.0051330210770134D+00, & 0.0068684889665150D+00, & 0.0068684889665150D+00, & 0.0068684889665150D+00, & 0.0027248852604065D+00, & 0.0027248852604065D+00, & 0.0027248852604065D+00, & 0.0027248852604065D+00, & 0.0027248852604065D+00, & 0.0027248852604065D+00, & 0.0016143072439158D+00, & 0.0016143072439158D+00, & 0.0016143072439158D+00, & 0.0030819278277026D+00, & 0.0030819278277026D+00, & 0.0030819278277026D+00, & 0.0030819278277026D+00, & 0.0030819278277026D+00, & 0.0030819278277026D+00, & 0.0010836224292710D+00, & 0.0010836224292710D+00, & 0.0010836224292710D+00, & 0.0021960146608965D+00, & 0.0021960146608965D+00, & 0.0021960146608965D+00, & 0.0021960146608965D+00, & 0.0021960146608965D+00, & 0.0021960146608965D+00, & 0.0027071716291895D+00, & 0.0027071716291895D+00, & 0.0027071716291895D+00, & 0.0027071716291895D+00, & 0.0027071716291895D+00, & 0.0027071716291895D+00, & 0.0017732505663030D+00, & 0.0017732505663030D+00, & 0.0017732505663030D+00, & 0.0017732505663030D+00, & 0.0017732505663030D+00, & 0.0017732505663030D+00, & 0.0027166050682952D+00, & 0.0027166050682952D+00, & 0.0027166050682952D+00, & 0.0021194095320856D+00, & 0.0021194095320856D+00, & 0.0021194095320856D+00, & 0.0021194095320856D+00, & 0.0021194095320856D+00, & 0.0021194095320856D+00, & 0.0020243293045497D+00, & 0.0020243293045497D+00, & 0.0020243293045497D+00, & 0.0013822658273997D+00, & 0.0013822658273997D+00, & 0.0013822658273997D+00, & 0.0013822658273997D+00, & 0.0013822658273997D+00, & 0.0013822658273997D+00, & 0.0008287796022760D+00, & 0.0008287796022760D+00, & 0.0008287796022760D+00, & 0.0008287796022760D+00, & 0.0008287796022760D+00, & 0.0008287796022760D+00, & 0.0042454319210643D+00, & 0.0042454319210643D+00, & 0.0042454319210643D+00, & 0.0057609299703683D+00, & 0.0057609299703683D+00, & 0.0057609299703683D+00, & 0.0057609299703683D+00, & 0.0057609299703683D+00, & 0.0057609299703683D+00, & 0.0004721021055792D+00, & 0.0004721021055792D+00, & 0.0004721021055792D+00, & 0.0004866406535789D+00, & 0.0004866406535789D+00, & 0.0004866406535789D+00, & 0.0004866406535789D+00, & 0.0004866406535789D+00, & 0.0004866406535789D+00, & 0.0060611706044967D+00, & 0.0060611706044967D+00, & 0.0060611706044967D+00, & 0.0060611706044967D+00, & 0.0060611706044967D+00, & 0.0060611706044967D+00, & 0.0039591603530013D+00, & 0.0039591603530013D+00, & 0.0039591603530013D+00, & 0.0039591603530013D+00, & 0.0039591603530013D+00, & 0.0039591603530013D+00, & 0.0019515305614847D+00, & 0.0019515305614847D+00, & 0.0019515305614847D+00, & 0.0019515305614847D+00, & 0.0019515305614847D+00, & 0.0019515305614847D+00, & 0.0031758640195785D+00, & 0.0031758640195785D+00, & 0.0031758640195785D+00, & 0.0031758640195785D+00, & 0.0031758640195785D+00, & 0.0031758640195785D+00, & 0.0004177689784025D+00, & 0.0004177689784025D+00, & 0.0004177689784025D+00, & 0.0004177689784025D+00, & 0.0004177689784025D+00, & 0.0004177689784025D+00, & 0.0028037985130037D+00, & 0.0028037985130037D+00, & 0.0028037985130037D+00, & 0.0028037985130037D+00, & 0.0028037985130037D+00, & 0.0028037985130037D+00, & 0.0003074323001241D+00, & 0.0003074323001241D+00, & 0.0003074323001241D+00, & 0.0003074323001241D+00, & 0.0003074323001241D+00, & 0.0003074323001241D+00, & 0.0007580478745157D+00, & 0.0007580478745157D+00, & 0.0007580478745157D+00, & 0.0007580478745157D+00, & 0.0007580478745157D+00, & 0.0007580478745157D+00, & 0.0016285601871914D+00, & 0.0016285601871914D+00, & 0.0016285601871914D+00, & 0.0016285601871914D+00, & 0.0016285601871914D+00, & 0.0016285601871914D+00, & 0.0010015815151317D+00, & 0.0010015815151317D+00, & 0.0010015815151317D+00, & 0.0010015815151317D+00, & 0.0010015815151317D+00, & 0.0010015815151317D+00, & 0.0001897035092211D+00, & 0.0001897035092211D+00, & 0.0001897035092211D+00, & 0.0001897035092211D+00, & 0.0001897035092211D+00, & 0.0001897035092211D+00, & 0.0000857325766799D+00, & 0.0000857325766799D+00, & 0.0000857325766799D+00, & 0.0053352753423962D+00, & 0.0053352753423962D+00, & 0.0053352753423962D+00, & 0.0039225937188264D+00, & 0.0039225937188264D+00, & 0.0039225937188264D+00, & 0.0039225937188264D+00, & 0.0039225937188264D+00, & 0.0039225937188264D+00, & 0.0007352644490711D+00, & 0.0007352644490711D+00, & 0.0007352644490711D+00, & 0.0007352644490711D+00, & 0.0007352644490711D+00, & 0.0007352644490711D+00, & 0.0069496808690566D+00, & 0.0069496808690566D+00, & 0.0069496808690566D+00, & 0.0026277500982666D+00, & 0.0026277500982666D+00, & 0.0026277500982666D+00, & 0.0026277500982666D+00, & 0.0026277500982666D+00, & 0.0026277500982666D+00, & 0.0018416339190279D+00, & 0.0018416339190279D+00, & 0.0018416339190279D+00, & 0.0018416339190279D+00, & 0.0018416339190279D+00, & 0.0018416339190279D+00, & 0.0059250327726738D+00, & 0.0059250327726738D+00, & 0.0059250327726738D+00, & 0.0059250327726738D+00, & 0.0059250327726738D+00, & 0.0059250327726738D+00, & 0.0006123388408143D+00, & 0.0006123388408143D+00, & 0.0006123388408143D+00, & 0.0006123388408143D+00, & 0.0006123388408143D+00, & 0.0006123388408143D+00, & 0.0038249634484789D+00, & 0.0038249634484789D+00, & 0.0038249634484789D+00, & 0.0038249634484789D+00, & 0.0038249634484789D+00, & 0.0038249634484789D+00, & 0.0041283032222063D+00, & 0.0041283032222063D+00, & 0.0041283032222063D+00, & 0.0041283032222063D+00, & 0.0041283032222063D+00, & 0.0041283032222063D+00, & 0.0066920320417412D+00, & 0.0066920320417412D+00, & 0.0066920320417412D+00, & 0.0066920320417412D+00, & 0.0066920320417412D+00, & 0.0066920320417412D+00, & 0.0020472829473930D+00, & 0.0020472829473930D+00, & 0.0020472829473930D+00, & 0.0020472829473930D+00, & 0.0020472829473930D+00, & 0.0020472829473930D+00, & 0.0008780156791651D+00, & 0.0008780156791651D+00, & 0.0008780156791651D+00, & 0.0008780156791651D+00, & 0.0008780156791651D+00, & 0.0008780156791651D+00, & 0.0015777851185459D+00, & 0.0015777851185459D+00, & 0.0015777851185459D+00, & 0.0015777851185459D+00, & 0.0015777851185459D+00, & 0.0015777851185459D+00, & 0.0063074359109884D+00, & 0.0063074359109884D+00, & 0.0063074359109884D+00, & 0.0063074359109884D+00, & 0.0063074359109884D+00, & 0.0063074359109884D+00, & 0.0042726398210532D+00, & 0.0042726398210532D+00, & 0.0042726398210532D+00, & 0.0042726398210532D+00, & 0.0042726398210532D+00, & 0.0042726398210532D+00, & 0.0009698373462393D+00, & 0.0009698373462393D+00, & 0.0009698373462393D+00, & 0.0009698373462393D+00, & 0.0009698373462393D+00, & 0.0009698373462393D+00, & 0.0007380182704579D+00, & 0.0007380182704579D+00, & 0.0007380182704579D+00, & 0.0007380182704579D+00, & 0.0007380182704579D+00, & 0.0007380182704579D+00, & 0.0052618813601275D+00, & 0.0052618813601275D+00, & 0.0052618813601275D+00, & 0.0052618813601275D+00, & 0.0052618813601275D+00, & 0.0052618813601275D+00, & 0.0053002719749983D+00, & 0.0053002719749983D+00, & 0.0053002719749983D+00, & 0.0053002719749983D+00, & 0.0053002719749983D+00, & 0.0053002719749983D+00, & 0.0024558010102792D+00, & 0.0024558010102792D+00, & 0.0024558010102792D+00, & 0.0024558010102792D+00, & 0.0024558010102792D+00, & 0.0024558010102792D+00, & 0.0053328054204010D+00, & 0.0053328054204010D+00, & 0.0053328054204010D+00, & 0.0050556103951577D+00, & 0.0050556103951577D+00, & 0.0050556103951577D+00, & 0.0050556103951577D+00, & 0.0050556103951577D+00, & 0.0050556103951577D+00, & 0.0044341909691302D+00, & 0.0044341909691302D+00, & 0.0044341909691302D+00, & 0.0044341909691302D+00, & 0.0044341909691302D+00, & 0.0044341909691302D+00, & 0.0032907061458540D+00, & 0.0032907061458540D+00, & 0.0032907061458540D+00, & 0.0073142091431203D+00, & 0.0073142091431203D+00, & 0.0073142091431203D+00 /) return end subroutine rule44 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule44() returns the rule of precision 44. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0017123075799637D+00, & 0.9965753848400722D+00, & 0.0017123075799641D+00, & 0.0197551676157197D+00, & 0.9694881128275959D+00, & 0.0107567195566844D+00, & 0.9694881128275961D+00, & 0.0197551676157198D+00, & 0.0107567195566840D+00, & 0.0995165813818446D+00, & 0.8997028327182934D+00, & 0.0007805858998620D+00, & 0.8997028327182934D+00, & 0.0995165813818448D+00, & 0.0007805858998617D+00, & 0.1534945447552139D+00, & 0.8445671223319955D+00, & 0.0019383329127907D+00, & 0.8445671223319955D+00, & 0.1534945447552140D+00, & 0.0019383329127904D+00, & 0.4606074520039989D+00, & 0.5376064055154758D+00, & 0.0017861424805254D+00, & 0.5376064055154757D+00, & 0.4606074520039989D+00, & 0.0017861424805253D+00, & 0.0296420604264444D+00, & 0.9686037144025027D+00, & 0.0017542251710529D+00, & 0.9686037144025029D+00, & 0.0296420604264444D+00, & 0.0017542251710524D+00, & 0.3338406248248118D+00, & 0.6656420809155281D+00, & 0.0005172942596601D+00, & 0.6656420809155281D+00, & 0.3338406248248119D+00, & 0.0005172942596599D+00, & 0.0291673514653005D+00, & 0.9416652970693987D+00, & 0.0291673514653009D+00, & 0.0495499879123024D+00, & 0.9009000241753948D+00, & 0.0495499879123029D+00, & 0.1194266872274120D+00, & 0.8730274418468819D+00, & 0.0075458709257062D+00, & 0.8730274418468820D+00, & 0.1194266872274120D+00, & 0.0075458709257059D+00, & 0.1733118066994289D+00, & 0.8151956468477657D+00, & 0.0114925464528055D+00, & 0.8151956468477658D+00, & 0.1733118066994291D+00, & 0.0114925464528051D+00, & 0.0593978633857566D+00, & 0.9163391688931388D+00, & 0.0242629677211046D+00, & 0.9163391688931388D+00, & 0.0593978633857567D+00, & 0.0242629677211044D+00, & 0.2594461646278431D+00, & 0.7307561420696972D+00, & 0.0097976933024596D+00, & 0.7307561420696972D+00, & 0.2594461646278433D+00, & 0.0097976933024595D+00, & 0.2696648795311178D+00, & 0.7284359696406738D+00, & 0.0018991508282084D+00, & 0.7284359696406739D+00, & 0.2696648795311180D+00, & 0.0018991508282082D+00, & 0.3234284104109564D+00, & 0.6688969097328992D+00, & 0.0076746798561443D+00, & 0.6688969097328992D+00, & 0.3234284104109564D+00, & 0.0076746798561442D+00, & 0.2093976094351925D+00, & 0.7878951862570389D+00, & 0.0027072043077686D+00, & 0.7878951862570389D+00, & 0.2093976094351925D+00, & 0.0027072043077684D+00, & 0.0107937373867395D+00, & 0.9864998660560905D+00, & 0.0027063965571701D+00, & 0.9864998660560905D+00, & 0.0107937373867397D+00, & 0.0027063965571697D+00, & 0.0416577600266789D+00, & 0.9478795059436815D+00, & 0.0104627340296397D+00, & 0.9478795059436816D+00, & 0.0416577600266790D+00, & 0.0104627340296393D+00, & 0.1393007744184822D+00, & 0.8391863652965978D+00, & 0.0215128602849200D+00, & 0.8391863652965978D+00, & 0.1393007744184823D+00, & 0.0215128602849197D+00, & 0.4877239805831534D+00, & 0.4877239805831534D+00, & 0.0245520388336932D+00, & 0.0971407574555291D+00, & 0.8800347069095190D+00, & 0.0228245356349520D+00, & 0.8800347069095190D+00, & 0.0971407574555291D+00, & 0.0228245356349517D+00, & 0.1511248097389706D+00, & 0.7487866599562394D+00, & 0.1000885303047901D+00, & 0.7487866599562394D+00, & 0.1511248097389706D+00, & 0.1000885303047898D+00, & 0.4960618044654749D+00, & 0.4960618044654750D+00, & 0.0078763910690500D+00, & 0.3939323955351545D+00, & 0.6029080349282100D+00, & 0.0031595695366355D+00, & 0.6029080349282100D+00, & 0.3939323955351544D+00, & 0.0031595695366353D+00, & 0.1276374594173248D+00, & 0.8287949653018399D+00, & 0.0435675752808352D+00, & 0.8287949653018402D+00, & 0.1276374594173247D+00, & 0.0435675752808349D+00, & 0.2153427859170523D+00, & 0.7218418378371082D+00, & 0.0628153762458395D+00, & 0.7218418378371081D+00, & 0.2153427859170524D+00, & 0.0628153762458394D+00, & 0.1805238872560285D+00, & 0.7847849261270403D+00, & 0.0346911866169312D+00, & 0.7847849261270403D+00, & 0.1805238872560286D+00, & 0.0346911866169310D+00, & 0.3706974787497283D+00, & 0.6133503854822405D+00, & 0.0159521357680312D+00, & 0.6133503854822404D+00, & 0.3706974787497284D+00, & 0.0159521357680310D+00, & 0.2389043466345939D+00, & 0.7245299623844421D+00, & 0.0365656909809640D+00, & 0.7245299623844421D+00, & 0.2389043466345939D+00, & 0.0365656909809638D+00, & 0.0765961156051737D+00, & 0.8468077687896521D+00, & 0.0765961156051742D+00, & 0.4035445047649169D+00, & 0.4735882468281119D+00, & 0.1228672484069711D+00, & 0.4735882468281119D+00, & 0.4035445047649169D+00, & 0.1228672484069711D+00, & 0.2510886184010617D+00, & 0.6268501895654275D+00, & 0.1220611920335108D+00, & 0.6268501895654275D+00, & 0.2510886184010617D+00, & 0.1220611920335106D+00, & 0.3100924603530019D+00, & 0.6020796526141913D+00, & 0.0878278870328068D+00, & 0.6020796526141913D+00, & 0.3100924603530019D+00, & 0.0878278870328066D+00, & 0.4171889370681111D+00, & 0.5171299598756924D+00, & 0.0656811030561965D+00, & 0.5171299598756924D+00, & 0.4171889370681111D+00, & 0.0656811030561964D+00, & 0.4759518460527712D+00, & 0.4759518460527714D+00, & 0.0480963078944574D+00, & 0.0842771975158688D+00, & 0.8700026552993007D+00, & 0.0457201471848306D+00, & 0.8700026552993007D+00, & 0.0842771975158688D+00, & 0.0457201471848303D+00, & 0.2875172818904952D+00, & 0.6596793072144378D+00, & 0.0528034108950670D+00, & 0.6596793072144378D+00, & 0.2875172818904952D+00, & 0.0528034108950669D+00, & 0.1090955419572377D+00, & 0.7818089160855244D+00, & 0.1090955419572380D+00, & 0.3421421849069924D+00, & 0.6245951075427290D+00, & 0.0332627075502785D+00, & 0.6245951075427290D+00, & 0.3421421849069924D+00, & 0.0332627075502785D+00, & 0.2312470036938409D+00, & 0.5375059926123180D+00, & 0.2312470036938411D+00, & 0.1959081982236505D+00, & 0.6081836035526987D+00, & 0.1959081982236506D+00, & 0.2907813356274843D+00, & 0.6861277132074860D+00, & 0.0230909511650299D+00, & 0.6861277132074859D+00, & 0.2907813356274844D+00, & 0.0230909511650297D+00, & 0.0777385297161003D+00, & 0.9138493473952539D+00, & 0.0084121228886461D+00, & 0.9138493473952539D+00, & 0.0777385297161003D+00, & 0.0084121228886456D+00, & 0.0583538087981567D+00, & 0.9397903465114041D+00, & 0.0018558446904393D+00, & 0.9397903465114043D+00, & 0.0583538087981568D+00, & 0.0018558446904388D+00, & 0.3537362173911874D+00, & 0.4944025611096592D+00, & 0.1518612214991533D+00, & 0.4944025611096592D+00, & 0.3537362173911875D+00, & 0.1518612214991532D+00, & 0.1941036834219221D+00, & 0.6592024700825740D+00, & 0.1466938464955038D+00, & 0.6592024700825740D+00, & 0.1941036834219222D+00, & 0.1466938464955036D+00, & 0.1152446802620743D+00, & 0.8116970473144409D+00, & 0.0730582724234849D+00, & 0.8116970473144409D+00, & 0.1152446802620743D+00, & 0.0730582724234846D+00, & 0.2526489188568274D+00, & 0.6640305665631259D+00, & 0.0833205145800467D+00, & 0.6640305665631260D+00, & 0.2526489188568274D+00, & 0.0833205145800466D+00, & 0.3706381279110351D+00, & 0.5316917725696112D+00, & 0.0976700995193537D+00, & 0.5316917725696112D+00, & 0.3706381279110351D+00, & 0.0976700995193536D+00, & 0.1975107662353285D+00, & 0.7003617605288512D+00, & 0.1021274732358203D+00, & 0.7003617605288514D+00, & 0.1975107662353285D+00, & 0.1021274732358200D+00, & 0.2191021787766396D+00, & 0.7639576985765668D+00, & 0.0169401226467936D+00, & 0.7639576985765668D+00, & 0.2191021787766396D+00, & 0.0169401226467933D+00, & 0.1647494714555341D+00, & 0.7706431138900716D+00, & 0.0646074146543943D+00, & 0.7706431138900717D+00, & 0.1647494714555343D+00, & 0.0646074146543940D+00, & 0.3487568874306149D+00, & 0.4569496207074597D+00, & 0.1942934918619253D+00, & 0.4569496207074596D+00, & 0.3487568874306151D+00, & 0.1942934918619253D+00, & 0.3558533300586623D+00, & 0.5853570821660166D+00, & 0.0587895877753212D+00, & 0.5853570821660165D+00, & 0.3558533300586624D+00, & 0.0587895877753211D+00, & 0.3487165289854694D+00, & 0.4076984951293575D+00, & 0.2435849758851730D+00, & 0.4076984951293575D+00, & 0.3487165289854693D+00, & 0.2435849758851730D+00, & 0.4223218082071514D+00, & 0.4223218082071514D+00, & 0.1553563835856973D+00, & 0.4548817499595059D+00, & 0.4548817499595060D+00, & 0.0902365000809880D+00, & 0.2907043355496960D+00, & 0.5231696984941406D+00, & 0.1861259659561632D+00, & 0.5231696984941406D+00, & 0.2907043355496960D+00, & 0.1861259659561631D+00, & 0.1439001195404208D+00, & 0.7121997609191582D+00, & 0.1439001195404210D+00, & 0.2898629348171137D+00, & 0.4717800456303300D+00, & 0.2383570195525562D+00, & 0.4717800456303302D+00, & 0.2898629348171137D+00, & 0.2383570195525561D+00, & 0.4023404478547354D+00, & 0.4023404478547353D+00, & 0.1953191042905292D+00, & 0.3093835754454580D+00, & 0.5593868077625690D+00, & 0.1312296167919730D+00, & 0.5593868077625690D+00, & 0.3093835754454579D+00, & 0.1312296167919728D+00, & 0.2469795390992444D+00, & 0.5845614823482763D+00, & 0.1684589785524792D+00, & 0.5845614823482763D+00, & 0.2469795390992445D+00, & 0.1684589785524790D+00, & 0.4353451951214652D+00, & 0.5515293353673113D+00, & 0.0131254695112235D+00, & 0.5515293353673113D+00, & 0.4353451951214652D+00, & 0.0131254695112233D+00, & 0.2942957656908339D+00, & 0.4114084686183320D+00, & 0.2942957656908339D+00, & 0.3516157887957689D+00, & 0.3516157887957689D+00, & 0.2967684224084619D+00, & 0.4137012893148831D+00, & 0.5518852701665368D+00, & 0.0344134405185802D+00, & 0.5518852701665367D+00, & 0.4137012893148831D+00, & 0.0344134405185801D+00 /) b = (/ & 0.0017123075799640D+00, & 0.0017123075799637D+00, & 0.9965753848400725D+00, & 0.0107567195566843D+00, & 0.0197551676157197D+00, & 0.9694881128275962D+00, & 0.0107567195566843D+00, & 0.9694881128275962D+00, & 0.0197551676157201D+00, & 0.0007805858998619D+00, & 0.0995165813818446D+00, & 0.8997028327182935D+00, & 0.0007805858998619D+00, & 0.8997028327182935D+00, & 0.0995165813818450D+00, & 0.0019383329127906D+00, & 0.1534945447552139D+00, & 0.8445671223319957D+00, & 0.0019383329127906D+00, & 0.8445671223319957D+00, & 0.1534945447552142D+00, & 0.0017861424805254D+00, & 0.4606074520039989D+00, & 0.5376064055154759D+00, & 0.0017861424805254D+00, & 0.5376064055154758D+00, & 0.4606074520039992D+00, & 0.0017542251710528D+00, & 0.0296420604264444D+00, & 0.9686037144025029D+00, & 0.0017542251710528D+00, & 0.9686037144025031D+00, & 0.0296420604264447D+00, & 0.0005172942596601D+00, & 0.3338406248248119D+00, & 0.6656420809155283D+00, & 0.0005172942596601D+00, & 0.6656420809155282D+00, & 0.3338406248248121D+00, & 0.0291673514653008D+00, & 0.0291673514653005D+00, & 0.9416652970693989D+00, & 0.0495499879123027D+00, & 0.0495499879123024D+00, & 0.9009000241753949D+00, & 0.0075458709257061D+00, & 0.1194266872274120D+00, & 0.8730274418468821D+00, & 0.0075458709257061D+00, & 0.8730274418468821D+00, & 0.1194266872274123D+00, & 0.0114925464528053D+00, & 0.1733118066994289D+00, & 0.8151956468477658D+00, & 0.0114925464528053D+00, & 0.8151956468477658D+00, & 0.1733118066994292D+00, & 0.0242629677211045D+00, & 0.0593978633857566D+00, & 0.9163391688931390D+00, & 0.0242629677211045D+00, & 0.9163391688931390D+00, & 0.0593978633857569D+00, & 0.0097976933024596D+00, & 0.2594461646278432D+00, & 0.7307561420696975D+00, & 0.0097976933024596D+00, & 0.7307561420696972D+00, & 0.2594461646278435D+00, & 0.0018991508282083D+00, & 0.2696648795311178D+00, & 0.7284359696406740D+00, & 0.0018991508282083D+00, & 0.7284359696406739D+00, & 0.2696648795311181D+00, & 0.0076746798561443D+00, & 0.3234284104109565D+00, & 0.6688969097328994D+00, & 0.0076746798561443D+00, & 0.6688969097328994D+00, & 0.3234284104109568D+00, & 0.0027072043077686D+00, & 0.2093976094351925D+00, & 0.7878951862570391D+00, & 0.0027072043077686D+00, & 0.7878951862570391D+00, & 0.2093976094351928D+00, & 0.0027063965571699D+00, & 0.0107937373867395D+00, & 0.9864998660560906D+00, & 0.0027063965571699D+00, & 0.9864998660560906D+00, & 0.0107937373867399D+00, & 0.0104627340296395D+00, & 0.0416577600266789D+00, & 0.9478795059436816D+00, & 0.0104627340296395D+00, & 0.9478795059436816D+00, & 0.0416577600266793D+00, & 0.0215128602849199D+00, & 0.1393007744184823D+00, & 0.8391863652965980D+00, & 0.0215128602849199D+00, & 0.8391863652965980D+00, & 0.1393007744184826D+00, & 0.0245520388336933D+00, & 0.4877239805831535D+00, & 0.4877239805831536D+00, & 0.0228245356349520D+00, & 0.0971407574555291D+00, & 0.8800347069095191D+00, & 0.0228245356349520D+00, & 0.8800347069095191D+00, & 0.0971407574555294D+00, & 0.1000885303047900D+00, & 0.1511248097389706D+00, & 0.7487866599562395D+00, & 0.1000885303047900D+00, & 0.7487866599562395D+00, & 0.1511248097389709D+00, & 0.0078763910690501D+00, & 0.4960618044654750D+00, & 0.4960618044654752D+00, & 0.0031595695366355D+00, & 0.3939323955351545D+00, & 0.6029080349282102D+00, & 0.0031595695366355D+00, & 0.6029080349282102D+00, & 0.3939323955351547D+00, & 0.0435675752808352D+00, & 0.1276374594173248D+00, & 0.8287949653018403D+00, & 0.0435675752808352D+00, & 0.8287949653018403D+00, & 0.1276374594173251D+00, & 0.0628153762458396D+00, & 0.2153427859170523D+00, & 0.7218418378371083D+00, & 0.0628153762458396D+00, & 0.7218418378371083D+00, & 0.2153427859170526D+00, & 0.0346911866169312D+00, & 0.1805238872560285D+00, & 0.7847849261270404D+00, & 0.0346911866169312D+00, & 0.7847849261270404D+00, & 0.1805238872560288D+00, & 0.0159521357680312D+00, & 0.3706974787497284D+00, & 0.6133503854822406D+00, & 0.0159521357680312D+00, & 0.6133503854822405D+00, & 0.3706974787497286D+00, & 0.0365656909809640D+00, & 0.2389043466345939D+00, & 0.7245299623844423D+00, & 0.0365656909809640D+00, & 0.7245299623844423D+00, & 0.2389043466345942D+00, & 0.0765961156051741D+00, & 0.0765961156051737D+00, & 0.8468077687896522D+00, & 0.1228672484069712D+00, & 0.4035445047649170D+00, & 0.4735882468281121D+00, & 0.1228672484069712D+00, & 0.4735882468281120D+00, & 0.4035445047649171D+00, & 0.1220611920335108D+00, & 0.2510886184010618D+00, & 0.6268501895654277D+00, & 0.1220611920335108D+00, & 0.6268501895654277D+00, & 0.2510886184010619D+00, & 0.0878278870328068D+00, & 0.3100924603530020D+00, & 0.6020796526141915D+00, & 0.0878278870328068D+00, & 0.6020796526141915D+00, & 0.3100924603530022D+00, & 0.0656811030561965D+00, & 0.4171889370681111D+00, & 0.5171299598756927D+00, & 0.0656811030561965D+00, & 0.5171299598756924D+00, & 0.4171889370681113D+00, & 0.0480963078944575D+00, & 0.4759518460527713D+00, & 0.4759518460527715D+00, & 0.0457201471848306D+00, & 0.0842771975158688D+00, & 0.8700026552993009D+00, & 0.0457201471848306D+00, & 0.8700026552993009D+00, & 0.0842771975158691D+00, & 0.0528034108950670D+00, & 0.2875172818904953D+00, & 0.6596793072144379D+00, & 0.0528034108950670D+00, & 0.6596793072144379D+00, & 0.2875172818904955D+00, & 0.1090955419572379D+00, & 0.1090955419572376D+00, & 0.7818089160855246D+00, & 0.0332627075502786D+00, & 0.3421421849069925D+00, & 0.6245951075427292D+00, & 0.0332627075502786D+00, & 0.6245951075427292D+00, & 0.3421421849069927D+00, & 0.2312470036938411D+00, & 0.2312470036938410D+00, & 0.5375059926123180D+00, & 0.1959081982236507D+00, & 0.1959081982236506D+00, & 0.6081836035526990D+00, & 0.0230909511650298D+00, & 0.2907813356274843D+00, & 0.6861277132074860D+00, & 0.0230909511650298D+00, & 0.6861277132074860D+00, & 0.2907813356274845D+00, & 0.0084121228886458D+00, & 0.0777385297161002D+00, & 0.9138493473952539D+00, & 0.0084121228886458D+00, & 0.9138493473952539D+00, & 0.0777385297161006D+00, & 0.0018558446904391D+00, & 0.0583538087981567D+00, & 0.9397903465114043D+00, & 0.0018558446904391D+00, & 0.9397903465114043D+00, & 0.0583538087981571D+00, & 0.1518612214991534D+00, & 0.3537362173911875D+00, & 0.4944025611096594D+00, & 0.1518612214991534D+00, & 0.4944025611096593D+00, & 0.3537362173911877D+00, & 0.1466938464955038D+00, & 0.1941036834219222D+00, & 0.6592024700825742D+00, & 0.1466938464955038D+00, & 0.6592024700825742D+00, & 0.1941036834219224D+00, & 0.0730582724234848D+00, & 0.1152446802620743D+00, & 0.8116970473144410D+00, & 0.0730582724234848D+00, & 0.8116970473144410D+00, & 0.1152446802620745D+00, & 0.0833205145800467D+00, & 0.2526489188568274D+00, & 0.6640305665631261D+00, & 0.0833205145800467D+00, & 0.6640305665631261D+00, & 0.2526489188568276D+00, & 0.0976700995193538D+00, & 0.3706381279110351D+00, & 0.5316917725696113D+00, & 0.0976700995193538D+00, & 0.5316917725696113D+00, & 0.3706381279110353D+00, & 0.1021274732358202D+00, & 0.1975107662353285D+00, & 0.7003617605288514D+00, & 0.1021274732358202D+00, & 0.7003617605288514D+00, & 0.1975107662353287D+00, & 0.0169401226467935D+00, & 0.2191021787766396D+00, & 0.7639576985765670D+00, & 0.0169401226467935D+00, & 0.7639576985765670D+00, & 0.2191021787766399D+00, & 0.0646074146543942D+00, & 0.1647494714555342D+00, & 0.7706431138900717D+00, & 0.0646074146543942D+00, & 0.7706431138900717D+00, & 0.1647494714555344D+00, & 0.1942934918619254D+00, & 0.3487568874306151D+00, & 0.4569496207074598D+00, & 0.1942934918619254D+00, & 0.4569496207074597D+00, & 0.3487568874306152D+00, & 0.0587895877753212D+00, & 0.3558533300586624D+00, & 0.5853570821660167D+00, & 0.0587895877753212D+00, & 0.5853570821660166D+00, & 0.3558533300586625D+00, & 0.2435849758851731D+00, & 0.3487165289854695D+00, & 0.4076984951293576D+00, & 0.2435849758851731D+00, & 0.4076984951293576D+00, & 0.3487165289854696D+00, & 0.1553563835856973D+00, & 0.4223218082071514D+00, & 0.4223218082071515D+00, & 0.0902365000809881D+00, & 0.4548817499595060D+00, & 0.4548817499595061D+00, & 0.1861259659561633D+00, & 0.2907043355496962D+00, & 0.5231696984941409D+00, & 0.1861259659561633D+00, & 0.5231696984941409D+00, & 0.2907043355496963D+00, & 0.1439001195404211D+00, & 0.1439001195404208D+00, & 0.7121997609191584D+00, & 0.2383570195525562D+00, & 0.2898629348171138D+00, & 0.4717800456303302D+00, & 0.2383570195525562D+00, & 0.4717800456303302D+00, & 0.2898629348171138D+00, & 0.1953191042905293D+00, & 0.4023404478547354D+00, & 0.4023404478547355D+00, & 0.1312296167919730D+00, & 0.3093835754454580D+00, & 0.5593868077625692D+00, & 0.1312296167919730D+00, & 0.5593868077625692D+00, & 0.3093835754454582D+00, & 0.1684589785524792D+00, & 0.2469795390992445D+00, & 0.5845614823482764D+00, & 0.1684589785524792D+00, & 0.5845614823482764D+00, & 0.2469795390992447D+00, & 0.0131254695112235D+00, & 0.4353451951214652D+00, & 0.5515293353673115D+00, & 0.0131254695112235D+00, & 0.5515293353673113D+00, & 0.4353451951214655D+00, & 0.2942957656908340D+00, & 0.2942957656908340D+00, & 0.4114084686183322D+00, & 0.2967684224084621D+00, & 0.3516157887957691D+00, & 0.3516157887957691D+00, & 0.0344134405185802D+00, & 0.4137012893148831D+00, & 0.5518852701665369D+00, & 0.0344134405185802D+00, & 0.5518852701665368D+00, & 0.4137012893148834D+00 /) c = (/ & 0.9965753848400724D+00, & 0.0017123075799641D+00, & 0.0017123075799634D+00, & 0.9694881128275959D+00, & 0.0107567195566844D+00, & 0.0197551676157194D+00, & 0.0197551676157196D+00, & 0.0107567195566841D+00, & 0.9694881128275959D+00, & 0.8997028327182934D+00, & 0.0007805858998619D+00, & 0.0995165813818445D+00, & 0.0995165813818446D+00, & 0.0007805858998616D+00, & 0.8997028327182933D+00, & 0.8445671223319956D+00, & 0.0019383329127906D+00, & 0.1534945447552136D+00, & 0.1534945447552139D+00, & 0.0019383329127903D+00, & 0.8445671223319955D+00, & 0.5376064055154757D+00, & 0.0017861424805253D+00, & 0.4606074520039987D+00, & 0.4606074520039989D+00, & 0.0017861424805253D+00, & 0.5376064055154756D+00, & 0.9686037144025029D+00, & 0.0017542251710529D+00, & 0.0296420604264441D+00, & 0.0296420604264443D+00, & 0.0017542251710524D+00, & 0.9686037144025029D+00, & 0.6656420809155281D+00, & 0.0005172942596600D+00, & 0.3338406248248116D+00, & 0.3338406248248118D+00, & 0.0005172942596600D+00, & 0.6656420809155280D+00, & 0.9416652970693987D+00, & 0.0291673514653008D+00, & 0.0291673514653003D+00, & 0.9009000241753948D+00, & 0.0495499879123028D+00, & 0.0495499879123021D+00, & 0.8730274418468819D+00, & 0.0075458709257062D+00, & 0.1194266872274118D+00, & 0.1194266872274119D+00, & 0.0075458709257060D+00, & 0.8730274418468817D+00, & 0.8151956468477658D+00, & 0.0114925464528054D+00, & 0.1733118066994287D+00, & 0.1733118066994289D+00, & 0.0114925464528052D+00, & 0.8151956468477657D+00, & 0.9163391688931388D+00, & 0.0242629677211045D+00, & 0.0593978633857564D+00, & 0.0593978633857566D+00, & 0.0242629677211043D+00, & 0.9163391688931387D+00, & 0.7307561420696972D+00, & 0.0097976933024596D+00, & 0.2594461646278429D+00, & 0.2594461646278431D+00, & 0.0097976933024596D+00, & 0.7307561420696971D+00, & 0.7284359696406738D+00, & 0.0018991508282084D+00, & 0.2696648795311175D+00, & 0.2696648795311177D+00, & 0.0018991508282081D+00, & 0.7284359696406737D+00, & 0.6688969097328993D+00, & 0.0076746798561443D+00, & 0.3234284104109563D+00, & 0.3234284104109565D+00, & 0.0076746798561442D+00, & 0.6688969097328989D+00, & 0.7878951862570389D+00, & 0.0027072043077686D+00, & 0.2093976094351923D+00, & 0.2093976094351925D+00, & 0.0027072043077684D+00, & 0.7878951862570389D+00, & 0.9864998660560906D+00, & 0.0027063965571700D+00, & 0.0107937373867393D+00, & 0.0107937373867396D+00, & 0.0027063965571696D+00, & 0.9864998660560905D+00, & 0.9478795059436815D+00, & 0.0104627340296396D+00, & 0.0416577600266786D+00, & 0.0416577600266789D+00, & 0.0104627340296394D+00, & 0.9478795059436814D+00, & 0.8391863652965978D+00, & 0.0215128602849199D+00, & 0.1393007744184821D+00, & 0.1393007744184823D+00, & 0.0215128602849198D+00, & 0.8391863652965976D+00, & 0.4877239805831534D+00, & 0.0245520388336932D+00, & 0.4877239805831531D+00, & 0.8800347069095189D+00, & 0.0228245356349519D+00, & 0.0971407574555289D+00, & 0.0971407574555290D+00, & 0.0228245356349518D+00, & 0.8800347069095188D+00, & 0.7487866599562394D+00, & 0.1000885303047900D+00, & 0.1511248097389705D+00, & 0.1511248097389706D+00, & 0.1000885303047899D+00, & 0.7487866599562393D+00, & 0.4960618044654749D+00, & 0.0078763910690500D+00, & 0.4960618044654748D+00, & 0.6029080349282100D+00, & 0.0031595695366355D+00, & 0.3939323955351542D+00, & 0.3939323955351545D+00, & 0.0031595695366354D+00, & 0.6029080349282099D+00, & 0.8287949653018400D+00, & 0.0435675752808353D+00, & 0.1276374594173245D+00, & 0.1276374594173247D+00, & 0.0435675752808350D+00, & 0.8287949653018400D+00, & 0.7218418378371082D+00, & 0.0628153762458395D+00, & 0.2153427859170521D+00, & 0.2153427859170524D+00, & 0.0628153762458393D+00, & 0.7218418378371080D+00, & 0.7847849261270403D+00, & 0.0346911866169312D+00, & 0.1805238872560283D+00, & 0.1805238872560285D+00, & 0.0346911866169309D+00, & 0.7847849261270403D+00, & 0.6133503854822404D+00, & 0.0159521357680311D+00, & 0.3706974787497281D+00, & 0.3706974787497284D+00, & 0.0159521357680311D+00, & 0.6133503854822404D+00, & 0.7245299623844421D+00, & 0.0365656909809640D+00, & 0.2389043466345937D+00, & 0.2389043466345939D+00, & 0.0365656909809637D+00, & 0.7245299623844421D+00, & 0.8468077687896521D+00, & 0.0765961156051742D+00, & 0.0765961156051735D+00, & 0.4735882468281119D+00, & 0.1228672484069712D+00, & 0.4035445047649167D+00, & 0.4035445047649169D+00, & 0.1228672484069712D+00, & 0.4735882468281118D+00, & 0.6268501895654275D+00, & 0.1220611920335107D+00, & 0.2510886184010614D+00, & 0.2510886184010617D+00, & 0.1220611920335106D+00, & 0.6268501895654275D+00, & 0.6020796526141913D+00, & 0.0878278870328068D+00, & 0.3100924603530018D+00, & 0.3100924603530019D+00, & 0.0878278870328065D+00, & 0.6020796526141912D+00, & 0.5171299598756924D+00, & 0.0656811030561965D+00, & 0.4171889370681109D+00, & 0.4171889370681111D+00, & 0.0656811030561965D+00, & 0.5171299598756923D+00, & 0.4759518460527713D+00, & 0.0480963078944573D+00, & 0.4759518460527711D+00, & 0.8700026552993007D+00, & 0.0457201471848306D+00, & 0.0842771975158686D+00, & 0.0842771975158688D+00, & 0.0457201471848304D+00, & 0.8700026552993005D+00, & 0.6596793072144378D+00, & 0.0528034108950669D+00, & 0.2875172818904951D+00, & 0.2875172818904952D+00, & 0.0528034108950669D+00, & 0.6596793072144376D+00, & 0.7818089160855244D+00, & 0.1090955419572380D+00, & 0.1090955419572374D+00, & 0.6245951075427290D+00, & 0.0332627075502785D+00, & 0.3421421849069923D+00, & 0.3421421849069924D+00, & 0.0332627075502784D+00, & 0.6245951075427288D+00, & 0.5375059926123179D+00, & 0.2312470036938410D+00, & 0.2312470036938409D+00, & 0.6081836035526988D+00, & 0.1959081982236507D+00, & 0.1959081982236505D+00, & 0.6861277132074860D+00, & 0.0230909511650297D+00, & 0.2907813356274841D+00, & 0.2907813356274843D+00, & 0.0230909511650296D+00, & 0.6861277132074858D+00, & 0.9138493473952539D+00, & 0.0084121228886459D+00, & 0.0777385297161001D+00, & 0.0777385297161002D+00, & 0.0084121228886457D+00, & 0.9138493473952537D+00, & 0.9397903465114041D+00, & 0.0018558446904391D+00, & 0.0583538087981564D+00, & 0.0583538087981567D+00, & 0.0018558446904390D+00, & 0.9397903465114040D+00, & 0.4944025611096592D+00, & 0.1518612214991533D+00, & 0.3537362173911873D+00, & 0.3537362173911874D+00, & 0.1518612214991532D+00, & 0.4944025611096591D+00, & 0.6592024700825742D+00, & 0.1466938464955038D+00, & 0.1941036834219220D+00, & 0.1941036834219222D+00, & 0.1466938464955035D+00, & 0.6592024700825739D+00, & 0.8116970473144409D+00, & 0.0730582724234848D+00, & 0.1152446802620740D+00, & 0.1152446802620743D+00, & 0.0730582724234846D+00, & 0.8116970473144408D+00, & 0.6640305665631259D+00, & 0.0833205145800467D+00, & 0.2526489188568272D+00, & 0.2526489188568273D+00, & 0.0833205145800465D+00, & 0.6640305665631258D+00, & 0.5316917725696111D+00, & 0.0976700995193537D+00, & 0.3706381279110349D+00, & 0.3706381279110350D+00, & 0.0976700995193536D+00, & 0.5316917725696111D+00, & 0.7003617605288512D+00, & 0.1021274732358203D+00, & 0.1975107662353283D+00, & 0.1975107662353284D+00, & 0.1021274732358201D+00, & 0.7003617605288512D+00, & 0.7639576985765669D+00, & 0.0169401226467936D+00, & 0.2191021787766394D+00, & 0.2191021787766397D+00, & 0.0169401226467933D+00, & 0.7639576985765668D+00, & 0.7706431138900716D+00, & 0.0646074146543943D+00, & 0.1647494714555340D+00, & 0.1647494714555341D+00, & 0.0646074146543941D+00, & 0.7706431138900716D+00, & 0.4569496207074596D+00, & 0.1942934918619252D+00, & 0.3487568874306149D+00, & 0.3487568874306150D+00, & 0.1942934918619252D+00, & 0.4569496207074596D+00, & 0.5853570821660165D+00, & 0.0587895877753211D+00, & 0.3558533300586620D+00, & 0.3558533300586623D+00, & 0.0587895877753211D+00, & 0.5853570821660163D+00, & 0.4076984951293574D+00, & 0.2435849758851730D+00, & 0.3487165289854693D+00, & 0.3487165289854693D+00, & 0.2435849758851731D+00, & 0.4076984951293575D+00, & 0.4223218082071513D+00, & 0.1553563835856972D+00, & 0.4223218082071513D+00, & 0.4548817499595059D+00, & 0.0902365000809880D+00, & 0.4548817499595058D+00, & 0.5231696984941406D+00, & 0.1861259659561632D+00, & 0.2907043355496960D+00, & 0.2907043355496961D+00, & 0.1861259659561630D+00, & 0.5231696984941407D+00, & 0.7121997609191582D+00, & 0.1439001195404210D+00, & 0.1439001195404206D+00, & 0.4717800456303301D+00, & 0.2383570195525562D+00, & 0.2898629348171136D+00, & 0.2898629348171136D+00, & 0.2383570195525561D+00, & 0.4717800456303301D+00, & 0.4023404478547353D+00, & 0.1953191042905292D+00, & 0.4023404478547353D+00, & 0.5593868077625691D+00, & 0.1312296167919730D+00, & 0.3093835754454578D+00, & 0.3093835754454580D+00, & 0.1312296167919729D+00, & 0.5593868077625690D+00, & 0.5845614823482763D+00, & 0.1684589785524792D+00, & 0.2469795390992443D+00, & 0.2469795390992445D+00, & 0.1684589785524792D+00, & 0.5845614823482763D+00, & 0.5515293353673113D+00, & 0.0131254695112235D+00, & 0.4353451951214650D+00, & 0.4353451951214652D+00, & 0.0131254695112234D+00, & 0.5515293353673112D+00, & 0.4114084686183320D+00, & 0.2942957656908339D+00, & 0.2942957656908339D+00, & 0.3516157887957689D+00, & 0.2967684224084620D+00, & 0.3516157887957690D+00, & 0.5518852701665368D+00, & 0.0344134405185801D+00, & 0.4137012893148829D+00, & 0.4137012893148831D+00, & 0.0344134405185802D+00, & 0.5518852701665365D+00 /) w = (/ & 0.0000443040909141D+00, & 0.0000443040909141D+00, & 0.0000443040909141D+00, & 0.0004119756464370D+00, & 0.0004119756464370D+00, & 0.0004119756464370D+00, & 0.0004119756464370D+00, & 0.0004119756464370D+00, & 0.0004119756464370D+00, & 0.0002732408460037D+00, & 0.0002732408460037D+00, & 0.0002732408460037D+00, & 0.0002732408460037D+00, & 0.0002732408460037D+00, & 0.0002732408460037D+00, & 0.0005393284439299D+00, & 0.0005393284439299D+00, & 0.0005393284439299D+00, & 0.0005393284439299D+00, & 0.0005393284439299D+00, & 0.0005393284439299D+00, & 0.0006709789705820D+00, & 0.0006709789705820D+00, & 0.0006709789705820D+00, & 0.0006709789705820D+00, & 0.0006709789705820D+00, & 0.0006709789705820D+00, & 0.0002259315361139D+00, & 0.0002259315361139D+00, & 0.0002259315361139D+00, & 0.0002259315361139D+00, & 0.0002259315361139D+00, & 0.0002259315361139D+00, & 0.0003220663094183D+00, & 0.0003220663094183D+00, & 0.0003220663094183D+00, & 0.0003220663094183D+00, & 0.0003220663094183D+00, & 0.0003220663094183D+00, & 0.0011229773828237D+00, & 0.0011229773828237D+00, & 0.0011229773828237D+00, & 0.0017451515655329D+00, & 0.0017451515655329D+00, & 0.0017451515655329D+00, & 0.0009677673027951D+00, & 0.0009677673027951D+00, & 0.0009677673027951D+00, & 0.0009677673027951D+00, & 0.0009677673027951D+00, & 0.0009677673027951D+00, & 0.0013466648921818D+00, & 0.0013466648921818D+00, & 0.0013466648921818D+00, & 0.0013466648921818D+00, & 0.0013466648921818D+00, & 0.0013466648921818D+00, & 0.0013375082839812D+00, & 0.0013375082839812D+00, & 0.0013375082839812D+00, & 0.0013375082839812D+00, & 0.0013375082839812D+00, & 0.0013375082839812D+00, & 0.0012094280366882D+00, & 0.0012094280366882D+00, & 0.0012094280366882D+00, & 0.0012094280366882D+00, & 0.0012094280366882D+00, & 0.0012094280366882D+00, & 0.0005973761417619D+00, & 0.0005973761417619D+00, & 0.0005973761417619D+00, & 0.0005973761417619D+00, & 0.0005973761417619D+00, & 0.0005973761417619D+00, & 0.0014682010637336D+00, & 0.0014682010637336D+00, & 0.0014682010637336D+00, & 0.0014682010637336D+00, & 0.0014682010637336D+00, & 0.0014682010637336D+00, & 0.0008010544852012D+00, & 0.0008010544852012D+00, & 0.0008010544852012D+00, & 0.0008010544852012D+00, & 0.0008010544852012D+00, & 0.0008010544852012D+00, & 0.0001855670423377D+00, & 0.0001855670423377D+00, & 0.0001855670423377D+00, & 0.0001855670423377D+00, & 0.0001855670423377D+00, & 0.0001855670423377D+00, & 0.0007214220264261D+00, & 0.0007214220264261D+00, & 0.0007214220264261D+00, & 0.0007214220264261D+00, & 0.0007214220264261D+00, & 0.0007214220264261D+00, & 0.0015321667240474D+00, & 0.0015321667240474D+00, & 0.0015321667240474D+00, & 0.0015321667240474D+00, & 0.0015321667240474D+00, & 0.0015321667240474D+00, & 0.0027296527164899D+00, & 0.0027296527164899D+00, & 0.0027296527164899D+00, & 0.0015090266204283D+00, & 0.0015090266204283D+00, & 0.0015090266204283D+00, & 0.0015090266204283D+00, & 0.0015090266204283D+00, & 0.0015090266204283D+00, & 0.0034017224729490D+00, & 0.0034017224729490D+00, & 0.0034017224729490D+00, & 0.0034017224729490D+00, & 0.0034017224729490D+00, & 0.0034017224729490D+00, & 0.0012045060134119D+00, & 0.0012045060134119D+00, & 0.0012045060134119D+00, & 0.0010359881638064D+00, & 0.0010359881638064D+00, & 0.0010359881638064D+00, & 0.0010359881638064D+00, & 0.0010359881638064D+00, & 0.0010359881638064D+00, & 0.0023774876927799D+00, & 0.0023774876927799D+00, & 0.0023774876927799D+00, & 0.0023774876927799D+00, & 0.0023774876927799D+00, & 0.0023774876927799D+00, & 0.0033953912341847D+00, & 0.0033953912341847D+00, & 0.0033953912341847D+00, & 0.0033953912341847D+00, & 0.0033953912341847D+00, & 0.0033953912341847D+00, & 0.0027040883824818D+00, & 0.0027040883824818D+00, & 0.0027040883824818D+00, & 0.0027040883824818D+00, & 0.0027040883824818D+00, & 0.0027040883824818D+00, & 0.0020170033902913D+00, & 0.0020170033902913D+00, & 0.0020170033902913D+00, & 0.0020170033902913D+00, & 0.0020170033902913D+00, & 0.0020170033902913D+00, & 0.0027918811324258D+00, & 0.0027918811324258D+00, & 0.0027918811324258D+00, & 0.0027918811324258D+00, & 0.0027918811324258D+00, & 0.0027918811324258D+00, & 0.0023657933107792D+00, & 0.0023657933107792D+00, & 0.0023657933107792D+00, & 0.0043004588657305D+00, & 0.0043004588657305D+00, & 0.0043004588657305D+00, & 0.0043004588657305D+00, & 0.0043004588657305D+00, & 0.0043004588657305D+00, & 0.0049838565291938D+00, & 0.0049838565291938D+00, & 0.0049838565291938D+00, & 0.0049838565291938D+00, & 0.0049838565291938D+00, & 0.0049838565291938D+00, & 0.0046532962756670D+00, & 0.0046532962756670D+00, & 0.0046532962756670D+00, & 0.0046532962756670D+00, & 0.0046532962756670D+00, & 0.0046532962756670D+00, & 0.0041278760422565D+00, & 0.0041278760422565D+00, & 0.0041278760422565D+00, & 0.0041278760422565D+00, & 0.0041278760422565D+00, & 0.0041278760422565D+00, & 0.0035111942683412D+00, & 0.0035111942683412D+00, & 0.0035111942683412D+00, & 0.0020578217623525D+00, & 0.0020578217623525D+00, & 0.0020578217623525D+00, & 0.0020578217623525D+00, & 0.0020578217623525D+00, & 0.0020578217623525D+00, & 0.0038938204584288D+00, & 0.0038938204584288D+00, & 0.0038938204584288D+00, & 0.0038938204584288D+00, & 0.0038938204584288D+00, & 0.0038938204584288D+00, & 0.0029434680471958D+00, & 0.0029434680471958D+00, & 0.0029434680471958D+00, & 0.0027707613965555D+00, & 0.0027707613965555D+00, & 0.0027707613965555D+00, & 0.0027707613965555D+00, & 0.0027707613965555D+00, & 0.0027707613965555D+00, & 0.0067232428984731D+00, & 0.0067232428984731D+00, & 0.0067232428984731D+00, & 0.0049798588125189D+00, & 0.0049798588125189D+00, & 0.0049798588125189D+00, & 0.0024801439985068D+00, & 0.0024801439985068D+00, & 0.0024801439985068D+00, & 0.0024801439985068D+00, & 0.0024801439985068D+00, & 0.0024801439985068D+00, & 0.0008629021808335D+00, & 0.0008629021808335D+00, & 0.0008629021808335D+00, & 0.0008629021808335D+00, & 0.0008629021808335D+00, & 0.0008629021808335D+00, & 0.0003209331775743D+00, & 0.0003209331775743D+00, & 0.0003209331775743D+00, & 0.0003209331775743D+00, & 0.0003209331775743D+00, & 0.0003209331775743D+00, & 0.0049810086106174D+00, & 0.0049810086106174D+00, & 0.0049810086106174D+00, & 0.0049810086106174D+00, & 0.0049810086106174D+00, & 0.0049810086106174D+00, & 0.0050195779180815D+00, & 0.0050195779180815D+00, & 0.0050195779180815D+00, & 0.0050195779180815D+00, & 0.0050195779180815D+00, & 0.0050195779180815D+00, & 0.0027692328182935D+00, & 0.0027692328182935D+00, & 0.0027692328182935D+00, & 0.0027692328182935D+00, & 0.0027692328182935D+00, & 0.0027692328182935D+00, & 0.0037015806596788D+00, & 0.0037015806596788D+00, & 0.0037015806596788D+00, & 0.0037015806596788D+00, & 0.0037015806596788D+00, & 0.0037015806596788D+00, & 0.0050750374591620D+00, & 0.0050750374591620D+00, & 0.0050750374591620D+00, & 0.0050750374591620D+00, & 0.0050750374591620D+00, & 0.0050750374591620D+00, & 0.0042676766915482D+00, & 0.0042676766915482D+00, & 0.0042676766915482D+00, & 0.0042676766915482D+00, & 0.0042676766915482D+00, & 0.0042676766915482D+00, & 0.0017292273039881D+00, & 0.0017292273039881D+00, & 0.0017292273039881D+00, & 0.0017292273039881D+00, & 0.0017292273039881D+00, & 0.0017292273039881D+00, & 0.0032247399122439D+00, & 0.0032247399122439D+00, & 0.0032247399122439D+00, & 0.0032247399122439D+00, & 0.0032247399122439D+00, & 0.0032247399122439D+00, & 0.0052879477129619D+00, & 0.0052879477129619D+00, & 0.0052879477129619D+00, & 0.0052879477129619D+00, & 0.0052879477129619D+00, & 0.0052879477129619D+00, & 0.0040195842863651D+00, & 0.0040195842863651D+00, & 0.0040195842863651D+00, & 0.0040195842863651D+00, & 0.0040195842863651D+00, & 0.0040195842863651D+00, & 0.0060608332073000D+00, & 0.0060608332073000D+00, & 0.0060608332073000D+00, & 0.0060608332073000D+00, & 0.0060608332073000D+00, & 0.0060608332073000D+00, & 0.0049208372452468D+00, & 0.0049208372452468D+00, & 0.0049208372452468D+00, & 0.0050214750285976D+00, & 0.0050214750285976D+00, & 0.0050214750285976D+00, & 0.0057991370585633D+00, & 0.0057991370585633D+00, & 0.0057991370585633D+00, & 0.0057991370585633D+00, & 0.0057991370585633D+00, & 0.0057991370585633D+00, & 0.0044465932407613D+00, & 0.0044465932407613D+00, & 0.0044465932407613D+00, & 0.0063931475211100D+00, & 0.0063931475211100D+00, & 0.0063931475211100D+00, & 0.0063931475211100D+00, & 0.0063931475211100D+00, & 0.0063931475211100D+00, & 0.0046466127645844D+00, & 0.0046466127645844D+00, & 0.0046466127645844D+00, & 0.0056546750089884D+00, & 0.0056546750089884D+00, & 0.0056546750089884D+00, & 0.0056546750089884D+00, & 0.0056546750089884D+00, & 0.0056546750089884D+00, & 0.0053110494169000D+00, & 0.0053110494169000D+00, & 0.0053110494169000D+00, & 0.0053110494169000D+00, & 0.0053110494169000D+00, & 0.0053110494169000D+00, & 0.0019732304214759D+00, & 0.0019732304214759D+00, & 0.0019732304214759D+00, & 0.0019732304214759D+00, & 0.0019732304214759D+00, & 0.0019732304214759D+00, & 0.0064254720501743D+00, & 0.0064254720501743D+00, & 0.0064254720501743D+00, & 0.0062655878836268D+00, & 0.0062655878836268D+00, & 0.0062655878836268D+00, & 0.0035554794715669D+00, & 0.0035554794715669D+00, & 0.0035554794715669D+00, & 0.0035554794715669D+00, & 0.0035554794715669D+00, & 0.0035554794715669D+00 /) return end subroutine rule45 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule45() returns the rule of precision 45. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.0126048038307362D+00, & 0.9801027666184203D+00, & 0.0072924295508435D+00, & 0.9801027666184204D+00, & 0.0126048038307363D+00, & 0.0072924295508431D+00, & 0.0046054766314413D+00, & 0.9940445261864481D+00, & 0.0013499971821107D+00, & 0.9940445261864482D+00, & 0.0046054766314413D+00, & 0.0013499971821102D+00, & 0.0679464966039112D+00, & 0.9251943274580282D+00, & 0.0068591759380607D+00, & 0.9251943274580283D+00, & 0.0679464966039112D+00, & 0.0068591759380603D+00, & 0.0693380043634408D+00, & 0.9294322276406242D+00, & 0.0012297679959350D+00, & 0.9294322276406243D+00, & 0.0693380043634408D+00, & 0.0012297679959347D+00, & 0.4682708598709480D+00, & 0.5229490399283573D+00, & 0.0087801002006947D+00, & 0.5229490399283572D+00, & 0.4682708598709480D+00, & 0.0087801002006947D+00, & 0.2504951703352215D+00, & 0.7478218033035982D+00, & 0.0016830263611803D+00, & 0.7478218033035983D+00, & 0.2504951703352215D+00, & 0.0016830263611800D+00, & 0.0179231013398374D+00, & 0.9803189260766274D+00, & 0.0017579725835354D+00, & 0.9803189260766274D+00, & 0.0179231013398374D+00, & 0.0017579725835349D+00, & 0.3594568419950528D+00, & 0.6390675443517843D+00, & 0.0014756136531630D+00, & 0.6390675443517843D+00, & 0.3594568419950528D+00, & 0.0014756136531628D+00, & 0.2211539847849475D+00, & 0.6251828877524599D+00, & 0.1536631274625926D+00, & 0.6251828877524600D+00, & 0.2211539847849475D+00, & 0.1536631274625923D+00, & 0.2389731948786961D+00, & 0.5334015889840547D+00, & 0.2276252161372492D+00, & 0.5334015889840547D+00, & 0.2389731948786961D+00, & 0.2276252161372491D+00, & 0.1298066533002767D+00, & 0.7403866933994464D+00, & 0.1298066533002770D+00, & 0.2265228859811758D+00, & 0.6592740762673123D+00, & 0.1142030377515119D+00, & 0.6592740762673124D+00, & 0.2265228859811758D+00, & 0.1142030377515117D+00, & 0.2395905240377902D+00, & 0.6800344164936584D+00, & 0.0803750594685514D+00, & 0.6800344164936585D+00, & 0.2395905240377902D+00, & 0.0803750594685512D+00, & 0.1782914029925923D+00, & 0.7910902333249177D+00, & 0.0306183636824901D+00, & 0.7910902333249177D+00, & 0.1782914029925923D+00, & 0.0306183636824899D+00, & 0.2063496656308830D+00, & 0.5873006687382336D+00, & 0.2063496656308832D+00, & 0.1750845888069398D+00, & 0.6498308223861201D+00, & 0.1750845888069402D+00, & 0.2825866891204175D+00, & 0.6904712080981594D+00, & 0.0269421027814231D+00, & 0.6904712080981593D+00, & 0.2825866891204175D+00, & 0.0269421027814229D+00, & 0.1372571102587296D+00, & 0.8299456761943377D+00, & 0.0327972135469328D+00, & 0.8299456761943378D+00, & 0.1372571102587296D+00, & 0.0327972135469324D+00, & 0.4995045768679594D+00, & 0.4995045768679594D+00, & 0.0009908462640811D+00, & 0.1002544152365696D+00, & 0.8670184720297813D+00, & 0.0327271127336490D+00, & 0.8670184720297813D+00, & 0.1002544152365697D+00, & 0.0327271127336487D+00, & 0.0517074765599653D+00, & 0.9331324221261621D+00, & 0.0151601013138727D+00, & 0.9331324221261622D+00, & 0.0517074765599654D+00, & 0.0151601013138723D+00, & 0.2606148551376569D+00, & 0.5685004919093655D+00, & 0.1708846529529776D+00, & 0.5685004919093656D+00, & 0.2606148551376569D+00, & 0.1708846529529774D+00, & 0.2272143249599573D+00, & 0.7441223888358753D+00, & 0.0286632862041673D+00, & 0.7441223888358756D+00, & 0.2272143249599574D+00, & 0.0286632862041670D+00, & 0.3110404872350509D+00, & 0.6762638411989882D+00, & 0.0126956715659609D+00, & 0.6762638411989881D+00, & 0.3110404872350510D+00, & 0.0126956715659608D+00, & 0.0552204190605028D+00, & 0.8895591618789941D+00, & 0.0552204190605031D+00, & 0.1856238762990532D+00, & 0.7264745884520657D+00, & 0.0879015352488812D+00, & 0.7264745884520657D+00, & 0.1856238762990533D+00, & 0.0879015352488808D+00, & 0.0658626437608178D+00, & 0.9034170100624399D+00, & 0.0307203461767425D+00, & 0.9034170100624398D+00, & 0.0658626437608178D+00, & 0.0307203461767422D+00, & 0.3015904700953623D+00, & 0.6955949792647613D+00, & 0.0028145506398765D+00, & 0.6955949792647613D+00, & 0.3015904700953622D+00, & 0.0028145506398762D+00, & 0.2925426576542363D+00, & 0.6276179259734721D+00, & 0.0798394163722916D+00, & 0.6276179259734721D+00, & 0.2925426576542364D+00, & 0.0798394163722914D+00, & 0.0273024847528849D+00, & 0.9593763173443479D+00, & 0.0133211979027673D+00, & 0.9593763173443479D+00, & 0.0273024847528850D+00, & 0.0133211979027669D+00, & 0.2991527658365939D+00, & 0.4016944683268121D+00, & 0.2991527658365939D+00, & 0.3715719205775442D+00, & 0.6188258934043402D+00, & 0.0096021860181155D+00, & 0.6188258934043402D+00, & 0.3715719205775442D+00, & 0.0096021860181154D+00, & 0.2010073039936871D+00, & 0.7964902586210802D+00, & 0.0025024373852327D+00, & 0.7964902586210802D+00, & 0.2010073039936872D+00, & 0.0025024373852325D+00, & 0.2931831293722664D+00, & 0.5050860425617371D+00, & 0.2017308280659965D+00, & 0.5050860425617371D+00, & 0.2931831293722664D+00, & 0.2017308280659964D+00, & 0.2333318911036226D+00, & 0.7139904265957288D+00, & 0.0526776823006487D+00, & 0.7139904265957289D+00, & 0.2333318911036226D+00, & 0.0526776823006484D+00, & 0.1792991418970043D+00, & 0.7649317119922271D+00, & 0.0557691461107687D+00, & 0.7649317119922271D+00, & 0.1792991418970044D+00, & 0.0557691461107684D+00, & 0.3669822772564582D+00, & 0.3669822772564582D+00, & 0.2660354454870835D+00, & 0.2934353311290930D+00, & 0.6583279675616898D+00, & 0.0482367013092171D+00, & 0.6583279675616899D+00, & 0.2934353311290930D+00, & 0.0482367013092171D+00, & 0.3298405962756192D+00, & 0.4364618201712586D+00, & 0.2336975835531220D+00, & 0.4364618201712586D+00, & 0.3298405962756192D+00, & 0.2336975835531221D+00, & 0.1381756936115276D+00, & 0.7691621557796962D+00, & 0.0926621506087763D+00, & 0.7691621557796963D+00, & 0.1381756936115277D+00, & 0.0926621506087759D+00, & 0.3585128657761011D+00, & 0.4680323661208265D+00, & 0.1734547681030723D+00, & 0.4680323661208265D+00, & 0.3585128657761011D+00, & 0.1734547681030723D+00, & 0.4203377834665488D+00, & 0.5618113228868684D+00, & 0.0178508936465827D+00, & 0.5618113228868684D+00, & 0.4203377834665488D+00, & 0.0178508936465827D+00, & 0.2790511330034806D+00, & 0.6010021745006722D+00, & 0.1199466924958471D+00, & 0.6010021745006722D+00, & 0.2790511330034807D+00, & 0.1199466924958470D+00, & 0.0934626722493711D+00, & 0.8925527104988681D+00, & 0.0139846172517610D+00, & 0.8925527104988681D+00, & 0.0934626722493711D+00, & 0.0139846172517607D+00, & 0.3874089876890199D+00, & 0.4932332479959026D+00, & 0.1193577643150775D+00, & 0.4932332479959027D+00, & 0.3874089876890199D+00, & 0.1193577643150774D+00, & 0.4071846956615202D+00, & 0.5192306493531181D+00, & 0.0735846549853617D+00, & 0.5192306493531181D+00, & 0.4071846956615202D+00, & 0.0735846549853617D+00, & 0.1876405833897097D+00, & 0.7996426687617495D+00, & 0.0127167478485408D+00, & 0.7996426687617495D+00, & 0.1876405833897097D+00, & 0.0127167478485406D+00, & 0.2649216423903805D+00, & 0.4701567152192389D+00, & 0.2649216423903806D+00, & 0.1522255260382763D+00, & 0.8453340935540358D+00, & 0.0024403804076879D+00, & 0.8453340935540359D+00, & 0.1522255260382763D+00, & 0.0024403804076877D+00, & 0.1741420017865634D+00, & 0.6959673722361421D+00, & 0.1298906259772944D+00, & 0.6959673722361421D+00, & 0.1741420017865634D+00, & 0.1298906259772943D+00, & 0.3984690684139450D+00, & 0.3984690684139450D+00, & 0.2030618631721098D+00, & 0.3214081551755261D+00, & 0.5347112144371693D+00, & 0.1438806303873045D+00, & 0.5347112144371693D+00, & 0.3214081551755262D+00, & 0.1438806303873043D+00, & 0.0888043361734265D+00, & 0.8523358545382167D+00, & 0.0588598092883569D+00, & 0.8523358545382167D+00, & 0.0888043361734265D+00, & 0.0588598092883565D+00, & 0.1304289155517122D+00, & 0.8092737430634784D+00, & 0.0602973413848094D+00, & 0.8092737430634784D+00, & 0.1304289155517123D+00, & 0.0602973413848091D+00, & 0.4526201907514942D+00, & 0.4526201907514942D+00, & 0.0947596184970115D+00, & 0.1368379127222100D+00, & 0.8499366346784312D+00, & 0.0132254525993589D+00, & 0.8499366346784312D+00, & 0.1368379127222101D+00, & 0.0132254525993586D+00, & 0.3528533591796706D+00, & 0.5898753813183408D+00, & 0.0572712595019886D+00, & 0.5898753813183407D+00, & 0.3528533591796706D+00, & 0.0572712595019886D+00, & 0.2463869002171422D+00, & 0.7426794521965718D+00, & 0.0109336475862860D+00, & 0.7426794521965718D+00, & 0.2463869002171423D+00, & 0.0109336475862858D+00, & 0.4268610495333074D+00, & 0.4268610495333074D+00, & 0.1462779009333850D+00, & 0.3333333333333333D+00, & 0.3435200440594713D+00, & 0.5605547908509811D+00, & 0.0959251650895475D+00, & 0.5605547908509811D+00, & 0.3435200440594713D+00, & 0.0959251650895474D+00, & 0.4162089636364642D+00, & 0.5441206066477789D+00, & 0.0396704297157567D+00, & 0.5441206066477789D+00, & 0.4162089636364643D+00, & 0.0396704297157567D+00, & 0.0945724371334944D+00, & 0.8108551257330109D+00, & 0.0945724371334948D+00, & 0.4729894708688973D+00, & 0.4729894708688974D+00, & 0.0540210582622052D+00, & 0.0390118106999858D+00, & 0.9581931415494848D+00, & 0.0027950477505296D+00, & 0.9581931415494848D+00, & 0.0390118106999859D+00, & 0.0027950477505291D+00, & 0.1071807141346061D+00, & 0.8901526742127170D+00, & 0.0026666116526771D+00, & 0.8901526742127172D+00, & 0.1071807141346060D+00, & 0.0026666116526766D+00, & 0.4264238197063261D+00, & 0.5710366502174161D+00, & 0.0025395300762577D+00, & 0.5710366502174161D+00, & 0.4264238197063261D+00, & 0.0025395300762577D+00, & 0.0340851411567991D+00, & 0.9318297176864013D+00, & 0.0340851411567996D+00, & 0.3519601313638296D+00, & 0.6193084930778816D+00, & 0.0287313755582888D+00, & 0.6193084930778816D+00, & 0.3519601313638297D+00, & 0.0287313755582886D+00, & 0.4869989968257815D+00, & 0.4869989968257815D+00, & 0.0260020063484370D+00 /) b = (/ & 0.0072924295508434D+00, & 0.0126048038307362D+00, & 0.9801027666184206D+00, & 0.0072924295508434D+00, & 0.9801027666184206D+00, & 0.0126048038307365D+00, & 0.0013499971821105D+00, & 0.0046054766314413D+00, & 0.9940445261864482D+00, & 0.0013499971821105D+00, & 0.9940445261864485D+00, & 0.0046054766314416D+00, & 0.0068591759380605D+00, & 0.0679464966039111D+00, & 0.9251943274580284D+00, & 0.0068591759380605D+00, & 0.9251943274580284D+00, & 0.0679464966039115D+00, & 0.0012297679959349D+00, & 0.0693380043634408D+00, & 0.9294322276406244D+00, & 0.0012297679959349D+00, & 0.9294322276406244D+00, & 0.0693380043634411D+00, & 0.0087801002006948D+00, & 0.4682708598709480D+00, & 0.5229490399283575D+00, & 0.0087801002006948D+00, & 0.5229490399283574D+00, & 0.4682708598709482D+00, & 0.0016830263611803D+00, & 0.2504951703352215D+00, & 0.7478218033035984D+00, & 0.0016830263611803D+00, & 0.7478218033035984D+00, & 0.2504951703352218D+00, & 0.0017579725835351D+00, & 0.0179231013398374D+00, & 0.9803189260766274D+00, & 0.0017579725835351D+00, & 0.9803189260766277D+00, & 0.0179231013398377D+00, & 0.0014756136531629D+00, & 0.3594568419950528D+00, & 0.6390675443517844D+00, & 0.0014756136531629D+00, & 0.6390675443517843D+00, & 0.3594568419950530D+00, & 0.1536631274625925D+00, & 0.2211539847849475D+00, & 0.6251828877524600D+00, & 0.1536631274625925D+00, & 0.6251828877524601D+00, & 0.2211539847849477D+00, & 0.2276252161372493D+00, & 0.2389731948786962D+00, & 0.5334015889840548D+00, & 0.2276252161372493D+00, & 0.5334015889840548D+00, & 0.2389731948786963D+00, & 0.1298066533002769D+00, & 0.1298066533002767D+00, & 0.7403866933994465D+00, & 0.1142030377515119D+00, & 0.2265228859811758D+00, & 0.6592740762673125D+00, & 0.1142030377515119D+00, & 0.6592740762673125D+00, & 0.2265228859811760D+00, & 0.0803750594685514D+00, & 0.2395905240377902D+00, & 0.6800344164936586D+00, & 0.0803750594685514D+00, & 0.6800344164936585D+00, & 0.2395905240377905D+00, & 0.0306183636824900D+00, & 0.1782914029925923D+00, & 0.7910902333249178D+00, & 0.0306183636824900D+00, & 0.7910902333249178D+00, & 0.1782914029925926D+00, & 0.2063496656308833D+00, & 0.2063496656308831D+00, & 0.5873006687382338D+00, & 0.1750845888069401D+00, & 0.1750845888069399D+00, & 0.6498308223861201D+00, & 0.0269421027814231D+00, & 0.2825866891204175D+00, & 0.6904712080981597D+00, & 0.0269421027814231D+00, & 0.6904712080981594D+00, & 0.2825866891204177D+00, & 0.0327972135469327D+00, & 0.1372571102587296D+00, & 0.8299456761943379D+00, & 0.0327972135469327D+00, & 0.8299456761943380D+00, & 0.1372571102587299D+00, & 0.0009908462640811D+00, & 0.4995045768679595D+00, & 0.4995045768679597D+00, & 0.0327271127336490D+00, & 0.1002544152365696D+00, & 0.8670184720297816D+00, & 0.0327271127336490D+00, & 0.8670184720297816D+00, & 0.1002544152365700D+00, & 0.0151601013138726D+00, & 0.0517074765599653D+00, & 0.9331324221261622D+00, & 0.0151601013138726D+00, & 0.9331324221261622D+00, & 0.0517074765599656D+00, & 0.1708846529529776D+00, & 0.2606148551376569D+00, & 0.5685004919093657D+00, & 0.1708846529529776D+00, & 0.5685004919093657D+00, & 0.2606148551376571D+00, & 0.0286632862041672D+00, & 0.2272143249599573D+00, & 0.7441223888358756D+00, & 0.0286632862041672D+00, & 0.7441223888358756D+00, & 0.2272143249599576D+00, & 0.0126956715659609D+00, & 0.3110404872350509D+00, & 0.6762638411989884D+00, & 0.0126956715659609D+00, & 0.6762638411989882D+00, & 0.3110404872350512D+00, & 0.0552204190605031D+00, & 0.0552204190605028D+00, & 0.8895591618789943D+00, & 0.0879015352488811D+00, & 0.1856238762990532D+00, & 0.7264745884520658D+00, & 0.0879015352488811D+00, & 0.7264745884520658D+00, & 0.1856238762990535D+00, & 0.0307203461767424D+00, & 0.0658626437608177D+00, & 0.9034170100624400D+00, & 0.0307203461767424D+00, & 0.9034170100624400D+00, & 0.0658626437608181D+00, & 0.0028145506398764D+00, & 0.3015904700953623D+00, & 0.6955949792647615D+00, & 0.0028145506398764D+00, & 0.6955949792647615D+00, & 0.3015904700953626D+00, & 0.0798394163722916D+00, & 0.2925426576542363D+00, & 0.6276179259734722D+00, & 0.0798394163722916D+00, & 0.6276179259734722D+00, & 0.2925426576542366D+00, & 0.0133211979027671D+00, & 0.0273024847528849D+00, & 0.9593763173443480D+00, & 0.0133211979027671D+00, & 0.9593763173443480D+00, & 0.0273024847528853D+00, & 0.2991527658365941D+00, & 0.2991527658365941D+00, & 0.4016944683268122D+00, & 0.0096021860181156D+00, & 0.3715719205775442D+00, & 0.6188258934043405D+00, & 0.0096021860181156D+00, & 0.6188258934043404D+00, & 0.3715719205775445D+00, & 0.0025024373852327D+00, & 0.2010073039936871D+00, & 0.7964902586210805D+00, & 0.0025024373852327D+00, & 0.7964902586210802D+00, & 0.2010073039936874D+00, & 0.2017308280659965D+00, & 0.2931831293722665D+00, & 0.5050860425617372D+00, & 0.2017308280659965D+00, & 0.5050860425617372D+00, & 0.2931831293722666D+00, & 0.0526776823006486D+00, & 0.2333318911036226D+00, & 0.7139904265957290D+00, & 0.0526776823006486D+00, & 0.7139904265957289D+00, & 0.2333318911036229D+00, & 0.0557691461107686D+00, & 0.1792991418970043D+00, & 0.7649317119922272D+00, & 0.0557691461107686D+00, & 0.7649317119922272D+00, & 0.1792991418970046D+00, & 0.2660354454870836D+00, & 0.3669822772564583D+00, & 0.3669822772564584D+00, & 0.0482367013092172D+00, & 0.2934353311290930D+00, & 0.6583279675616901D+00, & 0.0482367013092172D+00, & 0.6583279675616900D+00, & 0.2934353311290932D+00, & 0.2336975835531222D+00, & 0.3298405962756193D+00, & 0.4364618201712588D+00, & 0.2336975835531222D+00, & 0.4364618201712587D+00, & 0.3298405962756194D+00, & 0.0926621506087761D+00, & 0.1381756936115276D+00, & 0.7691621557796964D+00, & 0.0926621506087761D+00, & 0.7691621557796964D+00, & 0.1381756936115279D+00, & 0.1734547681030724D+00, & 0.3585128657761012D+00, & 0.4680323661208267D+00, & 0.1734547681030724D+00, & 0.4680323661208267D+00, & 0.3585128657761013D+00, & 0.0178508936465828D+00, & 0.4203377834665488D+00, & 0.5618113228868687D+00, & 0.0178508936465828D+00, & 0.5618113228868685D+00, & 0.4203377834665490D+00, & 0.1199466924958472D+00, & 0.2790511330034807D+00, & 0.6010021745006724D+00, & 0.1199466924958472D+00, & 0.6010021745006723D+00, & 0.2790511330034809D+00, & 0.0139846172517609D+00, & 0.0934626722493711D+00, & 0.8925527104988682D+00, & 0.0139846172517609D+00, & 0.8925527104988682D+00, & 0.0934626722493714D+00, & 0.1193577643150775D+00, & 0.3874089876890200D+00, & 0.4932332479959028D+00, & 0.1193577643150775D+00, & 0.4932332479959027D+00, & 0.3874089876890201D+00, & 0.0735846549853618D+00, & 0.4071846956615202D+00, & 0.5192306493531184D+00, & 0.0735846549853618D+00, & 0.5192306493531181D+00, & 0.4071846956615204D+00, & 0.0127167478485408D+00, & 0.1876405833897097D+00, & 0.7996426687617497D+00, & 0.0127167478485408D+00, & 0.7996426687617497D+00, & 0.1876405833897100D+00, & 0.2649216423903806D+00, & 0.2649216423903806D+00, & 0.4701567152192390D+00, & 0.0024403804076879D+00, & 0.1522255260382763D+00, & 0.8453340935540361D+00, & 0.0024403804076879D+00, & 0.8453340935540361D+00, & 0.1522255260382766D+00, & 0.1298906259772945D+00, & 0.1741420017865634D+00, & 0.6959673722361424D+00, & 0.1298906259772945D+00, & 0.6959673722361424D+00, & 0.1741420017865636D+00, & 0.2030618631721099D+00, & 0.3984690684139451D+00, & 0.3984690684139452D+00, & 0.1438806303873045D+00, & 0.3214081551755262D+00, & 0.5347112144371695D+00, & 0.1438806303873045D+00, & 0.5347112144371694D+00, & 0.3214081551755264D+00, & 0.0588598092883568D+00, & 0.0888043361734265D+00, & 0.8523358545382169D+00, & 0.0588598092883568D+00, & 0.8523358545382169D+00, & 0.0888043361734268D+00, & 0.0602973413848094D+00, & 0.1304289155517122D+00, & 0.8092737430634785D+00, & 0.0602973413848094D+00, & 0.8092737430634785D+00, & 0.1304289155517125D+00, & 0.0947596184970116D+00, & 0.4526201907514942D+00, & 0.4526201907514944D+00, & 0.0132254525993588D+00, & 0.1368379127222100D+00, & 0.8499366346784313D+00, & 0.0132254525993588D+00, & 0.8499366346784313D+00, & 0.1368379127222104D+00, & 0.0572712595019887D+00, & 0.3528533591796706D+00, & 0.5898753813183411D+00, & 0.0572712595019887D+00, & 0.5898753813183409D+00, & 0.3528533591796708D+00, & 0.0109336475862860D+00, & 0.2463869002171422D+00, & 0.7426794521965722D+00, & 0.0109336475862860D+00, & 0.7426794521965718D+00, & 0.2463869002171425D+00, & 0.1462779009333851D+00, & 0.4268610495333075D+00, & 0.4268610495333077D+00, & 0.3333333333333334D+00, & 0.0959251650895476D+00, & 0.3435200440594713D+00, & 0.5605547908509814D+00, & 0.0959251650895476D+00, & 0.5605547908509813D+00, & 0.3435200440594715D+00, & 0.0396704297157568D+00, & 0.4162089636364643D+00, & 0.5441206066477793D+00, & 0.0396704297157568D+00, & 0.5441206066477792D+00, & 0.4162089636364644D+00, & 0.0945724371334947D+00, & 0.0945724371334944D+00, & 0.8108551257330111D+00, & 0.0540210582622053D+00, & 0.4729894708688974D+00, & 0.4729894708688976D+00, & 0.0027950477505294D+00, & 0.0390118106999857D+00, & 0.9581931415494850D+00, & 0.0027950477505294D+00, & 0.9581931415494850D+00, & 0.0390118106999862D+00, & 0.0026666116526769D+00, & 0.1071807141346060D+00, & 0.8901526742127170D+00, & 0.0026666116526769D+00, & 0.8901526742127174D+00, & 0.1071807141346064D+00, & 0.0025395300762578D+00, & 0.4264238197063261D+00, & 0.5710366502174163D+00, & 0.0025395300762578D+00, & 0.5710366502174162D+00, & 0.4264238197063264D+00, & 0.0340851411567994D+00, & 0.0340851411567991D+00, & 0.9318297176864015D+00, & 0.0287313755582888D+00, & 0.3519601313638296D+00, & 0.6193084930778818D+00, & 0.0287313755582888D+00, & 0.6193084930778817D+00, & 0.3519601313638299D+00, & 0.0260020063484371D+00, & 0.4869989968257816D+00, & 0.4869989968257817D+00 /) c = (/ & 0.9801027666184204D+00, & 0.0072924295508435D+00, & 0.0126048038307359D+00, & 0.0126048038307362D+00, & 0.0072924295508432D+00, & 0.9801027666184203D+00, & 0.9940445261864482D+00, & 0.0013499971821106D+00, & 0.0046054766314411D+00, & 0.0046054766314413D+00, & 0.0013499971821102D+00, & 0.9940445261864481D+00, & 0.9251943274580283D+00, & 0.0068591759380607D+00, & 0.0679464966039108D+00, & 0.0679464966039111D+00, & 0.0068591759380604D+00, & 0.9251943274580282D+00, & 0.9294322276406243D+00, & 0.0012297679959350D+00, & 0.0693380043634406D+00, & 0.0693380043634408D+00, & 0.0012297679959348D+00, & 0.9294322276406242D+00, & 0.5229490399283573D+00, & 0.0087801002006947D+00, & 0.4682708598709479D+00, & 0.4682708598709481D+00, & 0.0087801002006946D+00, & 0.5229490399283572D+00, & 0.7478218033035983D+00, & 0.0016830263611803D+00, & 0.2504951703352213D+00, & 0.2504951703352215D+00, & 0.0016830263611801D+00, & 0.7478218033035982D+00, & 0.9803189260766274D+00, & 0.0017579725835352D+00, & 0.0179231013398372D+00, & 0.0179231013398374D+00, & 0.0017579725835349D+00, & 0.9803189260766273D+00, & 0.6390675443517843D+00, & 0.0014756136531629D+00, & 0.3594568419950526D+00, & 0.3594568419950528D+00, & 0.0014756136531630D+00, & 0.6390675443517841D+00, & 0.6251828877524599D+00, & 0.1536631274625926D+00, & 0.2211539847849474D+00, & 0.2211539847849475D+00, & 0.1536631274625924D+00, & 0.6251828877524599D+00, & 0.5334015889840545D+00, & 0.2276252161372492D+00, & 0.2389731948786961D+00, & 0.2389731948786961D+00, & 0.2276252161372491D+00, & 0.5334015889840545D+00, & 0.7403866933994465D+00, & 0.1298066533002769D+00, & 0.1298066533002765D+00, & 0.6592740762673124D+00, & 0.1142030377515119D+00, & 0.2265228859811755D+00, & 0.2265228859811758D+00, & 0.1142030377515116D+00, & 0.6592740762673124D+00, & 0.6800344164936584D+00, & 0.0803750594685514D+00, & 0.2395905240377899D+00, & 0.2395905240377901D+00, & 0.0803750594685513D+00, & 0.6800344164936583D+00, & 0.7910902333249177D+00, & 0.0306183636824900D+00, & 0.1782914029925921D+00, & 0.1782914029925923D+00, & 0.0306183636824898D+00, & 0.7910902333249177D+00, & 0.5873006687382337D+00, & 0.2063496656308832D+00, & 0.2063496656308830D+00, & 0.6498308223861200D+00, & 0.1750845888069400D+00, & 0.1750845888069398D+00, & 0.6904712080981594D+00, & 0.0269421027814231D+00, & 0.2825866891204173D+00, & 0.2825866891204176D+00, & 0.0269421027814231D+00, & 0.6904712080981593D+00, & 0.8299456761943378D+00, & 0.0327972135469327D+00, & 0.1372571102587293D+00, & 0.1372571102587296D+00, & 0.0327972135469324D+00, & 0.8299456761943377D+00, & 0.4995045768679595D+00, & 0.0009908462640812D+00, & 0.4995045768679592D+00, & 0.8670184720297814D+00, & 0.0327271127336490D+00, & 0.1002544152365694D+00, & 0.1002544152365697D+00, & 0.0327271127336487D+00, & 0.8670184720297813D+00, & 0.9331324221261621D+00, & 0.0151601013138726D+00, & 0.0517074765599651D+00, & 0.0517074765599652D+00, & 0.0151601013138724D+00, & 0.9331324221261621D+00, & 0.5685004919093655D+00, & 0.1708846529529776D+00, & 0.2606148551376568D+00, & 0.2606148551376569D+00, & 0.1708846529529774D+00, & 0.5685004919093655D+00, & 0.7441223888358754D+00, & 0.0286632862041673D+00, & 0.2272143249599571D+00, & 0.2272143249599572D+00, & 0.0286632862041670D+00, & 0.7441223888358753D+00, & 0.6762638411989881D+00, & 0.0126956715659609D+00, & 0.3110404872350506D+00, & 0.3110404872350510D+00, & 0.0126956715659609D+00, & 0.6762638411989881D+00, & 0.8895591618789941D+00, & 0.0552204190605031D+00, & 0.0552204190605027D+00, & 0.7264745884520657D+00, & 0.0879015352488811D+00, & 0.1856238762990530D+00, & 0.1856238762990532D+00, & 0.0879015352488809D+00, & 0.7264745884520658D+00, & 0.9034170100624398D+00, & 0.0307203461767424D+00, & 0.0658626437608175D+00, & 0.0658626437608178D+00, & 0.0307203461767421D+00, & 0.9034170100624398D+00, & 0.6955949792647614D+00, & 0.0028145506398763D+00, & 0.3015904700953620D+00, & 0.3015904700953623D+00, & 0.0028145506398762D+00, & 0.6955949792647612D+00, & 0.6276179259734721D+00, & 0.0798394163722916D+00, & 0.2925426576542361D+00, & 0.2925426576542363D+00, & 0.0798394163722914D+00, & 0.6276179259734720D+00, & 0.9593763173443480D+00, & 0.0133211979027672D+00, & 0.0273024847528847D+00, & 0.0273024847528849D+00, & 0.0133211979027669D+00, & 0.9593763173443478D+00, & 0.4016944683268120D+00, & 0.2991527658365938D+00, & 0.2991527658365939D+00, & 0.6188258934043401D+00, & 0.0096021860181155D+00, & 0.3715719205775441D+00, & 0.3715719205775442D+00, & 0.0096021860181154D+00, & 0.6188258934043400D+00, & 0.7964902586210802D+00, & 0.0025024373852326D+00, & 0.2010073039936868D+00, & 0.2010073039936870D+00, & 0.0025024373852326D+00, & 0.7964902586210801D+00, & 0.5050860425617371D+00, & 0.2017308280659965D+00, & 0.2931831293722663D+00, & 0.2931831293722664D+00, & 0.2017308280659964D+00, & 0.5050860425617369D+00, & 0.7139904265957288D+00, & 0.0526776823006486D+00, & 0.2333318911036223D+00, & 0.2333318911036225D+00, & 0.0526776823006485D+00, & 0.7139904265957286D+00, & 0.7649317119922271D+00, & 0.0557691461107686D+00, & 0.1792991418970041D+00, & 0.1792991418970043D+00, & 0.0557691461107684D+00, & 0.7649317119922271D+00, & 0.3669822772564583D+00, & 0.2660354454870835D+00, & 0.3669822772564582D+00, & 0.6583279675616899D+00, & 0.0482367013092172D+00, & 0.2934353311290928D+00, & 0.2934353311290929D+00, & 0.0482367013092170D+00, & 0.6583279675616898D+00, & 0.4364618201712586D+00, & 0.2336975835531220D+00, & 0.3298405962756191D+00, & 0.3298405962756191D+00, & 0.2336975835531220D+00, & 0.4364618201712585D+00, & 0.7691621557796963D+00, & 0.0926621506087762D+00, & 0.1381756936115274D+00, & 0.1381756936115276D+00, & 0.0926621506087759D+00, & 0.7691621557796962D+00, & 0.4680323661208265D+00, & 0.1734547681030723D+00, & 0.3585128657761010D+00, & 0.3585128657761011D+00, & 0.1734547681030721D+00, & 0.4680323661208264D+00, & 0.5618113228868685D+00, & 0.0178508936465828D+00, & 0.4203377834665486D+00, & 0.4203377834665488D+00, & 0.0178508936465828D+00, & 0.5618113228868683D+00, & 0.6010021745006722D+00, & 0.1199466924958471D+00, & 0.2790511330034805D+00, & 0.2790511330034807D+00, & 0.1199466924958471D+00, & 0.6010021745006722D+00, & 0.8925527104988680D+00, & 0.0139846172517608D+00, & 0.0934626722493708D+00, & 0.0934626722493710D+00, & 0.0139846172517607D+00, & 0.8925527104988679D+00, & 0.4932332479959026D+00, & 0.1193577643150775D+00, & 0.3874089876890197D+00, & 0.3874089876890198D+00, & 0.1193577643150774D+00, & 0.4932332479959025D+00, & 0.5192306493531180D+00, & 0.0735846549853617D+00, & 0.4071846956615199D+00, & 0.4071846956615201D+00, & 0.0735846549853617D+00, & 0.5192306493531180D+00, & 0.7996426687617495D+00, & 0.0127167478485408D+00, & 0.1876405833897095D+00, & 0.1876405833897097D+00, & 0.0127167478485406D+00, & 0.7996426687617494D+00, & 0.4701567152192389D+00, & 0.2649216423903806D+00, & 0.2649216423903804D+00, & 0.8453340935540358D+00, & 0.0024403804076879D+00, & 0.1522255260382760D+00, & 0.1522255260382763D+00, & 0.0024403804076876D+00, & 0.8453340935540357D+00, & 0.6959673722361421D+00, & 0.1298906259772944D+00, & 0.1741420017865631D+00, & 0.1741420017865634D+00, & 0.1298906259772943D+00, & 0.6959673722361421D+00, & 0.3984690684139450D+00, & 0.2030618631721098D+00, & 0.3984690684139450D+00, & 0.5347112144371693D+00, & 0.1438806303873045D+00, & 0.3214081551755260D+00, & 0.3214081551755262D+00, & 0.1438806303873045D+00, & 0.5347112144371693D+00, & 0.8523358545382167D+00, & 0.0588598092883569D+00, & 0.0888043361734262D+00, & 0.0888043361734265D+00, & 0.0588598092883565D+00, & 0.8523358545382168D+00, & 0.8092737430634784D+00, & 0.0602973413848094D+00, & 0.1304289155517121D+00, & 0.1304289155517122D+00, & 0.0602973413848092D+00, & 0.8092737430634783D+00, & 0.4526201907514942D+00, & 0.0947596184970116D+00, & 0.4526201907514941D+00, & 0.8499366346784312D+00, & 0.0132254525993588D+00, & 0.1368379127222098D+00, & 0.1368379127222100D+00, & 0.0132254525993586D+00, & 0.8499366346784311D+00, & 0.5898753813183408D+00, & 0.0572712595019885D+00, & 0.3528533591796703D+00, & 0.3528533591796706D+00, & 0.0572712595019885D+00, & 0.5898753813183406D+00, & 0.7426794521965718D+00, & 0.0109336475862860D+00, & 0.2463869002171418D+00, & 0.2463869002171422D+00, & 0.0109336475862859D+00, & 0.7426794521965717D+00, & 0.4268610495333075D+00, & 0.1462779009333851D+00, & 0.4268610495333073D+00, & 0.3333333333333333D+00, & 0.5605547908509813D+00, & 0.0959251650895475D+00, & 0.3435200440594711D+00, & 0.3435200440594713D+00, & 0.0959251650895475D+00, & 0.5605547908509811D+00, & 0.5441206066477791D+00, & 0.0396704297157568D+00, & 0.4162089636364640D+00, & 0.4162089636364643D+00, & 0.0396704297157565D+00, & 0.5441206066477789D+00, & 0.8108551257330110D+00, & 0.0945724371334948D+00, & 0.0945724371334941D+00, & 0.4729894708688974D+00, & 0.0540210582622052D+00, & 0.4729894708688971D+00, & 0.9581931415494849D+00, & 0.0027950477505295D+00, & 0.0390118106999854D+00, & 0.0390118106999858D+00, & 0.0027950477505291D+00, & 0.9581931415494848D+00, & 0.8901526742127170D+00, & 0.0026666116526769D+00, & 0.1071807141346058D+00, & 0.1071807141346060D+00, & 0.0026666116526767D+00, & 0.8901526742127169D+00, & 0.5710366502174161D+00, & 0.0025395300762577D+00, & 0.4264238197063259D+00, & 0.4264238197063261D+00, & 0.0025395300762576D+00, & 0.5710366502174160D+00, & 0.9318297176864014D+00, & 0.0340851411567995D+00, & 0.0340851411567989D+00, & 0.6193084930778816D+00, & 0.0287313755582888D+00, & 0.3519601313638294D+00, & 0.3519601313638296D+00, & 0.0287313755582886D+00, & 0.6193084930778815D+00, & 0.4869989968257814D+00, & 0.0260020063484369D+00, & 0.4869989968257813D+00 /) w = (/ & 0.0001943064247755D+00, & 0.0001943064247755D+00, & 0.0001943064247755D+00, & 0.0001943064247755D+00, & 0.0001943064247755D+00, & 0.0001943064247755D+00, & 0.0000593664802978D+00, & 0.0000593664802978D+00, & 0.0000593664802978D+00, & 0.0000593664802978D+00, & 0.0000593664802978D+00, & 0.0000593664802978D+00, & 0.0004806887075027D+00, & 0.0004806887075027D+00, & 0.0004806887075027D+00, & 0.0004806887075027D+00, & 0.0004806887075027D+00, & 0.0004806887075027D+00, & 0.0002301249335002D+00, & 0.0002301249335002D+00, & 0.0002301249335002D+00, & 0.0002301249335002D+00, & 0.0002301249335002D+00, & 0.0002301249335002D+00, & 0.0012944627170681D+00, & 0.0012944627170681D+00, & 0.0012944627170681D+00, & 0.0012944627170681D+00, & 0.0012944627170681D+00, & 0.0012944627170681D+00, & 0.0004605208982907D+00, & 0.0004605208982907D+00, & 0.0004605208982907D+00, & 0.0004605208982907D+00, & 0.0004605208982907D+00, & 0.0004605208982907D+00, & 0.0001550690080029D+00, & 0.0001550690080029D+00, & 0.0001550690080029D+00, & 0.0001550690080029D+00, & 0.0001550690080029D+00, & 0.0001550690080029D+00, & 0.0005264320168997D+00, & 0.0005264320168997D+00, & 0.0005264320168997D+00, & 0.0005264320168997D+00, & 0.0005264320168997D+00, & 0.0005264320168997D+00, & 0.0040776028008772D+00, & 0.0040776028008772D+00, & 0.0040776028008772D+00, & 0.0040776028008772D+00, & 0.0040776028008772D+00, & 0.0040776028008772D+00, & 0.0027273371555633D+00, & 0.0027273371555633D+00, & 0.0027273371555633D+00, & 0.0027273371555633D+00, & 0.0027273371555633D+00, & 0.0027273371555633D+00, & 0.0032024171503526D+00, & 0.0032024171503526D+00, & 0.0032024171503526D+00, & 0.0038178383600418D+00, & 0.0038178383600418D+00, & 0.0038178383600418D+00, & 0.0038178383600418D+00, & 0.0038178383600418D+00, & 0.0038178383600418D+00, & 0.0032435899284887D+00, & 0.0032435899284887D+00, & 0.0032435899284887D+00, & 0.0032435899284887D+00, & 0.0032435899284887D+00, & 0.0032435899284887D+00, & 0.0018849657183849D+00, & 0.0018849657183849D+00, & 0.0018849657183849D+00, & 0.0018849657183849D+00, & 0.0018849657183849D+00, & 0.0018849657183849D+00, & 0.0046373488411220D+00, & 0.0046373488411220D+00, & 0.0046373488411220D+00, & 0.0040870604654873D+00, & 0.0040870604654873D+00, & 0.0040870604654873D+00, & 0.0021807223876070D+00, & 0.0021807223876070D+00, & 0.0021807223876070D+00, & 0.0021807223876070D+00, & 0.0021807223876070D+00, & 0.0021807223876070D+00, & 0.0018345812391610D+00, & 0.0018345812391610D+00, & 0.0018345812391610D+00, & 0.0018345812391610D+00, & 0.0018345812391610D+00, & 0.0018345812391610D+00, & 0.0004831135230320D+00, & 0.0004831135230320D+00, & 0.0004831135230320D+00, & 0.0016273397954327D+00, & 0.0016273397954327D+00, & 0.0016273397954327D+00, & 0.0016273397954327D+00, & 0.0016273397954327D+00, & 0.0016273397954327D+00, & 0.0008285328211727D+00, & 0.0008285328211727D+00, & 0.0008285328211727D+00, & 0.0008285328211727D+00, & 0.0008285328211727D+00, & 0.0008285328211727D+00, & 0.0051074900867677D+00, & 0.0051074900867677D+00, & 0.0051074900867677D+00, & 0.0051074900867677D+00, & 0.0051074900867677D+00, & 0.0051074900867677D+00, & 0.0022391133588916D+00, & 0.0022391133588916D+00, & 0.0022391133588916D+00, & 0.0022391133588916D+00, & 0.0022391133588916D+00, & 0.0022391133588916D+00, & 0.0016401723644210D+00, & 0.0016401723644210D+00, & 0.0016401723644210D+00, & 0.0016401723644210D+00, & 0.0016401723644210D+00, & 0.0016401723644210D+00, & 0.0016926101405552D+00, & 0.0016926101405552D+00, & 0.0016926101405552D+00, & 0.0036716713931777D+00, & 0.0036716713931777D+00, & 0.0036716713931777D+00, & 0.0036716713931777D+00, & 0.0036716713931777D+00, & 0.0036716713931777D+00, & 0.0014130049415994D+00, & 0.0014130049415994D+00, & 0.0014130049415994D+00, & 0.0014130049415994D+00, & 0.0014130049415994D+00, & 0.0014130049415994D+00, & 0.0007644420008621D+00, & 0.0007644420008621D+00, & 0.0007644420008621D+00, & 0.0007644420008621D+00, & 0.0007644420008621D+00, & 0.0007644420008621D+00, & 0.0039540316260532D+00, & 0.0039540316260532D+00, & 0.0039540316260532D+00, & 0.0039540316260532D+00, & 0.0039540316260532D+00, & 0.0039540316260532D+00, & 0.0006448335449571D+00, & 0.0006448335449571D+00, & 0.0006448335449571D+00, & 0.0006448335449571D+00, & 0.0006448335449571D+00, & 0.0006448335449571D+00, & 0.0068337553756981D+00, & 0.0068337553756981D+00, & 0.0068337553756981D+00, & 0.0015547569025381D+00, & 0.0015547569025381D+00, & 0.0015547569025381D+00, & 0.0015547569025381D+00, & 0.0015547569025381D+00, & 0.0015547569025381D+00, & 0.0006264797924812D+00, & 0.0006264797924812D+00, & 0.0006264797924812D+00, & 0.0006264797924812D+00, & 0.0006264797924812D+00, & 0.0006264797924812D+00, & 0.0059918057501739D+00, & 0.0059918057501739D+00, & 0.0059918057501739D+00, & 0.0059918057501739D+00, & 0.0059918057501739D+00, & 0.0059918057501739D+00, & 0.0030584178145640D+00, & 0.0030584178145640D+00, & 0.0030584178145640D+00, & 0.0030584178145640D+00, & 0.0030584178145640D+00, & 0.0030584178145640D+00, & 0.0029964079041531D+00, & 0.0029964079041531D+00, & 0.0029964079041531D+00, & 0.0029964079041531D+00, & 0.0029964079041531D+00, & 0.0029964079041531D+00, & 0.0068925047985870D+00, & 0.0068925047985870D+00, & 0.0068925047985870D+00, & 0.0032333735833172D+00, & 0.0032333735833172D+00, & 0.0032333735833172D+00, & 0.0032333735833172D+00, & 0.0032333735833172D+00, & 0.0032333735833172D+00, & 0.0066463643649800D+00, & 0.0066463643649800D+00, & 0.0066463643649800D+00, & 0.0066463643649800D+00, & 0.0066463643649800D+00, & 0.0066463643649800D+00, & 0.0031949049329089D+00, & 0.0031949049329089D+00, & 0.0031949049329089D+00, & 0.0031949049329089D+00, & 0.0031949049329089D+00, & 0.0031949049329089D+00, & 0.0061619916829777D+00, & 0.0061619916829777D+00, & 0.0061619916829777D+00, & 0.0061619916829777D+00, & 0.0061619916829777D+00, & 0.0061619916829777D+00, & 0.0021838177312897D+00, & 0.0021838177312897D+00, & 0.0021838177312897D+00, & 0.0021838177312897D+00, & 0.0021838177312897D+00, & 0.0021838177312897D+00, & 0.0048382287535973D+00, & 0.0048382287535973D+00, & 0.0048382287535973D+00, & 0.0048382287535973D+00, & 0.0048382287535973D+00, & 0.0048382287535973D+00, & 0.0011709435195081D+00, & 0.0011709435195081D+00, & 0.0011709435195081D+00, & 0.0011709435195081D+00, & 0.0011709435195081D+00, & 0.0011709435195081D+00, & 0.0054074968564398D+00, & 0.0054074968564398D+00, & 0.0054074968564398D+00, & 0.0054074968564398D+00, & 0.0054074968564398D+00, & 0.0054074968564398D+00, & 0.0045333891237490D+00, & 0.0045333891237490D+00, & 0.0045333891237490D+00, & 0.0045333891237490D+00, & 0.0045333891237490D+00, & 0.0045333891237490D+00, & 0.0015268444445366D+00, & 0.0015268444445366D+00, & 0.0015268444445366D+00, & 0.0015268444445366D+00, & 0.0015268444445366D+00, & 0.0015268444445366D+00, & 0.0063146569930329D+00, & 0.0063146569930329D+00, & 0.0063146569930329D+00, & 0.0005985557587521D+00, & 0.0005985557587521D+00, & 0.0005985557587521D+00, & 0.0005985557587521D+00, & 0.0005985557587521D+00, & 0.0005985557587521D+00, & 0.0042213374314073D+00, & 0.0042213374314073D+00, & 0.0042213374314073D+00, & 0.0042213374314073D+00, & 0.0042213374314073D+00, & 0.0042213374314073D+00, & 0.0065583075001979D+00, & 0.0065583075001979D+00, & 0.0065583075001979D+00, & 0.0055145622313395D+00, & 0.0055145622313395D+00, & 0.0055145622313395D+00, & 0.0055145622313395D+00, & 0.0055145622313395D+00, & 0.0055145622313395D+00, & 0.0023371778099107D+00, & 0.0023371778099107D+00, & 0.0023371778099107D+00, & 0.0023371778099107D+00, & 0.0023371778099107D+00, & 0.0023371778099107D+00, & 0.0027879889526797D+00, & 0.0027879889526797D+00, & 0.0027879889526797D+00, & 0.0027879889526797D+00, & 0.0027879889526797D+00, & 0.0027879889526797D+00, & 0.0050168594859682D+00, & 0.0050168594859682D+00, & 0.0050168594859682D+00, & 0.0014305749953706D+00, & 0.0014305749953706D+00, & 0.0014305749953706D+00, & 0.0014305749953706D+00, & 0.0014305749953706D+00, & 0.0014305749953706D+00, & 0.0039720422418774D+00, & 0.0039720422418774D+00, & 0.0039720422418774D+00, & 0.0039720422418774D+00, & 0.0039720422418774D+00, & 0.0039720422418774D+00, & 0.0016230214293911D+00, & 0.0016230214293911D+00, & 0.0016230214293911D+00, & 0.0016230214293911D+00, & 0.0016230214293911D+00, & 0.0016230214293911D+00, & 0.0058825091261753D+00, & 0.0058825091261753D+00, & 0.0058825091261753D+00, & 0.0069414696543850D+00, & 0.0048308548778951D+00, & 0.0048308548778951D+00, & 0.0048308548778951D+00, & 0.0048308548778951D+00, & 0.0048308548778951D+00, & 0.0048308548778951D+00, & 0.0035396788161465D+00, & 0.0035396788161465D+00, & 0.0035396788161465D+00, & 0.0035396788161465D+00, & 0.0035396788161465D+00, & 0.0035396788161465D+00, & 0.0031371434621643D+00, & 0.0031371434621643D+00, & 0.0031371434621643D+00, & 0.0040930651478197D+00, & 0.0040930651478197D+00, & 0.0040930651478197D+00, & 0.0003670659894181D+00, & 0.0003670659894181D+00, & 0.0003670659894181D+00, & 0.0003670659894181D+00, & 0.0003670659894181D+00, & 0.0003670659894181D+00, & 0.0005709699094042D+00, & 0.0005709699094042D+00, & 0.0005709699094042D+00, & 0.0005709699094042D+00, & 0.0005709699094042D+00, & 0.0005709699094042D+00, & 0.0008761135391688D+00, & 0.0008761135391688D+00, & 0.0008761135391688D+00, & 0.0008761135391688D+00, & 0.0008761135391688D+00, & 0.0008761135391688D+00, & 0.0012513146853205D+00, & 0.0012513146853205D+00, & 0.0012513146853205D+00, & 0.0030871109749242D+00, & 0.0030871109749242D+00, & 0.0030871109749242D+00, & 0.0030871109749242D+00, & 0.0030871109749242D+00, & 0.0030871109749242D+00, & 0.0030558057702988D+00, & 0.0030558057702988D+00, & 0.0030558057702988D+00 /) return end subroutine rule46 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule46() returns the rule of precision 46. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.4791627094810211D+00, & 0.4791627094810211D+00, & 0.0416745810379577D+00, & 0.3979697646407098D+00, & 0.4479070861932129D+00, & 0.1541231491660771D+00, & 0.4479070861932128D+00, & 0.3979697646407099D+00, & 0.1541231491660771D+00, & 0.4143076079881758D+00, & 0.4725556860878008D+00, & 0.1131367059240233D+00, & 0.4725556860878007D+00, & 0.4143076079881759D+00, & 0.1131367059240234D+00, & 0.3297282498766237D+00, & 0.5972534223436730D+00, & 0.0730183277797033D+00, & 0.5972534223436731D+00, & 0.3297282498766237D+00, & 0.0730183277797032D+00, & 0.2257592423300578D+00, & 0.6644373808625786D+00, & 0.1098033768073635D+00, & 0.6644373808625786D+00, & 0.2257592423300578D+00, & 0.1098033768073634D+00, & 0.0486830795833199D+00, & 0.9026338408333598D+00, & 0.0486830795833202D+00, & 0.4868494344525785D+00, & 0.4868494344525786D+00, & 0.0263011310948430D+00, & 0.3286993475605237D+00, & 0.5684647770684034D+00, & 0.1028358753710730D+00, & 0.5684647770684034D+00, & 0.3286993475605237D+00, & 0.1028358753710729D+00, & 0.0570245183292809D+00, & 0.9325204663263090D+00, & 0.0104550153444102D+00, & 0.9325204663263090D+00, & 0.0570245183292810D+00, & 0.0104550153444098D+00, & 0.2181534906276071D+00, & 0.6343242478263365D+00, & 0.1475222615460565D+00, & 0.6343242478263365D+00, & 0.2181534906276072D+00, & 0.1475222615460563D+00, & 0.2023063458834636D+00, & 0.7455675573091064D+00, & 0.0521260968074301D+00, & 0.7455675573091063D+00, & 0.2023063458834636D+00, & 0.0521260968074299D+00, & 0.2132832098088080D+00, & 0.7066325944250231D+00, & 0.0800841957661689D+00, & 0.7066325944250231D+00, & 0.2132832098088080D+00, & 0.0800841957661687D+00, & 0.0082133588712220D+00, & 0.9896258607741097D+00, & 0.0021607803546684D+00, & 0.9896258607741097D+00, & 0.0082133588712220D+00, & 0.0021607803546680D+00, & 0.4615153616123003D+00, & 0.5271208360379724D+00, & 0.0113638023497272D+00, & 0.5271208360379723D+00, & 0.4615153616123003D+00, & 0.0113638023497272D+00, & 0.3546224673127057D+00, & 0.5155990090696432D+00, & 0.1297785236176510D+00, & 0.5155990090696433D+00, & 0.3546224673127058D+00, & 0.1297785236176509D+00, & 0.3109206435860316D+00, & 0.6401420778067229D+00, & 0.0489372786072454D+00, & 0.6401420778067229D+00, & 0.3109206435860316D+00, & 0.0489372786072453D+00, & 0.3049557841332307D+00, & 0.5366266568593034D+00, & 0.1584175590074660D+00, & 0.5366266568593034D+00, & 0.3049557841332306D+00, & 0.1584175590074658D+00, & 0.2507944375639041D+00, & 0.5737054769976868D+00, & 0.1755000854384091D+00, & 0.5737054769976868D+00, & 0.2507944375639042D+00, & 0.1755000854384089D+00, & 0.1962948092294495D+00, & 0.6074103815411007D+00, & 0.1962948092294496D+00, & 0.1657987165670959D+00, & 0.6684025668658078D+00, & 0.1657987165670963D+00, & 0.4338692218644805D+00, & 0.5130043968250232D+00, & 0.0531263813104962D+00, & 0.5130043968250232D+00, & 0.4338692218644806D+00, & 0.0531263813104962D+00, & 0.0770376986253196D+00, & 0.8720533240163508D+00, & 0.0509089773583296D+00, & 0.8720533240163508D+00, & 0.0770376986253197D+00, & 0.0509089773583293D+00, & 0.2768361860195224D+00, & 0.7120424143833398D+00, & 0.0111213995971378D+00, & 0.7120424143833398D+00, & 0.2768361860195226D+00, & 0.0111213995971376D+00, & 0.1736371621034214D+00, & 0.8145830842158606D+00, & 0.0117797536807180D+00, & 0.8145830842158606D+00, & 0.1736371621034215D+00, & 0.0117797536807177D+00, & 0.3354336886613770D+00, & 0.6527581850349298D+00, & 0.0118081263036934D+00, & 0.6527581850349297D+00, & 0.3354336886613770D+00, & 0.0118081263036932D+00, & 0.3750642184523966D+00, & 0.5736918975567098D+00, & 0.0512438839908936D+00, & 0.5736918975567098D+00, & 0.3750642184523967D+00, & 0.0512438839908935D+00, & 0.3467112861299004D+00, & 0.4707474573939668D+00, & 0.1825412564761328D+00, & 0.4707474573939667D+00, & 0.3467112861299005D+00, & 0.1825412564761327D+00, & 0.2559685112606641D+00, & 0.6901296172890430D+00, & 0.0539018714502929D+00, & 0.6901296172890431D+00, & 0.2559685112606642D+00, & 0.0539018714502927D+00, & 0.2920069207885316D+00, & 0.6806497657499146D+00, & 0.0273433134615538D+00, & 0.6806497657499146D+00, & 0.2920069207885317D+00, & 0.0273433134615535D+00, & 0.2364172395795756D+00, & 0.7338403785411441D+00, & 0.0297423818792803D+00, & 0.7338403785411441D+00, & 0.2364172395795756D+00, & 0.0297423818792801D+00, & 0.4661508981294354D+00, & 0.5316578071895072D+00, & 0.0021912946810573D+00, & 0.5316578071895072D+00, & 0.4661508981294354D+00, & 0.0021912946810573D+00, & 0.2234826291455856D+00, & 0.7639437050178102D+00, & 0.0125736658366042D+00, & 0.7639437050178102D+00, & 0.2234826291455856D+00, & 0.0125736658366041D+00, & 0.3973680138780006D+00, & 0.5911123169924868D+00, & 0.0115196691295125D+00, & 0.5911123169924869D+00, & 0.3973680138780006D+00, & 0.0115196691295124D+00, & 0.2856792432449899D+00, & 0.5036527190882436D+00, & 0.2106680376667663D+00, & 0.5036527190882436D+00, & 0.2856792432449899D+00, & 0.2106680376667662D+00, & 0.2290071177870446D+00, & 0.5419857644259105D+00, & 0.2290071177870448D+00, & 0.2998981018797286D+00, & 0.4002037962405427D+00, & 0.2998981018797286D+00, & 0.4009919122964068D+00, & 0.5968372374211253D+00, & 0.0021708502824680D+00, & 0.5968372374211253D+00, & 0.4009919122964067D+00, & 0.0021708502824680D+00, & 0.1562735104040767D+00, & 0.7879600672161253D+00, & 0.0557664223797980D+00, & 0.7879600672161253D+00, & 0.1562735104040768D+00, & 0.0557664223797977D+00, & 0.0477858936846818D+00, & 0.9501161980450165D+00, & 0.0020979082703018D+00, & 0.9501161980450166D+00, & 0.0477858936846819D+00, & 0.0020979082703013D+00, & 0.1822491599313741D+00, & 0.7886726424890335D+00, & 0.0290781975795925D+00, & 0.7886726424890333D+00, & 0.1822491599313742D+00, & 0.0290781975795923D+00, & 0.3660812614114254D+00, & 0.3660812614114254D+00, & 0.2678374771771491D+00, & 0.0893475681919859D+00, & 0.8990694649639888D+00, & 0.0115829668440254D+00, & 0.8990694649639889D+00, & 0.0893475681919860D+00, & 0.0115829668440250D+00, & 0.1652198812399128D+00, & 0.7473177571098144D+00, & 0.0874623616502729D+00, & 0.7473177571098144D+00, & 0.1652198812399128D+00, & 0.0874623616502726D+00, & 0.0805280047391684D+00, & 0.9173934916626123D+00, & 0.0020785035982195D+00, & 0.9173934916626122D+00, & 0.0805280047391685D+00, & 0.0020785035982190D+00, & 0.3305415015675990D+00, & 0.4329807146876172D+00, & 0.2364777837447837D+00, & 0.4329807146876172D+00, & 0.3305415015675991D+00, & 0.2364777837447836D+00, & 0.1750740132522936D+00, & 0.7021169686939935D+00, & 0.1228090180537130D+00, & 0.7021169686939934D+00, & 0.1750740132522937D+00, & 0.1228090180537126D+00, & 0.1133949730294224D+00, & 0.8315999985260938D+00, & 0.0550050284444840D+00, & 0.8315999985260938D+00, & 0.1133949730294224D+00, & 0.0550050284444836D+00, & 0.0945442284064488D+00, & 0.8766622383664391D+00, & 0.0287935332271122D+00, & 0.8766622383664391D+00, & 0.0945442284064488D+00, & 0.0287935332271118D+00, & 0.0589589423608463D+00, & 0.9147477258472858D+00, & 0.0262933317918678D+00, & 0.9147477258472859D+00, & 0.0589589423608463D+00, & 0.0262933317918676D+00, & 0.3554461171023697D+00, & 0.6162465555124068D+00, & 0.0283073273852236D+00, & 0.6162465555124067D+00, & 0.3554461171023696D+00, & 0.0283073273852235D+00, & 0.4206278444454289D+00, & 0.5512452167474322D+00, & 0.0281269388071388D+00, & 0.5512452167474322D+00, & 0.4206278444454289D+00, & 0.0281269388071388D+00, & 0.0307693439520818D+00, & 0.9384613120958362D+00, & 0.0307693439520821D+00, & 0.2763424771664457D+00, & 0.7215566217404850D+00, & 0.0021009010930694D+00, & 0.7215566217404851D+00, & 0.2763424771664458D+00, & 0.0021009010930691D+00, & 0.1358344051381373D+00, & 0.8336434944596028D+00, & 0.0305221004022600D+00, & 0.8336434944596030D+00, & 0.1358344051381374D+00, & 0.0305221004022596D+00, & 0.1214324449203873D+00, & 0.7904245130980823D+00, & 0.0881430419815304D+00, & 0.7904245130980824D+00, & 0.1214324449203874D+00, & 0.0881430419815301D+00, & 0.0824986937635583D+00, & 0.8350026124728831D+00, & 0.0824986937635587D+00, & 0.1292544813329482D+00, & 0.8581647113948480D+00, & 0.0125808072722039D+00, & 0.8581647113948480D+00, & 0.1292544813329483D+00, & 0.0125808072722036D+00, & 0.2729393183303263D+00, & 0.6431846260118416D+00, & 0.0838760556578322D+00, & 0.6431846260118415D+00, & 0.2729393183303264D+00, & 0.0838760556578320D+00, & 0.4608230043475881D+00, & 0.4608230043475881D+00, & 0.0783539913048237D+00, & 0.2762244316742870D+00, & 0.5989839678810083D+00, & 0.1247916004447048D+00, & 0.5989839678810083D+00, & 0.2762244316742870D+00, & 0.1247916004447046D+00, & 0.1665310619918011D+00, & 0.8312386887187595D+00, & 0.0022302492894395D+00, & 0.8312386887187594D+00, & 0.1665310619918010D+00, & 0.0022302492894393D+00, & 0.3373238618789556D+00, & 0.6603914710100434D+00, & 0.0022846671110011D+00, & 0.6603914710100434D+00, & 0.3373238618789556D+00, & 0.0022846671110009D+00, & 0.2666157086976967D+00, & 0.4667685826046064D+00, & 0.2666157086976969D+00, & 0.1284394349475123D+00, & 0.7431211301049753D+00, & 0.1284394349475125D+00, & 0.3899848376803788D+00, & 0.5268218597395553D+00, & 0.0831933025800658D+00, & 0.5268218597395553D+00, & 0.3899848376803788D+00, & 0.0831933025800657D+00, & 0.3333333333333333D+00, & 0.2190574020296069D+00, & 0.7785355668785605D+00, & 0.0024070310918327D+00, & 0.7785355668785605D+00, & 0.2190574020296069D+00, & 0.0024070310918324D+00, & 0.1203413424430903D+00, & 0.8772415939384313D+00, & 0.0024170636184784D+00, & 0.8772415939384313D+00, & 0.1203413424430904D+00, & 0.0024170636184781D+00, & 0.3975115754020483D+00, & 0.3975115754020484D+00, & 0.2049768491959033D+00, & 0.0321434597854268D+00, & 0.9549696683961201D+00, & 0.0128868718184532D+00, & 0.9549696683961202D+00, & 0.0321434597854269D+00, & 0.0128868718184528D+00, & 0.0128796984358850D+00, & 0.9742406031282296D+00, & 0.0128796984358854D+00, & 0.0239783625881974D+00, & 0.9734342386997918D+00, & 0.0025873987120110D+00, & 0.9734342386997918D+00, & 0.0239783625881975D+00, & 0.0025873987120104D+00, & 0.0004929222424058D+00, & 0.9990141555151880D+00, & 0.0004929222424063D+00 /) b = (/ & 0.0416745810379578D+00, & 0.4791627094810212D+00, & 0.4791627094810214D+00, & 0.1541231491660773D+00, & 0.3979697646407100D+00, & 0.4479070861932131D+00, & 0.1541231491660773D+00, & 0.4479070861932130D+00, & 0.3979697646407100D+00, & 0.1131367059240234D+00, & 0.4143076079881759D+00, & 0.4725556860878009D+00, & 0.1131367059240234D+00, & 0.4725556860878009D+00, & 0.4143076079881760D+00, & 0.0730183277797033D+00, & 0.3297282498766238D+00, & 0.5972534223436732D+00, & 0.0730183277797033D+00, & 0.5972534223436731D+00, & 0.3297282498766239D+00, & 0.1098033768073636D+00, & 0.2257592423300578D+00, & 0.6644373808625790D+00, & 0.1098033768073636D+00, & 0.6644373808625788D+00, & 0.2257592423300580D+00, & 0.0486830795833202D+00, & 0.0486830795833199D+00, & 0.9026338408333601D+00, & 0.0263011310948430D+00, & 0.4868494344525785D+00, & 0.4868494344525787D+00, & 0.1028358753710730D+00, & 0.3286993475605237D+00, & 0.5684647770684035D+00, & 0.1028358753710730D+00, & 0.5684647770684035D+00, & 0.3286993475605239D+00, & 0.0104550153444101D+00, & 0.0570245183292809D+00, & 0.9325204663263091D+00, & 0.0104550153444101D+00, & 0.9325204663263091D+00, & 0.0570245183292812D+00, & 0.1475222615460564D+00, & 0.2181534906276071D+00, & 0.6343242478263366D+00, & 0.1475222615460564D+00, & 0.6343242478263366D+00, & 0.2181534906276073D+00, & 0.0521260968074301D+00, & 0.2023063458834636D+00, & 0.7455675573091065D+00, & 0.0521260968074301D+00, & 0.7455675573091065D+00, & 0.2023063458834639D+00, & 0.0800841957661689D+00, & 0.2132832098088080D+00, & 0.7066325944250232D+00, & 0.0800841957661689D+00, & 0.7066325944250232D+00, & 0.2132832098088083D+00, & 0.0021607803546683D+00, & 0.0082133588712219D+00, & 0.9896258607741099D+00, & 0.0021607803546683D+00, & 0.9896258607741099D+00, & 0.0082133588712223D+00, & 0.0113638023497273D+00, & 0.4615153616123004D+00, & 0.5271208360379727D+00, & 0.0113638023497273D+00, & 0.5271208360379724D+00, & 0.4615153616123006D+00, & 0.1297785236176510D+00, & 0.3546224673127058D+00, & 0.5155990090696434D+00, & 0.1297785236176510D+00, & 0.5155990090696433D+00, & 0.3546224673127060D+00, & 0.0489372786072454D+00, & 0.3109206435860317D+00, & 0.6401420778067232D+00, & 0.0489372786072454D+00, & 0.6401420778067232D+00, & 0.3109206435860319D+00, & 0.1584175590074660D+00, & 0.3049557841332307D+00, & 0.5366266568593036D+00, & 0.1584175590074660D+00, & 0.5366266568593036D+00, & 0.3049557841332309D+00, & 0.1755000854384091D+00, & 0.2507944375639042D+00, & 0.5737054769976869D+00, & 0.1755000854384091D+00, & 0.5737054769976868D+00, & 0.2507944375639043D+00, & 0.1962948092294497D+00, & 0.1962948092294495D+00, & 0.6074103815411009D+00, & 0.1657987165670962D+00, & 0.1657987165670960D+00, & 0.6684025668658079D+00, & 0.0531263813104963D+00, & 0.4338692218644806D+00, & 0.5130043968250234D+00, & 0.0531263813104963D+00, & 0.5130043968250232D+00, & 0.4338692218644807D+00, & 0.0509089773583296D+00, & 0.0770376986253196D+00, & 0.8720533240163509D+00, & 0.0509089773583296D+00, & 0.8720533240163509D+00, & 0.0770376986253199D+00, & 0.0111213995971377D+00, & 0.2768361860195225D+00, & 0.7120424143833399D+00, & 0.0111213995971377D+00, & 0.7120424143833398D+00, & 0.2768361860195228D+00, & 0.0117797536807180D+00, & 0.1736371621034214D+00, & 0.8145830842158608D+00, & 0.0117797536807180D+00, & 0.8145830842158608D+00, & 0.1736371621034218D+00, & 0.0118081263036934D+00, & 0.3354336886613770D+00, & 0.6527581850349299D+00, & 0.0118081263036934D+00, & 0.6527581850349298D+00, & 0.3354336886613772D+00, & 0.0512438839908936D+00, & 0.3750642184523967D+00, & 0.5736918975567099D+00, & 0.0512438839908936D+00, & 0.5736918975567098D+00, & 0.3750642184523969D+00, & 0.1825412564761328D+00, & 0.3467112861299005D+00, & 0.4707474573939669D+00, & 0.1825412564761328D+00, & 0.4707474573939668D+00, & 0.3467112861299007D+00, & 0.0539018714502929D+00, & 0.2559685112606642D+00, & 0.6901296172890432D+00, & 0.0539018714502929D+00, & 0.6901296172890431D+00, & 0.2559685112606644D+00, & 0.0273433134615537D+00, & 0.2920069207885316D+00, & 0.6806497657499148D+00, & 0.0273433134615537D+00, & 0.6806497657499148D+00, & 0.2920069207885319D+00, & 0.0297423818792803D+00, & 0.2364172395795756D+00, & 0.7338403785411444D+00, & 0.0297423818792803D+00, & 0.7338403785411444D+00, & 0.2364172395795759D+00, & 0.0021912946810574D+00, & 0.4661508981294356D+00, & 0.5316578071895074D+00, & 0.0021912946810574D+00, & 0.5316578071895073D+00, & 0.4661508981294357D+00, & 0.0125736658366043D+00, & 0.2234826291455856D+00, & 0.7639437050178104D+00, & 0.0125736658366043D+00, & 0.7639437050178103D+00, & 0.2234826291455859D+00, & 0.0115196691295125D+00, & 0.3973680138780006D+00, & 0.5911123169924871D+00, & 0.0115196691295125D+00, & 0.5911123169924870D+00, & 0.3973680138780009D+00, & 0.2106680376667663D+00, & 0.2856792432449901D+00, & 0.5036527190882438D+00, & 0.2106680376667663D+00, & 0.5036527190882438D+00, & 0.2856792432449901D+00, & 0.2290071177870448D+00, & 0.2290071177870447D+00, & 0.5419857644259106D+00, & 0.2998981018797288D+00, & 0.2998981018797287D+00, & 0.4002037962405428D+00, & 0.0021708502824680D+00, & 0.4009919122964068D+00, & 0.5968372374211254D+00, & 0.0021708502824680D+00, & 0.5968372374211253D+00, & 0.4009919122964070D+00, & 0.0557664223797979D+00, & 0.1562735104040768D+00, & 0.7879600672161254D+00, & 0.0557664223797979D+00, & 0.7879600672161254D+00, & 0.1562735104040771D+00, & 0.0020979082703016D+00, & 0.0477858936846818D+00, & 0.9501161980450167D+00, & 0.0020979082703016D+00, & 0.9501161980450167D+00, & 0.0477858936846822D+00, & 0.0290781975795925D+00, & 0.1822491599313741D+00, & 0.7886726424890337D+00, & 0.0290781975795925D+00, & 0.7886726424890335D+00, & 0.1822491599313744D+00, & 0.2678374771771493D+00, & 0.3660812614114254D+00, & 0.3660812614114256D+00, & 0.0115829668440253D+00, & 0.0893475681919859D+00, & 0.8990694649639890D+00, & 0.0115829668440253D+00, & 0.8990694649639890D+00, & 0.0893475681919862D+00, & 0.0874623616502728D+00, & 0.1652198812399128D+00, & 0.7473177571098146D+00, & 0.0874623616502728D+00, & 0.7473177571098146D+00, & 0.1652198812399130D+00, & 0.0020785035982193D+00, & 0.0805280047391684D+00, & 0.9173934916626123D+00, & 0.0020785035982193D+00, & 0.9173934916626123D+00, & 0.0805280047391688D+00, & 0.2364777837447838D+00, & 0.3305415015675991D+00, & 0.4329807146876173D+00, & 0.2364777837447838D+00, & 0.4329807146876173D+00, & 0.3305415015675992D+00, & 0.1228090180537129D+00, & 0.1750740132522937D+00, & 0.7021169686939935D+00, & 0.1228090180537129D+00, & 0.7021169686939936D+00, & 0.1750740132522939D+00, & 0.0550050284444838D+00, & 0.1133949730294223D+00, & 0.8315999985260939D+00, & 0.0550050284444838D+00, & 0.8315999985260939D+00, & 0.1133949730294226D+00, & 0.0287935332271121D+00, & 0.0945442284064488D+00, & 0.8766622383664393D+00, & 0.0287935332271121D+00, & 0.8766622383664393D+00, & 0.0945442284064491D+00, & 0.0262933317918678D+00, & 0.0589589423608463D+00, & 0.9147477258472861D+00, & 0.0262933317918678D+00, & 0.9147477258472861D+00, & 0.0589589423608466D+00, & 0.0283073273852236D+00, & 0.3554461171023697D+00, & 0.6162465555124070D+00, & 0.0283073273852236D+00, & 0.6162465555124069D+00, & 0.3554461171023699D+00, & 0.0281269388071389D+00, & 0.4206278444454289D+00, & 0.5512452167474324D+00, & 0.0281269388071389D+00, & 0.5512452167474323D+00, & 0.4206278444454292D+00, & 0.0307693439520821D+00, & 0.0307693439520817D+00, & 0.9384613120958364D+00, & 0.0021009010930693D+00, & 0.2763424771664457D+00, & 0.7215566217404851D+00, & 0.0021009010930693D+00, & 0.7215566217404851D+00, & 0.2763424771664461D+00, & 0.0305221004022599D+00, & 0.1358344051381373D+00, & 0.8336434944596030D+00, & 0.0305221004022599D+00, & 0.8336434944596030D+00, & 0.1358344051381376D+00, & 0.0881430419815303D+00, & 0.1214324449203873D+00, & 0.7904245130980825D+00, & 0.0881430419815303D+00, & 0.7904245130980825D+00, & 0.1214324449203876D+00, & 0.0824986937635586D+00, & 0.0824986937635583D+00, & 0.8350026124728833D+00, & 0.0125808072722039D+00, & 0.1292544813329482D+00, & 0.8581647113948481D+00, & 0.0125808072722039D+00, & 0.8581647113948480D+00, & 0.1292544813329486D+00, & 0.0838760556578322D+00, & 0.2729393183303264D+00, & 0.6431846260118417D+00, & 0.0838760556578322D+00, & 0.6431846260118417D+00, & 0.2729393183303265D+00, & 0.0783539913048238D+00, & 0.4608230043475882D+00, & 0.4608230043475884D+00, & 0.1247916004447048D+00, & 0.2762244316742871D+00, & 0.5989839678810084D+00, & 0.1247916004447048D+00, & 0.5989839678810084D+00, & 0.2762244316742872D+00, & 0.0022302492894395D+00, & 0.1665310619918011D+00, & 0.8312386887187597D+00, & 0.0022302492894395D+00, & 0.8312386887187597D+00, & 0.1665310619918013D+00, & 0.0022846671110010D+00, & 0.3373238618789556D+00, & 0.6603914710100435D+00, & 0.0022846671110010D+00, & 0.6603914710100435D+00, & 0.3373238618789559D+00, & 0.2666157086976969D+00, & 0.2666157086976969D+00, & 0.4667685826046065D+00, & 0.1284394349475125D+00, & 0.1284394349475123D+00, & 0.7431211301049754D+00, & 0.0831933025800659D+00, & 0.3899848376803789D+00, & 0.5268218597395556D+00, & 0.0831933025800659D+00, & 0.5268218597395554D+00, & 0.3899848376803791D+00, & 0.3333333333333334D+00, & 0.0024070310918326D+00, & 0.2190574020296069D+00, & 0.7785355668785606D+00, & 0.0024070310918326D+00, & 0.7785355668785606D+00, & 0.2190574020296072D+00, & 0.0024170636184783D+00, & 0.1203413424430903D+00, & 0.8772415939384315D+00, & 0.0024170636184783D+00, & 0.8772415939384315D+00, & 0.1203413424430907D+00, & 0.2049768491959034D+00, & 0.3975115754020485D+00, & 0.3975115754020485D+00, & 0.0128868718184530D+00, & 0.0321434597854268D+00, & 0.9549696683961202D+00, & 0.0128868718184530D+00, & 0.9549696683961204D+00, & 0.0321434597854271D+00, & 0.0128796984358853D+00, & 0.0128796984358850D+00, & 0.9742406031282298D+00, & 0.0025873987120107D+00, & 0.0239783625881974D+00, & 0.9734342386997918D+00, & 0.0025873987120107D+00, & 0.9734342386997921D+00, & 0.0239783625881978D+00, & 0.0004929222424061D+00, & 0.0004929222424058D+00, & 0.9990141555151881D+00 /) c = (/ & 0.4791627094810211D+00, & 0.0416745810379577D+00, & 0.4791627094810209D+00, & 0.4479070861932128D+00, & 0.1541231491660772D+00, & 0.3979697646407097D+00, & 0.3979697646407099D+00, & 0.1541231491660771D+00, & 0.4479070861932128D+00, & 0.4725556860878008D+00, & 0.1131367059240233D+00, & 0.4143076079881757D+00, & 0.4143076079881758D+00, & 0.1131367059240233D+00, & 0.4725556860878006D+00, & 0.5972534223436731D+00, & 0.0730183277797032D+00, & 0.3297282498766235D+00, & 0.3297282498766236D+00, & 0.0730183277797033D+00, & 0.5972534223436730D+00, & 0.6644373808625788D+00, & 0.1098033768073635D+00, & 0.2257592423300575D+00, & 0.2257592423300578D+00, & 0.1098033768073634D+00, & 0.6644373808625785D+00, & 0.9026338408333600D+00, & 0.0486830795833202D+00, & 0.0486830795833197D+00, & 0.4868494344525785D+00, & 0.0263011310948429D+00, & 0.4868494344525783D+00, & 0.5684647770684034D+00, & 0.1028358753710729D+00, & 0.3286993475605235D+00, & 0.3286993475605237D+00, & 0.1028358753710729D+00, & 0.5684647770684033D+00, & 0.9325204663263090D+00, & 0.0104550153444101D+00, & 0.0570245183292806D+00, & 0.0570245183292809D+00, & 0.0104550153444098D+00, & 0.9325204663263090D+00, & 0.6343242478263366D+00, & 0.1475222615460564D+00, & 0.2181534906276069D+00, & 0.2181534906276071D+00, & 0.1475222615460562D+00, & 0.6343242478263365D+00, & 0.7455675573091064D+00, & 0.0521260968074300D+00, & 0.2023063458834634D+00, & 0.2023063458834636D+00, & 0.0521260968074299D+00, & 0.7455675573091063D+00, & 0.7066325944250231D+00, & 0.0800841957661688D+00, & 0.2132832098088079D+00, & 0.2132832098088080D+00, & 0.0800841957661688D+00, & 0.7066325944250230D+00, & 0.9896258607741097D+00, & 0.0021607803546683D+00, & 0.0082133588712218D+00, & 0.0082133588712219D+00, & 0.0021607803546680D+00, & 0.9896258607741096D+00, & 0.5271208360379724D+00, & 0.0113638023497272D+00, & 0.4615153616123001D+00, & 0.4615153616123004D+00, & 0.0113638023497272D+00, & 0.5271208360379722D+00, & 0.5155990090696433D+00, & 0.1297785236176510D+00, & 0.3546224673127056D+00, & 0.3546224673127056D+00, & 0.1297785236176509D+00, & 0.5155990090696431D+00, & 0.6401420778067229D+00, & 0.0489372786072454D+00, & 0.3109206435860313D+00, & 0.3109206435860317D+00, & 0.0489372786072452D+00, & 0.6401420778067228D+00, & 0.5366266568593034D+00, & 0.1584175590074658D+00, & 0.3049557841332305D+00, & 0.3049557841332306D+00, & 0.1584175590074658D+00, & 0.5366266568593033D+00, & 0.5737054769976867D+00, & 0.1755000854384089D+00, & 0.2507944375639041D+00, & 0.2507944375639041D+00, & 0.1755000854384090D+00, & 0.5737054769976868D+00, & 0.6074103815411007D+00, & 0.1962948092294498D+00, & 0.1962948092294494D+00, & 0.6684025668658078D+00, & 0.1657987165670962D+00, & 0.1657987165670959D+00, & 0.5130043968250232D+00, & 0.0531263813104962D+00, & 0.4338692218644803D+00, & 0.4338692218644805D+00, & 0.0531263813104962D+00, & 0.5130043968250230D+00, & 0.8720533240163508D+00, & 0.0509089773583296D+00, & 0.0770376986253195D+00, & 0.0770376986253196D+00, & 0.0509089773583294D+00, & 0.8720533240163507D+00, & 0.7120424143833398D+00, & 0.0111213995971377D+00, & 0.2768361860195223D+00, & 0.2768361860195224D+00, & 0.0111213995971376D+00, & 0.7120424143833397D+00, & 0.8145830842158607D+00, & 0.0117797536807180D+00, & 0.1736371621034212D+00, & 0.1736371621034214D+00, & 0.0117797536807177D+00, & 0.8145830842158606D+00, & 0.6527581850349298D+00, & 0.0118081263036933D+00, & 0.3354336886613768D+00, & 0.3354336886613770D+00, & 0.0118081263036932D+00, & 0.6527581850349296D+00, & 0.5736918975567097D+00, & 0.0512438839908935D+00, & 0.3750642184523966D+00, & 0.3750642184523966D+00, & 0.0512438839908935D+00, & 0.5736918975567096D+00, & 0.4707474573939667D+00, & 0.1825412564761327D+00, & 0.3467112861299004D+00, & 0.3467112861299004D+00, & 0.1825412564761327D+00, & 0.4707474573939667D+00, & 0.6901296172890430D+00, & 0.0539018714502928D+00, & 0.2559685112606639D+00, & 0.2559685112606641D+00, & 0.0539018714502927D+00, & 0.6901296172890430D+00, & 0.6806497657499146D+00, & 0.0273433134615537D+00, & 0.2920069207885315D+00, & 0.2920069207885316D+00, & 0.0273433134615536D+00, & 0.6806497657499146D+00, & 0.7338403785411441D+00, & 0.0297423818792803D+00, & 0.2364172395795753D+00, & 0.2364172395795756D+00, & 0.0297423818792800D+00, & 0.7338403785411441D+00, & 0.5316578071895072D+00, & 0.0021912946810573D+00, & 0.4661508981294352D+00, & 0.4661508981294354D+00, & 0.0021912946810573D+00, & 0.5316578071895071D+00, & 0.7639437050178102D+00, & 0.0125736658366042D+00, & 0.2234826291455854D+00, & 0.2234826291455856D+00, & 0.0125736658366041D+00, & 0.7639437050178101D+00, & 0.5911123169924869D+00, & 0.0115196691295126D+00, & 0.3973680138780004D+00, & 0.3973680138780006D+00, & 0.0115196691295124D+00, & 0.5911123169924868D+00, & 0.5036527190882437D+00, & 0.2106680376667663D+00, & 0.2856792432449899D+00, & 0.2856792432449901D+00, & 0.2106680376667662D+00, & 0.5036527190882436D+00, & 0.5419857644259105D+00, & 0.2290071177870448D+00, & 0.2290071177870446D+00, & 0.4002037962405426D+00, & 0.2998981018797286D+00, & 0.2998981018797285D+00, & 0.5968372374211253D+00, & 0.0021708502824679D+00, & 0.4009919122964066D+00, & 0.4009919122964067D+00, & 0.0021708502824680D+00, & 0.5968372374211250D+00, & 0.7879600672161253D+00, & 0.0557664223797979D+00, & 0.1562735104040766D+00, & 0.1562735104040767D+00, & 0.0557664223797977D+00, & 0.7879600672161251D+00, & 0.9501161980450165D+00, & 0.0020979082703017D+00, & 0.0477858936846814D+00, & 0.0477858936846818D+00, & 0.0020979082703013D+00, & 0.9501161980450166D+00, & 0.7886726424890335D+00, & 0.0290781975795925D+00, & 0.1822491599313738D+00, & 0.1822491599313741D+00, & 0.0290781975795923D+00, & 0.7886726424890333D+00, & 0.3660812614114253D+00, & 0.2678374771771492D+00, & 0.3660812614114253D+00, & 0.8990694649639888D+00, & 0.0115829668440253D+00, & 0.0893475681919856D+00, & 0.0893475681919859D+00, & 0.0115829668440250D+00, & 0.8990694649639888D+00, & 0.7473177571098144D+00, & 0.0874623616502728D+00, & 0.1652198812399125D+00, & 0.1652198812399128D+00, & 0.0874623616502725D+00, & 0.7473177571098144D+00, & 0.9173934916626123D+00, & 0.0020785035982193D+00, & 0.0805280047391682D+00, & 0.0805280047391685D+00, & 0.0020785035982192D+00, & 0.9173934916626122D+00, & 0.4329807146876172D+00, & 0.2364777837447836D+00, & 0.3305415015675990D+00, & 0.3305415015675990D+00, & 0.2364777837447836D+00, & 0.4329807146876172D+00, & 0.7021169686939934D+00, & 0.1228090180537128D+00, & 0.1750740132522935D+00, & 0.1750740132522937D+00, & 0.1228090180537127D+00, & 0.7021169686939934D+00, & 0.8315999985260938D+00, & 0.0550050284444839D+00, & 0.1133949730294221D+00, & 0.1133949730294224D+00, & 0.0550050284444837D+00, & 0.8315999985260938D+00, & 0.8766622383664391D+00, & 0.0287935332271121D+00, & 0.0945442284064485D+00, & 0.0945442284064488D+00, & 0.0287935332271119D+00, & 0.8766622383664391D+00, & 0.9147477258472859D+00, & 0.0262933317918679D+00, & 0.0589589423608460D+00, & 0.0589589423608463D+00, & 0.0262933317918675D+00, & 0.9147477258472857D+00, & 0.6162465555124067D+00, & 0.0283073273852235D+00, & 0.3554461171023694D+00, & 0.3554461171023697D+00, & 0.0283073273852236D+00, & 0.6162465555124066D+00, & 0.5512452167474322D+00, & 0.0281269388071388D+00, & 0.4206278444454288D+00, & 0.4206278444454289D+00, & 0.0281269388071387D+00, & 0.5512452167474320D+00, & 0.9384613120958362D+00, & 0.0307693439520821D+00, & 0.0307693439520814D+00, & 0.7215566217404850D+00, & 0.0021009010930693D+00, & 0.2763424771664456D+00, & 0.2763424771664457D+00, & 0.0021009010930692D+00, & 0.7215566217404850D+00, & 0.8336434944596028D+00, & 0.0305221004022599D+00, & 0.1358344051381370D+00, & 0.1358344051381372D+00, & 0.0305221004022597D+00, & 0.8336434944596028D+00, & 0.7904245130980824D+00, & 0.0881430419815304D+00, & 0.1214324449203871D+00, & 0.1214324449203873D+00, & 0.0881430419815301D+00, & 0.7904245130980823D+00, & 0.8350026124728831D+00, & 0.0824986937635586D+00, & 0.0824986937635580D+00, & 0.8581647113948480D+00, & 0.0125808072722038D+00, & 0.1292544813329480D+00, & 0.1292544813329482D+00, & 0.0125808072722037D+00, & 0.8581647113948477D+00, & 0.6431846260118415D+00, & 0.0838760556578321D+00, & 0.2729393183303261D+00, & 0.2729393183303264D+00, & 0.0838760556578320D+00, & 0.6431846260118415D+00, & 0.4608230043475882D+00, & 0.0783539913048238D+00, & 0.4608230043475879D+00, & 0.5989839678810082D+00, & 0.1247916004447047D+00, & 0.2762244316742869D+00, & 0.2762244316742870D+00, & 0.1247916004447046D+00, & 0.5989839678810082D+00, & 0.8312386887187595D+00, & 0.0022302492894394D+00, & 0.1665310619918008D+00, & 0.1665310619918011D+00, & 0.0022302492894393D+00, & 0.8312386887187594D+00, & 0.6603914710100434D+00, & 0.0022846671110010D+00, & 0.3373238618789555D+00, & 0.3373238618789556D+00, & 0.0022846671110009D+00, & 0.6603914710100431D+00, & 0.4667685826046063D+00, & 0.2666157086976967D+00, & 0.2666157086976967D+00, & 0.7431211301049753D+00, & 0.1284394349475124D+00, & 0.1284394349475121D+00, & 0.5268218597395554D+00, & 0.0831933025800658D+00, & 0.3899848376803786D+00, & 0.3899848376803788D+00, & 0.0831933025800659D+00, & 0.5268218597395552D+00, & 0.3333333333333333D+00, & 0.7785355668785605D+00, & 0.0024070310918325D+00, & 0.2190574020296067D+00, & 0.2190574020296069D+00, & 0.0024070310918324D+00, & 0.7785355668785604D+00, & 0.8772415939384313D+00, & 0.0024170636184784D+00, & 0.1203413424430901D+00, & 0.1203413424430904D+00, & 0.0024170636184782D+00, & 0.8772415939384312D+00, & 0.3975115754020483D+00, & 0.2049768491959031D+00, & 0.3975115754020483D+00, & 0.9549696683961202D+00, & 0.0128868718184531D+00, & 0.0321434597854267D+00, & 0.0321434597854268D+00, & 0.0128868718184527D+00, & 0.9549696683961202D+00, & 0.9742406031282297D+00, & 0.0128796984358854D+00, & 0.0128796984358848D+00, & 0.9734342386997918D+00, & 0.0025873987120108D+00, & 0.0239783625881972D+00, & 0.0239783625881974D+00, & 0.0025873987120104D+00, & 0.9734342386997918D+00, & 0.9990141555151881D+00, & 0.0004929222424062D+00, & 0.0004929222424056D+00 /) w = (/ & 0.0015063623878996D+00, & 0.0015063623878996D+00, & 0.0015063623878996D+00, & 0.0044537081869330D+00, & 0.0044537081869330D+00, & 0.0044537081869330D+00, & 0.0044537081869330D+00, & 0.0044537081869330D+00, & 0.0044537081869330D+00, & 0.0043200095246416D+00, & 0.0043200095246416D+00, & 0.0043200095246416D+00, & 0.0043200095246416D+00, & 0.0043200095246416D+00, & 0.0043200095246416D+00, & 0.0030868796559389D+00, & 0.0030868796559389D+00, & 0.0030868796559389D+00, & 0.0030868796559389D+00, & 0.0030868796559389D+00, & 0.0030868796559389D+00, & 0.0034302258154803D+00, & 0.0034302258154803D+00, & 0.0034302258154803D+00, & 0.0034302258154803D+00, & 0.0034302258154803D+00, & 0.0034302258154803D+00, & 0.0012474691816453D+00, & 0.0012474691816453D+00, & 0.0012474691816453D+00, & 0.0021895163833001D+00, & 0.0021895163833001D+00, & 0.0021895163833001D+00, & 0.0037827619823913D+00, & 0.0037827619823913D+00, & 0.0037827619823913D+00, & 0.0037827619823913D+00, & 0.0037827619823913D+00, & 0.0037827619823913D+00, & 0.0006704306400626D+00, & 0.0006704306400626D+00, & 0.0006704306400626D+00, & 0.0006704306400626D+00, & 0.0006704306400626D+00, & 0.0006704306400626D+00, & 0.0041741147673405D+00, & 0.0041741147673405D+00, & 0.0041741147673405D+00, & 0.0041741147673405D+00, & 0.0041741147673405D+00, & 0.0041741147673405D+00, & 0.0025583666569760D+00, & 0.0025583666569760D+00, & 0.0025583666569760D+00, & 0.0025583666569760D+00, & 0.0025583666569760D+00, & 0.0025583666569760D+00, & 0.0031839869521233D+00, & 0.0031839869521233D+00, & 0.0031839869521233D+00, & 0.0031839869521233D+00, & 0.0031839869521233D+00, & 0.0031839869521233D+00, & 0.0001317170927954D+00, & 0.0001317170927954D+00, & 0.0001317170927954D+00, & 0.0001317170927954D+00, & 0.0001317170927954D+00, & 0.0001317170927954D+00, & 0.0016456723831060D+00, & 0.0016456723831060D+00, & 0.0016456723831060D+00, & 0.0016456723831060D+00, & 0.0016456723831060D+00, & 0.0016456723831060D+00, & 0.0045954830932586D+00, & 0.0045954830932586D+00, & 0.0045954830932586D+00, & 0.0045954830932586D+00, & 0.0045954830932586D+00, & 0.0045954830932586D+00, & 0.0028688601568156D+00, & 0.0028688601568156D+00, & 0.0028688601568156D+00, & 0.0028688601568156D+00, & 0.0028688601568156D+00, & 0.0028688601568156D+00, & 0.0047267340609202D+00, & 0.0047267340609202D+00, & 0.0047267340609202D+00, & 0.0047267340609202D+00, & 0.0047267340609202D+00, & 0.0047267340609202D+00, & 0.0048087317688295D+00, & 0.0048087317688295D+00, & 0.0048087317688295D+00, & 0.0048087317688295D+00, & 0.0048087317688295D+00, & 0.0048087317688295D+00, & 0.0045326165183418D+00, & 0.0045326165183418D+00, & 0.0045326165183418D+00, & 0.0041121335512161D+00, & 0.0041121335512161D+00, & 0.0041121335512161D+00, & 0.0031927670836935D+00, & 0.0031927670836935D+00, & 0.0031927670836935D+00, & 0.0031927670836935D+00, & 0.0031927670836935D+00, & 0.0031927670836935D+00, & 0.0017487650502894D+00, & 0.0017487650502894D+00, & 0.0017487650502894D+00, & 0.0017487650502894D+00, & 0.0017487650502894D+00, & 0.0017487650502894D+00, & 0.0014306703323830D+00, & 0.0014306703323830D+00, & 0.0014306703323830D+00, & 0.0014306703323830D+00, & 0.0014306703323830D+00, & 0.0014306703323830D+00, & 0.0012681752789353D+00, & 0.0012681752789353D+00, & 0.0012681752789353D+00, & 0.0012681752789353D+00, & 0.0012681752789353D+00, & 0.0012681752789353D+00, & 0.0015790337439117D+00, & 0.0015790337439117D+00, & 0.0015790337439117D+00, & 0.0015790337439117D+00, & 0.0015790337439117D+00, & 0.0015790337439117D+00, & 0.0032154452084321D+00, & 0.0032154452084321D+00, & 0.0032154452084321D+00, & 0.0032154452084321D+00, & 0.0032154452084321D+00, & 0.0032154452084321D+00, & 0.0053977058220170D+00, & 0.0053977058220170D+00, & 0.0053977058220170D+00, & 0.0053977058220170D+00, & 0.0053977058220170D+00, & 0.0053977058220170D+00, & 0.0030627052030109D+00, & 0.0030627052030109D+00, & 0.0030627052030109D+00, & 0.0030627052030109D+00, & 0.0030627052030109D+00, & 0.0030627052030109D+00, & 0.0023192184096375D+00, & 0.0023192184096375D+00, & 0.0023192184096375D+00, & 0.0023192184096375D+00, & 0.0023192184096375D+00, & 0.0023192184096375D+00, & 0.0022961002901773D+00, & 0.0022961002901773D+00, & 0.0022961002901773D+00, & 0.0022961002901773D+00, & 0.0022961002901773D+00, & 0.0022961002901773D+00, & 0.0007338103320712D+00, & 0.0007338103320712D+00, & 0.0007338103320712D+00, & 0.0007338103320712D+00, & 0.0007338103320712D+00, & 0.0007338103320712D+00, & 0.0014437602767408D+00, & 0.0014437602767408D+00, & 0.0014437602767408D+00, & 0.0014437602767408D+00, & 0.0014437602767408D+00, & 0.0014437602767408D+00, & 0.0016586663239643D+00, & 0.0016586663239643D+00, & 0.0016586663239643D+00, & 0.0016586663239643D+00, & 0.0016586663239643D+00, & 0.0016586663239643D+00, & 0.0055707293081133D+00, & 0.0055707293081133D+00, & 0.0055707293081133D+00, & 0.0055707293081133D+00, & 0.0055707293081133D+00, & 0.0055707293081133D+00, & 0.0053362839978633D+00, & 0.0053362839978633D+00, & 0.0053362839978633D+00, & 0.0064756219278226D+00, & 0.0064756219278226D+00, & 0.0064756219278226D+00, & 0.0007214374344646D+00, & 0.0007214374344646D+00, & 0.0007214374344646D+00, & 0.0007214374344646D+00, & 0.0007214374344646D+00, & 0.0007214374344646D+00, & 0.0026221278244148D+00, & 0.0026221278244148D+00, & 0.0026221278244148D+00, & 0.0026221278244148D+00, & 0.0026221278244148D+00, & 0.0026221278244148D+00, & 0.0003035796033724D+00, & 0.0003035796033724D+00, & 0.0003035796033724D+00, & 0.0003035796033724D+00, & 0.0003035796033724D+00, & 0.0003035796033724D+00, & 0.0021000870011484D+00, & 0.0021000870011484D+00, & 0.0021000870011484D+00, & 0.0021000870011484D+00, & 0.0021000870011484D+00, & 0.0021000870011484D+00, & 0.0065283169454314D+00, & 0.0065283169454314D+00, & 0.0065283169454314D+00, & 0.0009662986187413D+00, & 0.0009662986187413D+00, & 0.0009662986187413D+00, & 0.0009662986187413D+00, & 0.0009662986187413D+00, & 0.0009662986187413D+00, & 0.0032046723702290D+00, & 0.0032046723702290D+00, & 0.0032046723702290D+00, & 0.0032046723702290D+00, & 0.0032046723702290D+00, & 0.0032046723702290D+00, & 0.0003922950453873D+00, & 0.0003922950453873D+00, & 0.0003922950453873D+00, & 0.0003922950453873D+00, & 0.0003922950453873D+00, & 0.0003922950453873D+00, & 0.0062575812080365D+00, & 0.0062575812080365D+00, & 0.0062575812080365D+00, & 0.0062575812080365D+00, & 0.0062575812080365D+00, & 0.0062575812080365D+00, & 0.0037812405140909D+00, & 0.0037812405140909D+00, & 0.0037812405140909D+00, & 0.0037812405140909D+00, & 0.0037812405140909D+00, & 0.0037812405140909D+00, & 0.0023063619647722D+00, & 0.0023063619647722D+00, & 0.0023063619647722D+00, & 0.0023063619647722D+00, & 0.0023063619647722D+00, & 0.0023063619647722D+00, & 0.0015964303372989D+00, & 0.0015964303372989D+00, & 0.0015964303372989D+00, & 0.0015964303372989D+00, & 0.0015964303372989D+00, & 0.0015964303372989D+00, & 0.0012488360135939D+00, & 0.0012488360135939D+00, & 0.0012488360135939D+00, & 0.0012488360135939D+00, & 0.0012488360135939D+00, & 0.0012488360135939D+00, & 0.0025556284082945D+00, & 0.0025556284082945D+00, & 0.0025556284082945D+00, & 0.0025556284082945D+00, & 0.0025556284082945D+00, & 0.0025556284082945D+00, & 0.0026782849316906D+00, & 0.0026782849316906D+00, & 0.0026782849316906D+00, & 0.0026782849316906D+00, & 0.0026782849316906D+00, & 0.0026782849316906D+00, & 0.0009717097001371D+00, & 0.0009717097001371D+00, & 0.0009717097001371D+00, & 0.0006413900158338D+00, & 0.0006413900158338D+00, & 0.0006413900158338D+00, & 0.0006413900158338D+00, & 0.0006413900158338D+00, & 0.0006413900158338D+00, & 0.0019107173540585D+00, & 0.0019107173540585D+00, & 0.0019107173540585D+00, & 0.0019107173540585D+00, & 0.0019107173540585D+00, & 0.0019107173540585D+00, & 0.0030285648566490D+00, & 0.0030285648566490D+00, & 0.0030285648566490D+00, & 0.0030285648566490D+00, & 0.0030285648566490D+00, & 0.0030285648566490D+00, & 0.0024386979014754D+00, & 0.0024386979014754D+00, & 0.0024386979014754D+00, & 0.0011940194745138D+00, & 0.0011940194745138D+00, & 0.0011940194745138D+00, & 0.0011940194745138D+00, & 0.0011940194745138D+00, & 0.0011940194745138D+00, & 0.0039897861442201D+00, & 0.0039897861442201D+00, & 0.0039897861442201D+00, & 0.0039897861442201D+00, & 0.0039897861442201D+00, & 0.0039897861442201D+00, & 0.0041882040717764D+00, & 0.0041882040717764D+00, & 0.0041882040717764D+00, & 0.0047741598764475D+00, & 0.0047741598764475D+00, & 0.0047741598764475D+00, & 0.0047741598764475D+00, & 0.0047741598764475D+00, & 0.0047741598764475D+00, & 0.0005681012975307D+00, & 0.0005681012975307D+00, & 0.0005681012975307D+00, & 0.0005681012975307D+00, & 0.0005681012975307D+00, & 0.0005681012975307D+00, & 0.0007292897898915D+00, & 0.0007292897898915D+00, & 0.0007292897898915D+00, & 0.0007292897898915D+00, & 0.0007292897898915D+00, & 0.0007292897898915D+00, & 0.0059862742964751D+00, & 0.0059862742964751D+00, & 0.0059862742964751D+00, & 0.0037734801565331D+00, & 0.0037734801565331D+00, & 0.0037734801565331D+00, & 0.0043995561699861D+00, & 0.0043995561699861D+00, & 0.0043995561699861D+00, & 0.0043995561699861D+00, & 0.0043995561699861D+00, & 0.0043995561699861D+00, & 0.0066350471232072D+00, & 0.0006789589985773D+00, & 0.0006789589985773D+00, & 0.0006789589985773D+00, & 0.0006789589985773D+00, & 0.0006789589985773D+00, & 0.0006789589985773D+00, & 0.0005314441134062D+00, & 0.0005314441134062D+00, & 0.0005314441134062D+00, & 0.0005314441134062D+00, & 0.0005314441134062D+00, & 0.0005314441134062D+00, & 0.0064816472544865D+00, & 0.0064816472544865D+00, & 0.0064816472544865D+00, & 0.0006475246634133D+00, & 0.0006475246634133D+00, & 0.0006475246634133D+00, & 0.0006475246634133D+00, & 0.0006475246634133D+00, & 0.0006475246634133D+00, & 0.0004493467102800D+00, & 0.0004493467102800D+00, & 0.0004493467102800D+00, & 0.0002613279460023D+00, & 0.0002613279460023D+00, & 0.0002613279460023D+00, & 0.0002613279460023D+00, & 0.0002613279460023D+00, & 0.0002613279460023D+00, & 0.0000140952201360D+00, & 0.0000140952201360D+00, & 0.0000140952201360D+00 /) return end subroutine rule47 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule47() returns the rule of precision 47. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3491775041543910D+00, & 0.3491775041543910D+00, & 0.3016449916912180D+00, & 0.0132182347742615D+00, & 0.9798556571067439D+00, & 0.0069261081189949D+00, & 0.9798556571067438D+00, & 0.0132182347742616D+00, & 0.0069261081189944D+00, & 0.1820741432615592D+00, & 0.7362900096274552D+00, & 0.0816358471109855D+00, & 0.7362900096274553D+00, & 0.1820741432615592D+00, & 0.0816358471109853D+00, & 0.1505809273177014D+00, & 0.7632227066935655D+00, & 0.0861963659887331D+00, & 0.7632227066935656D+00, & 0.1505809273177015D+00, & 0.0861963659887328D+00, & 0.3028965441179143D+00, & 0.3942069117641712D+00, & 0.3028965441179143D+00, & 0.0764329826567075D+00, & 0.8732738368131011D+00, & 0.0502931805301914D+00, & 0.8732738368131011D+00, & 0.0764329826567076D+00, & 0.0502931805301912D+00, & 0.0138326160976293D+00, & 0.9851184849524532D+00, & 0.0010488989499177D+00, & 0.9851184849524532D+00, & 0.0138326160976294D+00, & 0.0010488989499173D+00, & 0.0267452272430761D+00, & 0.9632342751915716D+00, & 0.0100204975653523D+00, & 0.9632342751915717D+00, & 0.0267452272430762D+00, & 0.0100204975653520D+00, & 0.0505319024623014D+00, & 0.8989361950753969D+00, & 0.0505319024623018D+00, & 0.3711902367525145D+00, & 0.4251355102023056D+00, & 0.2036742530451798D+00, & 0.4251355102023055D+00, & 0.3711902367525146D+00, & 0.2036742530451798D+00, & 0.3688949727921184D+00, & 0.4717783433339480D+00, & 0.1593266838739336D+00, & 0.4717783433339479D+00, & 0.3688949727921184D+00, & 0.1593266838739335D+00, & 0.4215093928787094D+00, & 0.4215093928787095D+00, & 0.1569812142425811D+00, & 0.1070745798931199D+00, & 0.8395567175421841D+00, & 0.0533687025646961D+00, & 0.8395567175421841D+00, & 0.1070745798931200D+00, & 0.0533687025646957D+00, & 0.1152179121673602D+00, & 0.7994860233403234D+00, & 0.0852960644923165D+00, & 0.7994860233403234D+00, & 0.1152179121673603D+00, & 0.0852960644923162D+00, & 0.4746270243429588D+00, & 0.4746270243429588D+00, & 0.0507459513140823D+00, & 0.4179628539698995D+00, & 0.5305548481010338D+00, & 0.0514822979290668D+00, & 0.5305548481010337D+00, & 0.4179628539698995D+00, & 0.0514822979290667D+00, & 0.0795728420692438D+00, & 0.8408543158615120D+00, & 0.0795728420692443D+00, & 0.0462992599159319D+00, & 0.9261471086445946D+00, & 0.0275536314394737D+00, & 0.9261471086445946D+00, & 0.0462992599159320D+00, & 0.0275536314394733D+00, & 0.3250299373159994D+00, & 0.5562680355150597D+00, & 0.1187020271689408D+00, & 0.5562680355150598D+00, & 0.3250299373159994D+00, & 0.1187020271689407D+00, & 0.2230214568534538D+00, & 0.6919169659768531D+00, & 0.0850615771696930D+00, & 0.6919169659768531D+00, & 0.2230214568534538D+00, & 0.0850615771696929D+00, & 0.3822400802517831D+00, & 0.4996324113070245D+00, & 0.1181275084411924D+00, & 0.4996324113070245D+00, & 0.3822400802517831D+00, & 0.1181275084411923D+00, & 0.3186810168040575D+00, & 0.4286106325432008D+00, & 0.2527083506527416D+00, & 0.4286106325432009D+00, & 0.3186810168040575D+00, & 0.2527083506527416D+00, & 0.3161024291972920D+00, & 0.4781516295945364D+00, & 0.2057459412081715D+00, & 0.4781516295945364D+00, & 0.3161024291972920D+00, & 0.2057459412081715D+00, & 0.0236802291430403D+00, & 0.9526395417139191D+00, & 0.0236802291430406D+00, & 0.2017143602625017D+00, & 0.7696399026320835D+00, & 0.0286457371054150D+00, & 0.7696399026320834D+00, & 0.2017143602625018D+00, & 0.0286457371054148D+00, & 0.3040953744572968D+00, & 0.6672038004510813D+00, & 0.0287008250916218D+00, & 0.6672038004510813D+00, & 0.3040953744572970D+00, & 0.0287008250916217D+00, & 0.2509406000944529D+00, & 0.7199771640567535D+00, & 0.0290822358487937D+00, & 0.7199771640567536D+00, & 0.2509406000944530D+00, & 0.0290822358487933D+00, & 0.2701136854877469D+00, & 0.6081440785715926D+00, & 0.1217422359406605D+00, & 0.6081440785715926D+00, & 0.2701136854877470D+00, & 0.1217422359406603D+00, & 0.4230078867718429D+00, & 0.5490451947911587D+00, & 0.0279469184369985D+00, & 0.5490451947911587D+00, & 0.4230078867718429D+00, & 0.0279469184369984D+00, & 0.2188381084082620D+00, & 0.6590218248333656D+00, & 0.1221400667583725D+00, & 0.6590218248333655D+00, & 0.2188381084082620D+00, & 0.1221400667583722D+00, & 0.2630564357703722D+00, & 0.4738871284592553D+00, & 0.2630564357703724D+00, & 0.3155582824301563D+00, & 0.5240287324788191D+00, & 0.1604129850910246D+00, & 0.5240287324788190D+00, & 0.3155582824301562D+00, & 0.1604129850910245D+00, & 0.3599942050767867D+00, & 0.5879673898202077D+00, & 0.0520384051030056D+00, & 0.5879673898202077D+00, & 0.3599942050767868D+00, & 0.0520384051030055D+00, & 0.0761492805627097D+00, & 0.8958426221108554D+00, & 0.0280080973264349D+00, & 0.8958426221108555D+00, & 0.0761492805627098D+00, & 0.0280080973264346D+00, & 0.3616871250428565D+00, & 0.6099486756638904D+00, & 0.0283641992932530D+00, & 0.6099486756638904D+00, & 0.3616871250428564D+00, & 0.0283641992932528D+00, & 0.4420693972638305D+00, & 0.4420693972638306D+00, & 0.1158612054723388D+00, & 0.4861601074836898D+00, & 0.4861601074836898D+00, & 0.0276797850326204D+00, & 0.3969570429794791D+00, & 0.5212280019989164D+00, & 0.0818149550216045D+00, & 0.5212280019989164D+00, & 0.3969570429794791D+00, & 0.0818149550216044D+00, & 0.2635821046503857D+00, & 0.5242839990330530D+00, & 0.2121338963165611D+00, & 0.5242839990330530D+00, & 0.2635821046503858D+00, & 0.2121338963165610D+00, & 0.1925350542122712D+00, & 0.7550197415648126D+00, & 0.0524452042229163D+00, & 0.7550197415648127D+00, & 0.1925350542122711D+00, & 0.0524452042229161D+00, & 0.1550537980019329D+00, & 0.8157685255653345D+00, & 0.0291776764327327D+00, & 0.8157685255653344D+00, & 0.1550537980019330D+00, & 0.0291776764327324D+00, & 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0.3013661191750608D+00, & 0.6458926721701389D+00, & 0.0527412086548005D+00, & 0.6458926721701388D+00, & 0.3013661191750611D+00, & 0.2125512689048139D+00, & 0.2125512689048138D+00, & 0.5748974621903725D+00, & 0.0539363844971338D+00, & 0.1455590941243064D+00, & 0.8005045213785600D+00, & 0.0539363844971338D+00, & 0.8005045213785600D+00, & 0.1455590941243067D+00, & 0.0020268965838007D+00, & 0.0339239311459583D+00, & 0.9640491722702410D+00, & 0.0020268965838007D+00, & 0.9640491722702410D+00, & 0.0339239311459588D+00, & 0.0803356517009978D+00, & 0.4598321741495012D+00, & 0.4598321741495013D+00, & 0.0113741139787509D+00, & 0.4609203982983522D+00, & 0.5277054877228973D+00, & 0.0113741139787509D+00, & 0.5277054877228970D+00, & 0.4609203982983524D+00, & 0.1647197357980591D+00, & 0.2096506369927426D+00, & 0.6256296272091985D+00, & 0.1647197357980591D+00, & 0.6256296272091985D+00, & 0.2096506369927428D+00, & 0.0824852827778116D+00, & 0.3356188307276364D+00, & 0.5818958864945523D+00, & 0.0824852827778116D+00, & 0.5818958864945523D+00, & 0.3356188307276366D+00, & 0.0118660258094384D+00, & 0.1191983560948026D+00, & 0.8689356180957590D+00, & 0.0118660258094384D+00, & 0.8689356180957590D+00, & 0.1191983560948030D+00, & 0.0289885801232180D+00, & 0.1127517427175889D+00, & 0.8582596771591934D+00, & 0.0289885801232180D+00, & 0.8582596771591934D+00, & 0.1127517427175892D+00, & 0.0536092519706684D+00, & 0.2446044849937105D+00, & 0.7017862630356213D+00, & 0.0536092519706684D+00, & 0.7017862630356212D+00, & 0.2446044849937108D+00, & 0.1649672925863881D+00, & 0.2613278952130155D+00, & 0.5737048122005965D+00, & 0.1649672925863881D+00, & 0.5737048122005965D+00, & 0.2613278952130156D+00, & 0.0841334586353880D+00, & 0.2767102223588471D+00, & 0.6391563190057651D+00, & 0.0841334586353880D+00, & 0.6391563190057651D+00, & 0.2767102223588473D+00, & 0.0117181407852650D+00, & 0.3310576983055140D+00, & 0.6572241609092212D+00, & 0.0117181407852650D+00, & 0.6572241609092211D+00, & 0.3310576983055142D+00, & 0.1198251592753853D+00, & 0.1711659603535231D+00, & 0.7090088803710918D+00, & 0.1198251592753853D+00, & 0.7090088803710918D+00, & 0.1711659603535233D+00, & 0.0118084740509012D+00, & 0.2148380935404156D+00, & 0.7733534324086834D+00, & 0.0118084740509012D+00, & 0.7733534324086833D+00, & 0.2148380935404159D+00, & 0.0118982357159540D+00, & 0.1640325957882373D+00, & 0.8240691684958088D+00, & 0.0118982357159540D+00, & 0.8240691684958088D+00, & 0.1640325957882376D+00, & 0.0118476002079960D+00, & 0.2705995205192745D+00, & 0.7175528792727297D+00, & 0.0118476002079960D+00, & 0.7175528792727297D+00, & 0.2705995205192748D+00, & 0.0115294467270000D+00, & 0.3948815299054213D+00, & 0.5935890233675789D+00, & 0.0115294467270000D+00, & 0.5935890233675788D+00, & 0.3948815299054215D+00, & 0.0021629417026532D+00, & 0.4989185291486735D+00, & 0.4989185291486736D+00, & 0.0022497058285755D+00, & 0.0976801440609630D+00, & 0.9000701501104617D+00, & 0.0022497058285755D+00, & 0.9000701501104617D+00, & 0.0976801440609633D+00, & 0.0021780831191386D+00, & 0.4316631884764962D+00, & 0.5661587284043654D+00, & 0.0021780831191386D+00, & 0.5661587284043653D+00, & 0.4316631884764964D+00, & 0.0022594310974726D+00, & 0.1403238605725803D+00, & 0.8574167083299473D+00, & 0.0022594310974726D+00, & 0.8574167083299473D+00, & 0.1403238605725806D+00, & 0.1249745067489116D+00, & 0.1249745067489113D+00, & 0.7500509865021772D+00, & 0.0022489510449106D+00, & 0.2437969001075017D+00, & 0.7539541488475879D+00, & 0.0022489510449106D+00, & 0.7539541488475878D+00, & 0.2437969001075020D+00, & 0.0022107829440680D+00, & 0.0619939934379152D+00, & 0.9357952236180170D+00, & 0.0022107829440680D+00, & 0.9357952236180170D+00, & 0.0619939934379155D+00, & 0.0022499314295439D+00, & 0.3029504928419904D+00, & 0.6947995757284657D+00, & 0.0022499314295439D+00, & 0.6947995757284657D+00, & 0.3029504928419907D+00, & 0.0022640392620408D+00, & 0.1892661005029103D+00, & 0.8084698602350490D+00, & 0.0022640392620408D+00, & 0.8084698602350490D+00, & 0.1892661005029106D+00, & 0.0022135119210076D+00, & 0.3659190279368091D+00, & 0.6318674601421835D+00, & 0.0022135119210076D+00, & 0.6318674601421833D+00, & 0.3659190279368094D+00, & 0.0026050966947363D+00, & 0.0026050966947360D+00, & 0.9947898066105276D+00 /) c = (/ & 0.3491775041543909D+00, & 0.3016449916912180D+00, & 0.3491775041543909D+00, & 0.9798556571067439D+00, & 0.0069261081189946D+00, & 0.0132182347742612D+00, & 0.0132182347742615D+00, & 0.0069261081189945D+00, & 0.9798556571067437D+00, & 0.7362900096274552D+00, & 0.0816358471109856D+00, & 0.1820741432615590D+00, & 0.1820741432615592D+00, & 0.0816358471109854D+00, & 0.7362900096274553D+00, & 0.7632227066935656D+00, & 0.0861963659887331D+00, & 0.1505809273177011D+00, & 0.1505809273177013D+00, & 0.0861963659887328D+00, & 0.7632227066935655D+00, & 0.3942069117641712D+00, & 0.3028965441179144D+00, & 0.3028965441179144D+00, & 0.8732738368131011D+00, & 0.0502931805301914D+00, & 0.0764329826567073D+00, & 0.0764329826567075D+00, & 0.0502931805301911D+00, & 0.8732738368131009D+00, & 0.9851184849524532D+00, & 0.0010488989499175D+00, & 0.0138326160976291D+00, & 0.0138326160976293D+00, & 0.0010488989499173D+00, & 0.9851184849524531D+00, & 0.9632342751915716D+00, & 0.0100204975653523D+00, & 0.0267452272430758D+00, & 0.0267452272430761D+00, & 0.0100204975653521D+00, & 0.9632342751915716D+00, & 0.8989361950753969D+00, & 0.0505319024623018D+00, & 0.0505319024623011D+00, & 0.4251355102023056D+00, & 0.2036742530451798D+00, & 0.3711902367525145D+00, & 0.3711902367525145D+00, & 0.2036742530451797D+00, & 0.4251355102023054D+00, & 0.4717783433339480D+00, & 0.1593266838739336D+00, & 0.3688949727921183D+00, & 0.3688949727921184D+00, & 0.1593266838739335D+00, & 0.4717783433339479D+00, & 0.4215093928787094D+00, & 0.1569812142425810D+00, & 0.4215093928787093D+00, & 0.8395567175421841D+00, & 0.0533687025646960D+00, & 0.1070745798931196D+00, & 0.1070745798931199D+00, & 0.0533687025646957D+00, & 0.8395567175421840D+00, & 0.7994860233403234D+00, & 0.0852960644923164D+00, & 0.1152179121673601D+00, & 0.1152179121673602D+00, & 0.0852960644923163D+00, & 0.7994860233403233D+00, & 0.4746270243429588D+00, & 0.0507459513140824D+00, & 0.4746270243429587D+00, & 0.5305548481010337D+00, & 0.0514822979290667D+00, & 0.4179628539698993D+00, & 0.4179628539698995D+00, & 0.0514822979290667D+00, & 0.5305548481010335D+00, & 0.8408543158615120D+00, & 0.0795728420692441D+00, & 0.0795728420692435D+00, & 0.9261471086445946D+00, & 0.0275536314394736D+00, & 0.0462992599159315D+00, & 0.0462992599159319D+00, & 0.0275536314394733D+00, & 0.9261471086445946D+00, & 0.5562680355150597D+00, & 0.1187020271689408D+00, & 0.3250299373159993D+00, & 0.3250299373159994D+00, & 0.1187020271689406D+00, & 0.5562680355150597D+00, & 0.6919169659768531D+00, & 0.0850615771696930D+00, & 0.2230214568534536D+00, & 0.2230214568534538D+00, & 0.0850615771696929D+00, & 0.6919169659768531D+00, & 0.4996324113070245D+00, & 0.1181275084411924D+00, & 0.3822400802517830D+00, & 0.3822400802517831D+00, & 0.1181275084411922D+00, & 0.4996324113070245D+00, & 0.4286106325432009D+00, & 0.2527083506527416D+00, & 0.3186810168040574D+00, & 0.3186810168040575D+00, & 0.2527083506527415D+00, & 0.4286106325432008D+00, & 0.4781516295945364D+00, & 0.2057459412081716D+00, & 0.3161024291972919D+00, & 0.3161024291972919D+00, & 0.2057459412081715D+00, & 0.4781516295945364D+00, & 0.9526395417139192D+00, & 0.0236802291430407D+00, & 0.0236802291430399D+00, & 0.7696399026320834D+00, & 0.0286457371054148D+00, & 0.2017143602625014D+00, & 0.2017143602625017D+00, & 0.0286457371054148D+00, & 0.7696399026320832D+00, & 0.6672038004510813D+00, & 0.0287008250916218D+00, & 0.3040953744572966D+00, & 0.3040953744572968D+00, & 0.0287008250916218D+00, & 0.6672038004510812D+00, & 0.7199771640567535D+00, & 0.0290822358487935D+00, & 0.2509406000944527D+00, & 0.2509406000944528D+00, & 0.0290822358487934D+00, & 0.7199771640567535D+00, & 0.6081440785715926D+00, & 0.1217422359406605D+00, & 0.2701136854877467D+00, & 0.2701136854877469D+00, & 0.1217422359406602D+00, & 0.6081440785715925D+00, & 0.5490451947911585D+00, & 0.0279469184369984D+00, & 0.4230078867718428D+00, & 0.4230078867718428D+00, & 0.0279469184369984D+00, & 0.5490451947911585D+00, & 0.6590218248333655D+00, & 0.1221400667583724D+00, & 0.2188381084082618D+00, & 0.2188381084082621D+00, & 0.1221400667583723D+00, & 0.6590218248333655D+00, & 0.4738871284592553D+00, & 0.2630564357703724D+00, & 0.2630564357703721D+00, & 0.5240287324788191D+00, & 0.1604129850910246D+00, & 0.3155582824301562D+00, & 0.3155582824301563D+00, & 0.1604129850910246D+00, & 0.5240287324788190D+00, & 0.5879673898202077D+00, & 0.0520384051030055D+00, & 0.3599942050767865D+00, & 0.3599942050767868D+00, & 0.0520384051030055D+00, & 0.5879673898202076D+00, & 0.8958426221108555D+00, & 0.0280080973264349D+00, & 0.0761492805627094D+00, & 0.0761492805627097D+00, & 0.0280080973264346D+00, & 0.8958426221108554D+00, & 0.6099486756638904D+00, & 0.0283641992932530D+00, & 0.3616871250428563D+00, & 0.3616871250428565D+00, & 0.0283641992932530D+00, & 0.6099486756638903D+00, & 0.4420693972638305D+00, & 0.1158612054723388D+00, & 0.4420693972638304D+00, & 0.4861601074836898D+00, & 0.0276797850326204D+00, & 0.4861601074836896D+00, & 0.5212280019989164D+00, & 0.0818149550216044D+00, & 0.3969570429794790D+00, & 0.3969570429794791D+00, & 0.0818149550216044D+00, & 0.5212280019989163D+00, & 0.5242839990330531D+00, & 0.2121338963165612D+00, & 0.2635821046503857D+00, & 0.2635821046503858D+00, & 0.2121338963165610D+00, & 0.5242839990330529D+00, & 0.7550197415648126D+00, & 0.0524452042229163D+00, & 0.1925350542122709D+00, & 0.1925350542122711D+00, & 0.0524452042229161D+00, & 0.7550197415648124D+00, & 0.8157685255653345D+00, & 0.0291776764327325D+00, & 0.1550537980019326D+00, & 0.1550537980019330D+00, & 0.0291776764327324D+00, & 0.8157685255653343D+00, & 0.9075107861434475D+00, & 0.0116752954894914D+00, & 0.0808139183670606D+00, & 0.0808139183670610D+00, & 0.0116752954894913D+00, & 0.9075107861434475D+00, & 0.6757077549550992D+00, & 0.1621461225224504D+00, & 0.1621461225224502D+00, & 0.9391567442455215D+00, & 0.0113529551848957D+00, & 0.0494903005695825D+00, & 0.0494903005695828D+00, & 0.0113529551848954D+00, & 0.9391567442455216D+00, & 0.3736911818051820D+00, & 0.2526176363896359D+00, & 0.3736911818051819D+00, & 0.6458926721701387D+00, & 0.0527412086548004D+00, & 0.3013661191750606D+00, & 0.3013661191750608D+00, & 0.0527412086548004D+00, & 0.6458926721701386D+00, & 0.5748974621903724D+00, & 0.2125512689048138D+00, & 0.2125512689048136D+00, & 0.8005045213785599D+00, & 0.0539363844971338D+00, & 0.1455590941243061D+00, & 0.1455590941243064D+00, & 0.0539363844971336D+00, & 0.8005045213785598D+00, & 0.9640491722702410D+00, & 0.0020268965838008D+00, & 0.0339239311459582D+00, & 0.0339239311459583D+00, & 0.0020268965838005D+00, & 0.9640491722702408D+00, & 0.4598321741495012D+00, & 0.0803356517009977D+00, & 0.4598321741495010D+00, & 0.5277054877228970D+00, & 0.0113741139787508D+00, & 0.4609203982983520D+00, & 0.4609203982983522D+00, & 0.0113741139787508D+00, & 0.5277054877228968D+00, & 0.6256296272091982D+00, & 0.1647197357980590D+00, & 0.2096506369927426D+00, & 0.2096506369927426D+00, & 0.1647197357980589D+00, & 0.6256296272091983D+00, & 0.5818958864945520D+00, & 0.0824852827778115D+00, & 0.3356188307276362D+00, & 0.3356188307276363D+00, & 0.0824852827778114D+00, & 0.5818958864945520D+00, & 0.8689356180957589D+00, & 0.0118660258094384D+00, & 0.1191983560948024D+00, & 0.1191983560948026D+00, & 0.0118660258094382D+00, & 0.8689356180957588D+00, & 0.8582596771591932D+00, & 0.0289885801232179D+00, & 0.1127517427175887D+00, & 0.1127517427175889D+00, & 0.0289885801232178D+00, & 0.8582596771591930D+00, & 0.7017862630356212D+00, & 0.0536092519706684D+00, & 0.2446044849937103D+00, & 0.2446044849937104D+00, & 0.0536092519706682D+00, & 0.7017862630356210D+00, & 0.5737048122005965D+00, & 0.1649672925863880D+00, & 0.2613278952130154D+00, & 0.2613278952130155D+00, & 0.1649672925863880D+00, & 0.5737048122005964D+00, & 0.6391563190057650D+00, & 0.0841334586353881D+00, & 0.2767102223588469D+00, & 0.2767102223588470D+00, & 0.0841334586353878D+00, & 0.6391563190057650D+00, & 0.6572241609092210D+00, & 0.0117181407852650D+00, & 0.3310576983055137D+00, & 0.3310576983055140D+00, & 0.0117181407852649D+00, & 0.6572241609092209D+00, & 0.7090088803710918D+00, & 0.1198251592753853D+00, & 0.1711659603535228D+00, & 0.1711659603535229D+00, & 0.1198251592753851D+00, & 0.7090088803710917D+00, & 0.7733534324086833D+00, & 0.0118084740509012D+00, & 0.2148380935404154D+00, & 0.2148380935404157D+00, & 0.0118084740509010D+00, & 0.7733534324086830D+00, & 0.8240691684958087D+00, & 0.0118982357159540D+00, & 0.1640325957882370D+00, & 0.1640325957882373D+00, & 0.0118982357159538D+00, & 0.8240691684958086D+00, & 0.7175528792727296D+00, & 0.0118476002079960D+00, & 0.2705995205192742D+00, & 0.2705995205192744D+00, & 0.0118476002079958D+00, & 0.7175528792727295D+00, & 0.5935890233675787D+00, & 0.0115294467270000D+00, & 0.3948815299054211D+00, & 0.3948815299054212D+00, & 0.0115294467269998D+00, & 0.5935890233675787D+00, & 0.4989185291486735D+00, & 0.0021629417026531D+00, & 0.4989185291486732D+00, & 0.9000701501104614D+00, & 0.0022497058285755D+00, & 0.0976801440609628D+00, & 0.0976801440609630D+00, & 0.0022497058285752D+00, & 0.9000701501104615D+00, & 0.5661587284043652D+00, & 0.0021780831191386D+00, & 0.4316631884764959D+00, & 0.4316631884764962D+00, & 0.0021780831191386D+00, & 0.5661587284043650D+00, & 0.8574167083299471D+00, & 0.0022594310974726D+00, & 0.1403238605725801D+00, & 0.1403238605725803D+00, & 0.0022594310974724D+00, & 0.8574167083299470D+00, & 0.7500509865021772D+00, & 0.1249745067489115D+00, & 0.1249745067489112D+00, & 0.7539541488475877D+00, & 0.0022489510449106D+00, & 0.2437969001075014D+00, & 0.2437969001075017D+00, & 0.0022489510449104D+00, & 0.7539541488475876D+00, & 0.9357952236180168D+00, & 0.0022107829440681D+00, & 0.0619939934379149D+00, & 0.0619939934379153D+00, & 0.0022107829440677D+00, & 0.9357952236180168D+00, & 0.6947995757284657D+00, & 0.0022499314295438D+00, & 0.3029504928419903D+00, & 0.3029504928419904D+00, & 0.0022499314295438D+00, & 0.6947995757284655D+00, & 0.8084698602350490D+00, & 0.0022640392620409D+00, & 0.1892661005029100D+00, & 0.1892661005029102D+00, & 0.0022640392620407D+00, & 0.8084698602350489D+00, & 0.6318674601421833D+00, & 0.0022135119210077D+00, & 0.3659190279368089D+00, & 0.3659190279368091D+00, & 0.0022135119210075D+00, & 0.6318674601421832D+00, & 0.9947898066105277D+00, & 0.0026050966947364D+00, & 0.0026050966947359D+00 /) w = (/ & 0.0043146569583335D+00, & 0.0043146569583335D+00, & 0.0043146569583335D+00, & 0.0002127820065249D+00, & 0.0002127820065249D+00, & 0.0002127820065249D+00, & 0.0002127820065249D+00, & 0.0002127820065249D+00, & 0.0002127820065249D+00, & 0.0022514827449286D+00, & 0.0022514827449286D+00, & 0.0022514827449286D+00, & 0.0022514827449286D+00, & 0.0022514827449286D+00, & 0.0022514827449286D+00, & 0.0022650701154880D+00, & 0.0022650701154880D+00, & 0.0022650701154880D+00, & 0.0022650701154880D+00, & 0.0022650701154880D+00, & 0.0022650701154880D+00, & 0.0046991712312519D+00, & 0.0046991712312519D+00, & 0.0046991712312519D+00, & 0.0014027295746802D+00, & 0.0014027295746802D+00, & 0.0014027295746802D+00, & 0.0014027295746802D+00, & 0.0014027295746802D+00, & 0.0014027295746802D+00, & 0.0000978099168127D+00, & 0.0000978099168127D+00, & 0.0000978099168127D+00, & 0.0000978099168127D+00, & 0.0000978099168127D+00, & 0.0000978099168127D+00, & 0.0004038629868035D+00, & 0.0004038629868035D+00, & 0.0004038629868035D+00, & 0.0004038629868035D+00, & 0.0004038629868035D+00, & 0.0004038629868035D+00, & 0.0012364924097053D+00, & 0.0012364924097053D+00, & 0.0012364924097053D+00, & 0.0051536553206131D+00, & 0.0051536553206131D+00, & 0.0051536553206131D+00, & 0.0051536553206131D+00, & 0.0051536553206131D+00, & 0.0051536553206131D+00, & 0.0045094710563839D+00, & 0.0045094710563839D+00, & 0.0045094710563839D+00, & 0.0045094710563839D+00, & 0.0045094710563839D+00, & 0.0045094710563839D+00, & 0.0045159973781931D+00, & 0.0045159973781931D+00, & 0.0045159973781931D+00, & 0.0019145889672060D+00, & 0.0019145889672060D+00, & 0.0019145889672060D+00, & 0.0019145889672060D+00, & 0.0019145889672060D+00, & 0.0019145889672060D+00, & 0.0026062651829993D+00, & 0.0026062651829993D+00, & 0.0026062651829993D+00, & 0.0026062651829993D+00, & 0.0026062651829993D+00, & 0.0026062651829993D+00, & 0.0029444810662743D+00, & 0.0029444810662743D+00, & 0.0029444810662743D+00, & 0.0030761572742866D+00, & 0.0030761572742866D+00, & 0.0030761572742866D+00, & 0.0030761572742866D+00, & 0.0030761572742866D+00, & 0.0030761572742866D+00, & 0.0020830024863947D+00, & 0.0020830024863947D+00, & 0.0020830024863947D+00, & 0.0010328123125119D+00, & 0.0010328123125119D+00, & 0.0010328123125119D+00, & 0.0010328123125119D+00, & 0.0010328123125119D+00, & 0.0010328123125119D+00, & 0.0043543612304128D+00, & 0.0043543612304128D+00, & 0.0043543612304128D+00, & 0.0043543612304128D+00, & 0.0043543612304128D+00, & 0.0043543612304128D+00, & 0.0033920879178230D+00, & 0.0033920879178230D+00, & 0.0033920879178230D+00, & 0.0033920879178230D+00, & 0.0033920879178230D+00, & 0.0033920879178230D+00, & 0.0045331567046035D+00, & 0.0045331567046035D+00, & 0.0045331567046035D+00, & 0.0045331567046035D+00, & 0.0045331567046035D+00, & 0.0045331567046035D+00, & 0.0053697193075647D+00, & 0.0053697193075647D+00, & 0.0053697193075647D+00, & 0.0053697193075647D+00, & 0.0053697193075647D+00, & 0.0053697193075647D+00, & 0.0050112518902677D+00, & 0.0050112518902677D+00, & 0.0050112518902677D+00, & 0.0050112518902677D+00, & 0.0050112518902677D+00, & 0.0050112518902677D+00, & 0.0006630078632668D+00, & 0.0006630078632668D+00, & 0.0006630078632668D+00, & 0.0019533942747889D+00, & 0.0019533942747889D+00, & 0.0019533942747889D+00, & 0.0019533942747889D+00, & 0.0019533942747889D+00, & 0.0019533942747889D+00, & 0.0022701532915994D+00, & 0.0022701532915994D+00, & 0.0022701532915994D+00, & 0.0022701532915994D+00, & 0.0022701532915994D+00, & 0.0022701532915994D+00, & 0.0021386729830485D+00, & 0.0021386729830485D+00, & 0.0021386729830485D+00, & 0.0021386729830485D+00, & 0.0021386729830485D+00, & 0.0021386729830485D+00, & 0.0042781341832724D+00, & 0.0042781341832724D+00, & 0.0042781341832724D+00, & 0.0042781341832724D+00, & 0.0042781341832724D+00, & 0.0042781341832724D+00, & 0.0025070193444428D+00, & 0.0025070193444428D+00, & 0.0025070193444428D+00, & 0.0025070193444428D+00, & 0.0025070193444428D+00, & 0.0025070193444428D+00, & 0.0039737311003985D+00, & 0.0039737311003985D+00, & 0.0039737311003985D+00, & 0.0039737311003985D+00, & 0.0039737311003985D+00, & 0.0039737311003985D+00, & 0.0055982544326031D+00, & 0.0055982544326031D+00, & 0.0055982544326031D+00, & 0.0047404136863378D+00, & 0.0047404136863378D+00, & 0.0047404136863378D+00, & 0.0047404136863378D+00, & 0.0047404136863378D+00, & 0.0047404136863378D+00, & 0.0031609021577845D+00, & 0.0031609021577845D+00, & 0.0031609021577845D+00, & 0.0031609021577845D+00, & 0.0031609021577845D+00, & 0.0031609021577845D+00, & 0.0013064930317837D+00, & 0.0013064930317837D+00, & 0.0013064930317837D+00, & 0.0013064930317837D+00, & 0.0013064930317837D+00, & 0.0013064930317837D+00, & 0.0024224165705941D+00, & 0.0024224165705941D+00, & 0.0024224165705941D+00, & 0.0024224165705941D+00, & 0.0024224165705941D+00, & 0.0024224165705941D+00, & 0.0045518145135699D+00, & 0.0045518145135699D+00, & 0.0045518145135699D+00, & 0.0025072813505809D+00, & 0.0025072813505809D+00, & 0.0025072813505809D+00, & 0.0041337585903884D+00, & 0.0041337585903884D+00, & 0.0041337585903884D+00, & 0.0041337585903884D+00, & 0.0041337585903884D+00, & 0.0041337585903884D+00, & 0.0051051331812112D+00, & 0.0051051331812112D+00, & 0.0051051331812112D+00, & 0.0051051331812112D+00, & 0.0051051331812112D+00, & 0.0051051331812112D+00, & 0.0026976233339834D+00, & 0.0026976233339834D+00, & 0.0026976233339834D+00, & 0.0026976233339834D+00, & 0.0026976233339834D+00, & 0.0026976233339834D+00, & 0.0018809643979073D+00, & 0.0018809643979073D+00, & 0.0018809643979073D+00, & 0.0018809643979073D+00, & 0.0018809643979073D+00, & 0.0018809643979073D+00, & 0.0009142190102743D+00, & 0.0009142190102743D+00, & 0.0009142190102743D+00, & 0.0009142190102743D+00, & 0.0009142190102743D+00, & 0.0009142190102743D+00, & 0.0040644299258672D+00, & 0.0040644299258672D+00, & 0.0040644299258672D+00, & 0.0007010656028691D+00, & 0.0007010656028691D+00, & 0.0007010656028691D+00, & 0.0007010656028691D+00, & 0.0007010656028691D+00, & 0.0007010656028691D+00, & 0.0055051135413514D+00, & 0.0055051135413514D+00, & 0.0055051135413514D+00, & 0.0031901056487151D+00, & 0.0031901056487151D+00, & 0.0031901056487151D+00, & 0.0031901056487151D+00, & 0.0031901056487151D+00, & 0.0031901056487151D+00, & 0.0049446615998697D+00, & 0.0049446615998697D+00, & 0.0049446615998697D+00, & 0.0024338258411055D+00, & 0.0024338258411055D+00, & 0.0024338258411055D+00, & 0.0024338258411055D+00, & 0.0024338258411055D+00, & 0.0024338258411055D+00, & 0.0002508474514575D+00, & 0.0002508474514575D+00, & 0.0002508474514575D+00, & 0.0002508474514575D+00, & 0.0002508474514575D+00, & 0.0002508474514575D+00, & 0.0040657898075942D+00, & 0.0040657898075942D+00, & 0.0040657898075942D+00, & 0.0017108131277605D+00, & 0.0017108131277605D+00, & 0.0017108131277605D+00, & 0.0017108131277605D+00, & 0.0017108131277605D+00, & 0.0017108131277605D+00, & 0.0045280121334294D+00, & 0.0045280121334294D+00, & 0.0045280121334294D+00, & 0.0045280121334294D+00, & 0.0045280121334294D+00, & 0.0045280121334294D+00, & 0.0040081392301490D+00, & 0.0040081392301490D+00, & 0.0040081392301490D+00, & 0.0040081392301490D+00, & 0.0040081392301490D+00, & 0.0040081392301490D+00, & 0.0011195403999073D+00, & 0.0011195403999073D+00, & 0.0011195403999073D+00, & 0.0011195403999073D+00, & 0.0011195403999073D+00, & 0.0011195403999073D+00, & 0.0016556490812277D+00, & 0.0016556490812277D+00, & 0.0016556490812277D+00, & 0.0016556490812277D+00, & 0.0016556490812277D+00, & 0.0016556490812277D+00, & 0.0030745572112736D+00, & 0.0030745572112736D+00, & 0.0030745572112736D+00, & 0.0030745572112736D+00, & 0.0030745572112736D+00, & 0.0030745572112736D+00, & 0.0048300704241971D+00, & 0.0048300704241971D+00, & 0.0048300704241971D+00, & 0.0048300704241971D+00, & 0.0048300704241971D+00, & 0.0048300704241971D+00, & 0.0038986974038214D+00, & 0.0038986974038214D+00, & 0.0038986974038214D+00, & 0.0038986974038214D+00, & 0.0038986974038214D+00, & 0.0038986974038214D+00, & 0.0016458519911547D+00, & 0.0016458519911547D+00, & 0.0016458519911547D+00, & 0.0016458519911547D+00, & 0.0016458519911547D+00, & 0.0016458519911547D+00, & 0.0037119048709275D+00, & 0.0037119048709275D+00, & 0.0037119048709275D+00, & 0.0037119048709275D+00, & 0.0037119048709275D+00, & 0.0037119048709275D+00, & 0.0014185756078616D+00, & 0.0014185756078616D+00, & 0.0014185756078616D+00, & 0.0014185756078616D+00, & 0.0014185756078616D+00, & 0.0014185756078616D+00, & 0.0012890581955709D+00, & 0.0012890581955709D+00, & 0.0012890581955709D+00, & 0.0012890581955709D+00, & 0.0012890581955709D+00, & 0.0012890581955709D+00, & 0.0015614900549058D+00, & 0.0015614900549058D+00, & 0.0015614900549058D+00, & 0.0015614900549058D+00, & 0.0015614900549058D+00, & 0.0015614900549058D+00, & 0.0016952718909460D+00, & 0.0016952718909460D+00, & 0.0016952718909460D+00, & 0.0016952718909460D+00, & 0.0016952718909460D+00, & 0.0016952718909460D+00, & 0.0007488308612040D+00, & 0.0007488308612040D+00, & 0.0007488308612040D+00, & 0.0004528022725679D+00, & 0.0004528022725679D+00, & 0.0004528022725679D+00, & 0.0004528022725679D+00, & 0.0004528022725679D+00, & 0.0004528022725679D+00, & 0.0007453398310664D+00, & 0.0007453398310664D+00, & 0.0007453398310664D+00, & 0.0007453398310664D+00, & 0.0007453398310664D+00, & 0.0007453398310664D+00, & 0.0005323481472587D+00, & 0.0005323481472587D+00, & 0.0005323481472587D+00, & 0.0005323481472587D+00, & 0.0005323481472587D+00, & 0.0005323481472587D+00, & 0.0036321398556638D+00, & 0.0036321398556638D+00, & 0.0036321398556638D+00, & 0.0006576196836264D+00, & 0.0006576196836264D+00, & 0.0006576196836264D+00, & 0.0006576196836264D+00, & 0.0006576196836264D+00, & 0.0006576196836264D+00, & 0.0003620690511307D+00, & 0.0003620690511307D+00, & 0.0003620690511307D+00, & 0.0003620690511307D+00, & 0.0003620690511307D+00, & 0.0003620690511307D+00, & 0.0007060119456705D+00, & 0.0007060119456705D+00, & 0.0007060119456705D+00, & 0.0007060119456705D+00, & 0.0007060119456705D+00, & 0.0007060119456705D+00, & 0.0006018771022200D+00, & 0.0006018771022200D+00, & 0.0006018771022200D+00, & 0.0006018771022200D+00, & 0.0006018771022200D+00, & 0.0006018771022200D+00, & 0.0007326393465497D+00, & 0.0007326393465497D+00, & 0.0007326393465497D+00, & 0.0007326393465497D+00, & 0.0007326393465497D+00, & 0.0007326393465497D+00, & 0.0000892536614181D+00, & 0.0000892536614181D+00, & 0.0000892536614181D+00 /) return end subroutine rule48 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule48() returns the rule of precision 48. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.3477244587108094D+00, & 0.3477244587108095D+00, & 0.3045510825783810D+00, & 0.3695672915901662D+00, & 0.4147320642402169D+00, & 0.2157006441696168D+00, & 0.4147320642402170D+00, & 0.3695672915901662D+00, & 0.2157006441696168D+00, & 0.3084818979933622D+00, & 0.5832166020846338D+00, & 0.1083014999220039D+00, & 0.5832166020846338D+00, & 0.3084818979933622D+00, & 0.1083014999220039D+00, & 0.3196427292245513D+00, & 0.6456613180043123D+00, & 0.0346959527711365D+00, & 0.6456613180043123D+00, & 0.3196427292245514D+00, & 0.0346959527711363D+00, & 0.3734312712553221D+00, & 0.3734312712553221D+00, & 0.2531374574893558D+00, & 0.9962559654771519D+00, & 0.0023979705918987D+00, & 0.0013460639309493D+00, & 0.0023979705918986D+00, & 0.9962559654771519D+00, & 0.0013460639309497D+00, & 0.3280848178088313D+00, & 0.6527443981108471D+00, & 0.0191707840803216D+00, & 0.6527443981108471D+00, & 0.3280848178088314D+00, & 0.0191707840803215D+00, & 0.3198129082727195D+00, & 0.4038255264164708D+00, & 0.2763615653108096D+00, & 0.4038255264164707D+00, & 0.3198129082727195D+00, & 0.2763615653108096D+00, & 0.1589266013618200D+00, & 0.8394322302943624D+00, & 0.0016411683438175D+00, & 0.8394322302943625D+00, & 0.1589266013618200D+00, & 0.0016411683438173D+00, & 0.1962759771972356D+00, & 0.7504008293814409D+00, & 0.0533231934213236D+00, & 0.7504008293814409D+00, & 0.1962759771972357D+00, & 0.0533231934213233D+00, & 0.4893390535628532D+00, & 0.4893390535628532D+00, & 0.0213218928742936D+00, & 0.2933421845901817D+00, & 0.6237289790086799D+00, & 0.0829288364011385D+00, & 0.6237289790086799D+00, & 0.2933421845901818D+00, & 0.0829288364011382D+00, & 0.0484109248251399D+00, & 0.9031781503497199D+00, & 0.0484109248251403D+00, & 0.0801595487479756D+00, & 0.8396809025040485D+00, & 0.0801595487479760D+00, & 0.1247273258813976D+00, & 0.8519536569694208D+00, & 0.0233190171491816D+00, & 0.8519536569694209D+00, & 0.1247273258813976D+00, & 0.0233190171491812D+00, & 0.3115932459432796D+00, & 0.5496936600973348D+00, & 0.1387130939593856D+00, & 0.5496936600973348D+00, & 0.3115932459432795D+00, & 0.1387130939593854D+00, & 0.4790902659592135D+00, & 0.4790902659592136D+00, & 0.0418194680815729D+00, & 0.4666424153484346D+00, & 0.4666424153484346D+00, & 0.0667151693031307D+00, & 0.1105414410318808D+00, & 0.8789179195599967D+00, & 0.0105406394081227D+00, & 0.8789179195599968D+00, & 0.1105414410318809D+00, & 0.0105406394081222D+00, & 0.2974171962759172D+00, & 0.6922355531565748D+00, & 0.0103472505675080D+00, & 0.6922355531565748D+00, & 0.2974171962759173D+00, & 0.0103472505675078D+00, & 0.2940680586522785D+00, & 0.6521500596889448D+00, & 0.0537818816587767D+00, & 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0.2088908643844065D+00, & 0.1643344616867154D+00, & 0.6267746739288779D+00, & 0.7839057415153878D+00, & 0.1080471292423063D+00, & 0.1080471292423058D+00, & 0.6227789405605143D+00, & 0.1238874588376768D+00, & 0.2533336006018087D+00, & 0.2533336006018090D+00, & 0.1238874588376765D+00, & 0.6227789405605142D+00, & 0.4971756372384660D+00, & 0.0056487255230678D+00, & 0.4971756372384659D+00, & 0.5360438668640494D+00, & 0.0001600103893843D+00, & 0.4637961227465662D+00, & 0.4637961227465663D+00, & 0.0001600103893842D+00, & 0.5360438668640493D+00, & 0.6161736917477099D+00, & 0.0001085092017437D+00, & 0.3837177990505463D+00, & 0.3837177990505465D+00, & 0.0001085092017435D+00, & 0.6161736917477098D+00 /) w = (/ & 0.0043651387537827D+00, & 0.0043651387537827D+00, & 0.0043651387537827D+00, & 0.0037199314122967D+00, & 0.0037199314122967D+00, & 0.0037199314122967D+00, & 0.0037199314122967D+00, & 0.0037199314122967D+00, & 0.0037199314122967D+00, & 0.0030326109445702D+00, & 0.0030326109445702D+00, & 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0.0004233009914606D+00, & 0.0004233009914606D+00, & 0.0004233009914606D+00, & 0.0004233009914606D+00, & 0.0010664611871638D+00, & 0.0010664611871638D+00, & 0.0010664611871638D+00, & 0.0010664611871638D+00, & 0.0010664611871638D+00, & 0.0010664611871638D+00, & 0.0013824010733117D+00, & 0.0013824010733117D+00, & 0.0013824010733117D+00, & 0.0013824010733117D+00, & 0.0013824010733117D+00, & 0.0013824010733117D+00, & 0.0036585117930270D+00, & 0.0036585117930270D+00, & 0.0036585117930270D+00, & 0.0036585117930270D+00, & 0.0036585117930270D+00, & 0.0036585117930270D+00, & 0.0052100048548666D+00, & 0.0052100048548666D+00, & 0.0052100048548666D+00, & 0.0052100048548666D+00, & 0.0052100048548666D+00, & 0.0052100048548666D+00, & 0.0002073105605908D+00, & 0.0002073105605908D+00, & 0.0002073105605908D+00, & 0.0002073105605908D+00, & 0.0002073105605908D+00, & 0.0002073105605908D+00, & 0.0019583162868632D+00, & 0.0019583162868632D+00, & 0.0019583162868632D+00, & 0.0019583162868632D+00, & 0.0019583162868632D+00, & 0.0019583162868632D+00, & 0.0032089225299188D+00, & 0.0032089225299188D+00, & 0.0032089225299188D+00, & 0.0032089225299188D+00, & 0.0032089225299188D+00, & 0.0032089225299188D+00, & 0.0003144151546132D+00, & 0.0003144151546132D+00, & 0.0003144151546132D+00, & 0.0003144151546132D+00, & 0.0003144151546132D+00, & 0.0003144151546132D+00, & 0.0010785145551204D+00, & 0.0010785145551204D+00, & 0.0010785145551204D+00, & 0.0010785145551204D+00, & 0.0010785145551204D+00, & 0.0010785145551204D+00, & 0.0036004269766152D+00, & 0.0036004269766152D+00, & 0.0036004269766152D+00, & 0.0036004269766152D+00, & 0.0036004269766152D+00, & 0.0036004269766152D+00, & 0.0036611914178426D+00, & 0.0036611914178426D+00, & 0.0036611914178426D+00, & 0.0036611914178426D+00, & 0.0036611914178426D+00, & 0.0036611914178426D+00, & 0.0021617123138751D+00, & 0.0021617123138751D+00, & 0.0021617123138751D+00, & 0.0021617123138751D+00, & 0.0021617123138751D+00, & 0.0021617123138751D+00, & 0.0018010562763862D+00, & 0.0018010562763862D+00, & 0.0018010562763862D+00, & 0.0018010562763862D+00, & 0.0018010562763862D+00, & 0.0018010562763862D+00, & 0.0054475592942759D+00, & 0.0054475592942759D+00, & 0.0054475592942759D+00, & 0.0054475592942759D+00, & 0.0054475592942759D+00, & 0.0054475592942759D+00, & 0.0051525605444838D+00, & 0.0051525605444838D+00, & 0.0051525605444838D+00, & 0.0001397852015244D+00, & 0.0001397852015244D+00, & 0.0001397852015244D+00, & 0.0001397852015244D+00, & 0.0001397852015244D+00, & 0.0001397852015244D+00, & 0.0049930051499418D+00, & 0.0049930051499418D+00, & 0.0049930051499418D+00, & 0.0011962011851953D+00, & 0.0011962011851953D+00, & 0.0011962011851953D+00, & 0.0011962011851953D+00, & 0.0011962011851953D+00, & 0.0011962011851953D+00, & 0.0049525658235836D+00, & 0.0049525658235836D+00, & 0.0049525658235836D+00, & 0.0049525658235836D+00, & 0.0049525658235836D+00, & 0.0049525658235836D+00, & 0.0042434984918542D+00, & 0.0042434984918542D+00, & 0.0042434984918542D+00, & 0.0008876005610246D+00, & 0.0008876005610246D+00, & 0.0008876005610246D+00, & 0.0050552058738964D+00, & 0.0050552058738964D+00, & 0.0050552058738964D+00, & 0.0050552058738964D+00, & 0.0050552058738964D+00, & 0.0050552058738964D+00, & 0.0006055910618992D+00, & 0.0006055910618992D+00, & 0.0006055910618992D+00, & 0.0006055910618992D+00, & 0.0006055910618992D+00, & 0.0006055910618992D+00, & 0.0053577902109237D+00, & 0.0053577902109237D+00, & 0.0053577902109237D+00, & 0.0053577902109237D+00, & 0.0053577902109237D+00, & 0.0053577902109237D+00, & 0.0023655352245003D+00, & 0.0023655352245003D+00, & 0.0023655352245003D+00, & 0.0023655352245003D+00, & 0.0023655352245003D+00, & 0.0023655352245003D+00, & 0.0006361760556450D+00, & 0.0006361760556450D+00, & 0.0006361760556450D+00, & 0.0006361760556450D+00, & 0.0006361760556450D+00, & 0.0006361760556450D+00, & 0.0041167794317584D+00, & 0.0041167794317584D+00, & 0.0041167794317584D+00, & 0.0041167794317584D+00, & 0.0041167794317584D+00, & 0.0041167794317584D+00, & 0.0047435661701725D+00, & 0.0047435661701725D+00, & 0.0047435661701725D+00, & 0.0047435661701725D+00, & 0.0047435661701725D+00, & 0.0047435661701725D+00, & 0.0031739283489719D+00, & 0.0031739283489719D+00, & 0.0031739283489719D+00, & 0.0046022674251482D+00, & 0.0046022674251482D+00, & 0.0046022674251482D+00, & 0.0046022674251482D+00, & 0.0046022674251482D+00, & 0.0046022674251482D+00, & 0.0012950799113896D+00, & 0.0012950799113896D+00, & 0.0012950799113896D+00, & 0.0002350089224806D+00, & 0.0002350089224806D+00, & 0.0002350089224806D+00, & 0.0002350089224806D+00, & 0.0002350089224806D+00, & 0.0002350089224806D+00, & 0.0002398736789311D+00, & 0.0002398736789311D+00, & 0.0002398736789311D+00, & 0.0002398736789311D+00, & 0.0002398736789311D+00, & 0.0002398736789311D+00 /) return end subroutine rule49 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule49() returns the rule of precision 49. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.1747098543071731D+00, & 0.7852819906358907D+00, & 0.0400081550569363D+00, & 0.7852819906358907D+00, & 0.1747098543071732D+00, & 0.0400081550569361D+00, & 0.3869650571638262D+00, & 0.6043725256047221D+00, & 0.0086624172314518D+00, & 0.6043725256047220D+00, & 0.3869650571638262D+00, & 0.0086624172314517D+00, & 0.1260609334354054D+00, & 0.8726379574162407D+00, & 0.0013011091483540D+00, & 0.8726379574162407D+00, & 0.1260609334354055D+00, & 0.0013011091483536D+00, & 0.1783730162296315D+00, & 0.6432539675407367D+00, & 0.1783730162296319D+00, & 0.2839249520005005D+00, & 0.4704465426211537D+00, & 0.2456285053783458D+00, & 0.4704465426211537D+00, & 0.2839249520005004D+00, & 0.2456285053783457D+00, & 0.3302482693344623D+00, & 0.4190100944919284D+00, & 0.2507416361736092D+00, & 0.4190100944919285D+00, & 0.3302482693344623D+00, & 0.2507416361736091D+00, & 0.0728406536060113D+00, & 0.8543186927879770D+00, & 0.0728406536060117D+00, & 0.2560459410681578D+00, & 0.7424443214379617D+00, & 0.0015097374938804D+00, & 0.7424443214379618D+00, & 0.2560459410681578D+00, & 0.0015097374938802D+00, & 0.2603953161344762D+00, & 0.6306213036525985D+00, & 0.1089833802129252D+00, & 0.6306213036525986D+00, & 0.2603953161344763D+00, & 0.1089833802129251D+00, & 0.4289883556394070D+00, & 0.4289883556394070D+00, & 0.1420232887211859D+00, & 0.1707126963793420D+00, & 0.7273185867118819D+00, & 0.1019687169087761D+00, & 0.7273185867118819D+00, & 0.1707126963793419D+00, & 0.1019687169087760D+00, & 0.3746440580951249D+00, & 0.6055836533300153D+00, & 0.0197722885748599D+00, & 0.6055836533300152D+00, & 0.3746440580951250D+00, & 0.0197722885748598D+00, & 0.4351684572939831D+00, & 0.5634773574179233D+00, & 0.0013541852880936D+00, & 0.5634773574179233D+00, & 0.4351684572939831D+00, & 0.0013541852880936D+00, & 0.1390923912291039D+00, & 0.7732647562548985D+00, & 0.0876428525159975D+00, & 0.7732647562548985D+00, & 0.1390923912291041D+00, & 0.0876428525159973D+00, & 0.2801506543012279D+00, & 0.6414337667335724D+00, & 0.0784155789651995D+00, & 0.6414337667335726D+00, & 0.2801506543012280D+00, & 0.0784155789651994D+00, & 0.3463311874275595D+00, & 0.5909210399343486D+00, & 0.0627477726380918D+00, & 0.5909210399343486D+00, & 0.3463311874275596D+00, & 0.0627477726380916D+00, & 0.3811688378455703D+00, & 0.3811688378455702D+00, & 0.2376623243088594D+00, & 0.1142447933587818D+00, & 0.8786494761873791D+00, & 0.0071057304538392D+00, & 0.8786494761873791D+00, & 0.1142447933587818D+00, & 0.0071057304538389D+00, & 0.2601477827144039D+00, & 0.6989617430573259D+00, & 0.0408904742282701D+00, & 0.6989617430573259D+00, & 0.2601477827144039D+00, & 0.0408904742282700D+00, & 0.3385954503697221D+00, & 0.6289096666027175D+00, & 0.0324948830275603D+00, & 0.6289096666027175D+00, & 0.3385954503697222D+00, & 0.0324948830275602D+00, & 0.4405249471606921D+00, & 0.5507460085493718D+00, & 0.0087290442899361D+00, & 0.5507460085493717D+00, & 0.4405249471606921D+00, & 0.0087290442899361D+00, & 0.0857234837407636D+00, & 0.9127017575952171D+00, & 0.0015747586640192D+00, & 0.9127017575952172D+00, & 0.0857234837407637D+00, & 0.0015747586640189D+00, & 0.2007383675971185D+00, & 0.5985232648057627D+00, & 0.2007383675971187D+00, & 0.2859840866397785D+00, & 0.5124837078245130D+00, & 0.2015322055357083D+00, & 0.5124837078245130D+00, & 0.2859840866397785D+00, & 0.2015322055357083D+00, & 0.3022430648527080D+00, & 0.6463387716329330D+00, & 0.0514181635143590D+00, & 0.6463387716329331D+00, & 0.3022430648527081D+00, & 0.0514181635143589D+00, & 0.1145574257288858D+00, & 0.8664138254475557D+00, & 0.0190287488235586D+00, & 0.8664138254475557D+00, & 0.1145574257288858D+00, & 0.0190287488235582D+00, & 0.2122964300195307D+00, & 0.7469155107726292D+00, & 0.0407880592078402D+00, & 0.7469155107726291D+00, & 0.2122964300195309D+00, & 0.0407880592078400D+00, & 0.0462782231758691D+00, & 0.9074435536482615D+00, & 0.0462782231758695D+00, & 0.2971430888632479D+00, & 0.4057138222735041D+00, & 0.2971430888632479D+00, & 0.1465284297099020D+00, & 0.8249569583935215D+00, & 0.0285146118965767D+00, & 0.8249569583935213D+00, & 0.1465284297099020D+00, & 0.0285146118965764D+00, & 0.3740816461088270D+00, & 0.4722096952795328D+00, & 0.1537086586116402D+00, & 0.4722096952795327D+00, & 0.3740816461088270D+00, & 0.1537086586116402D+00, & 0.0817068303997551D+00, & 0.8936878492161561D+00, & 0.0246053203840890D+00, & 0.8936878492161561D+00, & 0.0817068303997551D+00, & 0.0246053203840887D+00, & 0.0108421217690070D+00, & 0.9783157564619855D+00, & 0.0108421217690075D+00, & 0.2941474788808447D+00, & 0.6823170191891728D+00, & 0.0235355019299825D+00, & 0.6823170191891728D+00, & 0.2941474788808447D+00, & 0.0235355019299824D+00, & 0.1750703694826515D+00, & 0.6872129092572276D+00, & 0.1377167212601208D+00, & 0.6872129092572277D+00, & 0.1750703694826515D+00, & 0.1377167212601206D+00, & 0.1028533816631290D+00, & 0.7942932366737417D+00, & 0.1028533816631293D+00, & 0.0476205378057730D+00, & 0.9414041521049951D+00, & 0.0109753100892320D+00, & 0.9414041521049952D+00, & 0.0476205378057731D+00, & 0.0109753100892315D+00, & 0.3175724815133269D+00, & 0.5219618612839483D+00, & 0.1604656572027248D+00, & 0.5219618612839483D+00, & 0.3175724815133269D+00, & 0.1604656572027247D+00, & 0.2881380539950774D+00, & 0.5789126782672228D+00, & 0.1329492677376997D+00, & 0.5789126782672228D+00, & 0.2881380539950775D+00, & 0.1329492677376996D+00, & 0.2679708893032962D+00, & 0.7232741594653924D+00, & 0.0087549512313114D+00, & 0.7232741594653924D+00, & 0.2679708893032962D+00, & 0.0087549512313113D+00, & 0.4841735634166949D+00, & 0.4841735634166949D+00, & 0.0316528731666102D+00, & 0.2393790592030269D+00, & 0.7398771788136165D+00, & 0.0207437619833566D+00, & 0.7398771788136166D+00, & 0.2393790592030269D+00, & 0.0207437619833564D+00, & 0.1918532715697031D+00, & 0.7883864387462218D+00, & 0.0197602896840751D+00, & 0.7883864387462219D+00, & 0.1918532715697031D+00, & 0.0197602896840748D+00, & 0.3873242425341850D+00, & 0.5697364716889479D+00, & 0.0429392857768670D+00, & 0.5697364716889479D+00, & 0.3873242425341850D+00, & 0.0429392857768670D+00, & 0.3535324158284108D+00, & 0.5285751660132987D+00, & 0.1178924181582904D+00, & 0.5285751660132987D+00, & 0.3535324158284108D+00, & 0.1178924181582903D+00, & 0.0521774890148561D+00, & 0.9224477815225601D+00, & 0.0253747294625839D+00, & 0.9224477815225601D+00, & 0.0521774890148562D+00, & 0.0253747294625835D+00, & 0.3237021161513139D+00, & 0.5827685017638400D+00, & 0.0935293820848460D+00, & 0.5827685017638401D+00, & 0.3237021161513140D+00, & 0.0935293820848459D+00, & 0.3720593606748486D+00, & 0.6259535358370784D+00, & 0.0019871034880730D+00, & 0.6259535358370782D+00, & 0.3720593606748486D+00, & 0.0019871034880730D+00, & 0.4136925346071049D+00, & 0.4776172690993892D+00, & 0.1086901962935059D+00, & 0.4776172690993891D+00, & 0.4136925346071050D+00, & 0.1086901962935058D+00, & 0.2508654436414371D+00, & 0.5742322222075992D+00, & 0.1749023341509636D+00, & 0.5742322222075992D+00, & 0.2508654436414372D+00, & 0.1749023341509635D+00, & 0.2368477035387836D+00, & 0.6961863830895678D+00, & 0.0669659133716486D+00, & 0.6961863830895679D+00, & 0.2368477035387836D+00, & 0.0669659133716483D+00, & 0.1099576830426482D+00, & 0.8490631831866196D+00, & 0.0409791337707323D+00, & 0.8490631831866197D+00, & 0.1099576830426484D+00, & 0.0409791337707320D+00, & 0.4297319028951815D+00, & 0.5458016820289727D+00, & 0.0244664150758457D+00, & 0.5458016820289727D+00, & 0.4297319028951816D+00, & 0.0244664150758457D+00, & 0.1437680374333725D+00, & 0.7995438742256191D+00, & 0.0566880883410085D+00, & 0.7995438742256191D+00, & 0.1437680374333726D+00, & 0.0566880883410082D+00, & 0.0774106779986908D+00, & 0.9129368386397628D+00, & 0.0096524833615466D+00, & 0.9129368386397629D+00, & 0.0774106779986908D+00, & 0.0096524833615462D+00, & 0.1557060056653469D+00, & 0.8331944267073318D+00, & 0.0110995676273212D+00, & 0.8331944267073320D+00, & 0.1557060056653469D+00, & 0.0110995676273209D+00, & 0.3128533024496512D+00, & 0.6851726257624122D+00, & 0.0019740717879365D+00, & 0.6851726257624123D+00, & 0.3128533024496513D+00, & 0.0019740717879363D+00, & 0.0260902661381798D+00, & 0.9628508665812467D+00, & 0.0110588672805734D+00, & 0.9628508665812469D+00, & 0.0260902661381799D+00, & 0.0110588672805730D+00, & 0.1656728608179916D+00, & 0.8318645947596423D+00, & 0.0024625444223663D+00, & 0.8318645947596421D+00, & 0.1656728608179916D+00, & 0.0024625444223660D+00, & 0.4932611955660527D+00, & 0.4932611955660527D+00, & 0.0134776088678945D+00, & 0.0742257546763114D+00, & 0.8793792323410512D+00, & 0.0463950129826375D+00, & 0.8793792323410513D+00, & 0.0742257546763114D+00, & 0.0463950129826371D+00, & 0.0288339172370140D+00, & 0.9690874828381117D+00, & 0.0020785999248743D+00, & 0.9690874828381117D+00, & 0.0288339172370142D+00, & 0.0020785999248739D+00, & 0.1868226606723151D+00, & 0.7448240425293629D+00, & 0.0683532967983221D+00, & 0.7448240425293629D+00, & 0.1868226606723152D+00, & 0.0683532967983218D+00, & 0.3270839281856873D+00, & 0.6622397675113322D+00, & 0.0106763043029805D+00, & 0.6622397675113322D+00, & 0.3270839281856875D+00, & 0.0106763043029803D+00, & 0.1038911034338268D+00, & 0.8269396131025599D+00, & 0.0691692834636134D+00, & 0.8269396131025599D+00, & 0.1038911034338268D+00, & 0.0691692834636131D+00, & 0.2155342882429546D+00, & 0.6837969023224015D+00, & 0.1006688094346437D+00, & 0.6837969023224016D+00, & 0.2155342882429546D+00, & 0.1006688094346435D+00, & 0.4057324719755224D+00, & 0.4057324719755224D+00, & 0.1885350560489550D+00, & 0.3431516130273899D+00, & 0.4556304494441659D+00, & 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0.0691692834636133D+00, & 0.1038911034338268D+00, & 0.8269396131025600D+00, & 0.0691692834636133D+00, & 0.8269396131025600D+00, & 0.1038911034338271D+00, & 0.1006688094346437D+00, & 0.2155342882429546D+00, & 0.6837969023224019D+00, & 0.1006688094346437D+00, & 0.6837969023224019D+00, & 0.2155342882429548D+00, & 0.1885350560489551D+00, & 0.4057324719755226D+00, & 0.4057324719755226D+00, & 0.2012179375284443D+00, & 0.3431516130273900D+00, & 0.4556304494441660D+00, & 0.2012179375284443D+00, & 0.4556304494441659D+00, & 0.3431516130273902D+00, & 0.1434532484926369D+00, & 0.2224087587233255D+00, & 0.6341379927840379D+00, & 0.1434532484926369D+00, & 0.6341379927840379D+00, & 0.2224087587233256D+00, & 0.0021251605376943D+00, & 0.0534809769143942D+00, & 0.9443938625479115D+00, & 0.0021251605376943D+00, & 0.9443938625479115D+00, & 0.0534809769143946D+00, & 0.1304216449251317D+00, & 0.1304216449251314D+00, & 0.7391567101497369D+00, & 0.0514225024494020D+00, & 0.4387889688450270D+00, & 0.5097885287055712D+00, & 0.0514225024494020D+00, & 0.5097885287055710D+00, & 0.4387889688450272D+00, & 0.0771303887394075D+00, & 0.4614348056302963D+00, & 0.4614348056302964D+00, & 0.0275739602431115D+00, & 0.0275739602431112D+00, & 0.9448520795137775D+00, & 0.2318424453754741D+00, & 0.2318424453754740D+00, & 0.5363151092490521D+00, & 0.2965564467444571D+00, & 0.3517217766277715D+00, & 0.3517217766277716D+00, & 0.0022124213099821D+00, & 0.0022124213099817D+00, & 0.9955751573800363D+00, & 0.0781526329255783D+00, & 0.3919321013755560D+00, & 0.5299152656988662D+00, & 0.0781526329255783D+00, & 0.5299152656988660D+00, & 0.3919321013755561D+00, & 0.0064969244459218D+00, & 0.2110821798970346D+00, & 0.7824208956570438D+00, & 0.0064969244459218D+00, & 0.7824208956570438D+00, & 0.2110821798970349D+00, & 0.0020903064191529D+00, & 0.0117098573109518D+00, & 0.9861998362698955D+00, & 0.0020903064191529D+00, & 0.9861998362698955D+00, & 0.0117098573109521D+00, & 0.0024208706169743D+00, & 0.4987895646915129D+00, & 0.4987895646915131D+00, & 0.0001398635181475D+00, & 0.2063833537599899D+00, & 0.7934767827218628D+00, & 0.0001398635181475D+00, & 0.7934767827218628D+00, & 0.2063833537599901D+00 /) c = (/ & 0.7852819906358905D+00, & 0.0400081550569363D+00, & 0.1747098543071729D+00, & 0.1747098543071730D+00, & 0.0400081550569361D+00, & 0.7852819906358905D+00, & 0.6043725256047220D+00, & 0.0086624172314517D+00, & 0.3869650571638260D+00, & 0.3869650571638262D+00, & 0.0086624172314517D+00, & 0.6043725256047218D+00, & 0.8726379574162407D+00, & 0.0013011091483539D+00, & 0.1260609334354051D+00, & 0.1260609334354054D+00, & 0.0013011091483537D+00, & 0.8726379574162407D+00, & 0.6432539675407367D+00, & 0.1783730162296317D+00, & 0.1783730162296314D+00, & 0.4704465426211537D+00, & 0.2456285053783457D+00, & 0.2839249520005004D+00, & 0.2839249520005004D+00, & 0.2456285053783457D+00, & 0.4704465426211537D+00, & 0.4190100944919284D+00, & 0.2507416361736092D+00, & 0.3302482693344622D+00, & 0.3302482693344622D+00, & 0.2507416361736092D+00, & 0.4190100944919284D+00, & 0.8543186927879770D+00, & 0.0728406536060116D+00, & 0.0728406536060112D+00, & 0.7424443214379618D+00, & 0.0015097374938805D+00, & 0.2560459410681576D+00, & 0.2560459410681578D+00, & 0.0015097374938803D+00, & 0.7424443214379617D+00, & 0.6306213036525986D+00, & 0.1089833802129253D+00, & 0.2603953161344761D+00, & 0.2603953161344762D+00, & 0.1089833802129251D+00, & 0.6306213036525985D+00, & 0.4289883556394071D+00, & 0.1420232887211860D+00, & 0.4289883556394070D+00, & 0.7273185867118819D+00, & 0.1019687169087761D+00, & 0.1707126963793417D+00, & 0.1707126963793420D+00, & 0.1019687169087760D+00, & 0.7273185867118818D+00, & 0.6055836533300152D+00, & 0.0197722885748597D+00, & 0.3746440580951246D+00, & 0.3746440580951249D+00, & 0.0197722885748598D+00, & 0.6055836533300151D+00, & 0.5634773574179232D+00, & 0.0013541852880936D+00, & 0.4351684572939829D+00, & 0.4351684572939831D+00, & 0.0013541852880936D+00, & 0.5634773574179230D+00, & 0.7732647562548985D+00, & 0.0876428525159975D+00, & 0.1390923912291037D+00, & 0.1390923912291040D+00, & 0.0876428525159972D+00, & 0.7732647562548985D+00, & 0.6414337667335724D+00, & 0.0784155789651995D+00, & 0.2801506543012278D+00, & 0.2801506543012279D+00, & 0.0784155789651994D+00, & 0.6414337667335724D+00, & 0.5909210399343487D+00, & 0.0627477726380918D+00, & 0.3463311874275593D+00, & 0.3463311874275596D+00, & 0.0627477726380915D+00, & 0.5909210399343485D+00, & 0.3811688378455703D+00, & 0.2376623243088594D+00, & 0.3811688378455702D+00, & 0.8786494761873791D+00, & 0.0071057304538391D+00, & 0.1142447933587816D+00, & 0.1142447933587818D+00, & 0.0071057304538390D+00, & 0.8786494761873790D+00, & 0.6989617430573259D+00, & 0.0408904742282701D+00, & 0.2601477827144038D+00, & 0.2601477827144039D+00, & 0.0408904742282700D+00, & 0.6989617430573258D+00, & 0.6289096666027175D+00, & 0.0324948830275603D+00, & 0.3385954503697218D+00, & 0.3385954503697221D+00, & 0.0324948830275603D+00, & 0.6289096666027174D+00, & 0.5507460085493718D+00, & 0.0087290442899360D+00, & 0.4405249471606919D+00, & 0.4405249471606921D+00, & 0.0087290442899360D+00, & 0.5507460085493715D+00, & 0.9127017575952171D+00, & 0.0015747586640193D+00, & 0.0857234837407633D+00, & 0.0857234837407636D+00, & 0.0015747586640189D+00, & 0.9127017575952171D+00, & 0.5985232648057627D+00, & 0.2007383675971187D+00, & 0.2007383675971185D+00, & 0.5124837078245131D+00, & 0.2015322055357084D+00, & 0.2859840866397785D+00, & 0.2859840866397786D+00, & 0.2015322055357083D+00, & 0.5124837078245130D+00, & 0.6463387716329331D+00, & 0.0514181635143590D+00, & 0.3022430648527078D+00, & 0.3022430648527079D+00, & 0.0514181635143588D+00, & 0.6463387716329327D+00, & 0.8664138254475557D+00, & 0.0190287488235584D+00, & 0.1145574257288857D+00, & 0.1145574257288858D+00, & 0.0190287488235582D+00, & 0.8664138254475556D+00, & 0.7469155107726292D+00, & 0.0407880592078401D+00, & 0.2122964300195305D+00, & 0.2122964300195307D+00, & 0.0407880592078399D+00, & 0.7469155107726290D+00, & 0.9074435536482616D+00, & 0.0462782231758695D+00, & 0.0462782231758688D+00, & 0.4057138222735040D+00, & 0.2971430888632479D+00, & 0.2971430888632479D+00, & 0.8249569583935215D+00, & 0.0285146118965766D+00, & 0.1465284297099018D+00, & 0.1465284297099021D+00, & 0.0285146118965763D+00, & 0.8249569583935213D+00, & 0.4722096952795327D+00, & 0.1537086586116401D+00, & 0.3740816461088269D+00, & 0.3740816461088270D+00, & 0.1537086586116402D+00, & 0.4722096952795326D+00, & 0.8936878492161561D+00, & 0.0246053203840889D+00, & 0.0817068303997548D+00, & 0.0817068303997550D+00, & 0.0246053203840887D+00, & 0.8936878492161560D+00, & 0.9783157564619857D+00, & 0.0108421217690075D+00, & 0.0108421217690068D+00, & 0.6823170191891728D+00, & 0.0235355019299825D+00, & 0.2941474788808445D+00, & 0.2941474788808447D+00, & 0.0235355019299824D+00, & 0.6823170191891725D+00, & 0.6872129092572277D+00, & 0.1377167212601209D+00, & 0.1750703694826513D+00, & 0.1750703694826515D+00, & 0.1377167212601206D+00, & 0.6872129092572276D+00, & 0.7942932366737416D+00, & 0.1028533816631292D+00, & 0.1028533816631289D+00, & 0.9414041521049952D+00, & 0.0109753100892319D+00, & 0.0476205378057727D+00, & 0.0476205378057730D+00, & 0.0109753100892317D+00, & 0.9414041521049951D+00, & 0.5219618612839482D+00, & 0.1604656572027248D+00, & 0.3175724815133267D+00, & 0.3175724815133268D+00, & 0.1604656572027247D+00, & 0.5219618612839482D+00, & 0.5789126782672228D+00, & 0.1329492677376997D+00, & 0.2881380539950772D+00, & 0.2881380539950774D+00, & 0.1329492677376997D+00, & 0.5789126782672227D+00, & 0.7232741594653924D+00, & 0.0087549512313114D+00, & 0.2679708893032959D+00, & 0.2679708893032962D+00, & 0.0087549512313112D+00, & 0.7232741594653922D+00, & 0.4841735634166949D+00, & 0.0316528731666103D+00, & 0.4841735634166947D+00, & 0.7398771788136165D+00, & 0.0207437619833566D+00, & 0.2393790592030267D+00, & 0.2393790592030269D+00, & 0.0207437619833564D+00, & 0.7398771788136165D+00, & 0.7883864387462219D+00, & 0.0197602896840751D+00, & 0.1918532715697029D+00, & 0.1918532715697031D+00, & 0.0197602896840748D+00, & 0.7883864387462218D+00, & 0.5697364716889479D+00, & 0.0429392857768670D+00, & 0.3873242425341848D+00, & 0.3873242425341850D+00, & 0.0429392857768670D+00, & 0.5697364716889477D+00, & 0.5285751660132988D+00, & 0.1178924181582904D+00, & 0.3535324158284107D+00, & 0.3535324158284109D+00, & 0.1178924181582903D+00, & 0.5285751660132987D+00, & 0.9224477815225602D+00, & 0.0253747294625838D+00, & 0.0521774890148559D+00, & 0.0521774890148561D+00, & 0.0253747294625836D+00, & 0.9224477815225601D+00, & 0.5827685017638400D+00, & 0.0935293820848460D+00, & 0.3237021161513138D+00, & 0.3237021161513139D+00, & 0.0935293820848458D+00, & 0.5827685017638400D+00, & 0.6259535358370784D+00, & 0.0019871034880730D+00, & 0.3720593606748485D+00, & 0.3720593606748486D+00, & 0.0019871034880731D+00, & 0.6259535358370780D+00, & 0.4776172690993891D+00, & 0.1086901962935058D+00, & 0.4136925346071049D+00, & 0.4136925346071049D+00, & 0.1086901962935058D+00, & 0.4776172690993891D+00, & 0.5742322222075993D+00, & 0.1749023341509636D+00, & 0.2508654436414369D+00, & 0.2508654436414372D+00, & 0.1749023341509633D+00, & 0.5742322222075992D+00, & 0.6961863830895679D+00, & 0.0669659133716486D+00, & 0.2368477035387834D+00, & 0.2368477035387836D+00, & 0.0669659133716484D+00, & 0.6961863830895679D+00, & 0.8490631831866196D+00, & 0.0409791337707322D+00, & 0.1099576830426480D+00, & 0.1099576830426481D+00, & 0.0409791337707320D+00, & 0.8490631831866196D+00, & 0.5458016820289726D+00, & 0.0244664150758456D+00, & 0.4297319028951814D+00, & 0.4297319028951815D+00, & 0.0244664150758457D+00, & 0.5458016820289725D+00, & 0.7995438742256191D+00, & 0.0566880883410084D+00, & 0.1437680374333722D+00, & 0.1437680374333725D+00, & 0.0566880883410082D+00, & 0.7995438742256189D+00, & 0.9129368386397629D+00, & 0.0096524833615464D+00, & 0.0774106779986905D+00, & 0.0774106779986907D+00, & 0.0096524833615462D+00, & 0.9129368386397628D+00, & 0.8331944267073319D+00, & 0.0110995676273213D+00, & 0.1557060056653466D+00, & 0.1557060056653468D+00, & 0.0110995676273210D+00, & 0.8331944267073319D+00, & 0.6851726257624123D+00, & 0.0019740717879365D+00, & 0.3128533024496510D+00, & 0.3128533024496512D+00, & 0.0019740717879363D+00, & 0.6851726257624122D+00, & 0.9628508665812470D+00, & 0.0110588672805735D+00, & 0.0260902661381796D+00, & 0.0260902661381799D+00, & 0.0110588672805730D+00, & 0.9628508665812469D+00, & 0.8318645947596423D+00, & 0.0024625444223662D+00, & 0.1656728608179914D+00, & 0.1656728608179917D+00, & 0.0024625444223660D+00, & 0.8318645947596420D+00, & 0.4932611955660528D+00, & 0.0134776088678945D+00, & 0.4932611955660526D+00, & 0.8793792323410513D+00, & 0.0463950129826374D+00, & 0.0742257546763111D+00, & 0.0742257546763113D+00, & 0.0463950129826372D+00, & 0.8793792323410512D+00, & 0.9690874828381117D+00, & 0.0020785999248742D+00, & 0.0288339172370139D+00, & 0.0288339172370141D+00, & 0.0020785999248739D+00, & 0.9690874828381117D+00, & 0.7448240425293629D+00, & 0.0683532967983221D+00, & 0.1868226606723149D+00, & 0.1868226606723151D+00, & 0.0683532967983219D+00, & 0.7448240425293629D+00, & 0.6622397675113322D+00, & 0.0106763043029804D+00, & 0.3270839281856872D+00, & 0.3270839281856874D+00, & 0.0106763043029804D+00, & 0.6622397675113321D+00, & 0.8269396131025599D+00, & 0.0691692834636133D+00, & 0.1038911034338266D+00, & 0.1038911034338268D+00, & 0.0691692834636132D+00, & 0.8269396131025599D+00, & 0.6837969023224016D+00, & 0.1006688094346438D+00, & 0.2155342882429544D+00, & 0.2155342882429546D+00, & 0.1006688094346436D+00, & 0.6837969023224016D+00, & 0.4057324719755225D+00, & 0.1885350560489550D+00, & 0.4057324719755224D+00, & 0.4556304494441658D+00, & 0.2012179375284441D+00, & 0.3431516130273898D+00, & 0.3431516130273898D+00, & 0.2012179375284442D+00, & 0.4556304494441656D+00, & 0.6341379927840377D+00, & 0.1434532484926368D+00, & 0.2224087587233252D+00, & 0.2224087587233254D+00, & 0.1434532484926366D+00, & 0.6341379927840376D+00, & 0.9443938625479115D+00, & 0.0021251605376944D+00, & 0.0534809769143939D+00, & 0.0534809769143942D+00, & 0.0021251605376941D+00, & 0.9443938625479114D+00, & 0.7391567101497369D+00, & 0.1304216449251317D+00, & 0.1304216449251313D+00, & 0.5097885287055710D+00, & 0.0514225024494020D+00, & 0.4387889688450268D+00, & 0.4387889688450269D+00, & 0.0514225024494019D+00, & 0.5097885287055708D+00, & 0.4614348056302962D+00, & 0.0771303887394074D+00, & 0.4614348056302961D+00, & 0.9448520795137773D+00, & 0.0275739602431116D+00, & 0.0275739602431110D+00, & 0.5363151092490519D+00, & 0.2318424453754740D+00, & 0.2318424453754738D+00, & 0.3517217766277715D+00, & 0.2965564467444571D+00, & 0.3517217766277714D+00, & 0.9955751573800361D+00, & 0.0022124213099820D+00, & 0.0022124213099816D+00, & 0.5299152656988658D+00, & 0.0781526329255781D+00, & 0.3919321013755557D+00, & 0.3919321013755558D+00, & 0.0781526329255781D+00, & 0.5299152656988657D+00, & 0.7824208956570436D+00, & 0.0064969244459218D+00, & 0.2110821798970344D+00, & 0.2110821798970347D+00, & 0.0064969244459216D+00, & 0.7824208956570435D+00, & 0.9861998362698954D+00, & 0.0020903064191529D+00, & 0.0117098573109514D+00, & 0.0117098573109518D+00, & 0.0020903064191528D+00, & 0.9861998362698953D+00, & 0.4987895646915129D+00, & 0.0024208706169743D+00, & 0.4987895646915126D+00, & 0.7934767827218626D+00, & 0.0001398635181476D+00, & 0.2063833537599896D+00, & 0.2063833537599898D+00, & 0.0001398635181474D+00, & 0.7934767827218625D+00 /) w = (/ & 0.0015179493827508D+00, & 0.0015179493827508D+00, & 0.0015179493827508D+00, & 0.0015179493827508D+00, & 0.0015179493827508D+00, & 0.0015179493827508D+00, & 0.0009640363088870D+00, & 0.0009640363088870D+00, & 0.0009640363088870D+00, & 0.0009640363088870D+00, & 0.0009640363088870D+00, & 0.0009640363088870D+00, & 0.0002813503665322D+00, & 0.0002813503665322D+00, & 0.0002813503665322D+00, & 0.0002813503665322D+00, & 0.0002813503665322D+00, & 0.0002813503665322D+00, & 0.0032298776744525D+00, & 0.0032298776744525D+00, & 0.0032298776744525D+00, & 0.0046862213374651D+00, & 0.0046862213374651D+00, & 0.0046862213374651D+00, & 0.0046862213374651D+00, & 0.0046862213374651D+00, & 0.0046862213374651D+00, & 0.0045178989983832D+00, & 0.0045178989983832D+00, & 0.0045178989983832D+00, & 0.0045178989983832D+00, & 0.0045178989983832D+00, & 0.0045178989983832D+00, & 0.0015790917860184D+00, & 0.0015790917860184D+00, & 0.0015790917860184D+00, & 0.0004264134812992D+00, & 0.0004264134812992D+00, & 0.0004264134812992D+00, & 0.0004264134812992D+00, & 0.0004264134812992D+00, & 0.0004264134812992D+00, & 0.0032468366301052D+00, & 0.0032468366301052D+00, & 0.0032468366301052D+00, & 0.0032468366301052D+00, & 0.0032468366301052D+00, & 0.0032468366301052D+00, & 0.0039309054788202D+00, & 0.0039309054788202D+00, & 0.0039309054788202D+00, & 0.0027113498937414D+00, & 0.0027113498937414D+00, & 0.0027113498937414D+00, & 0.0027113498937414D+00, & 0.0027113498937414D+00, & 0.0027113498937414D+00, & 0.0016327582269425D+00, & 0.0016327582269425D+00, & 0.0016327582269425D+00, & 0.0016327582269425D+00, & 0.0016327582269425D+00, & 0.0016327582269425D+00, & 0.0004790301761790D+00, & 0.0004790301761790D+00, & 0.0004790301761790D+00, & 0.0004790301761790D+00, & 0.0004790301761790D+00, & 0.0004790301761790D+00, & 0.0026002718294388D+00, & 0.0026002718294388D+00, & 0.0026002718294388D+00, & 0.0026002718294388D+00, & 0.0026002718294388D+00, & 0.0026002718294388D+00, & 0.0030738076620057D+00, & 0.0030738076620057D+00, & 0.0030738076620057D+00, & 0.0030738076620057D+00, & 0.0030738076620057D+00, & 0.0030738076620057D+00, & 0.0029878198502273D+00, & 0.0029878198502273D+00, & 0.0029878198502273D+00, & 0.0029878198502273D+00, & 0.0029878198502273D+00, & 0.0029878198502273D+00, & 0.0049958592249662D+00, & 0.0049958592249662D+00, & 0.0049958592249662D+00, & 0.0006925913496786D+00, & 0.0006925913496786D+00, & 0.0006925913496786D+00, & 0.0006925913496786D+00, & 0.0006925913496786D+00, & 0.0006925913496786D+00, & 0.0022641894958966D+00, & 0.0022641894958966D+00, & 0.0022641894958966D+00, & 0.0022641894958966D+00, & 0.0022641894958966D+00, & 0.0022641894958966D+00, & 0.0021683619372714D+00, & 0.0021683619372714D+00, & 0.0021683619372714D+00, & 0.0021683619372714D+00, & 0.0021683619372714D+00, & 0.0021683619372714D+00, & 0.0012603344824756D+00, & 0.0012603344824756D+00, & 0.0012603344824756D+00, & 0.0012603344824756D+00, & 0.0012603344824756D+00, & 0.0012603344824756D+00, & 0.0003019280054420D+00, & 0.0003019280054420D+00, & 0.0003019280054420D+00, & 0.0003019280054420D+00, & 0.0003019280054420D+00, & 0.0003019280054420D+00, & 0.0040779189028797D+00, & 0.0040779189028797D+00, & 0.0040779189028797D+00, & 0.0045616230274563D+00, & 0.0045616230274563D+00, & 0.0045616230274563D+00, & 0.0045616230274563D+00, & 0.0045616230274563D+00, & 0.0045616230274563D+00, & 0.0026431427639031D+00, & 0.0026431427639031D+00, & 0.0026431427639031D+00, & 0.0026431427639031D+00, & 0.0026431427639031D+00, & 0.0026431427639031D+00, & 0.0011314599292834D+00, & 0.0011314599292834D+00, & 0.0011314599292834D+00, & 0.0011314599292834D+00, & 0.0011314599292834D+00, & 0.0011314599292834D+00, & 0.0021088731883819D+00, & 0.0021088731883819D+00, & 0.0021088731883819D+00, & 0.0021088731883819D+00, & 0.0021088731883819D+00, & 0.0021088731883819D+00, & 0.0011717865482745D+00, & 0.0011717865482745D+00, & 0.0011717865482745D+00, & 0.0050840537579920D+00, & 0.0050840537579920D+00, & 0.0050840537579920D+00, & 0.0015608187011213D+00, & 0.0015608187011213D+00, & 0.0015608187011213D+00, & 0.0015608187011213D+00, & 0.0015608187011213D+00, & 0.0015608187011213D+00, & 0.0046308511124104D+00, & 0.0046308511124104D+00, & 0.0046308511124104D+00, & 0.0046308511124104D+00, & 0.0046308511124104D+00, & 0.0046308511124104D+00, & 0.0011648378245234D+00, & 0.0011648378245234D+00, & 0.0011648378245234D+00, & 0.0011648378245234D+00, & 0.0011648378245234D+00, & 0.0011648378245234D+00, & 0.0002909934397913D+00, & 0.0002909934397913D+00, & 0.0002909934397913D+00, & 0.0019078475871128D+00, & 0.0019078475871128D+00, & 0.0019078475871128D+00, & 0.0019078475871128D+00, & 0.0019078475871128D+00, & 0.0019078475871128D+00, & 0.0036207359330354D+00, & 0.0036207359330354D+00, & 0.0036207359330354D+00, & 0.0036207359330354D+00, & 0.0036207359330354D+00, & 0.0036207359330354D+00, & 0.0024679826387392D+00, & 0.0024679826387392D+00, & 0.0024679826387392D+00, & 0.0006047059166113D+00, & 0.0006047059166113D+00, & 0.0006047059166113D+00, & 0.0006047059166113D+00, & 0.0006047059166113D+00, & 0.0006047059166113D+00, & 0.0044715780288226D+00, & 0.0044715780288226D+00, & 0.0044715780288226D+00, & 0.0044715780288226D+00, & 0.0044715780288226D+00, & 0.0044715780288226D+00, & 0.0043217865559446D+00, & 0.0043217865559446D+00, & 0.0043217865559446D+00, & 0.0043217865559446D+00, & 0.0043217865559446D+00, & 0.0043217865559446D+00, & 0.0011834459680029D+00, & 0.0011834459680029D+00, & 0.0011834459680029D+00, & 0.0011834459680029D+00, & 0.0011834459680029D+00, & 0.0011834459680029D+00, & 0.0024475548918752D+00, & 0.0024475548918752D+00, & 0.0024475548918752D+00, & 0.0017098461192591D+00, & 0.0017098461192591D+00, & 0.0017098461192591D+00, & 0.0017098461192591D+00, & 0.0017098461192591D+00, & 0.0017098461192591D+00, & 0.0015260667775320D+00, & 0.0015260667775320D+00, & 0.0015260667775320D+00, & 0.0015260667775320D+00, & 0.0015260667775320D+00, & 0.0015260667775320D+00, & 0.0027529020694636D+00, & 0.0027529020694636D+00, & 0.0027529020694636D+00, & 0.0027529020694636D+00, & 0.0027529020694636D+00, & 0.0027529020694636D+00, & 0.0043632272367912D+00, & 0.0043632272367912D+00, & 0.0043632272367912D+00, & 0.0043632272367912D+00, & 0.0043632272367912D+00, & 0.0043632272367912D+00, & 0.0009662853562326D+00, & 0.0009662853562326D+00, & 0.0009662853562326D+00, & 0.0009662853562326D+00, & 0.0009662853562326D+00, & 0.0009662853562326D+00, & 0.0037815526680686D+00, & 0.0037815526680686D+00, & 0.0037815526680686D+00, & 0.0037815526680686D+00, & 0.0037815526680686D+00, & 0.0037815526680686D+00, & 0.0006035693127469D+00, & 0.0006035693127469D+00, & 0.0006035693127469D+00, & 0.0006035693127469D+00, & 0.0006035693127469D+00, & 0.0006035693127469D+00, & 0.0042551639608390D+00, & 0.0042551639608390D+00, & 0.0042551639608390D+00, & 0.0042551639608390D+00, & 0.0042551639608390D+00, & 0.0042551639608390D+00, & 0.0048490533224092D+00, & 0.0048490533224092D+00, & 0.0048490533224092D+00, & 0.0048490533224092D+00, & 0.0048490533224092D+00, & 0.0048490533224092D+00, & 0.0030254918153352D+00, & 0.0030254918153352D+00, & 0.0030254918153352D+00, & 0.0030254918153352D+00, & 0.0030254918153352D+00, & 0.0030254918153352D+00, & 0.0018302659109492D+00, & 0.0018302659109492D+00, & 0.0018302659109492D+00, & 0.0018302659109492D+00, & 0.0018302659109492D+00, & 0.0018302659109492D+00, & 0.0023112911452725D+00, & 0.0023112911452725D+00, & 0.0023112911452725D+00, & 0.0023112911452725D+00, & 0.0023112911452725D+00, & 0.0023112911452725D+00, & 0.0022976181282931D+00, & 0.0022976181282931D+00, & 0.0022976181282931D+00, & 0.0022976181282931D+00, & 0.0022976181282931D+00, & 0.0022976181282931D+00, & 0.0007737426014553D+00, & 0.0007737426014553D+00, & 0.0007737426014553D+00, & 0.0007737426014553D+00, & 0.0007737426014553D+00, & 0.0007737426014553D+00, & 0.0011091107906633D+00, & 0.0011091107906633D+00, & 0.0011091107906633D+00, & 0.0011091107906633D+00, & 0.0011091107906633D+00, & 0.0011091107906633D+00, & 0.0005917280070787D+00, & 0.0005917280070787D+00, & 0.0005917280070787D+00, & 0.0005917280070787D+00, & 0.0005917280070787D+00, & 0.0005917280070787D+00, & 0.0004663290783398D+00, & 0.0004663290783398D+00, & 0.0004663290783398D+00, & 0.0004663290783398D+00, & 0.0004663290783398D+00, & 0.0004663290783398D+00, & 0.0005060545142142D+00, & 0.0005060545142142D+00, & 0.0005060545142142D+00, & 0.0005060545142142D+00, & 0.0005060545142142D+00, & 0.0005060545142142D+00, & 0.0016834711767858D+00, & 0.0016834711767858D+00, & 0.0016834711767858D+00, & 0.0015462052435902D+00, & 0.0015462052435902D+00, & 0.0015462052435902D+00, & 0.0015462052435902D+00, & 0.0015462052435902D+00, & 0.0015462052435902D+00, & 0.0002238167725271D+00, & 0.0002238167725271D+00, & 0.0002238167725271D+00, & 0.0002238167725271D+00, & 0.0002238167725271D+00, & 0.0002238167725271D+00, & 0.0029561851838940D+00, & 0.0029561851838940D+00, & 0.0029561851838940D+00, & 0.0029561851838940D+00, & 0.0029561851838940D+00, & 0.0029561851838940D+00, & 0.0014290418491702D+00, & 0.0014290418491702D+00, & 0.0014290418491702D+00, & 0.0014290418491702D+00, & 0.0014290418491702D+00, & 0.0014290418491702D+00, & 0.0021458693484176D+00, & 0.0021458693484176D+00, & 0.0021458693484176D+00, & 0.0021458693484176D+00, & 0.0021458693484176D+00, & 0.0021458693484176D+00, & 0.0035847674194570D+00, & 0.0035847674194570D+00, & 0.0035847674194570D+00, & 0.0035847674194570D+00, & 0.0035847674194570D+00, & 0.0035847674194570D+00, & 0.0053654225406028D+00, & 0.0053654225406028D+00, & 0.0053654225406028D+00, & 0.0054527357782272D+00, & 0.0054527357782272D+00, & 0.0054527357782272D+00, & 0.0054527357782272D+00, & 0.0054527357782272D+00, & 0.0054527357782272D+00, & 0.0043816657756572D+00, & 0.0043816657756572D+00, & 0.0043816657756572D+00, & 0.0043816657756572D+00, & 0.0043816657756572D+00, & 0.0043816657756572D+00, & 0.0003071745359645D+00, & 0.0003071745359645D+00, & 0.0003071745359645D+00, & 0.0003071745359645D+00, & 0.0003071745359645D+00, & 0.0003071745359645D+00, & 0.0034992680317617D+00, & 0.0034992680317617D+00, & 0.0034992680317617D+00, & 0.0032381770164589D+00, & 0.0032381770164589D+00, & 0.0032381770164589D+00, & 0.0032381770164589D+00, & 0.0032381770164589D+00, & 0.0032381770164589D+00, & 0.0039600197915087D+00, & 0.0039600197915087D+00, & 0.0039600197915087D+00, & 0.0008319508889038D+00, & 0.0008319508889038D+00, & 0.0008319508889038D+00, & 0.0053644090708949D+00, & 0.0053644090708949D+00, & 0.0053644090708949D+00, & 0.0061267736075541D+00, & 0.0061267736075541D+00, & 0.0061267736075541D+00, & 0.0000646114299085D+00, & 0.0000646114299085D+00, & 0.0000646114299085D+00, & 0.0041053828589275D+00, & 0.0041053828589275D+00, & 0.0041053828589275D+00, & 0.0041053828589275D+00, & 0.0041053828589275D+00, & 0.0041053828589275D+00, & 0.0010683587323421D+00, & 0.0010683587323421D+00, & 0.0010683587323421D+00, & 0.0010683587323421D+00, & 0.0010683587323421D+00, & 0.0010683587323421D+00, & 0.0001423198916150D+00, & 0.0001423198916150D+00, & 0.0001423198916150D+00, & 0.0001423198916150D+00, & 0.0001423198916150D+00, & 0.0001423198916150D+00, & 0.0007885551654533D+00, & 0.0007885551654533D+00, & 0.0007885551654533D+00, & 0.0001605584705522D+00, & 0.0001605584705522D+00, & 0.0001605584705522D+00, & 0.0001605584705522D+00, & 0.0001605584705522D+00, & 0.0001605584705522D+00 /) return end subroutine rule50 ( n, a, b, c, w ) !*****************************************************************************80 ! !! rule50() returns the rule of precision 50. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 09 June 2023 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient ! quadrature rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer n: the number of points. ! ! Output: ! ! real ( kind = 8 ) a(n), b(n), c(n): the barycentric coordinates of ! quadrature points. ! ! real ( kind = 8 ) w(n): the quadrature weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) real ( kind = rk ) w(n) a = (/ & 0.2563558633847908D+00, & 0.4872882732304182D+00, & 0.2563558633847909D+00, & 0.4433230868583420D+00, & 0.5557544570355875D+00, & 0.0009224561060704D+00, & 0.5557544570355875D+00, & 0.4433230868583420D+00, & 0.0009224561060704D+00, & 0.0259368938757904D+00, & 0.9516251148618965D+00, & 0.0224379912623133D+00, & 0.9516251148618965D+00, & 0.0259368938757906D+00, & 0.0224379912623128D+00, & 0.2401441052632695D+00, & 0.5370651664429976D+00, & 0.2227907282937328D+00, & 0.5370651664429976D+00, & 0.2401441052632695D+00, & 0.2227907282937327D+00, & 0.1345526180266427D+00, & 0.8423271680031109D+00, & 0.0231202139702464D+00, & 0.8423271680031110D+00, & 0.1345526180266427D+00, & 0.0231202139702461D+00, & 0.0450355724673314D+00, & 0.9541076477376595D+00, & 0.0008567797950091D+00, & 0.9541076477376597D+00, & 0.0450355724673315D+00, & 0.0008567797950087D+00, & 0.4087145665677719D+00, & 0.5864767957713561D+00, & 0.0048086376608720D+00, & 0.5864767957713561D+00, & 0.4087145665677719D+00, & 0.0048086376608719D+00, & 0.1714634577399832D+00, & 0.8050435299005781D+00, & 0.0234930123594386D+00, & 0.8050435299005783D+00, & 0.1714634577399832D+00, & 0.0234930123594384D+00, & 0.0016305781421460D+00, & 0.9967388437157076D+00, & 0.0016305781421465D+00, & 0.2101059247050331D+00, & 0.6964974281656032D+00, & 0.0933966471293636D+00, & 0.6964974281656033D+00, & 0.2101059247050331D+00, & 0.0933966471293634D+00, & 0.1392968201185850D+00, & 0.8189065432302668D+00, & 0.0417966366511482D+00, & 0.8189065432302668D+00, & 0.1392968201185851D+00, & 0.0417966366511480D+00, & 0.0703820539127592D+00, & 0.8802606341943795D+00, & 0.0493573118928615D+00, & 0.8802606341943796D+00, & 0.0703820539127593D+00, & 0.0493573118928611D+00, & 0.4903268692484512D+00, & 0.4903268692484513D+00, & 0.0193462615030975D+00, & 0.3726064881564940D+00, & 0.4745794048313449D+00, & 0.1528141070121611D+00, & 0.4745794048313449D+00, & 0.3726064881564940D+00, & 0.1528141070121610D+00, & 0.1479157172776441D+00, & 0.7869688527917342D+00, & 0.0651154299306216D+00, & 0.7869688527917343D+00, & 0.1479157172776442D+00, & 0.0651154299306213D+00, & 0.2140246435816437D+00, & 0.7625132132423355D+00, & 0.0234621431760209D+00, & 0.7625132132423355D+00, & 0.2140246435816437D+00, & 0.0234621431760206D+00, & 0.3302674030581440D+00, & 0.6177003187074449D+00, & 0.0520322782344111D+00, & 0.6177003187074449D+00, & 0.3302674030581441D+00, & 0.0520322782344110D+00, & 0.3699848635444039D+00, & 0.6285206173500637D+00, & 0.0014945191055323D+00, & 0.6285206173500638D+00, & 0.3699848635444039D+00, & 0.0014945191055322D+00, & 0.0675115690433361D+00, & 0.9204446840218713D+00, & 0.0120437469347927D+00, & 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0.0740590746798509D+00, & 0.0022261525470099D+00, & 0.9237147727731388D+00 /) w = (/ & 0.0033286951747132D+00, & 0.0033286951747132D+00, & 0.0033286951747132D+00, & 0.0003473281594925D+00, & 0.0003473281594925D+00, & 0.0003473281594925D+00, & 0.0003473281594925D+00, & 0.0003473281594925D+00, & 0.0003473281594925D+00, & 0.0003000501019099D+00, & 0.0003000501019099D+00, & 0.0003000501019099D+00, & 0.0003000501019099D+00, & 0.0003000501019099D+00, & 0.0003000501019099D+00, & 0.0027304020592298D+00, & 0.0027304020592298D+00, & 0.0027304020592298D+00, & 0.0027304020592298D+00, & 0.0027304020592298D+00, & 0.0027304020592298D+00, & 0.0011329714517846D+00, & 0.0011329714517846D+00, & 0.0011329714517846D+00, & 0.0011329714517846D+00, & 0.0011329714517846D+00, & 0.0011329714517846D+00, & 0.0001365218409967D+00, & 0.0001365218409967D+00, & 0.0001365218409967D+00, & 0.0001365218409967D+00, & 0.0001365218409967D+00, & 0.0001365218409967D+00, & 0.0007693760667843D+00, & 0.0007693760667843D+00, & 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0.0034396664292256D+00, & 0.0034396664292256D+00, & 0.0034396664292256D+00, & 0.0034396664292256D+00, & 0.0004380269370904D+00, & 0.0004380269370904D+00, & 0.0004380269370904D+00, & 0.0004380269370904D+00, & 0.0004380269370904D+00, & 0.0004380269370904D+00, & 0.0044060145278103D+00, & 0.0044060145278103D+00, & 0.0044060145278103D+00, & 0.0044060145278103D+00, & 0.0044060145278103D+00, & 0.0044060145278103D+00, & 0.0020175008084554D+00, & 0.0020175008084554D+00, & 0.0020175008084554D+00, & 0.0020175008084554D+00, & 0.0020175008084554D+00, & 0.0020175008084554D+00, & 0.0032382786045497D+00, & 0.0032382786045497D+00, & 0.0032382786045497D+00, & 0.0032382786045497D+00, & 0.0032382786045497D+00, & 0.0032382786045497D+00, & 0.0046662107991940D+00, & 0.0046662107991940D+00, & 0.0046662107991940D+00, & 0.0046662107991940D+00, & 0.0046662107991940D+00, & 0.0046662107991940D+00, & 0.0031592258177549D+00, & 0.0031592258177549D+00, & 0.0031592258177549D+00, & 0.0031592258177549D+00, & 0.0031592258177549D+00, & 0.0031592258177549D+00, & 0.0034735845184462D+00, & 0.0034735845184462D+00, & 0.0034735845184462D+00, & 0.0034735845184462D+00, & 0.0034735845184462D+00, & 0.0034735845184462D+00, & 0.0008953928804098D+00, & 0.0008953928804098D+00, & 0.0008953928804098D+00, & 0.0008953928804098D+00, & 0.0008953928804098D+00, & 0.0008953928804098D+00, & 0.0010804784836254D+00, & 0.0010804784836254D+00, & 0.0010804784836254D+00, & 0.0010804784836254D+00, & 0.0010804784836254D+00, & 0.0010804784836254D+00, & 0.0018129744491099D+00, & 0.0018129744491099D+00, & 0.0018129744491099D+00, & 0.0018129744491099D+00, & 0.0018129744491099D+00, & 0.0018129744491099D+00, & 0.0007651571304863D+00, & 0.0007651571304863D+00, & 0.0007651571304863D+00, & 0.0007651571304863D+00, & 0.0007651571304863D+00, & 0.0007651571304863D+00, & 0.0028576817042790D+00, & 0.0028576817042790D+00, & 0.0028576817042790D+00, & 0.0028576817042790D+00, & 0.0028576817042790D+00, & 0.0028576817042790D+00, & 0.0026558120905517D+00, & 0.0026558120905517D+00, & 0.0026558120905517D+00, & 0.0026558120905517D+00, & 0.0026558120905517D+00, & 0.0026558120905517D+00, & 0.0044774376211065D+00, & 0.0044774376211065D+00, & 0.0044774376211065D+00, & 0.0044774376211065D+00, & 0.0044774376211065D+00, & 0.0044774376211065D+00, & 0.0016535172612734D+00, & 0.0016535172612734D+00, & 0.0016535172612734D+00, & 0.0016535172612734D+00, & 0.0016535172612734D+00, & 0.0016535172612734D+00, & 0.0019449896357145D+00, & 0.0019449896357145D+00, & 0.0019449896357145D+00, & 0.0019449896357145D+00, & 0.0019449896357145D+00, & 0.0019449896357145D+00, & 0.0040545175807175D+00, & 0.0040545175807175D+00, & 0.0040545175807175D+00, & 0.0040545175807175D+00, & 0.0040545175807175D+00, & 0.0040545175807175D+00, & 0.0023471970098679D+00, & 0.0023471970098679D+00, & 0.0023471970098679D+00, & 0.0023471970098679D+00, & 0.0023471970098679D+00, & 0.0023471970098679D+00, & 0.0054197966818915D+00, & 0.0054197966818915D+00, & 0.0054197966818915D+00, & 0.0054197966818915D+00, & 0.0054197966818915D+00, & 0.0054197966818915D+00, & 0.0008214191155562D+00, & 0.0008214191155562D+00, & 0.0008214191155562D+00, & 0.0008214191155562D+00, & 0.0008214191155562D+00, & 0.0008214191155562D+00, & 0.0013331230747820D+00, & 0.0013331230747820D+00, & 0.0013331230747820D+00, & 0.0013331230747820D+00, & 0.0013331230747820D+00, & 0.0013331230747820D+00, & 0.0046726023038407D+00, & 0.0046726023038407D+00, & 0.0046726023038407D+00, & 0.0046726023038407D+00, & 0.0046726023038407D+00, & 0.0046726023038407D+00, & 0.0035827112110621D+00, & 0.0035827112110621D+00, & 0.0035827112110621D+00, & 0.0010473492443510D+00, & 0.0010473492443510D+00, & 0.0010473492443510D+00, & 0.0010473492443510D+00, & 0.0010473492443510D+00, & 0.0010473492443510D+00, & 0.0027795988004447D+00, & 0.0027795988004447D+00, & 0.0027795988004447D+00, & 0.0025570128208941D+00, & 0.0025570128208941D+00, & 0.0025570128208941D+00, & 0.0025570128208941D+00, & 0.0025570128208941D+00, & 0.0025570128208941D+00, & 0.0011537659281314D+00, & 0.0011537659281314D+00, & 0.0011537659281314D+00, & 0.0011537659281314D+00, & 0.0011537659281314D+00, & 0.0011537659281314D+00, & 0.0042237575830891D+00, & 0.0042237575830891D+00, & 0.0042237575830891D+00, & 0.0042237575830891D+00, & 0.0042237575830891D+00, & 0.0042237575830891D+00, & 0.0013374175145031D+00, & 0.0013374175145031D+00, & 0.0013374175145031D+00, & 0.0013374175145031D+00, & 0.0013374175145031D+00, & 0.0013374175145031D+00, & 0.0023814233045742D+00, & 0.0023814233045742D+00, & 0.0023814233045742D+00, & 0.0023814233045742D+00, & 0.0023814233045742D+00, & 0.0023814233045742D+00, & 0.0042828524520190D+00, & 0.0042828524520190D+00, & 0.0042828524520190D+00, & 0.0042828524520190D+00, & 0.0042828524520190D+00, & 0.0042828524520190D+00, & 0.0002999521869148D+00, & 0.0002999521869148D+00, & 0.0002999521869148D+00, & 0.0004406939585376D+00, & 0.0004406939585376D+00, & 0.0004406939585376D+00, & 0.0004406939585376D+00, & 0.0004406939585376D+00, & 0.0004406939585376D+00, & 0.0020678716670798D+00, & 0.0020678716670798D+00, & 0.0020678716670798D+00, & 0.0001156452577508D+00, & 0.0001156452577508D+00, & 0.0001156452577508D+00, & 0.0001156452577508D+00, & 0.0001156452577508D+00, & 0.0001156452577508D+00, & 0.0001824251018040D+00, & 0.0001824251018040D+00, & 0.0001824251018040D+00, & 0.0001824251018040D+00, & 0.0001824251018040D+00, & 0.0001824251018040D+00, & 0.0051351158472688D+00, & 0.0051351158472688D+00, & 0.0051351158472688D+00, & 0.0051351158472688D+00, & 0.0051351158472688D+00, & 0.0051351158472688D+00, & 0.0039050557101547D+00, & 0.0039050557101547D+00, & 0.0039050557101547D+00, & 0.0039050557101547D+00, & 0.0039050557101547D+00, & 0.0039050557101547D+00, & 0.0005282175598339D+00, & 0.0005282175598339D+00, & 0.0005282175598339D+00, & 0.0005282175598339D+00, & 0.0005282175598339D+00, & 0.0005282175598339D+00, & 0.0018990634758471D+00, & 0.0018990634758471D+00, & 0.0018990634758471D+00, & 0.0018990634758471D+00, & 0.0018990634758471D+00, & 0.0018990634758471D+00, & 0.0040277109885183D+00, & 0.0040277109885183D+00, & 0.0040277109885183D+00, & 0.0023340593121637D+00, & 0.0023340593121637D+00, & 0.0023340593121637D+00, & 0.0023340593121637D+00, & 0.0023340593121637D+00, & 0.0023340593121637D+00, & 0.0004826706779797D+00, & 0.0004826706779797D+00, & 0.0004826706779797D+00, & 0.0004826706779797D+00, & 0.0004826706779797D+00, & 0.0004826706779797D+00, & 0.0045706738891262D+00, & 0.0045706738891262D+00, & 0.0045706738891262D+00, & 0.0032490194493214D+00, & 0.0032490194493214D+00, & 0.0032490194493214D+00, & 0.0032490194493214D+00, & 0.0032490194493214D+00, & 0.0032490194493214D+00, & 0.0013197669167677D+00, & 0.0013197669167677D+00, & 0.0013197669167677D+00, & 0.0013197669167677D+00, & 0.0013197669167677D+00, & 0.0013197669167677D+00, & 0.0051653559274539D+00, & 0.0051653559274539D+00, & 0.0051653559274539D+00, & 0.0034852633534527D+00, & 0.0034852633534527D+00, & 0.0034852633534527D+00, & 0.0003967292610444D+00, & 0.0003967292610444D+00, & 0.0003967292610444D+00, & 0.0003967292610444D+00, & 0.0003967292610444D+00, & 0.0003967292610444D+00, & 0.0058568144539184D+00, & 0.0058568144539184D+00, & 0.0058568144539184D+00, & 0.0011989487838384D+00, & 0.0011989487838384D+00, & 0.0011989487838384D+00, & 0.0005855934410211D+00, & 0.0005855934410211D+00, & 0.0005855934410211D+00, & 0.0005855934410211D+00, & 0.0005855934410211D+00, & 0.0005855934410211D+00, & 0.0007493220541052D+00, & 0.0007493220541052D+00, & 0.0007493220541052D+00, & 0.0014007748847512D+00, & 0.0014007748847512D+00, & 0.0014007748847512D+00, & 0.0014007748847512D+00, & 0.0014007748847512D+00, & 0.0014007748847512D+00, & 0.0057736389035923D+00, & 0.0057736389035923D+00, & 0.0057736389035923D+00, & 0.0003705055488142D+00, & 0.0003705055488142D+00, & 0.0003705055488142D+00, & 0.0003705055488142D+00, & 0.0003705055488142D+00, & 0.0003705055488142D+00 /) return end subroutine triangle_symq_rule ( p, n, a, b, c, w ) !*****************************************************************************80 ! !! triangle_symq_rule() returns the requested quadrature rule. ! ! Licensing: ! ! This code is distributed under the GNU GPL license. ! ! Modified: ! ! 10 June 2023 ! ! Author: ! ! Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas. ! This version by John Burkardt. ! ! Reference: ! ! Hong Xiao, Zydrunas Gimbutas, ! A numerical algorithm for the construction of efficient quadrature ! rules in two and higher dimensions, ! Computers and Mathematics with Applications, ! Volume 59, 2010, pages 663-676. ! ! Input: ! ! integer p: the precision of the quadrature. 0 <= p <= 50. ! ! integer n: the number of nodes. ! ! Output: ! ! real ( kind = rk ) a(n), b(n), c(n): the barycentric coordinates ! of the nodes. ! ! real ( kind = rk ) w(n): the weights. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) real ( kind = rk ) b(n) real ( kind = rk ) c(n) integer p real ( kind = rk ) w(n) if ( p == 0 ) then call rule00 ( n, a, b, c, w ) else if ( p == 1 ) then call rule01 ( n, a, b, c, w ) else if ( p == 2 ) then call rule02 ( n, a, b, c, w ) else if ( p == 3 ) then call rule03 ( n, a, b, c, w ) else if ( p == 4 ) then call rule04 ( n, a, b, c, w ) else if ( p == 5 ) then call rule05 ( n, a, b, c, w ) else if ( p == 6 ) then call rule06 ( n, a, b, c, w ) else if ( p == 7 ) then call rule07 ( n, a, b, c, w ) else if ( p == 8 ) then call rule08 ( n, a, b, c, w ) else if ( p == 9 ) then call rule09 ( n, a, b, c, w ) else if ( p == 10 ) then call rule10 ( n, a, b, c, w ) else if ( p == 11 ) then call rule11 ( n, a, b, c, w ) else if ( p == 12 ) then call rule12 ( n, a, b, c, w ) else if ( p == 13 ) then call rule13 ( n, a, b, c, w ) else if ( p == 14 ) then call rule14 ( n, a, b, c, w ) else if ( p == 15 ) then call rule15 ( n, a, b, c, w ) else if ( p == 16 ) then call rule16 ( n, a, b, c, w ) else if ( p == 17 ) then call rule17 ( n, a, b, c, w ) else if ( p == 18 ) then call rule18 ( n, a, b, c, w ) else if ( p == 19 ) then call rule19 ( n, a, b, c, w ) else if ( p == 20 ) then call rule20 ( n, a, b, c, w ) else if ( p == 21 ) then call rule21 ( n, a, b, c, w ) else if ( p == 22 ) then call rule22 ( n, a, b, c, w ) else if ( p == 23 ) then call rule23 ( n, a, b, c, w ) else if ( p == 24 ) then call rule24 ( n, a, b, c, w ) else if ( p == 25 ) then call rule25 ( n, a, b, c, w ) else if ( p == 26 ) then call rule26 ( n, a, b, c, w ) else if ( p == 27 ) then call rule27 ( n, a, b, c, w ) else if ( p == 28 ) then call rule28 ( n, a, b, c, w ) else if ( p == 29 ) then call rule29 ( n, a, b, c, w ) else if ( p == 30 ) then call rule30 ( n, a, b, c, w ) else if ( p == 31 ) then call rule31 ( n, a, b, c, w ) else if ( p == 32 ) then call rule32 ( n, a, b, c, w ) else if ( p == 33 ) then call rule33 ( n, a, b, c, w ) else if ( p == 34 ) then call rule34 ( n, a, b, c, w ) else if ( p == 35 ) then call rule35 ( n, a, b, c, w ) else if ( p == 36 ) then call rule36 ( n, a, b, c, w ) else if ( p == 37 ) then call rule37 ( n, a, b, c, w ) else if ( p == 38 ) then call rule38 ( n, a, b, c, w ) else if ( p == 39 ) then call rule39 ( n, a, b, c, w ) else if ( p == 40 ) then call rule40 ( n, a, b, c, w ) else if ( p == 41 ) then call rule41 ( n, a, b, c, w ) else if ( p == 42 ) then call rule42 ( n, a, b, c, w ) else if ( p == 43 ) then call rule43 ( n, a, b, c, w ) else if ( p == 44 ) then call rule44 ( n, a, b, c, w ) else if ( p == 45 ) then call rule45 ( n, a, b, c, w ) else if ( p == 46 ) then call rule46 ( n, a, b, c, w ) else if ( p == 47 ) then call rule47 ( n, a, b, c, w ) else if ( p == 48 ) then call rule48 ( n, a, b, c, w ) else if ( p == 49 ) then call rule49 ( n, a, b, c, w ) else if ( p == 50 ) then call rule50 ( n, a, b, c, w ) else write ( *, '(a)' ) '' write ( *, '(a)' ) 'triangle_symq_rule(): Fatal error!' write ( *, '(a)' ) ' Illegal input value of p.' write ( *, '(a)' ) ' 0 <= p <= 50 required.' call exit ( 1 ) end if return end function triangle_unit_area ( ) !*****************************************************************************80 ! !! triangle_unit_area() returns the area of a unit triangle. ! ! Licensing: ! ! This code is distributed under the GNU GPL license. ! ! Modified: ! ! 24 May 2023 ! ! Author: ! ! John Burkardt. ! ! Output: ! ! real ( kind = rk ) triangle_unit_area: the area of the triangle. ! implicit none integer, parameter :: rk = kind ( 1.0D+00) real ( kind = rk ) triangle_unit_area triangle_unit_area = 0.5D+00 return end function triangle_unit_monomial_integral ( expon ) !*****************************************************************************80 ! !! triangle_unit_monomial_integral(): integral of a monomial over the unit triangle. ! ! Discussion: ! ! This routine integrates a monomial of the form ! ! product ( 1 <= dim <= dim_num ) x(dim)^expon(dim) ! ! where the exponents are nonnegative integers. Note that ! if the combination 0^0 is encountered, it should be treated ! as 1. ! ! Integral ( over unit triangle ) x^m y^n dx dy = m! * n! / ( m + n + 2 )! ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 04 July 2007 ! ! Author: ! ! John Burkardt ! ! Input: ! ! integer EXPON(3), the exponents. ! ! Output: ! ! real ( kind = rk ) triangle_unit_monomial_integral: ! the value of the integral. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer expon(3) integer i integer k real ( kind = rk ) triangle_unit_monomial_integral real ( kind = rk ) value ! ! The first computation ends with VALUE = 1.0; ! value = 1.0D+00 k = 0 do i = 1, expon(1) k = k + 1 ! value = value * real ( i, kind = rk ) / real ( k, kind = rk ) end do do i = 1, expon(2) k = k + 1 value = value * real ( i, kind = rk ) / real ( k, kind = rk ) end do k = k + 1 value = value / real ( k, kind = rk ) k = k + 1 value = value / real ( k, kind = rk ) triangle_unit_monomial_integral = value return end