subroutine monomial_value ( m, n, e, x, value ) !*****************************************************************************80 ! !! MONOMIAL_VALUE evaluates a monomial. ! ! Discussion: ! ! This routine evaluates a monomial of the form ! ! product ( 1 <= i <= m ) x(i)^e(i) ! ! where the exponents are nonnegative integers. Note that ! if the combination 0^0 is encountered, it should be treated ! as 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 07 May 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, the spatial dimension. ! ! Input, integer N, the number of points at which the ! monomial is to be evaluated. ! ! Input, integer E(M), the exponents. ! ! Input, real ( kind = rk ) X(M,N), the point coordinates. ! ! Output, real ( kind = rk ) VALUE(N), the value of the monomial. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer e(m) integer i real ( kind = rk ) value(n) real ( kind = rk ) x(m,n) value(1:n) = 1.0D+00 do i = 1, m if ( 0 /= e(i) ) then value(1:n) = value(1:n) * x(i,1:n) ** e(i) end if end do return end subroutine r8vec_uniform_01 ( n, seed, r ) !*****************************************************************************80 ! !! R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC. ! ! Discussion: ! ! An R8VEC is a vector of real ( kind = rk ) values. ! ! For now, the input quantity SEED is an integer variable. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 05 July 2006 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Paul Bratley, Bennett Fox, Linus Schrage, ! A Guide to Simulation, ! Springer Verlag, pages 201-202, 1983. ! ! Bennett Fox, ! Algorithm 647: ! Implementation and Relative Efficiency of Quasirandom ! Sequence Generators, ! ACM Transactions on Mathematical Software, ! Volume 12, Number 4, pages 362-376, 1986. ! ! Peter Lewis, Allen Goodman, James Miller ! A Pseudo-Random Number Generator for the System/360, ! IBM Systems Journal, ! Volume 8, pages 136-143, 1969. ! ! Parameters: ! ! Input, integer N, the number of entries in the vector. ! ! Input/output, integer SEED, the "seed" value, which ! should NOT be 0. On output, SEED has been updated. ! ! Output, real ( kind = rk ) R(N), the vector of pseudorandom values. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n integer i integer k integer seed real ( kind = rk ) r(n) if ( seed == 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8VEC_UNIFORM_01 - Fatal error!' write ( *, '(a)' ) ' Input value of SEED = 0.' stop 1 end if do i = 1, n k = seed / 127773 seed = 16807 * ( seed - k * 127773 ) - k * 2836 if ( seed < 0 ) then seed = seed + 2147483647 end if r(i) = real ( seed, kind = rk ) * 4.656612875D-10 end do return end subroutine tetrahedron01_monomial_integral ( e, integral ) !*****************************************************************************80 ! !! TETRAHEDRON01_MONOMIAL_INTEGRAL: monomial integral in unit tetrahedron in 3D. ! ! Discussion: ! ! The monomial is F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3). ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 January 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer E(3), the exponents. ! Each exponent must be nonnegative. ! ! Output, real ( kind = rk ) INTEGRAL, the integral. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 3 integer e(m) integer i real ( kind = rk ) integral integer j integer k if ( any ( e(1:m) < 0 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TETRAHEDRON01_MONOMIAL_INTEGRAL - Fatal error!' write ( *, '(a)' ) ' All exponents must be nonnegative.' stop 1 end if k = 0 integral = 1.0D+00 do i = 1, m do j = 1, e(i) k = k + 1 integral = integral * real ( j, kind = rk ) / real ( k, kind = rk ) end do end do do i = 1, m k = k + 1 integral = integral / real ( k, kind = rk ) end do return end subroutine tetrahedron01_sample ( n, seed, x ) !*****************************************************************************80 ! !! TETRAHEDRON01_SAMPLE samples points from the unit tetrahedron in 3D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 January 2014 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Reuven Rubinstein, ! Monte Carlo Optimization, Simulation, and Sensitivity ! of Queueing Networks, ! Krieger, 1992, ! ISBN: 0894647644, ! LC: QA298.R79. ! ! Parameters: ! ! Input, integer N, the number of points. ! ! Input/output, integer SEED, a seed for the random ! number generator. ! ! Output, real ( kind = rk ) X(3,N), the points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 3 integer n real ( kind = rk ) e(m+1) real ( kind = rk ) e_sum integer j integer seed real ( kind = rk ) x(m,n) do j = 1, n call r8vec_uniform_01 ( m + 1, seed, e ) e(1:m+1) = - log ( e(1:m+1) ) e_sum = sum ( e(1:m+1) ) x(1:m,j) = e(1:m) / e_sum end do return end function tetrahedron01_volume ( ) !*****************************************************************************80 ! !! TETRAHEDRON01_VOLUME computes the volume of the unit tetrahedron in 3D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 15 January 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, real ( kind = rk ) TETRAHEDRON01_VOLUME, the volume. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) real ( kind = rk ) tetrahedron01_volume tetrahedron01_volume = 1.0D+00 / 6.0D+00 return end subroutine timestamp ( ) !*****************************************************************************80 ! !! TIMESTAMP prints the current YMDHMS date as a time stamp. ! ! Example: ! ! 31 May 2001 9:45:54.872 AM ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 May 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character ( len = 8 ) ampm integer d integer h integer m integer mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer n integer s integer values(8) integer y call date_and_time ( values = values ) y = values(1) m = values(2) d = values(3) h = values(5) n = values(6) s = values(7) mm = values(8) if ( h < 12 ) then ampm = 'AM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Noon' else ampm = 'PM' end if else h = h - 12 if ( h < 12 ) then ampm = 'PM' else if ( h == 12 ) then if ( n == 0 .and. s == 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, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm ) return end