program main !*****************************************************************************80 ! !! MAIN is the main program for HYPERBALL_MONTE_CARLO_TEST. ! ! Discussion: ! ! HYPERBALL_MONTE_CARLO_TEST tests the HYPERBALL_MONTE_CARLO library. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 January 2014 ! ! Author: ! ! John Burkardt ! implicit none call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HYPERBALL_MONTE_CARLO_TEST' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Test the HYPERBALL_MONTE_CARLO library.' call test01 ( ) call test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HYPERBALL_MONTE_CARLO_TEST' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine test01 ( ) !*****************************************************************************80 ! !! TEST01 uses HYPERBALL01_SAMPLE to estimate integrals in 3D. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer ( kind = 4 ), parameter :: m = 3 real ( kind = 8 ) hyperball01_volume integer ( kind = 4 ) e(m) integer ( kind = 4 ) :: e_test(m,7) = reshape ( (/ & 0, 0, 0, & 2, 0, 0, & 0, 2, 0, & 0, 0, 2, & 4, 0, 0, & 2, 2, 0, & 0, 0, 4 /), (/ m, 7 /) ) integer ( kind = 4 ) j integer ( kind = 4 ) n real ( kind = 8 ) result(7) integer ( kind = 4 ) seed real ( kind = 8 ), allocatable :: value(:) real ( kind = 8 ), allocatable :: x(:,:) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST01' write ( *, '(a)' ) ' Use the Monte Carlo method to estimate integrals over' write ( *, '(a)' ) ' the interior of the unit hyperball in M dimensions.' write ( *, '(a)' ) '' write ( *, '(a,i4)' ) ' Spatial dimension M = ', m seed = 123456789 write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' N 1 X^2 Y^2' // & ' Z^2 X^4 X^2Y^2 Z^4' write ( *, '(a)' ) ' ' n = 1 do while ( n <= 65536 ) allocate ( value(1:n) ) allocate ( x(1:m,1:n) ) call hyperball01_sample ( m, n, seed, x ) do j = 1, 7 e(1:m) = e_test(1:m,j) call monomial_value ( m, n, e, x, value ) result(j) = hyperball01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = 8 ) end do write ( *, '(2x,i8,7(2x,g14.6))' ) n, result(1:7) deallocate ( value ) deallocate ( x ) n = 2 * n end do write ( *, '(a)' ) ' ' do j = 1, 7 e(1:m) = e_test(1:m,j) call hyperball01_monomial_integral ( m, e, result(j) ) end do write ( *, '(2x,a8,7(2x,g14.6))' ) ' Exact', result(1:7) return end subroutine test02 ( ) !*****************************************************************************80 ! !! TEST02 uses HYPERBALL01_SAMPLE to estimate integrals in 6D. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer ( kind = 4 ), parameter :: m = 6 real ( kind = 8 ) hyperball01_volume integer ( kind = 4 ) e(m) integer ( kind = 4 ) :: e_test(m,7) = reshape ( (/ & 0, 0, 0, 0, 0, 0, & 1, 0, 0, 0, 0, 0, & 0, 2, 0, 0, 0, 0, & 0, 2, 2, 0, 0, 0, & 0, 0, 0, 4, 0, 0, & 2, 0, 0, 0, 2, 2, & 0, 0, 0, 0, 0, 6 /), (/ m, 7 /) ) integer ( kind = 4 ) j integer ( kind = 4 ) n real ( kind = 8 ) result(7) integer ( kind = 4 ) seed real ( kind = 8 ), allocatable :: value(:) real ( kind = 8 ), allocatable :: x(:,:) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST02' write ( *, '(a)' ) ' Use the Monte Carlo method to estimate integrals over' write ( *, '(a)' ) ' the interior of the unit hyperball in M dimensions.' write ( *, '(a)' ) '' write ( *, '(a,i4)' ) ' Spatial dimension M = ', m seed = 123456789 write ( *, '(a)' ) ' ' write ( *, '(a)' ) & ' N' // & ' 1 ' // & ' U ' // & ' V^2 ' // & ' V^2W^2' // & ' X^4 ' // & ' Y^2Z^2' // & ' Z^6' write ( *, '(a)' ) ' ' n = 1 do while ( n <= 65536 ) allocate ( value(1:n) ) allocate ( x(1:m,1:n) ) call hyperball01_sample ( m, n, seed, x ) do j = 1, 7 e(1:m) = e_test(1:m,j) call monomial_value ( m, n, e, x, value ) result(j) = hyperball01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = 8 ) end do write ( *, '(2x,i8,7(2x,g14.6))' ) n, result(1:7) deallocate ( value ) deallocate ( x ) n = 2 * n end do write ( *, '(a)' ) ' ' do j = 1, 7 e(1:m) = e_test(1:m,j) call hyperball01_monomial_integral ( m, e, result(j) ) end do write ( *, '(2x,a8,7(2x,g14.6))' ) ' Exact', result(1:7) return end