subroutine get_unit ( iunit )

c*********************************************************************72
c
cc GET_UNIT returns a free Fortran unit number.
c
c  Discussion:
c
c    A "free" Fortran unit number is a value between 1 and 99 which
c    is not currently associated with an I/O device.  A free Fortran unit
c    number is needed in order to open a file with the OPEN command.
c
c    If IUNIT = 0, then no free Fortran unit could be found, although
c    all 99 units were checked (except for units 5, 6 and 9, which
c    are commonly reserved for console I/O).
c
c    Otherwise, IUNIT is a value between 1 and 99, representing a
c    free Fortran unit.  Note that GET_UNIT assumes that units 5 and 6
c    are special, and will never return those values.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    02 September 2013
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Output, integer IUNIT, the free unit number.
c
      implicit none

      integer i
      integer iunit
      logical value

      iunit = 0

      do i = 1, 99

        if ( i .ne. 5 .and. i .ne. 6 .and. i .ne. 9 ) then

          inquire ( unit = i, opened = value, err = 10 )

          if ( .not. value ) then
            iunit = i
            return
          end if

        end if

10      continue

      end do

      return
      end
      subroutine kjacoypols3 ( x, y, a, b, n, pols )

c*********************************************************************72
c
cc KJACOYPOLS3 evaluates modified Jacobi polynomials.
c
c  Discussion:
c
c    This procedure evaluates Jacobi polynomials multiplied by
c    specific polynomials given by the formula
c      P_n^{(a,b)} (x/y) y^n
c    at the user-provided point x/y.
c
c  Licensing:
c
c    This code is distributed under the GNU GPL license.
c
c  Modified:
c
c    13 June 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, double precision X, Y, define the evaluation point X/Y.
c
c    Input, double precision A, B, the parameters.
c
c    Input, integer N, the highest degree to compute.
c
c    Output, double precision POLS(N+1), the polynomial values.
c
      implicit none

      integer n

      double precision a
      double precision alpha
      double precision b
      double precision beta
      integer k
      double precision k_r8
      double precision pk
      double precision pkm1
      double precision pkp1
      double precision pols(n+1)
      double precision x
      double precision y

      pkp1 = 1.0D+00
      pols(1) = pkp1

      if ( n .eq. 0 ) then
        return
      end if

      pk = pkp1
      pkp1 = 0.5D+00 * ( ( a - b ) * y + ( 2.0D+00 + a + b ) * x )
      pols(2)= pkp1

      if ( n .eq. 1 ) then
        return
      end if

      do k = 2, n

        k_r8 = dble ( k )
  
        alpha = ( 2.0D+00 * k_r8 + a + b - 1.0D+00 ) 
     &    * ( a - b ) * ( a + b ) * y
     &    + ( 2.0D+00 * k_r8 + a + b - 1.0D+00 ) 
     &    * ( 2.0D+00 * k_r8 + a + b - 2.0D+00 ) 
     &    * ( 2.0D+00 * k_r8 + a + b ) * x

        beta = 2.0D+00 * ( k_r8 + a - 1.0D+00 ) 
     &    * ( k_r8 + b - 1.0D+00 ) 
     &    * ( 2.0D+00 * k_r8 + a + b ) * y * y

        pkm1 = pk
        pk = pkp1
        pkp1 = ( alpha * pk - beta * pkm1 ) 
     &    / ( 2.0D+00 * k_r8 * ( k_r8 + a + b ) 
     &    * ( 2.0D+00 * k_r8 + a + b - 2.0D+00 ) )

        pols(k+1) = pkp1

      end do

      return
      end
      subroutine klegeypols ( x, y, n, pols )

c*********************************************************************72
c
cc KLEGEYPOLS evaluates scaled Legendre polynomials.
c
c  Discussion:
c
c    This routine evaluate a sequence of scaled Legendre polynomials
c    P_n(x/y) y^n, with the parameter y in [0,1].
c
c  Licensing:
c
c    This code is distributed under the GNU GPL license.
c
c  Modified:
c
c    13 June 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, double precision X, the evaluation point.
c
c    Input, double precision Y, the parameter.
c
c    Input, integer N, the highest degree to be evaluated.
c
c    Output, double precision POLS(N+1), the polynomial values.
c
      implicit none

      integer n

      integer k
      double precision pk
      double precision pkm1
      double precision pkp1
      double precision pols(n+1)
      double precision x
      double precision y

      pkp1 = 1.0D+00
      pols(1) = pkp1
      if ( n .eq. 0 ) then
        return
      end if

      pk = pkp1
      pkp1 = x
      pols(2) = pkp1
      if ( n .eq. 1 ) then
        return
      end if

      do k = 1, n - 1
        pkm1 = pk
        pk = pkp1
        pkp1 = ( ( 2.0D+00 * k + 1.0D+00 ) * x * pk
     &    - k * pkm1 * y * y ) / ( k + 1.0D+00 )
        pols(k+2) = pkp1
      end do

      return
      end
      subroutine ortho3eva ( degree, xyz, fvals )

c*********************************************************************72
c
cc ORTHO3EVA evaluates polynomials orthogonal in the reference triangle.
c
c  Discussion:
c
c    This procedure evaluates the Koornwinder's orthogonal polynomial 
c    up to order DEGREE on the reference tetrahedron with vertices
c      (-1, -1/Sqrt(3), -1/Sqrt(6)), 
c      ( 0,  2/Sqrt(3), -1/Sqrt(6)), 
c      ( 1, -1/Sqrt(3), -1/Sqrt(6)),
c      ( 0,  0,          3/Sqrt(6))
c
c    The polynomials are ordered by their order, and in each order,
c    they are ordered lexicographically in terms of their indices
c    (m,n,k). 
c
c    The total number of polynomials should be
c      NVALS = ( ( DEGREE + 1 ) * ( DEGREE + 2 ) * ( DEGREE + 3 ) ) / 6.
c       
c    The calculations are based on Koornwinder's representation
c    of the orthogonal polynomials on the right triangle
c      (-1,-1,-1), (-1,1,-1), (1,-1,-1),(-1,-1,1)
c    given by:
c      K_mnk(x,y,z) = 
c        P_m ((2x+2+y+z)/(-y-z)) * ((-y-z)/2)^m *
C        P_n^{2m+1,0}((2y+1+z)/(1-z)) * ((1-z)/2)^{n}
C        P_k^{2m+2n+2,0} (z) 
c    with the input (x,y,z) transformed as
c      x = -1/2 + xold -yold/s3 - zold/s6
c      y = -1/2 + 2/s3 * yold - zold/s6
c      z = -1/2 + s6/2 * zold
c    where
c      s3=sqrt(3)
c      s6=sqrt(6)
c    and
c      P_m is the Legendre polynomial of degree m,
c      P_n^{2m+1,0} the Jacobi polynomial of degree n, parameters 2*m+1 and 0. 
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    10 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer DEGREE, the maximum degree.
c
c    Input, double precision XYZ(3), the evaluation point.
c
c    Output, double precision FVALS(NVALS), the polynomial values.
c
      implicit none

      integer degree

      double precision f1(degree+1)
      double precision f2s(degree+1,degree+1)
      double precision f3s(degree+1,degree+1)
      double precision fvals(((degree+1)*(degree+2)*(degree+3))/6)
      integer i
      integer j
      integer k
      integer m
      integer mmax
      integer n
      integer ncount
      double precision p1
      double precision p2
      double precision scale
      double precision uvw(3)
      double precision x1
      double precision xyz(3)
      double precision y1
c       
c  Convert coordinates from reference to Koornwinder tetrahedron.
c
      call ref_to_koorn ( xyz, uvw )
c  
c  Compute F1.
c
      p1 = 0.5D+00 * ( 2.0D+00 * uvw(1) + 2.0D+00 + uvw(2) + uvw(3) )
      p2 = - 0.5D+00 * ( uvw(2) + uvw(3) )

      call klegeypols ( p1, p2, degree, f1 )    
c       
c  Compute F2S.
c
      do j = 1, degree + 1
        do i = 1, degree + 1
          f2s(i,j) = 0.0D+00
        end do
      end do

      do m = 0, degree

        x1 = 0.5D+00 * ( 2.0D+00 * uvw(2) + 1.0D+00 + uvw(3) )
        y1 = 0.5D+00 * ( 1.0D+00 - uvw(3) )
        p1 = dble ( 2 * m + 1 )
        p2 = 0.0D+00

        call kjacoypols3 ( x1, y1, p1, p2, degree - m, f2s(1,m+1) )

      end do
c
c  Compute F3S.
c
      do j = 1, degree + 1
        do i = 1, degree + 1
          f3s(i,j) = 0.0D+00
        end do
      end do

      x1 = uvw(3)
      y1 = 1.0D+00
      p2 = 0.0D+00

      do j = 1, degree + 1

        p1 = dble ( 2 * j )

        call kjacoypols3 ( x1, y1, p1, p2, degree + 1 - j, f3s(1,j) )

      end do
c
c  Construct FVALS.
c
      ncount = 0

      do mmax = 0, degree

        do m = 0, mmax

          do n = 0, mmax - m

            k = mmax - m - n
            ncount = ncount + 1

            scale = sqrt 
     &      ( 
     &        4.0D+00
     &        / dble ( 2 * mmax + 3 ) 
     &        / dble ( 2 * m + 1 )
     &        / dble ( n + m + 1 )
     &        / sqrt ( 2.0D+00 ) 
     &      )

            fvals(ncount) = 
     &        f1(m+1) *
     &        f2s(n+1,m+1) *
     &        f3s(k+1,m+n+1) / scale


          end do
        end do
      end do

      return
      end
      subroutine r8mat_row_copy ( m, n, i, v, a )

c*********************************************************************72
c
cc R8MAT_ROW_COPY copies a vector into a row of an R8MAT.
c
c  Discussion:
c
c    An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M].
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    30 June 2014
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer M, N, the order of the matrix.
c
c    Input, integer I, the index of the row.
c    1 <= I <= M.
c
c    Input, double precision V(N), the row to be copied.
c
c    Input/output, double precision A(M,N), the matrix into which
c    the row is to be copied.
c
      implicit none

      integer m
      integer n

      double precision a(m,n)
      integer i
      integer j
      double precision v(n)

      do j = 1, n
        a(i,j) = v(j)
      end do

      return
      end
      subroutine r8vec_copy ( n, a1, a2 )

c*********************************************************************72
c
cc R8VEC_COPY copies an R8VEC.
c
c  Discussion:
c
c    An R8VEC is a vector of R8 values.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    13 August 2008
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the length of the vectors.
c
c    Input, double precision A1(N), the vector to be copied.
c
c    Output, double precision A2(N), a copy of A1.
c
      implicit none

      integer n

      double precision a1(n)
      double precision a2(n)
      integer i

      do i = 1, n
        a2(i) = a1(i)
      end do

      return
      end
      subroutine r8vec_print ( n, a, title )

c*********************************************************************72
c
cc R8VEC_PRINT prints an R8VEC.
c
c  Discussion:
c
c    An R8VEC is a vector of R8's.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 January 2007
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the number of components of the vector.
c
c    Input, double precision A(N), the vector to be printed.
c
c    Input, character * ( * ) TITLE, a title.
c
      implicit none

      integer n

      double precision a(n)
      integer i
      character * ( * ) title

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) trim ( title )
      write ( *, '(a)' ) ' '
      do i = 1, n
        write ( *, '(2x,i8,a,1x,g16.8)' ) i, ':', a(i)
      end do

      return
      end
      function r8vec_sum ( n, v1 )

c*********************************************************************72
c
cc R8VEC_SUM sums the entries of an R8VEC.
c
c  Discussion:
c
c    An R8VEC is a vector of R8's.
c
c    In Fortran90, the system routine SUM should be called
c    directly.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    22 July 2008
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the dimension of the vectors.
c
c    Input, double precision V1(N), the vector.
c
c    Output, double precision R8VEC_SUM, the sum of the entries.
c
      implicit none

      integer n

      integer i
      double precision r8vec_sum
      double precision v1(n)
      double precision value

      value = 0.0D+00
      do i = 1, n
        value = value + v1(i)
      end do

      r8vec_sum = value

      return
      end
      subroutine ref_to_koorn ( r, u )

c*********************************************************************72
c
cc REF_TO_KOORN maps points from the reference to Koornwinder's tetrahedron.
c
c  Discussion:
c
c    The reference tetrahedron has vertices:
c
c      (-1, -1/Sqrt(3), -1/Sqrt(6) )
c      ( 0,  2/Sqrt(3), -1/Sqrt(6) ) 
c      ( 1, -1/Sqrt(3), -1/Sqrt(6) )
c      ( 0,  0,          3/Sqrt(6) )
c
c    Koornwinder's tetrahedron has vertices:
c
c      ( -1, -1, -1 )
c      ( -1, +1, -1 )
c      ( +1, -1, -1 )
c      ( -1, -1, +1 )
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    10 July 2013
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, double precision R(3), the coordinates of a point in the
c    reference tetrahedron.
c
c    Output, double precision U(3), the coordinates of the point in
c    the Koornwinder tetrahedron.
c
      implicit none

      double precision a10
      double precision a11
      double precision a12
      double precision a13
      double precision a20
      double precision a21
      double precision a22
      double precision a23
      double precision a30
      double precision a31
      double precision a32
      double precision a33
      double precision s3
      double precision s6
      double precision r(3)
      double precision u(3)

      s3 = sqrt ( 3.0D+00 )
      s6 = sqrt ( 6.0D+00 )

      a10 = - 0.5D+00
      a11 =   1.0D+00
      a12 = - 1.0D+00 / s3
      a13 = - 1.0D+00 / s6

      a20 = - 0.5D+00
      a21 =   0.0D+00
      a22 =   2.0D+00 / s3
      a23 = - 1.0D+00 / s6

      a30 = - 0.5D+00
      a31 =   0.0D+00
      a32 =   0.0D+00
      a33 =   0.5D+00 * s6

      u(1) = a10 + a11 * r(1) + a12 * r(2) + a13 * r(3)
      u(2) = a20 +              a22 * r(2) + a23 * r(3)
      u(3) = a30 +                           a33 * r(3)

      return
      end
      subroutine rule01 ( n, x, w )

c*********************************************************************72
c
cc RULE01 returns the rule of degree 1.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 1 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     &     0.00000000000000000D+00 /
      data ys /
     &     0.00000000000000000D+00 /
      data zs /
     &     0.00000000000000000D+00 /
      data ws /
     &     0.9709835434146467D+00 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule02 ( n, x, w )

c*********************************************************************72
c
cc RULE02 returns the rule of degree 2.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 4 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.2677028585910073D+00,0.1510931841533142D+00,
     2  -.1367699195237390D+00,0.8067449309051964D+00 /
      data ys /
     1  0.5939017006199488D-01,0.4354087732476309D+00,
     2  -.3280341115590410D+00,-.3400977314285288D+00 /
      data zs /
     1  -.3969426941142150D+00,0.2151719254306919D+00,
     2  0.2950846519937133D+00,-.3430378951002550D+00 /
      data ws /
     1  0.2918008865477151D+00,0.2706884392356724D+00,
     2  0.3098349601753470D+00,0.9865925745591227D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule03 ( n, x, w )

c*********************************************************************72
c
cc RULE03 returns the rule of degree 3.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 6 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.1685037180276000D+00,0.2783799427534418D-01,
     2  -.3512216177343445D+00,0.4308532463549043D+00,
     3  -.4676763747967377D+00,0.1492831253848431D+00 /
      data ys /
     1  0.1910914916271708D+00,-.2304932838839657D-01,
     2  0.1835144026339993D+00,-.2474715823180446D+00,
     3  -.4235250827264375D+00,0.6397847685164516D+00 /
      data zs /
     1  -.3896267314585163D+00,0.5481350663241830D+00,
     2  0.5147815330343534D-01,-.1683315641007033D+00,
     3  -.1586973077889307D+00,-.1080219253055393D+00 /
      data ws /
     1  0.1287213727402025D+00,0.2179034339695993D+00,
     2  0.1243503792062836D+00,0.2446917182410072D+00,
     3  0.1365439875826512D+00,0.1187726516749031D+00 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule04 ( n, x, w )

c*********************************************************************72
c
cc RULE04 returns the rule of degree 4.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 11 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.1459612280979987D-01,-.2937244896309993D+00,
     2  0.3230878337158274D+00,-.8819654179396583D-01,
     3  0.1270203663314710D+00,-.4414307688091184D+00,
     4  0.3939418589633429D+00,-.6034469714614210D-01,
     5  -.8914059834601185D-01,0.6545213033603760D+00,
     6  -.7307642259677857D+00 /
      data ys /
     1  0.2426564579199708D-02,0.1764396506764613D+00,
     2  -.1932070410956556D+00,0.2317884270105980D-01,
     3  0.5451410677215219D+00,-.3848225631590180D+00,
     4  0.2068744670639530D+00,-.4573739074927080D+00,
     5  0.7268092659599459D+00,-.3970356243870571D+00,
     6  -.2669420088648982D+00 /
      data zs /
     1  0.7093565780103633D+00,0.1108860494941134D+00,
     2  0.1695426396704650D+00,-.2011819391325586D+00,
     3  0.1309503990759315D+00,0.9225429679162532D-01,
     4  -.3111560426198242D+00,-.3302215329322376D+00,
     5  -.3507931737363739D+00,-.2970424833951137D+00,
     6  -.3861037570241846D+00 /
      data ws /
     1  0.1033787090646894D+00,0.1070356256090164D+00,
     2  0.1504792582740940D+00,0.1877987156186583D+00,
     3  0.7395274312521298D-01,0.7712199925411270D-01,
     4  0.6745419368701999D-01,0.5819413648173244D-01,
     5  0.5378646711152148D-01,0.5366953183949744D-01,
     6  0.3811216334909158D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule05 ( n, x, w )

c*********************************************************************72
c
cc RULE05 returns the rule of degree 5.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 14 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.1664180721577685D-15,0.4089925917487008D+00,
     2  0.6338467275429999D-16,-.4089925917487006D+00,
     3  0.3723900931035782D-16,-.2435436770532023D+00,
     4  0.7718657600705262D-17,0.2435436770532026D+00,
     5  0.6290589987564350D+00,-.6290589987564351D+00,
     6  -.1407768953799327D-15,0.4089925917487006D+00,
     7  -.1047965211464895D-15,-.4089925917487007D+00 /
      data ys /
     1  0.1094362324146226D-15,-.2361319829426750D+00,
     2  0.4722639658853500D+00,-.2361319829426750D+00,
     3  0.3548001489301807D-16,0.1406100075060977D+00,
     4  -.2812200150121953D+00,0.1406100075060977D+00,
     5  -.3631873822681842D+00,-.3631873822681841D+00,
     6  0.7263747645363684D+00,0.2361319829426750D+00,
     7  -.4722639658853500D+00,0.2361319829426750D+00 /
      data zs /
     1  0.7704367825296720D+00,0.3339410527875835D+00,
     2  0.3339410527875834D+00,0.3339410527875834D+00,
     3  -.2982788694307592D+00,0.9942628981025299D-01,
     4  0.9942628981025306D-01,0.9942628981025299D-01,
     5  -.2568122608432240D+00,-.2568122608432239D+00,
     6  -.2568122608432239D+00,-.3339410527875835D+00,
     7  -.3339410527875834D+00,-.3339410527875835D+00 /
      data ws /
     1  0.7136053542145054D-01,0.4131148601232373D-01,
     2  0.4131148601232375D-01,0.4131148601232376D-01,
     3  0.1094181214137256D+00,0.1094181214137255D+00,
     4  0.1094181214137255D+00,0.1094181214137255D+00,
     5  0.7136053542145050D-01,0.7136053542145052D-01,
     6  0.7136053542145050D-01,0.4131148601232370D-01,
     7  0.4131148601232373D-01,0.4131148601232375D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule06 ( n, x, w )

c*********************************************************************72
c
cc RULE06 returns the rule of degree 6.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 23 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.4919941951523113D-02,0.3415058060219544D-01,
     2  -.4561198328617235D+00,0.2144499229769493D+00,
     3  -.1540693059995943D+00,0.3064525403222947D+00,
     4  -.1305882959514773D-01,0.1535244689838072D-01,
     5  -.1567784487775340D+00,-.3973616940506757D+00,
     6  0.9764884616649552D-02,-.5228087984647453D+00,
     7  0.5565605702210328D+00,0.8423081979023464D-01,
     8  0.2174166091160236D+00,0.3212158945225647D+00,
     9  -.2593648078545398D+00,0.5636454767202584D+00,
     *  -.6410949644625729D+00,-.3344151090582155D+00,
     1  -.1894588386892019D-01,-.8214655896199351D+00,
     *  0.8597415475615655D+00 /
      data ys /
     1  -.1392238503430922D-01,0.2542073830543402D+00,
     2  -.3110385447445375D+00,-.1234903873249722D+00,
     3  -.6865214472302168D-01,0.1818495501923178D+00,
     4  -.2488891169073396D-01,-.3261143100532925D+00,
     5  0.2522454301000923D+00,-.1977159083378496D+00,
     6  0.6504184291133676D+00,-.6635055304123420D-01,
     7  -.3186690054220115D+00,0.2138059822864521D-01,
     8  0.4599507004997997D+00,-.4260052421545051D+00,
     9  0.3851980211137577D+00,-.1111606227821696D+00,
     *  -.1934318338507612D+00,-.4491758699723651D+00,
     1  0.9010599459930961D+00,-.5109860359355179D+00,
     *  -.5208085141225744D+00 /
      data zs /
     1  0.1066228263967720D+01,0.6315886967039234D+00,
     2  0.2300267655106985D+00,0.5632351636302827D+00,
     3  0.6206264896282621D+00,0.1254685876442911D+00,
     4  -.3357705926282663D+00,0.1147788985927003D+00,
     5  0.2140597800705522D+00,-.7963361802882329D-01,
     6  0.5868446281578688D-02,0.1934272688455952D-02,
     7  0.1379740251424839D-01,0.3195756126912550D-01,
     8  -.3027232303753162D+00,-.2994855602604263D+00,
     9  -.2825197099253122D+00,-.3068140495300409D+00,
     *  -.3660473605161587D+00,-.3102423292746128D+00,
     1  -.3473952050436902D+00,-.2635645240101362D+00,
     *  -.3603432585369335D+00 /
      data ws /
     1  0.6889900028407776D-02,0.3059511845881479D-01,
     2  0.2352818079375775D-01,0.4747145913756433D-01,
     3  0.5149448476741100D-01,0.4198464552012798D-01,
     4  0.6518777271610311D-01,0.5808554412413398D-01,
     5  0.6079762507769643D-01,0.6246727661754427D-01,
     6  0.4232555916776466D-01,0.2191089157324707D-01,
     7  0.4526058614388953D-01,0.1093321687620292D+00,
     8  0.5237000773398501D-01,0.4832452079715138D-01,
     9  0.6123639953387314D-01,0.4577996169297793D-01,
     *  0.2476427914920903D-01,0.3856173525882120D-01,
     1  0.1546337820963114D-01,0.1012088745519476D-01,
     *  0.7031160695311595D-02 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule07 ( n, x, w )

c*********************************************************************72
c
cc RULE07 returns the rule of degree 7.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 31 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.3082522913562920D+00,0.3230068564765168D+00,
     2  0.1790030943099486D-02,-.1749858562850217D+00,
     3  0.3515818224512229D-01,-.1148912802505062D+00,
     4  0.1080242619580473D+00,0.9960886019209524D-01,
     5  0.2552589657173040D+00,0.3018972093964544D+00,
     6  -.3637995251662868D-01,-.1979748432674351D+00,
     7  0.1705547608587194D+00,0.5382714575357732D+00,
     8  -.5826255951559661D+00,-.6638827484255140D-01,
     9  0.1394865450483365D+00,-.2525448211561483D+00,
     *  -.3364179479356783D+00,0.5088174095091343D+00,
     1  -.3997676771299581D+00,0.2233579208997628D+00,
     2  -.2887689832327979D+00,0.2430056805988458D+00,
     3  -.2402459184668794D+00,-.5737122495168941D+00,
     4  0.5530740586345179D+00,0.7632160871540358D+00,
     5  0.1108323525316276D-02,-.7666589725519221D+00,
     *  0.3314379268437029D+00 /
      data ys /
     1  -.1978432879678884D+00,-.1166608144800289D+00,
     2  0.2760223041671345D-02,0.1492553071272583D+00,
     3  0.3222570009831960D+00,0.3598150246997987D-01,
     4  -.2123211082745265D+00,0.3370600346165786D+00,
     5  0.2345931387652712D-01,-.2797440812728529D+00,
     6  0.6784158147792628D+00,-.1099260120706853D+00,
     7  0.5854481149716676D-01,-.3326202438156060D+00,
     8  -.2866394288669600D+00,0.3396643732745171D+00,
     9  -.3078502318368667D+00,-.9687707852320762D-01,
     *  -.4222809305623556D+00,-.4607960014652947D-01,
     1  0.1694117934001565D+00,0.5070263922318456D+00,
     2  -.4320411612241725D+00,0.5262155488082486D+00,
     3  0.4919239659783042D+00,-.7453182334351910D-01,
     4  -.3355026530466742D-02,-.4345394288375978D+00,
     5  0.8835815093231754D+00,-.4540327424996255D+00,
     *  -.5419034033722774D+00 /
      data zs /
     1  0.6553771405341420D+00,0.5963217268212818D+00,
     2  0.9191670342435462D+00,0.5162921387398244D+00,
     3  0.5492103599470217D+00,-.3886917653966460D+00,
     4  0.5138214657068572D+00,-.2732502226402171D+00,
     5  -.1289266426427488D+00,-.3368155028155599D+00,
     6  0.4965154590499942D-01,0.3688101367310880D+00,
     7  0.3245398450336227D+00,0.6530998463389483D-01,
     8  0.4050073689194288D-01,0.4339137621154699D-01,
     9  -.8554188228126980D-02,-.1212234343128167D+00,
     *  0.2244936992133664D-01,-.5389155149780182D-01,
     1  -.1331769110761944D-01,-.3996173060097081D-01,
     2  -.3304370757138854D+00,-.3633697548034391D+00,
     3  -.3184670075538235D+00,-.3348000741414298D+00,
     4  -.3507444035401421D+00,-.3120479891575616D+00,
     5  -.3155336884007630D+00,-.3148702231578014D+00,
     *  -.3104410268762152D+00 /
      data ws /
     1  0.7484517057961263D-02,0.1165548467333077D-01,
     2  0.2254313978794985D-01,0.2176106698437745D-01,
     3  0.2261516504544270D-01,0.2653689704536702D-01,
     4  0.2796071748247393D-01,0.4174371077929897D-01,
     5  0.5125012874361469D-01,0.4062452567161350D-01,
     6  0.2011109093086575D-01,0.5855177928202636D-01,
     7  0.6477548431925077D-01,0.3049968783939012D-01,
     8  0.2749125083938057D-01,0.6480294592357103D-01,
     9  0.6232630627722486D-01,0.7994900688083093D-01,
     *  0.2026705321864424D-01,0.2384971520555609D-01,
     1  0.2170019222676944D-01,0.2153672490681497D-01,
     2  0.3586406280991152D-01,0.1621736817489311D-01,
     3  0.3281522904442925D-01,0.2724694235165297D-01,
     4  0.2048072851756261D-01,0.1999288967511468D-01,
     5  0.1864561424137827D-01,0.1753312507928042D-01,
     *  0.1215099239866789D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule08 ( n, x, w )

c*********************************************************************72
c
cc RULE08 returns the rule of degree 8.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 44 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.1611772551670525D-01,-.7148827236840712D-02,
     2  0.4589923372088558D+00,-.4520990492494178D+00,
     3  0.1109560356430631D+00,0.1825224293648890D+00,
     4  -.1507489805419971D+00,-.2877324734878600D+00,
     5  0.3680747212378487D+00,0.4788156424890513D+00,
     6  -.3478779367400819D+00,-.3548285868734744D-01,
     7  0.2591650442934043D+00,-.1305037378946309D-02,
     8  -.3493996070828597D-01,-.1660462859707297D+00,
     9  0.1010085522422429D+00,-.3587468163605144D+00,
     *  -.3473067563985682D+00,-.8635741121401184D-01,
     1  0.2901168201778487D+00,0.1042093355150105D+00,
     2  -.6419387451918364D-01,-.2016986972118968D+00,
     3  0.1846170677356399D+00,0.3788893958160157D+00,
     4  -.4818716163165796D+00,0.6821719050778170D+00,
     5  0.3978642293015137D+00,-.6975889470159129D+00,
     6  0.2742964749336314D-02,0.1645687860050991D-01,
     7  -.4618349214785903D+00,0.1575090568397094D+00,
     8  0.5399175203215238D+00,-.1403905262089725D+00,
     9  0.4453396570037857D-01,-.4234360302104348D+00,
     *  -.7214176376894034D+00,0.7278118716190342D+00,
     1  0.4901890779701343D+00,-.8758887352507779D+00,
     2  0.7632377205619759D-02,0.9317431147169187D+00 /
      data ys /
     1  0.7998600119500696D-03,0.1723914595007140D+00,
     2  -.1744716351651229D+00,-.2632941629071404D+00,
     3  -.6295720376005641D-01,0.1678382818593359D+00,
     4  -.7826941873249307D-01,-.1234686974783635D+00,
     5  -.2169876766339741D+00,-.4629437300594242D-01,
     6  -.1295630336164733D+00,-.2268108031307481D+00,
     7  0.1330071443027294D+00,0.4919409115894537D+00,
     8  0.3001995169122194D+00,0.1407736457687509D+00,
     9  -.2259257575315161D+00,-.1083199795573463D+00,
     *  -.3742304739030127D+00,-.1478062482085008D+00,
     1  -.3449512373726749D+00,0.2883671141680468D-01,
     2  0.2558125570853043D+00,0.4404368079041183D+00,
     3  0.3998568605285963D+00,-.9956585162815586D-01,
     4  -.1509747383909747D-01,-.3956518618817587D+00,
     5  0.2256616013248351D+00,-.3899651023918449D+00,
     6  0.8134998230879619D+00,-.4451036700294634D+00,
     7  -.4535647479937944D+00,0.6650145460171435D+00,
     8  -.4674624469973033D+00,0.7012653983759632D+00,
     9  -.5107241847309127D+00,0.2263324997687613D+00,
     *  -.2727155170636352D+00,-.2861627803070728D+00,
     1  0.1856306523332632D+00,-.5566374678887420D+00,
     2  0.1056056946669113D+01,-.5664247124705913D+00 /
      data zs /
     1  0.1140750120480647D+01,0.7860696072793454D+00,
     2  -.3991430912330994D+00,0.3536092960240441D+00,
     3  0.8189404142301465D+00,0.4764962716361752D+00,
     4  0.7628974295081231D+00,-.3880058323817796D+00,
     5  0.3997553695274408D+00,0.1144656464995089D+00,
     6  0.2509171968778639D+00,0.4174615578343315D+00,
     7  -.2747778345118032D+00,0.3031929324753210D+00,
     8  -.3442503524230918D+00,0.3970537434180833D+00,
     9  -.3070893258601431D+00,-.1989904396903917D+00,
     *  0.1526258958568332D-01,-.1542350189843949D-03,
     1  0.4121026001314489D-01,0.3248913848279931D+00,
     2  -.6957900515388780D-01,-.3340987564879216D-01,
     3  -.1303527431545757D-01,-.8390322512212595D-01,
     4  -.4501404031339341D-01,-.7451523522744341D-01,
     5  -.3993939022009145D+00,-.1254210458205579D+00,
     6  -.1415815795205319D+00,-.1858244299410800D+00,
     7  -.3245512424809017D+00,-.3317121001508232D+00,
     8  -.3168159505701121D+00,-.3372150239150091D+00,
     9  -.3950013670511707D+00,-.3336444006035868D+00,
     *  -.3519392970001664D+00,-.3226167582915808D+00,
     1  -.2780042325707565D+00,-.3720577799104590D+00,
     2  -.3972751008974220D+00,-.3821073616790632D+00 /
      data ws /
     1  0.1694544493019982D-02,0.1462667227182682D-01,
     2  0.9589935274093377D-02,0.9835015847019813D-02,
     3  0.1710148279355958D-01,0.1516325692442914D-01,
     4  0.1746691605511999D-01,0.1604974314640067D-01,
     5  0.2185156320663785D-01,0.1242799062066869D-01,
     6  0.2646409426919389D-01,0.3135597218974045D-01,
     7  0.2736783716876112D-01,0.2345735439005822D-01,
     8  0.3130572641601596D-01,0.3548953658742431D-01,
     9  0.4036134913447077D-01,0.3792924852161072D-01,
     *  0.2440963887102594D-01,0.5132903383025206D-01,
     1  0.3177764520649842D-01,0.5417358749775593D-01,
     2  0.5180566415546370D-01,0.2633068360731991D-01,
     3  0.3893527990282211D-01,0.5027716272897634D-01,
     4  0.2208377845212325D-01,0.1429278762793107D-01,
     5  0.6697289387082959D-02,0.1648266825522313D-01,
     6  0.1688462952130244D-01,0.2190464958161271D-01,
     7  0.2281706804403004D-01,0.1956212468616595D-01,
     8  0.1994889218942623D-01,0.1737944394368884D-01,
     9  0.7302913219204132D-02,0.2128832734454982D-01,
     *  0.1333720911018169D-01,0.1494192725418561D-01,
     1  0.1152112823254964D-01,0.2472998490996246D-02,
     2  0.2018756899942699D-02,0.1470016064285112D-02 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule09 ( n, x, w )

c*********************************************************************72
c
cc RULE09 returns the rule of degree 9.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 57 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.2108052017103265D+00,0.1283729355850052D-02,
     2  -.2918734175018473D-01,-.4357949297689266D+00,
     3  -.1799341637870203D+00,0.6942222186204158D-01,
     4  -.1005642991135230D+00,0.1904855696753355D+00,
     5  0.3231238851996552D+00,0.6819987943340138D-01,
     6  0.9708131623556143D-01,0.4246239788055203D+00,
     7  -.3569664256203109D+00,-.2145752061141752D+00,
     8  -.4818674305781609D-02,-.4314954104621454D+00,
     9  -.1312453567417025D+00,-.4083558222913988D+00,
     *  -.1245612605849638D+00,0.1136348780330888D+00,
     1  0.3351668846328467D+00,0.2159589333207287D+00,
     2  -.1228639493897767D+00,0.1380276243456064D+00,
     3  0.3905319783823730D+00,-.4580867844324543D+00,
     4  0.2310228564389770D+00,0.3554068884610396D+00,
     5  -.6505241861040961D-01,-.1786506541288197D+00,
     6  0.1265104521534247D-01,-.4573827823867556D+00,
     7  -.5542731199877091D-01,-.6387630000068671D-01,
     8  -.3413749732146179D+00,0.5966077890976830D+00,
     9  0.6917314710518101D+00,0.1078283022003015D-01,
     *  0.1833983579629060D+00,-.1566832100689738D+00,
     1  -.7215475195156269D+00,0.5634418100399829D+00,
     2  -.6038175317729408D+00,0.4424617155479634D+00,
     3  0.5376954508544742D+00,0.5801674951413821D+00,
     4  0.1418634443888370D+00,0.3802052805108170D-01,
     5  -.6766546338276799D+00,-.1483779428740810D+00,
     6  0.7588538984987838D+00,-.4009332704109223D+00,
     7  0.4294022281773516D+00,-.4911820218387012D+00,
     8  -.8230436696819400D+00,0.8307385272442451D+00,
     *  0.2847756354434797D-02 /
      data ys /
     1  -.8955776048075967D-01,0.6121197754911472D-03,
     2  0.2122758579659528D+00,-.2839355480318341D+00,
     3  -.9582556152029258D-01,-.1394666680707507D+00,
     4  0.4836397528261835D+00,0.3248843951738821D+00,
     5  -.3091097002134723D+00,-.1799541017656358D+00,
     6  0.1346690341273634D+00,-.1974037451364399D+00,
     7  0.5240665094885540D-01,0.2761387382865308D+00,
     8  0.4840041246351735D+00,-.3972752286396523D+00,
     9  0.7569076187744307D-01,-.1239859742013766D+00,
     *  -.2344790300437711D+00,-.3305476987034425D-01,
     1  0.1770622072827525D-01,0.2385246764606510D+00,
     2  0.5313763678851683D-01,0.7344859267512056D-02,
     3  -.2434286634053894D+00,-.2589556174266634D+00,
     4  -.2578369917972710D+00,0.1458366018963618D+00,
     5  -.3194064610603558D+00,-.8361295659204318D-01,
     6  0.2789606323941811D+00,-.3620544381079852D+00,
     7  0.4583494650640864D+00,-.4110512725485398D+00,
     8  0.1453586652323175D+00,-.2817335623108552D+00,
     9  -.4244951895917183D+00,0.7740686042096789D+00,
     *  0.5096501737807261D+00,0.5871627777302516D+00,
     1  -.4069288134308984D+00,-.8745287448038948D-01,
     2  -.1605011166676197D+00,-.4658949840050826D+00,
     3  -.4822919051612324D+00,-.2630487459758545D-01,
     4  0.7093134008050596D+00,-.4981319573109797D+00,
     5  -.1608102554139131D+00,0.7476578114817578D+00,
     6  -.2863864956290275D+00,0.3184909341350718D+00,
     7  0.3342451266830045D+00,-.5259906817121476D+00,
     8  -.4752298758892802D+00,-.4894484556416516D+00,
     *  0.9800293546928647D+00 /
      data zs /
     1  0.7735882074261043D+00,0.1020940836140086D+01,
     2  0.7799358723388078D+00,0.3644377643783332D+00,
     3  0.7572044348058194D+00,0.7055487604983020D+00,
     4  -.4071603611745789D+00,0.2784337835342537D+00,
     5  0.3220003691351323D+00,-.3955135683176328D+00,
     6  0.6632209417507691D+00,0.3671897521183273D+00,
     7  -.3747481356463467D+00,0.2325932263186099D+00,
     8  0.3487840306818015D+00,-.4035704541972099D+00,
     9  0.5374900196303547D+00,0.2654318104765763D+00,
     *  0.3698883029355781D+00,0.4369873036895401D+00,
     1  0.1860393220233105D+00,-.3479911186004724D+00,
     2  -.2731450419753432D+00,-.8193864872695196D-01,
     3  -.2812924318728223D+00,-.2546313790752990D+00,
     4  0.8678030145840356D-01,-.1428438498378993D+00,
     5  -.2156622116049685D+00,0.9674903232992661D-01,
     6  0.1583036737187768D+00,-.2371578880066309D-01,
     7  -.2083640565350588D+00,-.1327703130967625D-01,
     8  -.8664488303113425D-01,-.7748272430107629D-01,
     9  -.9669501947122619D-02,-.6316745396431407D-01,
     *  -.1041997605600258D+00,-.7558004547861685D-01,
     1  -.7999199041063003D-01,-.3751069250486347D+00,
     2  -.1299227031705554D+00,-.1892728310331580D+00,
     3  -.3910612496171095D+00,-.1907765273821742D+00,
     4  -.3477134529420335D+00,-.3474543531762018D+00,
     5  -.3606479588180986D+00,-.3440499686491684D+00,
     6  -.3474563411684222D+00,-.3276892436683218D+00,
     7  -.3542380917718721D+00,-.3040019129455090D+00,
     8  -.3440705957046394D+00,-.3298160634602457D+00,
     *  -.3378012113084769D+00 /
      data ws /
     1  0.5680408778529046D-02,0.6887854441113948D-02,
     2  0.6899595536569939D-02,0.6990873936739353D-02,
     3  0.1142122940842178D-01,0.1220808590880294D-01,
     4  0.7651487209643779D-02,0.9540263940869291D-02,
     5  0.9495638963926394D-02,0.1385248437188017D-01,
     6  0.1446333231867884D-01,0.1128763818550772D-01,
     7  0.1290073048331596D-01,0.1468008559737106D-01,
     8  0.1526131467815127D-01,0.7960414659472547D-02,
     9  0.2551792590874883D-01,0.1931170779707098D-01,
     *  0.2561026230172263D-01,0.3169262013385435D-01,
     1  0.2455872440888530D-01,0.2465571070153197D-01,
     2  0.3419839251013865D-01,0.4066027350436995D-01,
     3  0.3092126671144214D-01,0.2731106642703576D-01,
     4  0.3711204543388613D-01,0.2490755526192437D-01,
     5  0.3425568258765496D-01,0.4767735489615401D-01,
     6  0.4389950894493362D-01,0.2234183537671572D-01,
     7  0.3468016547781724D-01,0.1599733331684861D-01,
     8  0.3216001820424372D-01,0.2173130208768448D-01,
     9  0.4172519829863862D-02,0.1261067900439839D-01,
     *  0.2073467359947484D-01,0.1259876220642243D-01,
     1  0.6842300320404830D-02,0.1001228308171065D-01,
     2  0.1328037050111305D-01,0.1493735138014892D-01,
     3  0.6932861063756816D-02,0.6827617690151055D-02,
     4  0.1270616397760185D-01,0.1288875403806118D-01,
     5  0.8899252930026689D-02,0.8881169613715286D-02,
     6  0.5288619835392034D-02,0.1284718318260967D-01,
     7  0.6409598847098365D-02,0.8055508398015583D-02,
     8  0.7788463427997768D-02,0.6545788868966830D-02,
     *  0.5341431206058898D-02 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule10 ( n, x, w )

c*********************************************************************72
c
cc RULE10 returns the rule of degree 10.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 74 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.4135441926108436D+00,0.6920344574148628D-02,
     2  -.4204645371849727D+00,0.1212827019050737D+00,
     3  0.2550746585402268D+00,-.3763573604446380D+00,
     4  -.4793578815415788D-03,-.9545817212686222D-01,
     5  0.9593753000785579D-01,0.3126301401176562D+00,
     6  -.6029042538437952D+00,0.2902741137267026D+00,
     7  0.1793124962974703D+00,-.3341633308670676D+00,
     8  0.1548508345696874D+00,0.4006666604011494D+00,
     9  -.3875674230187136D+00,-.1309923738259358D-01,
     *  -.1159749898125322D+00,-.6294076737424348D+00,
     1  0.7453826635553922D+00,-.1465165887848432D+00,
     2  -.4643141868299223D+00,0.6108307756147643D+00,
     3  0.1526773226986329D+00,-.6092465369941313D+00,
     4  0.4565692142952937D+00,-.2349836288652037D+00,
     5  0.5557206177695652D+00,-.3207369889038079D+00,
     6  0.2617190792164227D+00,-.2353754650695125D+00,
     7  -.2634361414712093D-01,-.1518707842414898D+00,
     8  -.2491539125596758D+00,0.4010246968008866D+00,
     9  0.2108318943729519D+00,0.7968056612120857D-02,
     *  -.2187999509850842D+00,-.6451845341149960D+00,
     1  0.5779406907458116D+00,0.6724384336957467D-01,
     2  -.1117027003111241D+00,-.2717471055583957D+00,
     3  0.3834498058697393D+00,0.2353864631064914D+00,
     4  0.1649339445101810D+00,-.4003204076167762D+00,
     5  0.7813866474350551D+00,0.1310349087707534D-02,
     6  -.7826969965232643D+00,-.1446486485942199D+00,
     7  -.1795841794748884D-02,0.1464444903888344D+00,
     8  0.5662897411515679D+00,0.1839447497576211D-02,
     9  -.5681291886496517D+00,0.1959958820407995D-02,
     *  -.3041697942355038D+00,0.3022098354145521D+00,
     1  -.7138061627291874D-01,-.3075192230121023D+00,
     2  0.3788998392856530D+00,-.3187848524903898D-01,
     3  -.9081742825948123D+00,0.9400527678433584D+00,
     4  0.9976676831438748D-01,-.8701982408315725D+00,
     5  0.7704314725177221D+00,-.8207757778140335D-14,
     6  -.3478417597234231D-12,0.4790952016774938D-12,
     7  0.1374787712765062D-12,0.1420358457394610D-12 /
      data ys /
     1  -.2467507765313092D+00,0.4815151646539115D+00,
     2  -.2347643881227681D+00,-.3645574461360758D+00,
     3  0.2873126239566789D+00,0.7724482217897545D-01,
     4  0.1105023601492690D+00,-.5566631617759855D-01,
     5  -.5483604397160680D-01,0.5156767709512212D+00,
     6  0.1290725785546668D-01,-.5285840288063388D+00,
     7  0.2823324600522004D+00,0.1412294698335291D-01,
     8  -.2964554070359728D+00,0.2161993077800489D+00,
     9  0.2388878524669672D+00,-.4550871602470489D+00,
     *  0.7937355713187059D+00,-.4973050730407310D+00,
     1  -.2964304982776649D+00,0.6207352334853357D+00,
     2  -.4372547047061620D+00,-.1834805287791172D+00,
     3  0.6153490109135903D+00,-.1754520654179484D+00,
     4  -.4398969454955785D+00,-.5060230351463111D+00,
     5  0.4950972550220373D-01,0.4565133096445042D+00,
     6  0.1206845953990400D+00,0.1663130735568127D+00,
     7  -.2869976689562073D+00,0.3753807951356096D+00,
     8  -.3192143548135662D+00,-.5616644032198326D-01,
     9  -.1309245702301312D+00,0.2480480615696827D+00,
     *  -.1171234913398124D+00,-.2948509623067830D+00,
     1  -.4113207155193597D+00,0.7061716778256595D+00,
     2  0.3782781131850991D+00,-.2858764327334718D+00,
     3  -.9240168045211911D-01,-.3263497523611192D+00,
     4  0.3670255329377183D+00,-.4067578057659137D-01,
     5  -.4526468520348789D+00,0.9030241128745099D+00,
     6  -.4503772608395989D+00,0.8558659569093126D-01,
     7  -.1680627021511816D+00,0.8247610646027727D-01,
     8  -.3290715455089481D+00,0.6549570744945620D+00,
     9  -.3258855289855604D+00,0.3500934424096372D+00,
     *  -.1733493470760727D+00,-.1767440953334651D+00,
     1  0.3963042303943790D+00,-.2599695422276034D+00,
     2  -.1363346881672204D+00,0.1067074385094486D+01,
     3  -.5611447706066169D+00,-.5059296144870963D+00,
     4  0.9472180066426262D+00,-.3872084475068061D+00,
     5  -.5600095591352807D+00,-.1466739111569232D-12,
     6  0.2419854376387837D-13,-.1552488340937713D-12,
     7  -.2306323605219641D-12,-.1706174368865759D-12 /
      data zs /
     1  -.2246678712539802D-01,-.2246678712556187D-01,
     2  -.2246678712549978D-01,-.3674985430672734D+00,
     3  -.3674985430672704D+00,-.3674985430673924D+00,
     4  0.9168884763080956D+00,0.9168884763077307D+00,
     5  0.9168884763085783D+00,-.3553336558198409D+00,
     6  -.3553336558198190D+00,-.3553336558198354D+00,
     7  -.1983165808272536D+00,-.1983165808275630D+00,
     8  -.1983165808272446D+00,-.1447858405450569D+00,
     9  -.1447858405451866D+00,-.1447858405451966D+00,
     *  -.3542393281108072D+00,-.3542393281107521D+00,
     1  -.3542393281107588D+00,-.1251511927365907D+00,
     2  -.1251511927364737D+00,-.1251511927364298D+00,
     3  -.1387177797398434D+00,-.1387177797398834D+00,
     4  -.1387177797396668D+00,-.3549137865746493D+00,
     5  -.3549137865746083D+00,-.3549137865746373D+00,
     6  0.8659130596210637D-01,0.8659130596171444D-01,
     7  0.8659130596207916D-01,0.2597687530320102D+00,
     8  0.2597687530321350D+00,0.2597687530322305D+00,
     9  0.2630632081142404D+00,0.2630632081143893D+00,
     *  0.2630632081144756D+00,-.3453833089184027D+00,
     1  -.3453833089183551D+00,-.3453833089183527D+00,
     2  -.2327889534298980D+00,-.2327889534297419D+00,
     3  -.2327889534296802D+00,0.2415268120578684D+00,
     4  0.2415268120576211D+00,0.2415268120576665D+00,
     5  -.2133068003220094D+00,-.2133068003224423D+00,
     6  -.2133068003227821D+00,0.6055816506735499D+00,
     7  0.6055816506736809D+00,0.6055816506737702D+00,
     8  0.1414131684170811D+00,0.1414131684165572D+00,
     9  0.1414131684162387D+00,0.5593538346997974D+00,
     *  0.5593538346994973D+00,0.5593538347003276D+00,
     1  -.3961007879024273D+00,-.3961007879023746D+00,
     2  -.3961007879023505D+00,-.3950741090480416D+00,
     3  -.3950741090482457D+00,-.3950741090476022D+00,
     4  -.3779492208572051D+00,-.3779492208572193D+00,
     5  -.3779492208571862D+00,-.3464548867786856D-01,
     6  0.1201009856985286D+01,0.4068123865912653D+00,
     7  -.3341407786078385D+00,0.5699475205900819D+00 /
      data ws /
     1  0.2007080596188233D-01,0.2007080596192337D-01,
     2  0.2007080596192014D-01,0.1202850982705908D-01,
     3  0.1202850982706234D-01,0.1202850982703673D-01,
     4  0.6428246923028596D-02,0.6428246923032827D-02,
     5  0.6428246923025550D-02,0.5961017737373873D-02,
     6  0.5961017737376429D-02,0.5961017737354793D-02,
     7  0.2466985253776778D-01,0.2466985253776116D-01,
     8  0.2466985253775616D-01,0.1220343371669821D-01,
     9  0.1220343371668563D-01,0.1220343371666686D-01,
     *  0.6782282187245643D-02,0.6782282187250343D-02,
     1  0.6782282187251558D-02,0.1276699476009991D-01,
     2  0.1276699476009263D-01,0.1276699476009060D-01,
     3  0.1330898468041284D-01,0.1330898468040929D-01,
     4  0.1330898468040468D-01,0.8872828138103311D-02,
     5  0.8872828138107657D-02,0.8872828138112581D-02,
     6  0.2604852195750169D-01,0.2604852195750782D-01,
     7  0.2604852195751094D-01,0.1091598279364878D-01,
     8  0.1091598279363667D-01,0.1091598279364397D-01,
     9  0.2727741583607240D-01,0.2727741583609616D-01,
     *  0.2727741583610115D-01,0.1214067234472188D-01,
     1  0.1214067234470734D-01,0.1214067234471387D-01,
     2  0.2653047387010774D-01,0.2653047387011107D-01,
     3  0.2653047387012045D-01,0.1147407678956960D-01,
     4  0.1147407678960903D-01,0.1147407678957783D-01,
     5  0.6941339438094368D-02,0.6941339438087489D-02,
     6  0.6941339438089641D-02,0.1618088676127407D-01,
     7  0.1618088676125095D-01,0.1618088676125473D-01,
     8  0.9879744049167588D-02,0.9879744049174469D-02,
     9  0.9879744049169482D-02,0.1106165676903961D-01,
     *  0.1106165676903509D-01,0.1106165676904102D-01,
     1  0.7973762810133187D-02,0.7973762810143904D-02,
     2  0.7973762810145713D-02,0.7671732380845806D-03,
     3  0.7671732380905287D-03,0.7671732380951896D-03,
     4  0.1643453575966134D-02,0.1643453575957693D-02,
     5  0.1643453575955291D-02,0.4522697832344839D-01,
     6  0.3708344580879497D-03,0.1141401437229523D-01,
     7  0.2710167289616961D-01,0.1108569325544364D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule11 ( n, x, w )

c*********************************************************************72
c
cc RULE11 returns the rule of degree 11.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 95 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.9651177776899700D-01,-.7093619453993043D+00,
     2  0.6128501676297941D+00,-.4527836424396549D-02,
     3  -.4612438490926584D+00,0.4657716855189367D+00,
     4  0.2438655531438615D-01,0.3220723301923039D+00,
     5  -.3464588855081770D+00,-.1267500664585161D+00,
     6  -.5368057828378728D+00,0.6635558492970384D+00,
     7  -.9547972451775022D-01,-.2357077639614438D+00,
     8  0.3311874884792527D+00,-.7908328086591814D-02,
     9  -.7854922635641037D+00,0.7934005916498822D+00,
     *  -.1494644432070149D+00,-.3155198764172914D+00,
     1  0.4649843196230657D+00,0.1165276860785583D+00,
     2  -.4038862538014747D+00,0.2873585677227137D+00,
     3  -.2047755067090988D-02,-.9205200026937792D-01,
     4  0.9409975533966558D-01,0.3468354574885807D+00,
     5  0.1682368211989309D+00,-.5150722786890125D+00,
     6  -.1144319727418180D+00,-.7020417246489494D+00,
     7  0.8164736973908203D+00,-.3048702567593000D+00,
     8  -.1613129802547456D+00,0.4661832370146523D+00,
     9  0.2101640308259509D+00,0.3270815374994656D+00,
     *  -.5372455683250684D+00,-.6404070599046534D-01,
     1  -.5801912598472644D+00,0.6442319658370544D+00,
     2  0.5470009647103604D-02,-.2517469475214085D+00,
     3  0.2462769378777770D+00,0.1008461981380965D-01,
     4  0.1731441764929287D+00,-.1832287963083161D+00,
     5  0.1748982078445799D+00,-.3794913490849509D+00,
     6  0.2045931412407059D+00,0.1065391638487668D-01,
     7  -.3452291078932529D+00,0.3345751915058239D+00,
     8  -.7083686826885625D-03,0.2101573677291210D+00,
     9  -.2094489990466886D+00,-.2851273048890965D+00,
     *  -.3267460563855006D+00,0.6118733612746845D+00,
     1  -.2323209396920720D-02,-.2164769352136706D+00,
     2  0.2188001446096009D+00,-.2051577904029304D-01,
     3  -.5570838828147304D+00,0.5775996618543481D+00,
     4  -.3026455196997997D-02,0.1457949533626576D+00,
     5  -.1427684981666913D+00,-.1973538549140939D+00,
     6  -.1582348302473636D+00,0.3555886851614904D+00,
     7  0.1068857744362264D+00,-.4126086236419754D+00,
     8  0.3057228492051779D+00,-.3003364082942412D+00,
     9  0.3997857603256970D+00,-.9944935203203158D-01,
     *  0.1221835246093986D-01,-.8799955089249785D+00,
     1  0.8677771564639284D+00,0.1534568838650121D+00,
     2  -.7253511736488428D+00,0.5718942897840599D+00,
     3  0.2235456216473980D-02,-.5785135622840735D+00,
     4  0.5762781060658508D+00,0.9436416592156352D-01,
     5  0.3995572440244000D+00,-.4939214099453045D+00,
     6  0.1578951817317316D-11,-.7234508899977211D-12,
     7  -.1195010503052243D-12,0.1273193864088492D-12,
     *  -.1398313045262104D-12 /
      data ys /
     1  0.7633795193833395D+00,-.2981081083795290D+00,
     2  -.4652714110037153D+00,0.5352126684505152D+00,
     3  -.2715275555928822D+00,-.2636851128574337D+00,
     4  -.3859766773459927D+00,0.2141077150870582D+00,
     5  0.1718689622588539D+00,0.6930291114382893D+00,
     6  -.4562833332036821D+00,-.2367457782343889D+00,
     7  0.3272971265990525D+00,-.2463364302786462D+00,
     8  -.8096069632058686D-01,0.9115742149797984D+00,
     9  -.4626359205144959D+00,-.4489382944649009D+00,
     *  0.4506243076880464D+00,-.3547521586231100D+00,
     1  -.9587214906505584D-01,0.3990903837832518D+00,
     2  -.9862925550286258D-01,-.3004611282798994D+00,
     3  0.1074747662091034D+00,-.5551079101315480D-01,
     4  -.5196397519770712D-01,-.3945086927598004D+00,
     5  0.4976226634994518D+00,-.1031139707392109D+00,
     6  0.8767152876835527D+00,-.5374586392410802D+00,
     7  -.3392566484421098D+00,0.3622851099556234D+00,
     8  -.4451679421897679D+00,0.8288283223322354D-01,
     9  -.4990194872156122D+00,0.4315171332646398D+00,
     *  0.6750235395125617D-01,0.7069210789517217D+00,
     1  -.4089214177391241D+00,-.2979996612119608D+00,
     2  0.2875342242963981D+00,-.1390299448345922D+00,
     3  -.1485042794638735D+00,-.2057520317788134D+00,
     4  0.1116095528368255D+00,0.9414247894240614D-01,
     5  0.3372213377187678D+00,-.1714437779017452D-01,
     6  -.3200769599289869D+00,0.3924851952555710D+00,
     7  -.1870160353880812D+00,-.2054691598668353D+00,
     8  -.2422598488114232D+00,0.1205164591315570D+00,
     9  0.1217433896809788D+00,0.5419121734527502D+00,
     *  -.5178835760728716D+00,-.2402859737978143D-01,
     1  0.2513073392081394D+00,-.1276656279597885D+00,
     2  -.1236417112471668D+00,0.6551098499602489D+00,
     3  -.3453221108076170D+00,-.3097877391525884D+00,
     4  -.1666021864185573D+00,0.8068010612598300D-01,
     5  0.8592208029345208D-01,0.2966561449375769D+00,
     6  -.3192415243590572D+00,0.2258537942164062D-01,
     7  0.4147288692159332D+00,-.1147986386430089D+00,
     8  -.2999302305730746D+00,-.2882335265091744D+00,
     9  -.1159821960086673D+00,0.4042157225193962D+00,
     *  0.1009077018844530D+01,-.4939571057987255D+00,
     1  -.5151199130457724D+00,0.7489650175178515D+00,
     2  -.2415849489462737D+00,-.5073800685715635D+00,
     3  0.6667192805807411D+00,-.3314236784178127D+00,
     4  -.3352956021620059D+00,-.5158501413847826D+00,
     5  0.3396468355868865D+00,0.1762033057983631D+00,
     6  -.8069526265224892D-12,0.4596851666550035D-12,
     7  0.1156254386801148D-12,0.5765654131403360D-13,
     *  -.1226198587930237D-12 /
      data zs /
     1  -.1868268863122697D+00,-.1868268863123053D+00,
     2  -.1868268863112705D+00,0.4194136456710284D+00,
     3  0.4194136456717518D+00,0.4194136456711013D+00,
     4  0.5030086583798776D-01,0.5030086583729960D-01,
     5  0.5030086583707338D-01,-.1505956145194099D+00,
     6  -.1505956145190243D+00,-.1505956145192429D+00,
     7  -.1725275785423899D+00,-.1725275785429845D+00,
     8  -.1725275785414913D+00,-.1709810615420194D+00,
     9  -.1709810615421794D+00,-.1709810615408042D+00,
     *  0.7674742839401762D-01,0.7674742839470597D-01,
     1  0.7674742839681360D-01,-.3720134569923326D+00,
     2  -.3720134569922893D+00,-.3720134569921418D+00,
     3  0.9342960665019454D+00,0.9342960665021878D+00,
     4  0.9342960664953203D+00,-.3611736289802844D-01,
     5  -.3611736289860155D-01,-.3611736289902880D-01,
     6  -.3535560367475518D+00,-.3535560367476202D+00,
     7  -.3535560367476884D+00,-.1926114352197085D+00,
     8  -.1926114352198034D+00,-.1926114352197086D+00,
     9  -.2818523519641055D+00,-.2818523519643090D+00,
     *  -.2818523519648298D+00,-.3888552761464975D+00,
     1  -.3888552761464523D+00,-.3888552761454053D+00,
     2  0.6654848063127317D+00,0.6654848063130780D+00,
     3  0.6654848063078891D+00,0.1794683181875785D-01,
     4  0.1794683181975163D-01,0.1794683181866871D-01,
     5  -.2272794453431112D+00,-.2272794453432979D+00,
     6  -.2272794453429204D+00,0.8078480103364902D-01,
     7  0.8078480103319574D-01,0.8078480103608091D-01,
     8  0.3406111942551650D+00,0.3406111942551089D+00,
     9  0.3406111942537021D+00,-.3549131236009490D+00,
     *  -.3549131236011042D+00,-.3549131236012491D+00,
     1  0.4213057676587053D+00,0.4213057676584742D+00,
     2  0.4213057676619541D+00,-.2430250873757710D+00,
     3  -.2430250873755122D+00,-.2430250873736784D+00,
     4  0.6939507005767215D+00,0.6939507005768448D+00,
     5  0.6939507005757009D+00,-.3547895907184612D+00,
     6  -.3547895907186004D+00,-.3547895907184947D+00,
     7  0.3273634204692249D+00,0.3273634204691543D+00,
     8  0.3273634204697847D+00,0.3797479097987934D+00,
     9  0.3797479098019154D+00,0.3797479097984070D+00,
     *  -.3626672020688875D+00,-.3626672020689380D+00,
     1  -.3626672020686431D+00,-.3656623860600263D+00,
     2  -.3656623860600038D+00,-.3656623860598407D+00,
     3  0.1056953360682411D+00,0.1056953360682777D+00,
     4  0.1056953360707847D+00,-.4015122352990265D+00,
     5  -.4015122352990430D+00,-.4015122352995484D+00,
     6  0.1118223609071020D+01,0.6664104583675564D+00,
     7  -.3809990858052303D+00,-.2253945502682283D+00,
     *  0.2604940999755755D+00 /
      data ws /
     1  0.6188005592967251D-02,0.6188005592972490D-02,
     2  0.6188005592984317D-02,0.1421063031043561D-02,
     3  0.1421063031047919D-02,0.1421063030985486D-02,
     4  0.9481646089825704D-02,0.9481646089870772D-02,
     5  0.9481646089801222D-02,0.6814905118771046D-02,
     6  0.6814905118757536D-02,0.6814905118753749D-02,
     7  0.1912041674313553D-01,0.1912041674309802D-01,
     8  0.1912041674324984D-01,0.3076029506690844D-02,
     9  0.3076029506690773D-02,0.3076029506710983D-02,
     *  0.1135836724916717D-01,0.1135836724921729D-01,
     1  0.1135836724932070D-01,0.1091603321391938D-01,
     2  0.1091603321391454D-01,0.1091603321395138D-01,
     3  0.4213691001392970D-02,0.4213691001384827D-02,
     4  0.4213691001487200D-02,0.1206837849134008D-01,
     5  0.1206837849134312D-01,0.1206837849132945D-01,
     6  0.2578861292324762D-02,0.2578861292345221D-02,
     7  0.2578861292334968D-02,0.1252456101442731D-01,
     8  0.1252456101442267D-01,0.1252456101444618D-01,
     9  0.8063913155156468D-02,0.8063913155154395D-02,
     *  0.8063913155182456D-02,0.4993280626450522D-02,
     1  0.4993280626459499D-02,0.4993280626580781D-02,
     2  0.6150188384809636D-02,0.6150188384813883D-02,
     3  0.6150188384677927D-02,0.2678388417077401D-01,
     4  0.2678388417077927D-01,0.2678388417078649D-01,
     5  0.1946856127752551D-01,0.1946856127748248D-01,
     6  0.1946856127749281D-01,0.2102094189170934D-01,
     7  0.2102094189169974D-01,0.2102094189174428D-01,
     8  0.1685367818736497D-01,0.1685367818729912D-01,
     9  0.1685367818732997D-01,0.5900869705091857D-02,
     *  0.5900869705093673D-02,0.5900869705073673D-02,
     1  0.1690563324458130D-01,0.1690563324459602D-01,
     2  0.1690563324456019D-01,0.1476341187397782D-01,
     3  0.1476341187398414D-01,0.1476341187397479D-01,
     4  0.6992794755775152D-02,0.6992794755747075D-02,
     5  0.6992794755746150D-02,0.1513056742691520D-01,
     6  0.1513056742688911D-01,0.1513056742692685D-01,
     7  0.7015883109811540D-02,0.7015883109809210D-02,
     8  0.7015883109746114D-02,0.4965174122051565D-02,
     9  0.4965174121903291D-02,0.4965174122041231D-02,
     *  0.2712699778890213D-02,0.2712699778885687D-02,
     1  0.2712699778899985D-02,0.5900718944404856D-02,
     2  0.5900718944405426D-02,0.5900718944424988D-02,
     3  0.8768888887154097D-02,0.8768888887160882D-02,
     4  0.8768888887196669D-02,0.3175432879836244D-02,
     5  0.3175432879833069D-02,0.3175432879794895D-02,
     6  0.1078986495318477D-02,0.1747404076054822D-01,
     7  0.1129982873905144D-01,0.2890093028298477D-01,
     *  0.2624431483486055D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule12 ( n, x, w )

c*********************************************************************72
c
cc RULE12 returns the rule of degree 12.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 122 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.3958544098912666D+00,-.4870511331351648D+00,
     2  0.9119672324389515D-01,-.5926431804946591D+00,
     3  0.5193516147881150D+00,0.7329156570653904D-01,
     4  -.4544141850245140D-01,-.2756993864806933D+00,
     5  0.3211408049831440D+00,-.3413860630862161D+00,
     6  0.5248742662396945D+00,-.1834882031534880D+00,
     7  -.1319722431139201D+00,0.2771078804366659D+00,
     8  -.1451356373227354D+00,0.2916719156941026D+00,
     9  -.6416905801467393D+00,0.3500186644526196D+00,
     *  -.4070439485536645D-01,-.4815006651936328D+00,
     1  0.5222050600490048D+00,-.9820856549819251D-01,
     2  -.4276075601779065D+00,0.5258161256761047D+00,
     3  0.2184089033681613D+00,-.4656593625800790D+00,
     4  0.2472504592119225D+00,-.6606777491144762D-02,
     5  0.1271987824323769D+00,-.1205920049412379D+00,
     6  -.1862346674942773D+00,-.1097662119993451D+00,
     7  0.2960008794936306D+00,-.5890402754221185D+00,
     8  0.6424505517737594D+00,-.5341027635165645D-01,
     9  -.1196400210307819D-01,-.7808240524677493D+00,
     *  0.7927880545708264D+00,0.6235239461686299D-01,
     1  -.4408318818916021D+00,0.3784794872747496D+00,
     2  0.2235903863093564D+00,-.5240787479715297D-01,
     3  -.1711825115122079D+00,0.1666477050331823D+00,
     4  -.2729955606600447D+00,0.1063478556268736D+00,
     5  -.7415049139037595D-01,0.7389518464069887D-01,
     6  0.2553067496801190D-03,0.1955908717228039D+00,
     7  0.1141488778114551D+00,-.3097397495342445D+00,
     8  -.1802680258591541D-01,-.2161777731993448D+00,
     9  0.2342045757852541D+00,-.1532613811702923D+00,
     *  -.1800985367097719D+00,0.3333599178800782D+00,
     1  0.5776336665233524D-02,-.6762886678803212D+00,
     2  0.6705123312150877D+00,-.8304590790913337D-01,
     3  0.3554044991859694D+00,-.2723585912768360D+00,
     4  0.5423845315967933D+00,-.2526088517557438D+00,
     5  -.2897756798410528D+00,0.5573431967310101D+00,
     6  -.3595768372350124D+00,-.1977663594959926D+00,
     7  0.4731366238769863D+00,-.1975148047452081D-01,
     8  -.4533851434024622D+00,0.3153219324427421D+00,
     9  -.2494039878683618D-01,-.2903815336558955D+00,
     *  -.1831653764008917D-01,-.9317223914837645D+00,
     1  0.9500389291238570D+00,-.6699974553713883D+00,
     2  0.5322783600952914D+00,0.1377190952760970D+00,
     3  0.2782783282780965D+00,-.3217122219145910D+00,
     4  0.4343389363650290D-01,0.9746770878915403D-01,
     5  -.3733686186921615D+00,0.2759009099030095D+00,
     6  0.1089081465931238D-01,-.8195375330783097D+00,
     7  0.8086467184189974D+00,-.1251938886030335D+00,
     8  0.3429675592810749D-01,0.9089713267491691D-01,
     9  0.4868852723886817D+00,0.1198290818690802D+00,
     *  -.6067143542577578D+00,0.3382540465835279D+00,
     1  -.4603539675728300D+00,0.1220999209893009D+00,
     2  -.9480210749913888D-01,-.6451285680033118D+00,
     3  0.7399306755024498D+00,0.1140113067761596D+00,
     4  -.8552704011446526D+00,0.7412590943684850D+00,
     5  -.1658421801556803D+00,-.6245895743792733D+00,
     6  0.7904317545349575D+00,0.2557413056493574D+00,
     7  0.3270954418922731D-01,-.2884508498385872D+00,
     8  -.1613157569571640D+00,-.4583565335140027D+00,
     9  0.6196722904711670D+00,0.2156998987651826D-14,
     *  0.2157685773910294D-14,0.9329761593328095D-14,
     1  -.1937826095544789D-14,0.5112100598082816D-14 /
      data ys /
     1  0.3338515555387722D+00,0.1758941973965540D+00,
     2  -.5097457529353365D+00,-.2575328894119814D+00,
     3  -.3844776049819921D+00,0.6420104943939733D+00,
     4  0.3445858452048264D+00,-.2116463454095397D+00,
     5  -.1329394997952951D+00,-.4089732623879643D+00,
     6  -.9116237193661333D-01,0.5001356343245807D+00,
     7  -.2437824086419522D+00,0.7599889189904093D-02,
     8  0.2361825194520526D+00,0.5725635993272842D+00,
     9  -.3368651110208424D-01,-.5388770882252032D+00,
     *  0.5794897706560004D+00,-.3249959253184209D+00,
     1  -.2544938453375776D+00,0.5504594216795844D+00,
     2  -.3602808234304559D+00,-.1901785982491242D+00,
     3  0.4115986775195391D+00,-.1665168003024589D-01,
     4  -.3949469974892933D+00,-.1430620777928657D+00,
     5  0.6580940175195596D-01,0.7725267604090996D-01,
     6  0.2342697395017627D+00,-.2784188228662802D+00,
     7  0.4414908336450658D-01,-.4017554364367290D+00,
     8  -.3092461241493650D+00,0.7110015605860860D+00,
     9  0.9085253735987711D+00,-.4646238165515825D+00,
     *  -.4439015570471948D+00,0.4730296395382988D+00,
     1  -.1825160620441602D+00,-.2905135774941487D+00,
     2  -.6857456848032077D-01,0.2279222388260412D+00,
     3  -.1593476703457152D+00,0.2190140235085516D+00,
     4  0.3481413428683416D-01,-.2538281577953898D+00,
     5  -.4251600332346974D-01,-.4295820758543226D-01,
     6  0.8547421090889233D-01,-.2447322131044543D+00,
     7  0.2917527702125314D+00,-.4702055710805701D-01,
     8  0.2600283704245143D+00,-.1456258542006649D+00,
     9  -.1144025162238410D+00,0.2964453769751457D+00,
     *  -.2809509380001344D+00,-.1549443897500673D-01,
     1  0.7775759193725890D+00,-.3837855053933897D+00,
     2  -.3937904139792007D+00,-.3624391892660122D+00,
     3  0.1092997287033503D+00,0.2531394605626634D+00,
     4  -.2145827819997083D-01,0.4804479220825398D+00,
     5  -.4589896438825594D+00,0.9342132288033096D-01,
     6  0.4359627055553254D+00,-.5293840284356405D+00,
     7  -.2503585120211285D+00,0.5349275917488283D+00,
     8  -.2845690797277077D+00,-.1532525106706588D+00,
     9  0.3497030592011267D+00,-.1964505485304861D+00,
     *  0.1086435405003431D+01,-.5590802894074118D+00,
     1  -.5273551155960269D+00,-.2277988977546228D+00,
     2  -.4663353679452422D+00,0.6941342656998574D+00,
     3  0.2108172081069621D+00,0.1355874975580061D+00,
     4  -.3464047056649888D+00,0.3748559371110348D+00,
     5  -.1030184566954502D+00,-.2718374804155939D+00,
     6  0.9400326158922729D+00,-.4605845857832677D+00,
     7  -.4794480301090108D+00,0.3267824275100505D-01,
     8  -.1247602093042907D+00,0.9208196655328471D-01,
     9  -.4194700484257879D+00,0.6313900388299887D+00,
     *  -.2119199904042083D+00,0.3362799093518891D+00,
     1  0.1247966425982771D+00,-.4610765519501666D+00,
     2  0.7996643270816305D+00,-.4819331969673737D+00,
     3  -.3177311301142533D+00,0.9217567340036824D+00,
     4  -.3621416790150311D+00,-.5596150549886635D+00,
     5  0.8169629451576943D+00,-.5521050136126617D+00,
     6  -.2648579315450346D+00,-.1854220399449956D+00,
     7  0.3141894874618389D+00,-.1287674475168422D+00,
     8  0.6224002317220075D+00,-.4509036594166286D+00,
     9  -.1714965723053837D+00,-.1747363709921250D-14,
     *  -.7841339838758449D-14,-.1038742413216324D-13,
     1  -.6434088705165255D-14,0.8511611593137641D-14 /
      data zs /
     1  -.3905577451659811D+00,-.3905577451659810D+00,
     2  -.3905577451659885D+00,-.4194761577597843D-02,
     3  -.4194761577604291D-02,-.4194761577584145D-02,
     4  0.1874027021856000D+00,0.1874027021856146D+00,
     5  0.1874027021856214D+00,-.3071102013390232D+00,
     6  -.3071102013390279D+00,-.3071102013390283D+00,
     7  -.2701961597911837D-01,-.2701961597911512D-01,
     8  -.2701961597910549D-01,-.3650223874563840D+00,
     9  -.3650223874563843D+00,-.3650223874563830D+00,
     *  -.8612392000622994D-01,-.8612392000621880D-01,
     1  -.8612392000621745D-01,0.1070791221730147D+00,
     2  0.1070791221730203D+00,0.1070791221730225D+00,
     3  0.3230374822491166D-01,0.3230374822490626D-01,
     4  0.3230374822491062D-01,0.3289827199375365D+00,
     5  0.3289827199375268D+00,0.3289827199375392D+00,
     6  -.2002324469987915D+00,-.2002324469988037D+00,
     7  -.2002324469988010D+00,-.2771825970811163D+00,
     8  -.2771825970811178D+00,-.2771825970811177D+00,
     9  -.3794145952130761D+00,-.3794145952130777D+00,
     *  -.3794145952130777D+00,0.2887592197883361D+00,
     1  0.2887592197883261D+00,0.2887592197883259D+00,
     2  0.7307953050563157D+00,0.7307953050563196D+00,
     3  0.7307953050563138D+00,0.4124918246328610D+00,
     4  0.4124918246328517D+00,0.4124918246328527D+00,
     5  0.9839020121236216D+00,0.9839020121236166D+00,
     6  0.9839020121236378D+00,0.6829751492607604D-01,
     7  0.6829751492606395D-01,0.6829751492607447D-01,
     8  0.5090267712108498D+00,0.5090267712108671D+00,
     9  0.5090267712108663D+00,0.3851617855258526D+00,
     *  0.3851617855258565D+00,0.3851617855258507D+00,
     1  0.2348420776072121D-01,0.2348420776071207D-01,
     2  0.2348420776071097D-01,0.7747281662419676D-01,
     3  0.7747281662420324D-01,0.7747281662419568D-01,
     4  -.1630338566084656D+00,-.1630338566084718D+00,
     5  -.1630338566084695D+00,-.3584562395667113D+00,
     6  -.3584562395667106D+00,-.3584562395667084D+00,
     7  0.3698626219613211D+00,0.3698626219613297D+00,
     8  0.3698626219613188D+00,-.3667298228875690D+00,
     9  -.3667298228875713D+00,-.3667298228875721D+00,
     *  -.3790081337166384D+00,-.3790081337166408D+00,
     1  -.3790081337166418D+00,-.2197227060814419D+00,
     2  -.2197227060814434D+00,-.2197227060814370D+00,
     3  -.3654645869052863D+00,-.3654645869052863D+00,
     4  -.3654645869052867D+00,-.2014726326233556D+00,
     5  -.2014726326233535D+00,-.2014726326233503D+00,
     6  -.2464405285751480D+00,-.2464405285751552D+00,
     7  -.2464405285751559D+00,0.7375395719855852D+00,
     8  0.7375395719855836D+00,0.7375395719855902D+00,
     9  -.3689240261223760D+00,-.3689240261223751D+00,
     *  -.3689240261223750D+00,-.2202508600260902D+00,
     1  -.2202508600260935D+00,-.2202508600260907D+00,
     2  -.1594720366091775D+00,-.1594720366091723D+00,
     3  -.1594720366091740D+00,-.3758886073617869D+00,
     4  -.3758886073617894D+00,-.3758886073617892D+00,
     5  -.3542700621002714D+00,-.3542700621002700D+00,
     6  -.3542700621002702D+00,0.6895589091912253D+00,
     7  0.6895589091912366D+00,0.6895589091912278D+00,
     8  -.4073916692470354D+00,-.4073916692470370D+00,
     9  -.4073916692470400D+00,0.6482117053575507D+00,
     *  0.1198603539538932D+01,-.4041509145471567D+00,
     1  -.2710584986072719D+00,0.8757555073873696D-02 /
      data ws /
     1  0.2025764222341204D-02,0.2025764222341283D-02,
     2  0.2025764222340314D-02,0.6116300216663094D-02,
     3  0.6116300216663310D-02,0.6116300216663541D-02,
     4  0.1275819159212241D-01,0.1275819159212196D-01,
     5  0.1275819159212162D-01,0.8334684897884583D-02,
     6  0.8334684897884422D-02,0.8334684897884272D-02,
     7  0.1507614954107500D-01,0.1507614954107359D-01,
     8  0.1507614954107202D-01,0.2734637742973762D-02,
     9  0.2734637742973644D-02,0.2734637742974016D-02,
     *  0.1154303798541227D-01,0.1154303798541274D-01,
     1  0.1154303798541255D-01,0.7163952410599667D-02,
     2  0.7163952410599083D-02,0.7163952410598778D-02,
     3  0.7580503447649259D-02,0.7580503447650207D-02,
     4  0.7580503447650126D-02,0.1894249152240793D-01,
     5  0.1894249152240805D-01,0.1894249152240727D-01,
     6  0.1641784697591419D-01,0.1641784697591236D-01,
     7  0.1641784697591317D-01,0.8436640400263927D-02,
     8  0.8436640400264633D-02,0.8436640400264418D-02,
     9  0.3036004079076158D-02,0.3036004079076059D-02,
     *  0.3036004079076094D-02,0.7492415688372185D-02,
     1  0.7492415688372261D-02,0.7492415688372197D-02,
     2  0.3062456464426824D-02,0.3062456464427586D-02,
     3  0.3062456464427105D-02,0.8856133214568079D-02,
     4  0.8856133214567973D-02,0.8856133214568157D-02,
     5  0.3071402699546415D-02,0.3071402699546453D-02,
     6  0.3071402699546178D-02,0.1823835135198804D-01,
     7  0.1823835135198757D-01,0.1823835135198796D-01,
     8  0.1121658861163283D-01,0.1121658861163258D-01,
     9  0.1121658861163293D-01,0.5177567930581361D-02,
     *  0.5177567930581481D-02,0.5177567930580846D-02,
     1  0.3242723020974106D-02,0.3242723020974469D-02,
     2  0.3242723020974430D-02,0.1136422978208590D-01,
     3  0.1136422978208548D-01,0.1136422978208555D-01,
     4  0.8174247103577847D-02,0.8174247103578128D-02,
     5  0.8174247103578329D-02,0.4083194002127334D-02,
     6  0.4083194002127503D-02,0.4083194002128160D-02,
     7  0.3128101586450114D-02,0.3128101586450456D-02,
     8  0.3128101586450350D-02,0.1081664090579396D-01,
     9  0.1081664090579364D-01,0.1081664090579339D-01,
     *  0.4910680133298682D-03,0.4910680133297917D-03,
     1  0.4910680133297780D-03,0.8074513061447679D-02,
     2  0.8074513061447566D-02,0.8074513061448123D-02,
     3  0.1112708329974781D-01,0.1112708329974803D-01,
     4  0.1112708329974812D-01,0.2131526487678964D-01,
     5  0.2131526487679003D-01,0.2131526487678986D-01,
     6  0.3571026646377801D-02,0.3571026646377656D-02,
     7  0.3571026646377794D-02,0.7768447076866043D-02,
     8  0.7768447076865915D-02,0.7768447076866019D-02,
     9  0.7618830679555172D-02,0.7618830679555604D-02,
     *  0.7618830679555573D-02,0.1180399216908969D-01,
     1  0.1180399216908947D-01,0.1180399216908933D-01,
     2  0.2753708273597594D-02,0.2753708273597404D-02,
     3  0.2753708273597407D-02,0.1252040626033346D-02,
     4  0.1252040626033167D-02,0.1252040626033129D-02,
     5  0.2035505637330654D-02,0.2035505637330660D-02,
     6  0.2035505637330673D-02,0.2152733016776995D-02,
     7  0.2152733016776493D-02,0.2152733016776350D-02,
     8  0.2538969965943544D-02,0.2538969965943405D-02,
     9  0.2538969965943241D-02,0.1078372873958245D-01,
     *  0.1943908493037603D-03,0.4799528389705479D-02,
     1  0.2477673544485754D-01,0.2864883777302190D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule13 ( n, x, w )

c*********************************************************************72
c
cc RULE13 returns the rule of degree 13.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 146 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.4777385017466611D-01,-.7568808830760128D+00,
     2  0.8046547332507396D+00,0.3005907944967990D-01,
     3  -.3472424886466524D+00,0.3171834091971876D+00,
     4  -.3529824413110864D-01,-.4209487812102883D+00,
     5  0.4562470253414500D+00,-.7153537080888878D+00,
     6  0.5989558965388279D+00,0.1163978115501301D+00,
     7  0.3710519456025519D-02,0.4652335033519287D+00,
     8  -.4689440228078527D+00,-.3599160575353618D-01,
     9  0.1939924024452817D+00,-.1580007966914678D+00,
     *  -.2161537359848647D-01,0.2912599485905940D+00,
     1  -.2696445749921000D+00,-.4913573074965884D+00,
     2  0.2288888183023164D+00,0.2624684891944182D+00,
     3  -.1426281098822192D+00,-.3118486240867259D+00,
     4  0.4544767339690260D+00,0.7618754763810419D+00,
     5  -.1422306180040716D+00,-.6196448583768703D+00,
     6  0.5776897880027803D-01,0.1164689180950719D+00,
     7  -.1742378968955057D+00,-.1414719142296262D+00,
     8  -.3229372289650024D+00,0.4644091431945710D+00,
     9  -.1398258170326137D+00,-.5098850522745304D+00,
     *  0.6497108693071825D+00,0.3610318921371553D+00,
     1  0.1054629929099188D+00,-.4664948850470391D+00,
     2  0.2459013465212476D-01,-.7178146556427887D+00,
     3  0.6932245209907225D+00,-.1065595141175732D-01,
     4  -.9217121855780308D+00,0.9323681369897492D+00,
     5  -.4115285528872360D+00,0.2668526805669106D+00,
     6  0.1446758723202021D+00,0.1571190412397715D-02,
     7  -.6922217370423006D-01,0.6765098329171684D-01,
     8  -.2991189861629327D+00,-.1245621803681009D+00,
     9  0.4236811665311025D+00,0.3871696430393148D+00,
     *  0.1500785041234294D+00,-.5372481471625822D+00,
     1  -.8064886300342536D-01,-.4844598247542774D+00,
     2  0.5651086877577737D+00,0.6705603853993255D+00,
     3  -.2613693382805031D+00,-.4091910471186840D+00,
     4  -.2994914861160214D+00,-.2674832138785850D+00,
     5  0.5669746999946459D+00,0.4510147973428894D-01,
     6  0.2172069032075606D+00,-.2623083829418457D+00,
     7  -.2495785492724049D+00,-.2085110500880744D+00,
     8  0.4580895993605156D+00,0.2707504828489703D+00,
     9  -.4821600751443009D+00,0.2114095922954477D+00,
     *  -.4554280384514680D-01,-.7996627976605564D+00,
     1  0.8452056015056444D+00,0.2029674430134095D-01,
     2  -.7997175993984930D+00,0.7794208550971885D+00,
     3  0.1441756236446537D+00,-.6915442312985614D+00,
     4  0.5473686076540003D+00,0.3528170518753222D-01,
     5  -.3311753761570134D+00,0.2958936709696454D+00,
     6  -.7827835701762442D-02,0.2760083802741976D+00,
     7  -.2681805445724308D+00,0.6806655606966093D-01,
     8  -.5973241026022454D+00,0.5292575465325308D+00,
     9  -.9685067665231929D-01,0.2259602937925122D+00,
     *  -.1291096171402099D+00,-.1001708030503953D-01,
     1  -.5630399697700922D+00,0.5730570500751420D+00,
     2  0.3465920273834422D-01,-.1777529113458167D+00,
     3  0.1430937086076311D+00,0.7285263734559304D-01,
     4  -.8758889229618175D+00,0.8030362856162614D+00,
     5  0.1343389663918027D+00,0.3445210697535890D+00,
     6  -.4788600361453874D+00,-.1348321313217423D-01,
     7  0.1154680832801965D+00,-.1019848701479677D+00,
     8  -.5176848990301737D-01,-.2375948027597131D+00,
     9  0.2893632926627010D+00,0.1729207472857360D-01,
     *  -.4389324777852445D+00,0.4216404030566085D+00,
     1  -.3914791775164566D-02,-.2309684344749786D+00,
     2  0.2348832262501366D+00,-.6881144138718593D+00,
     3  0.4266860230809687D+00,0.2614283907909357D+00,
     4  0.4960973006288234D-02,-.2137441872471665D+00,
     5  0.2087832142407756D+00,-.7325006065249269D-01,
     6  -.2659488483143491D+00,0.3391989089668666D+00,
     7  -.4678501489682662D-01,-.5410293892575722D+00,
     8  0.5878144041543488D+00,-.2500405721723705D-01,
     9  -.6313699376952513D+00,0.6563739949124212D+00,
     *  0.1364199568193839D+00,-.2996193314702689D+00,
     1  0.1631993746509763D+00,0.1198743702984181D-12,
     2  -.7662979863046558D-13,-.4829662024390088D-14,
     3  -.2111050829994401D-13,-.1270671025297558D-13 /
      data ys /
     1  0.9015530084355994D+00,-.4921498721057091D+00,
     2  -.4094031363297998D+00,0.3836064709764307D+00,
     3  -.1657713090704851D+00,-.2178351619061508D+00,
     4  0.5064492350445715D+00,-.2837937936488191D+00,
     5  -.2226554413958301D+00,-.2786050402678961D+00,
     6  -.4802119637624816D+00,0.7588170040302994D+00,
     7  -.5393476461992264D+00,0.2728872272096964D+00,
     8  0.2664604189895141D+00,-.2032233682745297D+00,
     9  0.7044203923151297D-01,0.1327813290428652D+00,
     *  -.3238383776801540D+00,0.1431997261914898D+00,
     1  0.1806386514886541D+00,0.1938723202896774D-01,
     2  -.4352215266416702D+00,0.4158342946127344D+00,
     3  0.4424381517603146D+00,-.3447386423319839D+00,
     4  -.9769950942847148D-01,-.2756352401942940D+00,
     5  0.7976211371634238D+00,-.5219858969692130D+00,
     6  -.1678396578899558D+00,0.1339492321368408D+00,
     7  0.3389042575316226D-01,0.4545746399118207D+00,
     8  -.3498055916007531D+00,-.1047690483110467D+00,
     9  0.6694930174765074D+00,-.4558392183934259D+00,
     *  -.2136537990830517D+00,-.3302200348036231D+00,
     1  0.4777728075688429D+00,-.1475527727653846D+00,
     2  0.8146638484662959D+00,-.3860362429420576D+00,
     3  -.4286276055244945D+00,0.1070453773333782D+01,
     4  -.5444552112909320D+00,-.5259985620427312D+00,
     5  -.7053881312997473D-01,-.3211247746179037D+00,
     6  0.3916635877479940D+00,0.7902375403647920D-01,
     7  -.3815118620693258D-01,-.4087256782951131D-01,
     8  0.3165284439137526D+00,-.4173088627282204D+00,
     9  0.1007804188144937D+00,-.3968282271412536D+00,
     *  0.5337128600166933D+00,-.1368846328756112D+00,
     1  0.6059686632316962D+00,-.3728282957631877D+00,
     2  -.2331403674686730D+00,-.8534490338988292D-01,
     3  0.6233947802222222D+00,-.5380498768323672D+00,
     4  0.4817745012020841D+00,-.5002544857946896D+00,
     5  0.1847998459249884D-01,-.2768482795388788D+00,
     6  0.1774831669675317D+00,0.9936511257127259D-01,
     7  0.3848620644010382D+00,-.4085723961101285D+00,
     8  0.2371033170906487D-01,0.4004326341980497D+00,
     9  0.3426047913492075D-01,-.4346931133331124D+00,
     *  0.9496652130401684D+00,-.5142738316095435D+00,
     1  -.4353913814305450D+00,0.9117160117907287D+00,
     2  -.4382805097163334D+00,-.4734355020744341D+00,
     3  0.7152866610716716D+00,-.2327835778531099D+00,
     4  -.4825030832186010D+00,0.3620384831590592D+00,
     5  -.1504643885983839D+00,-.2115740945607743D+00,
     6  -.3141876222502283D+00,0.1503147065506677D+00,
     7  0.1638729156994478D+00,0.6504322183920584D+00,
     8  -.2662687424915907D+00,-.3841634759004985D+00,
     9  -.2049997086581880D+00,0.1862470797446676D-01,
     *  0.1863750006837488D+00,0.6559259202331654D+00,
     1  -.3366380061325622D+00,-.3192879141007369D+00,
     2  0.1852408823986869D+00,-.6260469115301880D-01,
     3  -.1226361912458057D+00,0.9693279211217602D+00,
     4  -.4215717258868716D+00,-.5477561952349157D+00,
     5  -.4753793031363919D+00,0.3540306091815932D+00,
     6  0.1213486939547357D+00,-.1255465211978510D+00,
     7  0.5109645550180968D-01,0.7445006569601835D-01,
     8  0.3042393982437668D+00,-.1969525264934776D+00,
     9  -.1072868717503699D+00,0.4968519844113532D+00,
     *  -.2334506162065882D+00,-.2634013682047193D+00,
     1  0.2689595817220580D+00,-.1378700999889159D+00,
     2  -.1310894817332517D+00,-.9541153848828572D-01,
     3  -.5482187938791565D+00,0.6436303323674273D+00,
     4  0.2439463089891027D+00,-.1176768258436301D+00,
     5  -.1262694831454210D+00,0.3493822205657847D+00,
     6  -.2381275236366834D+00,-.1112546969291192D+00,
     7  0.6517382679995124D+00,-.3663861454168269D+00,
     8  -.2853521225825763D+00,0.7434793061384100D+00,
     9  -.3933938018169897D+00,-.3500855043213671D+00,
     *  0.2672085045651081D+00,-.1546110409379758D-01,
     1  -.2517474004713509D+00,-.6195967642546056D-13,
     2  0.3002370388193685D-13,-.5457794979132388D-13,
     3  0.1164494042115649D-12,0.3123283355285955D-13 /
      data zs /
     1  -.2327715323996341D+00,-.2327715323996078D+00,
     2  -.2327715323995431D+00,0.3496762696550786D+00,
     3  0.3496762696549099D+00,0.3496762696549561D+00,
     4  0.2717988565409110D+00,0.2717988565409942D+00,
     5  0.2717988565407555D+00,-.3874128688211647D+00,
     6  -.3874128688212131D+00,-.3874128688212028D+00,
     7  -.3783145937148669D+00,-.3783145937148664D+00,
     8  -.3783145937148837D+00,-.3908054363428844D+00,
     9  -.3908054363428517D+00,-.3908054363428521D+00,
     *  0.2214621132658698D+00,0.2214621132658886D+00,
     1  0.2214621132658825D+00,-.5332156026748039D-01,
     2  -.5332156026744841D-01,-.5332156026745260D-01,
     3  -.1366126720097484D+00,-.1366126720097481D+00,
     4  -.1366126720097814D+00,-.3405718815923187D+00,
     5  -.3405718815923307D+00,-.3405718815923774D+00,
     6  0.2482158558753812D+00,0.2482158558753821D+00,
     7  0.2482158558753401D+00,0.1493078550521198D+00,
     8  0.1493078550521607D+00,0.1493078550521824D+00,
     9  -.1246861001425667D+00,-.1246861001425311D+00,
     *  -.1246861001424509D+00,-.8804090671666169D-01,
     1  -.8804090671661184D-01,-.8804090671646460D-01,
     2  -.2903904416529835D+00,-.2903904416529482D+00,
     3  -.2903904416530703D+00,-.3588716811515187D+00,
     4  -.3588716811515073D+00,-.3588716811515079D+00,
     5  0.1748649644824907D+00,0.1748649644825259D+00,
     6  0.1748649644824762D+00,0.1005626022480115D+01,
     7  0.1005626022480066D+01,0.1005626022480308D+01,
     8  -.6085363845277859D-01,-.6085363845275459D-01,
     9  -.6085363845275343D-01,-.2907416212662024D+00,
     *  -.2907416212662147D+00,-.2907416212661059D+00,
     1  -.2928675049685535D+00,-.2928675049684912D+00,
     2  -.2928675049686165D+00,-.3986190384060752D+00,
     3  -.3986190384060841D+00,-.3986190384061074D+00,
     4  -.2763005028815692D+00,-.2763005028815834D+00,
     5  -.2763005028815310D+00,-.3171132373617958D-01,
     6  -.3171132373613690D-01,-.3171132373618723D-01,
     7  -.3670072924650872D+00,-.3670072924650821D+00,
     8  -.3670072924650642D+00,-.3918966809387769D+00,
     9  -.3918966809387540D+00,-.3918966809387686D+00,
     *  -.3945112928982144D+00,-.3945112928982283D+00,
     1  -.3945112928982709D+00,-.1689813827450514D+00,
     2  -.1689813827450869D+00,-.1689813827450585D+00,
     3  -.1988456360856388D+00,-.1988456360856537D+00,
     4  -.1988456360856610D+00,-.3581788966687771D+00,
     5  -.3581788966687613D+00,-.3581788966687278D+00,
     6  -.2652570624981906D+00,-.2652570624981415D+00,
     7  -.2652570624981432D+00,0.9127655651197962D-01,
     8  0.9127655651192465D-01,0.9127655651200027D-01,
     9  0.4712027028361149D+00,0.4712027028361768D+00,
     *  0.4712027028361248D+00,-.4789101434801453D-01,
     1  -.4789101434802212D-01,-.4789101434808656D-01,
     2  0.5562071598537035D+00,0.5562071598536467D+00,
     3  0.5562071598533351D+00,-.3666902411131864D+00,
     4  -.3666902411132085D+00,-.3666902411132190D+00,
     5  -.2500081968302335D+00,-.2500081968302558D+00,
     6  -.2500081968302762D+00,0.7953910781041313D+00,
     7  0.7953910781041719D+00,0.7953910781041406D+00,
     8  0.1246295654192337D+00,0.1246295654192380D+00,
     9  0.1246295654192949D+00,0.4430780439124138D+00,
     *  0.4430780439124452D+00,0.4430780439125641D+00,
     1  -.1789190687389412D+00,-.1789190687388659D+00,
     2  -.1789190687388622D+00,-.3621753277358900D+00,
     3  -.3621753277358689D+00,-.3621753277358712D+00,
     4  0.7590201625172059D+00,0.7590201625171641D+00,
     5  0.7590201625173268D+00,0.5385097619725802D+00,
     6  0.5385097619725214D+00,0.5385097619724014D+00,
     7  -.4034889863680245D+00,-.4034889863679839D+00,
     8  -.4034889863680722D+00,0.9129480050841532D-01,
     9  0.9129480050844316D-01,0.9129480050850451D-01,
     *  0.5076476008019328D+00,0.5076476008020036D+00,
     1  0.5076476008019484D+00,0.7587686360919684D+00,
     2  0.1174064403165666D+01,-.2917588131252908D+00,
     3  0.4072850512806022D+00,-.2737975651676979D-02 /
      data ws /
     1  0.2068909148962774D-02,0.2068909148960302D-02,
     2  0.2068909148962221D-02,0.6862179883351744D-02,
     3  0.6862179883357749D-02,0.6862179883341077D-02,
     4  0.4745055930506758D-02,0.4745055930499521D-02,
     5  0.4745055930498638D-02,0.2639271833496386D-02,
     6  0.2639271833492975D-02,0.2639271833493415D-02,
     7  0.2420284628312029D-02,0.2420284628310808D-02,
     8  0.2420284628311964D-02,0.5428029730193044D-02,
     9  0.5428029730198515D-02,0.5428029730197811D-02,
     *  0.7363269664287002D-02,0.7363269664287796D-02,
     1  0.7363269664288242D-02,0.4622589345403796D-02,
     2  0.4622589345400746D-02,0.4622589345402929D-02,
     3  0.1113014179512893D-01,0.1113014179512515D-01,
     4  0.1113014179513268D-01,0.3019898782414975D-02,
     5  0.3019898782415646D-02,0.3019898782415196D-02,
     6  0.1497918593186746D-01,0.1497918593186317D-01,
     7  0.1497918593186622D-01,0.6570279132551560D-02,
     8  0.6570279132554112D-02,0.6570279132553927D-02,
     9  0.4504033084972921D-02,0.4504033084968776D-02,
     *  0.4504033084972839D-02,0.1239429415995445D-01,
     1  0.1239429415996196D-01,0.1239429415995679D-01,
     2  0.5367281142254301D-02,0.5367281142251953D-02,
     3  0.5367281142250357D-02,0.6316169904420855D-03,
     4  0.6316169904431759D-03,0.6316169904440820D-03,
     5  0.8876101030265546D-02,0.8876101030282007D-02,
     6  0.8876101030274161D-02,0.2162421606464688D-02,
     7  0.2162421606465037D-02,0.2162421606462924D-02,
     8  0.8054280667477870D-02,0.8054280667477506D-02,
     9  0.8054280667478849D-02,0.9049885628396499D-02,
     *  0.9049885628398672D-02,0.9049885628405025D-02,
     1  0.9196546074381425D-02,0.9196546074380063D-02,
     2  0.9196546074381355D-02,0.1389679560298547D-02,
     3  0.1389679560298251D-02,0.1389679560296835D-02,
     4  0.5469361348986402D-02,0.5469361348984248D-02,
     5  0.5469361348984599D-02,0.1725450508839409D-01,
     6  0.1725450508839278D-01,0.1725450508839148D-01,
     7  0.6733913747887457D-02,0.6733913747885728D-02,
     8  0.6733913747886398D-02,0.4022564578398640D-02,
     9  0.4022564578402713D-02,0.4022564578399363D-02,
     *  0.1301944787144861D-02,0.1301944787144253D-02,
     1  0.1301944787143136D-02,0.2027792916616635D-02,
     2  0.2027792916617886D-02,0.2027792916616735D-02,
     3  0.4379548102164245D-02,0.4379548102164029D-02,
     4  0.4379548102160293D-02,0.9788773323829804D-02,
     5  0.9788773323830982D-02,0.9788773323832441D-02,
     6  0.1491498412616913D-01,0.1491498412617151D-01,
     7  0.1491498412617137D-01,0.3816494659634458D-02,
     8  0.3816494659634902D-02,0.3816494659631925D-02,
     9  0.1053753256419563D-01,0.1053753256419800D-01,
     *  0.1053753256419685D-01,0.9378412737876001D-02,
     1  0.9378412737873921D-02,0.9378412737876034D-02,
     2  0.1034943926448387D-01,0.1034943926449078D-01,
     3  0.1034943926449734D-01,0.1253515438165336D-02,
     4  0.1253515438163976D-02,0.1253515438162651D-02,
     5  0.7631115735488028D-02,0.7631115735488942D-02,
     6  0.7631115735487678D-02,0.4662247664665583D-02,
     7  0.4662247664663175D-02,0.4662247664669866D-02,
     8  0.1924508745358327D-01,0.1924508745357723D-01,
     9  0.1924508745358518D-01,0.2150599791391388D-02,
     *  0.2150599791389261D-02,0.2150599791389503D-02,
     1  0.1815794181007045D-01,0.1815794181007355D-01,
     2  0.1815794181007060D-01,0.2074509937828351D-02,
     3  0.2074509937826631D-02,0.2074509937827053D-02,
     4  0.3856301126724407D-02,0.3856301126725213D-02,
     5  0.3856301126727490D-02,0.2342776832115179D-02,
     6  0.2342776832117610D-02,0.2342776832119853D-02,
     7  0.2485903899501151D-02,0.2485903899504086D-02,
     8  0.2485903899497665D-02,0.1958269886432824D-02,
     9  0.1958269886433108D-02,0.1958269886434393D-02,
     *  0.3112037442333638D-02,0.3112037442336383D-02,
     1  0.3112037442329971D-02,0.8380938111968996D-02,
     2  0.2408616607470909D-03,0.1651223797192308D-01,
     3  0.1363274166717042D-01,0.2507433395640973D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule14 ( n, x, w )

c*********************************************************************72
c
cc RULE14 returns the rule of degree 14.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 177 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  -.5752422835841802D+00,0.4314967658691802D+00,
     2  0.1437455177139820D+00,-.3303076984155172D+00,
     3  0.4866309056595519D+00,-.1563232072429510D+00,
     4  -.5770168798465761D-02,-.7016819527781105D+00,
     5  0.7074521215770434D+00,-.3032416710412216D+00,
     6  -.2339888323701999D+00,0.5372305034104569D+00,
     7  0.2995840525991514D+00,-.4325354814520043D+00,
     8  0.1329514288534004D+00,0.2313978508942549D+00,
     9  -.4060579401191659D-01,-.1907920568806182D+00,
     *  0.1198459969693036D+00,-.5485013403177168D+00,
     1  0.4286553433493205D+00,-.4223067018453286D+00,
     2  0.2051376117542425D+00,0.2171690900904567D+00,
     3  -.1995552059487330D+00,-.3336302067365579D+00,
     4  0.5331854126840413D+00,-.3362367775957516D-02,
     5  -.2082502914064486D+00,0.2116126591830406D+00,
     6  0.3901789196843061D+00,-.4123770748876975D-03,
     7  -.3897665426036371D+00,0.5440475521812093D-02,
     8  -.5671976659757272D+00,0.5617571904593656D+00,
     9  0.5109903009675820D-01,-.8812309166767075D+00,
     *  0.8301318865798517D+00,-.3334033396451877D+00,
     1  -.4849473999181729D-01,0.3818980796337723D+00,
     2  0.2967209217147687D+00,0.6320475373066934D-02,
     3  -.3030413970906470D+00,0.3947081540530285D+00,
     4  -.2978075731654519D+00,-.9690058088341083D-01,
     5  0.4602277425410929D+00,-.2588695285519879D+00,
     6  -.2013582139898412D+00,0.4320204013442107D+00,
     7  0.2158666376867163D+00,-.6478870390304328D+00,
     8  0.3243502588043465D-02,-.8153377567221353D+00,
     9  0.8120942541315551D+00,-.2929639748058975D+00,
     *  0.3937181324850053D-01,0.2535921615554882D+00,
     1  -.2911712364207900D+00,0.4448737339859005D+00,
     2  -.1537024975672874D+00,0.3770577628402459D+00,
     3  -.4566844608555435D+00,0.7962669801609278D-01,
     4  -.7343568438702067D-03,-.6012198115212343D-01,
     5  0.6085633799849959D-01,-.7860612444751536D+00,
     6  0.7072341550237046D+00,0.7882708945288715D-01,
     7  -.1798079430257987D+00,-.5716591672723068D+00,
     8  0.7514671102985679D+00,0.2349121749284232D-01,
     9  -.2977965988756665D+00,0.2743053813811669D+00,
     *  -.3508185900315901D+00,0.3561089208016359D+00,
     1  -.5290330768361618D-02,-.4799997070573949D+00,
     2  0.3284477153105494D+00,0.1515519917450605D+00,
     3  0.5503749362395663D+00,-.1236979845612246D+00,
     4  -.4266769516797990D+00,-.1160913996018244D+00,
     5  0.1218716230766462D+00,-.5780223478460763D-02,
     6  -.1795966192456130D+00,-.5071498846594161D+00,
     7  0.6867465039037227D+00,-.4731311596169461D-02,
     8  -.6889415863849245D+00,0.6936728979813912D+00,
     9  0.1838019755826437D+00,-.7414338401434005D+00,
     *  0.5576318645605018D+00,-.3157482778904093D+00,
     1  0.1186260398816200D-01,0.3038856739015107D+00,
     2  -.3760156844932397D+00,0.2533165859904101D+00,
     3  0.1226990985037814D+00,0.3132847887437243D-01,
     4  0.1567813343830147D+00,-.1881098132555542D+00,
     5  -.5940398288585815D+00,0.6767061397330466D+00,
     6  -.8266631087504343D-01,0.5799063749491890D+00,
     7  0.7755651500224905D-01,-.6574628899522570D+00,
     8  0.1959288531923632D+00,0.8941019681549953D-01,
     9  -.2853390500081148D+00,0.2938476934905306D+00,
     *  0.2019773488401272D-02,-.2958674669799366D+00,
     1  0.3655020525321305D+00,-.5615458414677339D+00,
     2  0.1960437889355228D+00,-.5706595245720943D-01,
     3  -.7715171223939032D+00,0.8285830748522059D+00,
     4  0.1011528057210596D+00,-.1051837271533038D+00,
     5  0.4030921431232027D-02,-.2124197258439737D+00,
     6  0.3605072524272380D+00,-.1480875265845512D+00,
     7  -.1651782199629099D+00,0.7878215733569789D-02,
     8  0.1573000042284481D+00,-.3617927525610758D+00,
     9  -.2009201308789826D+00,0.5627128834404685D+00,
     *  -.5015820600281335D+00,0.4144850071548899D+00,
     1  0.8709705287395679D-01,0.9434068372117834D+00,
     2  0.4463509082121593D-02,-.9478703462960307D+00,
     3  0.2005751720829750D+00,-.1945620110873523D+00,
     4  -.6013160997523850D-02,-.1255658338458569D-01,
     5  -.4674319437690188D+00,0.4799885271519170D+00,
     6  -.1716908737168969D-01,0.1956591346765856D+00,
     7  -.1784900473056204D+00,-.5462757915789873D-03,
     8  -.5780834828017836D+00,0.5786297585932533D+00,
     9  -.1833877013210589D+00,0.2818210581349795D+00,
     *  -.9843335681437262D-01,0.1916617895075464D+00,
     1  -.7885465203364792D-03,-.1908732429835174D+00,
     2  -.4813891231174998D-01,-.8618855209039119D+00,
     3  0.9100244332179739D+00,-.4424462871708599D+00,
     4  0.5232153544540827D+00,-.8076906728405848D-01,
     5  0.2330164669103972D+00,-.5137198179676699D+00,
     6  0.2807033510564895D+00,0.3967080654003286D-12,
     7  0.1722425458471176D-11,0.3502410373140708D-12,
     8  -.2947942461866533D-11,-.1032091026644403D-11,
     *  -.4359393565820349D-12 /
      data ys /
     1  -.1661332605832194D+00,-.4151078006247312D+00,
     2  0.5812410612053462D+00,-.3712097301616572D+00,
     3  -.1004499928153783D+00,0.4716597229753685D+00,
     4  0.8135639371543177D+00,-.4117790813394923D+00,
     5  -.4017848558132318D+00,0.4452636911188574D+00,
     6  -.4852468361674822D+00,0.3998314505168596D-01,
     7  0.3264840198869604D+00,0.9620539017564665D-01,
     8  -.4226894100630985D+00,-.8671007929617915D-01,
     9  0.2437514569045547D+00,-.1570413776087273D+00,
     *  0.5641616743542007D+00,-.1782911592597502D+00,
     1  -.3858705150939825D+00,0.6946377256844247D-02,
     2  -.3692015206135402D+00,0.3622551433574067D+00,
     3  0.5004562312099742D+00,-.4230479934143149D+00,
     4  -.7740823779440852D-01,0.2424079875448238D+00,
     5  -.1241158896833233D+00,-.1182920978621629D+00,
     6  -.2247937322813834D+00,0.4503017226062891D+00,
     7  -.2255079903239726D+00,0.6518023902669200D+00,
     8  -.3211896051207328D+00,-.3306127851443094D+00,
     9  0.9880557751410730D+00,-.4497748293987996D+00,
     *  -.5382809457428603D+00,0.2484874102685690D+00,
     1  -.4129794669742624D+00,0.1644920567082871D+00,
     2  -.1786101603431211D+00,0.3462729362116060D+00,
     3  -.1676627758691386D+00,0.1159937060740129D+00,
     4  0.2838304354535469D+00,-.3998241415280471D+00,
     5  0.3320417294495800D-01,0.3819668300942372D+00,
     6  -.4151710030395980D+00,-.4986884177668357D+00,
     7  0.6234848514007479D+00,-.1247964336323278D+00,
     8  0.9395983095546842D+00,-.4669901991392865D+00,
     9  -.4726081104148907D+00,0.1236801757609007D+00,
     *  -.3155543324553964D+00,0.1918741566946638D+00,
     1  -.3455881484181401D+00,-.7936761338079117D-01,
     2  0.4249557617992578D+00,0.3096393919455638D+00,
     3  0.1717219053442890D+00,-.4813612972863747D+00,
     4  0.6984686512807867D-01,-.3555940424550629D-01,
     5  -.3428746088226146D-01,-.3628109884665136D+00,
     6  -.4993435124130320D+00,0.8621545008801837D+00,
     7  0.7639073125277335D+00,-.5376719027263360D+00,
     8  -.2262354098013041D+00,0.3303032323049931D+00,
     9  -.1448076250378262D+00,-.1854956072669932D+00,
     *  -.2086539551781068D+00,-.1994908334986071D+00,
     1  0.4081447886767858D+00,-.1021307936198597D+00,
     2  -.3646265433107137D+00,0.4667573369306311D+00,
     3  -.1749249882226239D+00,0.5641011705032603D+00,
     4  -.3891761822782046D+00,-.7369982797233314D-01,
     5  -.6368818722810367D-01,0.1373880152000548D+00,
     6  0.6892964013212863D+00,-.5001834353611165D+00,
     7  -.1891129659598641D+00,0.7982528447344757D+00,
     8  -.4032238584029919D+00,-.3950289863308680D+00,
     9  0.7500159343054114D+00,-.2158307870331475D+00,
     *  -.5341851472730395D+00,0.1685995980230182D+00,
     1  -.3577458288655779D+00,0.1891462308433379D+00,
     2  -.7541204156110640D-01,-.2879331142125014D+00,
     3  0.3633451557721906D+00,-.1991229969303482D+00,
     4  0.1266927570309605D+00,0.7243023989959384D-01,
     5  -.4384238887740483D+00,-.2952416382641486D+00,
     6  0.7336655270377042D+00,-.4243636513101600D+00,
     7  0.7143954781786902D+00,-.2900318268675506D+00,
     8  -.2163615785319861D+00,0.2778601534641544D+00,
     9  -.6149857493356037D-01,-.1719852784726787D+00,
     *  0.3404722066425572D+00,-.1684869281697858D+00,
     1  0.4373945770482864D+00,0.9783677410376379D-01,
     2  -.5352313511523523D+00,0.9238182796099402D+00,
     3  -.5113297043238586D+00,-.4124885752868345D+00,
     4  0.6305510675913090D-01,0.5607334603928896D-01,
     5  -.1191284527989022D+00,-.2936373325714834D+00,
     6  -.3714221255853142D-01,0.3307795451305264D+00,
     7  0.8626870981050186D-01,-.1861828895445977D+00,
     8  0.9991417973422896D-01,0.4408837263795412D+00,
     9  -.5337635778128931D+00,0.9287985143315733D-01,
     *  -.1890175235323525D+00,-.3398740442993634D+00,
     1  0.5288915678318241D+00,-.5498302077599997D+00,
     2  0.1091929391010154D+01,-.5420991832506766D+00,
     3  0.1088587293550235D+00,0.1192738297139006D+00,
     4  -.2281325590696736D+00,0.5469934639217403D+00,
     5  -.2843710521572813D+00,-.2626224117648735D+00,
     6  -.2160151309343958D+00,0.9313869964408443D-01,
     7  0.1228764312899015D+00,0.6678287012945778D+00,
     8  -.3343874393606580D+00,-.3334412619346900D+00,
     9  -.2195399888316988D+00,-.4904841366906035D-01,
     *  0.2685884025019004D+00,-.1097454506740659D+00,
     1  0.2208567039838767D+00,-.1111112533091888D+00,
     2  0.1023012688991847D+01,-.5531958654682623D+00,
     3  -.4698168235239601D+00,-.3487105684781340D+00,
     4  -.2088144402600705D+00,0.5575250087387288D+00,
     5  0.4586604304883936D+00,-.2753203539748657D-01,
     6  -.4311283950878784D+00,0.1424849530503414D-12,
     7  0.4163207520226179D-12,0.2564407634679153D-12,
     8  -.9489253825677672D-12,0.5725707601904812D-12,
     *  -.4307858177802721D-12 /
      data zs /
     1  -.3002408419822953D+00,-.3002408419833086D+00,
     2  -.3002408419833821D+00,-.2367243537500485D+00,
     3  -.2367243537456669D+00,-.2367243537470976D+00,
     4  -.1124874139319764D-01,-.1124874139141120D-01,
     5  -.1124874139183386D-01,-.2091200491939335D+00,
     6  -.2091200491951212D+00,-.2091200491943568D+00,
     7  -.3871070169557922D+00,-.3871070169557220D+00,
     8  -.3871070169561885D+00,0.1576758205577684D+00,
     9  0.1576758205557184D+00,0.1576758205553296D+00,
     *  -.3804994466636671D+00,-.3804994466631279D+00,
     1  -.3804994466634047D+00,-.2566785126781401D+00,
     2  -.2566785126792934D+00,-.2566785126782982D+00,
     3  -.7550445623527601D-02,-.7550445625559176D-02,
     4  -.7550445625114355D-02,0.3966685271521035D+00,
     5  0.3966685271469443D+00,0.3966685271536675D+00,
     6  0.5436295368746583D+00,0.5436295368772041D+00,
     7  0.5436295368824269D+00,0.2108533972691848D+00,
     8  0.2108533972755834D+00,0.2108533972664533D+00,
     9  -.3846227632566736D+00,-.3846227632563715D+00,
     *  -.3846227632570768D+00,0.4320199156927147D-01,
     1  0.4320199156864359D-01,0.4320199157222126D-01,
     2  -.3942552261036596D+00,-.3942552261036111D+00,
     3  -.3942552261035123D+00,-.2900823721656310D+00,
     4  -.2900823721654074D+00,-.2900823721650085D+00,
     5  -.4001954700908103D+00,-.4001954700902223D+00,
     6  -.4001954700893645D+00,-.2514599966999538D+00,
     7  -.2514599967001752D+00,-.2514599967005651D+00,
     8  -.2052993465249218D+00,-.2052993465263826D+00,
     9  -.2052993465223245D+00,0.2946594740406009D+00,
     *  0.2946594740416467D+00,0.2946594740425612D+00,
     1  -.5795226862357377D-01,-.5795226862121653D-01,
     2  -.5795226862189089D-01,-.2212157144490026D+00,
     3  -.2212157144492802D+00,-.2212157144486162D+00,
     4  0.1031915041617615D+01,0.1031915041621368D+01,
     5  0.1031915041615854D+01,-.2843664701680810D+00,
     6  -.2843664701691355D+00,-.2843664701684534D+00,
     7  -.3916632709551901D+00,-.3916632709550742D+00,
     8  -.3916632709550005D+00,-.5853404503565347D-01,
     9  -.5853404503336719D-01,-.5853404503471410D-01,
     *  0.4349032593314631D+00,0.4349032593318472D+00,
     1  0.4349032593321483D+00,-.7166469320204438D-01,
     2  -.7166469320319802D-01,-.7166469320166638D-01,
     3  -.3651020078507813D+00,-.3651020078509204D+00,
     4  -.3651020078510956D+00,0.6666741608359100D+00,
     5  0.6666741608427517D+00,0.6666741608415513D+00,
     6  -.2850607980246553D+00,-.2850607980246767D+00,
     7  -.2850607980239678D+00,-.3767139049041499D+00,
     8  -.3767139049041446D+00,-.3767139049041464D+00,
     9  -.3847323113293710D+00,-.3847323113294659D+00,
     *  -.3847323113294736D+00,-.1430711791014896D-01,
     1  -.1430711790970269D-01,-.1430711791041984D-01,
     2  0.2226893434846138D+00,0.2226893434844011D+00,
     3  0.2226893434848597D+00,0.1861368718435910D+00,
     4  0.1861368718416253D+00,0.1861368718431125D+00,
     5  -.1072795622749953D+00,-.1072795622745489D+00,
     6  -.1072795622748554D+00,-.6485516948547954D-01,
     7  -.6485516948561629D-01,-.6485516948569679D-01,
     8  0.5725622693459446D+00,0.5725622693472699D+00,
     9  0.5725622693460108D+00,-.2791087112264201D+00,
     *  -.2791087112266160D+00,-.2791087112254542D+00,
     1  -.3714154371111505D+00,-.3714154371112492D+00,
     2  -.3714154371110855D+00,-.3161738417128371D+00,
     3  -.3161738417122791D+00,-.3161738417134797D+00,
     4  0.8373277100424955D+00,0.8373277100425663D+00,
     5  0.8373277100420310D+00,0.2498873918545072D+00,
     6  0.2498873918552929D+00,0.2498873918556660D+00,
     7  0.5108904140436563D+00,0.5108904140435110D+00,
     8  0.5108904140435037D+00,-.3706147756740159D+00,
     9  -.3706147756740524D+00,-.3706147756740479D+00,
     *  0.2433004560275582D+00,0.2433004560300772D+00,
     1  0.2433004560291551D+00,-.3538702545014873D+00,
     2  -.3538702545021283D+00,-.3538702545024522D+00,
     3  -.3582651744000784D+00,-.3582651743999515D+00,
     4  -.3582651744000865D+00,0.8755062971445479D-01,
     5  0.8755062971455986D-01,0.8755062971379197D-01,
     6  -.1397307998126365D+00,-.1397307998123260D+00,
     7  -.1397307998124737D+00,-.2183761124774179D+00,
     8  -.2183761124772129D+00,-.2183761124776710D+00,
     9  0.5763507816362148D+00,0.5763507816368744D+00,
     *  0.5763507816365103D+00,0.8062208425433149D+00,
     1  0.8062208425454057D+00,0.8062208425485021D+00,
     2  -.4049658784349283D+00,-.4049658784337947D+00,
     3  -.4049658784361176D+00,0.2225706813796632D+00,
     4  0.2225706813790471D+00,0.2225706813801265D+00,
     5  -.4096725239466332D-02,-.4096725240921904D-02,
     6  -.4096725238250503D-02,-.2592447810085974D+00,
     7  0.1191149121741652D+01,0.4120653127511454D+00,
     8  0.8435262601344188D+00,-.4003639673386698D+00,
     *  0.3321002545060888D-01 /
      data ws /
     1  0.4194830168311239D-02,0.4194830168326290D-02,
     2  0.4194830168354955D-02,0.6505251369757091D-02,
     3  0.6505251369749837D-02,0.6505251369724089D-02,
     4  0.1511857423469778D-02,0.1511857423531536D-02,
     5  0.1511857423435278D-02,0.3576693638591392D-02,
     6  0.3576693638610991D-02,0.3576693638618915D-02,
     7  0.3373656058688358D-02,0.3373656058691433D-02,
     8  0.3373656058671795D-02,0.1076784154760114D-01,
     9  0.1076784154761919D-01,0.1076784154751974D-01,
     *  0.3758938857122322D-02,0.3758938857165091D-02,
     1  0.3758938857143189D-02,0.8302444588410703D-02,
     2  0.8302444588357655D-02,0.8302444588429193D-02,
     3  0.2942777031213149D-02,0.2942777031243674D-02,
     4  0.2942777031245480D-02,0.8843589566618218D-02,
     5  0.8843589566569863D-02,0.8843589566624911D-02,
     6  0.9759028519288406D-03,0.9759028519397565D-03,
     7  0.9759028519575427D-03,0.2004802238525724D-02,
     8  0.2004802238518510D-02,0.2004802238530063D-02,
     9  0.9695765259457370D-03,0.9695765259577475D-03,
     *  0.9695765259399248D-03,0.1954897938090337D-02,
     1  0.1954897938078232D-02,0.1954897938036924D-02,
     2  0.3691846518220940D-02,0.3691846518218663D-02,
     3  0.3691846518232707D-02,0.7970801887754822D-02,
     4  0.7970801887704541D-02,0.7970801887626933D-02,
     5  0.1979189926163023D-02,0.1979189926220139D-02,
     6  0.1979189926268928D-02,0.3698742482337427D-02,
     7  0.3698742482364018D-02,0.3698742482353030D-02,
     8  0.1687317723859350D-02,0.1687317723863163D-02,
     9  0.1687317723875827D-02,0.3835254087109209D-02,
     *  0.3835254087144783D-02,0.3835254087114301D-02,
     1  0.1016260451104831D-01,0.1016260451098046D-01,
     2  0.1016260451102241D-01,0.5267012161743862D-02,
     3  0.5267012161757533D-02,0.5267012161774349D-02,
     4  0.1528430187195588D-02,0.1528430187157122D-02,
     5  0.1528430187208298D-02,0.2982437800867588D-02,
     6  0.2982437800865273D-02,0.2982437800863566D-02,
     7  0.1466557323209961D-02,0.1466557323217223D-02,
     8  0.1466557323219012D-02,0.1461057795662250D-01,
     9  0.1461057795662684D-01,0.1461057795667047D-01,
     *  0.5561076940885510D-02,0.5561076940819906D-02,
     1  0.5561076940859880D-02,0.9751977499183117D-02,
     2  0.9751977499261835D-02,0.9751977499259098D-02,
     3  0.5302530732607095D-02,0.5302530732562353D-02,
     4  0.5302530732501225D-02,0.7136244952723934D-02,
     5  0.7136244952687442D-02,0.7136244952687213D-02,
     6  0.3962851386077182D-02,0.3962851386075291D-02,
     7  0.3962851386117417D-02,0.3518864309482585D-02,
     8  0.3518864309488224D-02,0.3518864309487660D-02,
     9  0.1910503466789297D-02,0.1910503466785413D-02,
     *  0.1910503466785542D-02,0.1114372702758599D-01,
     1  0.1114372702763622D-01,0.1114372702759230D-01,
     2  0.9339073844350225D-02,0.9339073844312899D-02,
     3  0.9339073844325385D-02,0.1427519172629088D-01,
     4  0.1427519172633135D-01,0.1427519172637184D-01,
     5  0.4705321020321325D-02,0.4705321020382762D-02,
     6  0.4705321020369120D-02,0.4787930353379107D-02,
     7  0.4787930353341169D-02,0.4787930353337981D-02,
     8  0.3363836009342347D-02,0.3363836009325845D-02,
     9  0.3363836009335837D-02,0.1284569887457350D-01,
     *  0.1284569887456974D-01,0.1284569887463706D-01,
     1  0.2752818417406538D-02,0.2752818417393949D-02,
     2  0.2752818417406429D-02,0.2544892612698709D-02,
     3  0.2544892612676544D-02,0.2544892612707782D-02,
     4  0.3052619386398206D-02,0.3052619386307692D-02,
     5  0.3052619386349196D-02,0.8865680919273325D-02,
     6  0.8865680919243184D-02,0.8865680919267345D-02,
     7  0.9030103498125034D-02,0.9030103498122236D-02,
     8  0.9030103498131978D-02,0.2991177381103681D-02,
     9  0.2991177381087045D-02,0.2991177381095963D-02,
     *  0.2211164766946887D-02,0.2211164766969601D-02,
     1  0.2211164766996503D-02,0.2973562062279324D-03,
     2  0.2973562062207861D-03,0.2973562062075669D-03,
     3  0.9172628789611696D-02,0.9172628789611484D-02,
     4  0.9172628789627685D-02,0.9783236108387362D-02,
     5  0.9783236108363432D-02,0.9783236108405431D-02,
     6  0.1738125981964304D-01,0.1738125981965133D-01,
     7  0.1738125981965202D-01,0.9766706161581359D-02,
     8  0.9766706161581049D-02,0.9766706161590663D-02,
     9  0.3005216389199320D-02,0.3005216389178637D-02,
     *  0.3005216389160241D-02,0.2785222700150757D-02,
     1  0.2785222700144989D-02,0.2785222700178524D-02,
     2  0.3753359578155891D-03,0.3753359578293081D-03,
     3  0.3753359577958143D-03,0.2191182863239439D-02,
     4  0.2191182863316704D-02,0.2191182863281961D-02,
     5  0.2531026444894308D-02,0.2531026444936393D-02,
     6  0.2531026444945725D-02,0.1445748928029682D-01,
     7  0.1287820052356487D-03,0.1574864463007665D-01,
     8  0.4621613088145150D-02,0.2792502892512972D-02,
     *  0.1851564470805342D-01 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine rule15 ( n, x, w )

c*********************************************************************72
c
cc RULE15 returns the rule of degree 15.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    09 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer N, the number of nodes.
c
c    Output, double precision X(3,N), the coordinates of the nodes.
c
c    Output, double precision W(N), the weights.
c
      implicit none

      integer n
      integer ns
      parameter ( ns = 214 )

      double precision w(n)
      double precision ws(ns)
      double precision x(3,n)
      double precision xs(ns)
      double precision ys(ns)
      double precision zs(ns)

      save xs
      save ys
      save zs
      save ws

      data xs /
     1  0.2581521194788427D+00,-.3924996680742822D+00,
     2  0.1343475485954617D+00,0.1747936627600043D+00,
     3  -.3848787335398570D+00,0.2100850707798483D+00,
     4  -.2686158385486640D+00,0.3159539810469303D+00,
     5  -.4733814249823749D-01,0.5356808415765576D-02,
     6  -.8659172184635908D-01,0.8123491343054050D-01,
     7  -.8144631134845116D+00,0.8470041241206219D+00,
     8  -.3254101063610144D-01,0.2249358441935477D+00,
     9  -.7323416768865754D+00,0.5074058326930275D+00,
     *  -.5473570384341295D+00,0.4843265718105462D+00,
     1  0.6303046662358983D-01,-.2378791442311287D-01,
     2  -.2016252113668169D+00,0.2254131257898949D+00,
     3  -.7391871819240758D-01,0.5113049221289290D+00,
     4  -.4373862039365108D+00,-.2968004530699073D+00,
     5  0.1205383163903803D+00,0.1762621366794993D+00,
     6  -.4241098255347354D-02,-.3585193417940622D+00,
     7  0.3627604400494130D+00,0.4202386364031931D-02,
     8  0.1599370643332776D-01,-.2019609279738776D-01,
     9  -.5388551273867861D-01,-.7018353952881240D+00,
     *  0.7557209080267955D+00,0.3646027806298292D-01,
     1  -.6343658219832248D+00,0.5979055439202614D+00,
     2  0.1258503466822884D-01,0.2393555213511634D+00,
     3  -.2519405560194015D+00,0.3851625317792869D-02,
     4  0.1534194382150093D+00,-.1572710635328328D+00,
     5  -.3485301409937485D-02,0.1619818108911392D+00,
     6  -.1584965094812263D+00,0.5304635114647127D-01,
     7  0.3545913748848099D+00,-.4076377260313040D+00,
     8  0.6653928546486268D-01,-.2403180998360646D+00,
     9  0.1737788143712072D+00,-.1667348931062531D+00,
     *  -.2713747582479675D+00,0.4381096513542055D+00,
     1  0.9493532822319652D-01,0.1868738963948708D-02,
     2  -.9680406718713280D-01,-.5105981722468006D-01,
     3  0.3251121848754134D+00,-.2740523676507155D+00,
     4  -.2080245286773480D-01,-.1497129535134266D+00,
     5  0.1705154063812837D+00,0.2921781238709439D+00,
     6  0.1381062592802215D+00,-.4302843831511968D+00,
     7  -.8780905828000338D-01,0.2673000828923510D+00,
     8  -.1794910246123719D+00,-.1944587456799732D-01,
     9  -.2823011707456111D+00,0.3017470453136293D+00,
     *  -.7313431320411609D-01,-.5236633756518274D+00,
     1  0.5967976888559381D+00,-.3762507052448836D+00,
     2  0.2871315908267298D+00,0.8911911441816055D-01,
     3  -.3797896271838643D-01,-.4650879543817582D+00,
     4  0.5030669171001346D+00,0.2750555493489867D-02,
     5  -.7277556508895471D+00,0.7250050953960729D+00,
     6  0.6123006138565600D+00,-.1192649298638286D+00,
     7  -.4930356839927218D+00,-.2645727220089428D+00,
     8  -.1730736170401170D+00,0.4376463390490505D+00,
     9  -.6630962451131286D-01,-.1763224174379790D+00,
     *  0.2426320419492632D+00,-.4200384093190587D-02,
     1  -.5418782850881636D+00,0.5460786691813587D+00,
     2  0.5394663228522688D-01,0.1507657818092707D+00,
     3  -.2047124140944948D+00,0.1018171426999433D+00,
     4  -.5394039692520657D+00,0.4375868265521267D+00,
     5  0.1245513301303478D+00,-.6455557549708775D+00,
     6  0.5210044248405197D+00,-.9855929555799212D-01,
     7  -.7473211662573033D+00,0.8458804618152944D+00,
     8  -.1755388020283085D+00,-.5318861672552897D+00,
     9  0.7074249692836033D+00,-.6267629157220122D-02,
     *  0.6632219831012681D-01,-.6005456915289890D-01,
     1  -.2023381108267559D+00,0.1094534186561336D+00,
     2  0.9288469217061772D-01,-.6473499743579236D-01,
     3  -.3234505788317799D+00,0.3881855762675665D+00,
     4  -.1233025545427212D+00,-.2864321270324415D+00,
     5  0.4097346815751876D+00,0.1989648914526389D+00,
     6  -.5364226464888502D+00,0.3374577550361906D+00,
     7  0.2178991630195039D-01,-.5426229008583486D+00,
     8  0.5208329845563997D+00,-.2014523059829409D+00,
     9  -.1081005526244278D+00,0.3095528586073633D+00,
     *  -.1169567835631198D-01,0.1260374294457714D+00,
     1  -.1143417510894922D+00,0.6829681010950600D-01,
     2  -.2897229857831844D+00,0.2214261756736523D+00,
     3  -.4298175003068387D+00,0.2110526002984961D+00,
     4  0.2187649000083270D+00,0.6578307149076966D+00,
     5  -.1808749039318607D+00,-.4769558109758388D+00,
     6  -.3704630736636612D+00,0.3211543940711805D+00,
     7  0.4930867959248819D-01,-.1193005517808560D+00,
     8  -.3998990653549201D+00,0.5191996171357768D+00,
     9  -.1504520555101911D+00,0.4460532087610402D+00,
     *  -.2956011532508667D+00,0.1975830054753616D+00,
     1  -.6709593039696905D+00,0.4733762984943273D+00,
     2  -.7463137388742009D-02,-.4211815306853685D+00,
     3  0.4286446680740814D+00,0.2049473200886011D-02,
     4  -.2026603403979144D+00,0.2006108671970308D+00,
     5  0.7152086010197926D-01,-.7652447634530471D+00,
     6  0.6937239033510662D+00,0.2166839105383212D+00,
     7  0.3458968024421906D+00,-.5625807129804981D+00,
     8  0.1279853939984014D+00,0.3081799665774158D+00,
     9  -.4361653605757960D+00,-.1577812374505563D-01,
     *  -.6857246456300986D+00,0.7015027693751511D+00,
     1  -.7105996230949263D-03,-.9227565022751169D+00,
     2  0.9234671018982127D+00,-.1882955447783474D-01,
     3  -.7344571519218671D+00,0.7532867063996859D+00,
     4  -.3375217299349303D+00,-.2041740513278847D+00,
     5  0.5416957812628146D+00,0.4996795038021838D+00,
     6  0.1342360979189166D+00,-.6339156017211199D+00,
     7  0.7596408799506882D+00,0.8346506611711336D-01,
     8  -.8431059460678011D+00,-.8820027427037123D+00,
     9  0.8657493528015160D+00,0.1625338990220750D-01,
     *  0.7067742334596752D+00,-.2761780760336056D+00,
     1  -.4305961574260422D+00,-.9186459446440826D-01,
     2  -.1188760024130717D+00,0.2107405968774760D+00,
     3  0.5405133012525005D+00,-.2620825757773786D+00,
     4  -.2784307254751027D+00,0.1458059413495244D+00,
     5  0.3829161242112978D+00,-.5287220655607965D+00,
     6  -.1823158001392015D-13,-.1699106971810907D-13,
     7  0.1569922552833598D-12,0.5359985656924711D-13 /
      data ys /
     1  0.3041753823660573D+00,0.7147860232646702D-01,
     2  -.3756539846925305D+00,0.3435025125820099D+00,
     3  -.2037550392031693D-01,-.3231270086616979D+00,
     4  -.2097468053232621D+00,-.1277547373803833D+00,
     5  0.3375015427036143D+00,0.9689475305431051D-01,
     6  -.4380824435589394D-01,-.5308650869840935D-01,
     7  -.5078056203162217D+00,-.4514429365648450D+00,
     8  0.9592485568810678D+00,0.7157685583829504D+00,
     9  -.1630841238981528D+00,-.5526844344847958D+00,
     *  -.2432354197382121D+00,-.3524073903550577D+00,
     1  0.5956428100933059D+00,0.2465506989117151D+00,
     2  -.1438762876493171D+00,-.1026744112624022D+00,
     3  -.5477270770116898D+00,0.2098480507360208D+00,
     4  0.3378790262756754D+00,0.3217216264418476D-01,
     5  -.2731228135353417D+00,0.2409506508911702D+00,
     6  0.4164310762083722D+00,-.2118884369332560D+00,
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     5  0.2801823664802910D-02,0.2801823664803036D-02,
     6  0.3473047605746596D-02,0.3473047605746489D-02,
     7  0.3473047605747130D-02,0.8146696772355114D-02,
     8  0.8146696772356077D-02,0.8146696772355570D-02,
     9  0.4104346629768971D-02,0.4104346629769071D-02,
     *  0.4104346629768999D-02,0.3673293016416287D-02,
     1  0.3673293016415687D-02,0.3673293016415978D-02,
     2  0.7385814346097036D-02,0.7385814346096885D-02,
     3  0.7385814346097676D-02,0.1952835342529582D-02,
     4  0.1952835342529196D-02,0.1952835342529467D-02,
     5  0.2956577367937866D-02,0.2956577367938132D-02,
     6  0.2956577367937872D-02,0.2429727102722713D-02,
     7  0.2429727102722471D-02,0.2429727102722800D-02,
     8  0.7838569405690889D-02,0.7838569405690287D-02,
     9  0.7838569405690948D-02,0.4786830078294293D-02,
     *  0.4786830078294275D-02,0.4786830078294352D-02,
     1  0.6464879373388097D-03,0.6464879373388156D-03,
     2  0.6464879373387403D-03,0.1094759729336998D-02,
     3  0.1094759729336943D-02,0.1094759729337179D-02,
     4  0.4183486775030887D-02,0.4183486775030987D-02,
     5  0.4183486775031043D-02,0.1388382329059297D-02,
     6  0.1388382329058254D-02,0.1388382329057900D-02,
     7  0.1547261679853963D-02,0.1547261679853909D-02,
     8  0.1547261679853913D-02,0.5245559039887955D-03,
     9  0.5245559039888078D-03,0.5245559039885548D-03,
     *  0.4714073461717449D-03,0.4714073461717063D-03,
     1  0.4714073461712849D-03,0.1734297963526248D-02,
     2  0.1734297963526404D-02,0.1734297963527124D-02,
     3  0.2194380264311005D-02,0.2194380264311055D-02,
     4  0.2194380264311861D-02,0.1505920846848116D-02,
     5  0.1505920846847692D-02,0.1505920846848549D-02,
     6  0.1092191482369307D-01,0.1402579642206070D-01,
     7  0.9137907285788647D-02,0.8807144129412933D-02 /

      call r8mat_row_copy ( 3, n, 1, xs, x )
      call r8mat_row_copy ( 3, n, 2, ys, x )
      call r8mat_row_copy ( 3, n, 3, zs, x )
      call r8vec_copy ( n, ws, w )

      return
      end
      subroutine tetrahedron_arbq ( degree, n, x, w )

c*********************************************************************72
c
cc TETRAHEDRON_ARBQ returns a quadrature rule for a tetrahedron.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    08 July 2014
c
c  Author:
c
c    Original Fortran77 version by Hong Xiao, Zydrunas Gimbutas.
c    This version by John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer DEGREE, the desired degree of exactness.
c    1 <= DEGREE <= 15.
c
c    Input, integer N, the number of points in the rule.
c    This value should be requested first from TETRAHEDRON_ARBQ_SIZE.
c
c    Output, double precision X(3,N), the quadrature nodes.
c
c    Output, double precision W(N), the quadrature weights.
c
      implicit none

      integer n

      double precision d
      integer degree
      integer i
      double precision r8vec_sum
      double precision volume
      double precision w(n)
      double precision x(3,n)
 
      if( degree .eq. 1 ) then
        call rule01 ( n, x, w )
      else if ( degree .eq. 2 ) then
        call rule02 ( n, x, w )
      else if ( degree .eq. 3 ) then
        call rule03 ( n, x, w )
      else if ( degree .eq. 4 ) then
        call rule04 ( n, x, w )
      else if ( degree .eq. 5 ) then
        call rule05 ( n, x, w )
      else if ( degree .eq. 6 ) then
        call rule06 ( n, x, w )
      else if ( degree .eq. 7 ) then
        call rule07 ( n, x, w )
      else if ( degree .eq. 8 ) then
        call rule08 ( n, x, w )
      else if ( degree .eq. 9 ) then
        call rule09 ( n, x, w )
      else if ( degree .eq. 10 ) then
        call rule10 ( n, x, w )
      else if ( degree .eq. 11 ) then
        call rule11 ( n, x, w )
      else if ( degree .eq. 12 ) then
        call rule12 ( n, x, w )
      else if ( degree .eq. 13 ) then
        call rule13 ( n, x, w )
      else if ( degree .eq. 14 ) then
        call rule14 ( n, x, w )
      else if ( degree .eq. 15 ) then
        call rule15 ( n, x, w )
      else
        write ( *, '(a)' ) ''
        write ( *, '(a)' ) 'TETRAHEDRON_ARBQ - Fatal error!'
        write ( *, '(a)' ) '  Illegal value of DEGREE.'
        stop 1
      end if

      d = r8vec_sum ( n, w )

      volume = sqrt ( 8.0D+00 ) / 3.0D+00
      do i = 1, n
        w(i) = w(i) * volume / d
      end do

      return
      end
      subroutine tetrahedron_arbq_gnuplot ( n, x, header )

c*********************************************************************72
c
cc TETRAHEDRON_ARBQ_GNUPLOT: plot of a quadrature rule in the tetrahedron.
c
c  Licensing:
c
c    This code is distributed under the GNU GPL license.
c
c  Modified:
c
c    11 July 2014
c
c  Author:
c
c    John Burkardt
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, double precision N, the number of nodes.
c
c    Input, double precision X(3,N), the coordinates of the nodes.
c
c    Input, character * ( * ) HEADER, a string to be used to identify
c    the files created.
c
      implicit none

      integer n

      character * ( 255 ) command_filename
      integer command_unit
      character * ( * ) header
      integer j
      character * ( 255 ) node_filename
      integer node_unit
      character * ( 255 ) plot_filename
      double precision v1(3)
      double precision v2(3)
      double precision v3(3)
      double precision v4(3)
      character * ( 255 ) vertex_filename
      integer vertex_unit
      double precision x(3,n)
c
c  Create the tetrahedron file.
c
      call tetrahedron_ref ( v1, v2, v3, v4 )

      call get_unit ( vertex_unit )
      vertex_filename = trim ( header ) // '_vertices.txt'
      open ( unit = vertex_unit, file = vertex_filename,
     &  status = 'replace' )

      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v1(1), v1(2), v1(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v2(1), v2(2), v2(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v3(1), v3(2), v3(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v1(1), v1(2), v1(3)
      write ( vertex_unit, '(a)' ) ''

      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v1(1), v1(2), v1(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v4(1), v4(2), v4(3)
      write ( vertex_unit, '(a)' ) ''

      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v2(1), v2(2), v2(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v4(1), v4(2), v4(3)
      write ( vertex_unit, '(a)' ) ''

      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v3(1), v3(2), v3(3)
      write ( vertex_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) 
     &  v4(1), v4(2), v4(3)

      close ( unit = vertex_unit )
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) '  Created vertex file "' //
     &  trim ( vertex_filename ) // '".'
c
c  Create node file.
c
      call get_unit ( node_unit )
      node_filename = trim ( header ) // '_nodes.txt'
      open ( unit = node_unit, file = node_filename,
     &  status = 'replace' )
      do j = 1, n
        write ( node_unit, '(g14.6,2x,g14.6,2x,g14.6)' ) x(1:3,j)
      end do
      close ( unit = node_unit )
      write ( *, '(a)' ) '  Created node file "' //
     &  trim ( node_filename ) // '".'
c
c  Create graphics command file.
c
      call get_unit ( command_unit )
      command_filename = trim ( header ) // '_commands.txt'
      open ( unit = command_unit, file = command_filename,
     &  status = 'replace' )
      write ( command_unit, '(a)' ) '# ' // trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) '# Usage:'
      write ( command_unit, '(a)' ) '#  gnuplot < ' //
     &  trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) 'set term png'
      plot_filename = trim ( header ) // '.png'
      write ( command_unit, '(a)' ) 'set output "' //
     &  trim ( plot_filename ) // '"'
      write ( command_unit, '(a)' ) 'set xlabel "<--- X --->"'
      write ( command_unit, '(a)' ) 'set ylabel "<--- Y --->"'
      write ( command_unit, '(a)' ) 'set zlabel "<--- Z --->"'
      write ( command_unit, '(a)' )
     &  'set title "' // trim ( header ) // '"'
      write ( command_unit, '(a)' ) 'set grid'
      write ( command_unit, '(a)' ) 'set key off'
      write ( command_unit, '(a)' ) 'set view equal xyz'
      write ( command_unit, '(a)' ) 'set style data lines'
      write ( command_unit, '(a)' ) 'set timestamp'
      write ( command_unit, '(a)' ) 'splot "' //
     &  trim ( vertex_filename ) //
     &  '" with lines lw 3, \'
      write ( command_unit, '(a)' ) '     "' //
     &  trim ( node_filename ) // '" with points pt 7 lt 0'
      close ( unit = command_unit )

      write ( *, '(a)' )
     &  '  Created command file "' // trim ( command_filename ) // '".'

      return
      end
      function tetrahedron_arbq_size ( degree )

c*********************************************************************72
c
cc TETRAHEDRON_ARBQ_SIZE returns the size of quadrature rule for a tetrahedron.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    08 July 2014
c
c  Author:
c
c    John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Input, integer DEGREE, the desired degree of exactness.
c    1 <= DEGREE <= 15.
c
c    Output, integer TETRAHEDRON_ARBQ_SIZE, the number of points in the
c    corresponding rule.
c
      implicit none

      integer degree
      integer n_save(15)
      integer tetrahedron_arbq_size

      save n_save

      data n_save /
     &    1,   4,   6,  11,  14,
     &   23,  31,  44,  57,  74,
     &   95, 122, 146, 177, 214 /

      if ( degree .lt. 1 .or. 15 .lt. degree ) then
        write ( *, '(a)' ) ''
        write ( *, '(a)' ) 'TETRAHEDRON_ARBQ_SIZE - Fatal error!'
        write ( *, '(a)' ) '  Illegal value of DEGREE.'
        stop 1
      end if

      tetrahedron_arbq_size = n_save ( degree )
 
      return
      end
      subroutine tetrahedron_ref ( v1, v2, v3, v4 )

c*********************************************************************72
c
cc TETRAHEDRON_REF returns the vertices of the reference tetrahedron.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    08 July 2014
c
c  Author:
c
c    John Burkardt.
c
c  Reference:
c
c    Hong Xiao, Zydrunas Gimbutas,
c    A numerical algorithm for the construction of efficient quadrature
c    rules in two and higher dimensions,
c    Computers and Mathematics with Applications,
c    Volume 59, 2010, pages 663-676.
c
c  Parameters:
c
c    Output, double precision V1(3), V2(3), V3(3), V4(3), the vertices.
c
      implicit none

      double precision v1(3)
      double precision v2(3)
      double precision v3(3)
      double precision v4(3)

      v1(1) = - 1.0D+00
      v1(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
      v1(3) = - 1.0D+00 / sqrt ( 6.0D+00 )

      v2(1) =   0.0D+00
      v2(2) =   2.0D+00 / sqrt ( 3.0D+00 )
      v2(3) = - 1.0D+00 / sqrt ( 6.0D+00 )

      v3(1) =   1.0D+00
      v3(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
      v3(3) = - 1.0D+00 / sqrt ( 6.0D+00 )

      v4(1) =   0.0D+00
      v4(2) =   0.0D+00
      v4(3) =   3.0D+00 / sqrt ( 6.0D+00 )

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc TIMESTAMP prints out the current YMDHMS date as a timestamp.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 January 2007
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    None
c
      implicit none

      character * ( 8 ) ampm
      integer d
      character * ( 8 ) date
      integer h
      integer m
      integer mm
      character * ( 9 ) month(12)
      integer n
      integer s
      character * ( 10 ) time
      integer y

      save month

      data month /
     &  'January  ', 'February ', 'March    ', 'April    ',
     &  'May      ', 'June     ', 'July     ', 'August   ',
     &  'September', 'October  ', 'November ', 'December ' /

      call date_and_time ( date, time )

      read ( date, '(i4,i2,i2)' ) y, m, d
      read ( time, '(i2,i2,i2,1x,i3)' ) h, n, s, mm

      if ( h .lt. 12 ) then
        ampm = 'AM'
      else if ( h .eq. 12 ) then
        if ( n .eq. 0 .and. s .eq. 0 ) then
          ampm = 'Noon'
        else
          ampm = 'PM'
        end if
      else
        h = h - 12
        if ( h .lt. 12 ) then
          ampm = 'PM'
        else if ( h .eq. 12 ) then
          if ( n .eq. 0 .and. s .eq. 0 ) then
            ampm = 'Midnight'
          else
            ampm = 'AM'
          end if
        end if
      end if

      write ( *,
     &  '(i2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' )
     &  d, month(m), y, h, ':', n, ':', s, '.', mm, ampm

      return
      end