program main !*****************************************************************************80 ! !! SIMPLEX_INTEGRALS_TEST tests the SIMPLEX_INTEGRALS library. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 13 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'SIMPLEX_INTEGRALS_TEST' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Test the SIMPLEX_INTEGRALS library.' call test01 ( ) call test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'SIMPLEX_INTEGRALS_TEST' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine test01 ( ) !*****************************************************************************80 ! !! TEST01 compares exact and estimated integrals in 3D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 13 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 3 integer, parameter :: n = 4192 integer e(m) real ( kind = rk ) error real ( kind = rk ) exact real ( kind = rk ) result integer seed real ( kind = rk ) simplex01_volume integer test integer, parameter :: test_num = 20 real ( kind = rk ) value(n) real ( kind = rk ) x(m,n) write ( *, '(a)' ) '' write ( *, '(a)' ) 'TEST01' write ( *, '(a)' ) ' Estimate monomial integrals using Monte Carlo' write ( *, '(a)' ) ' over the interior of the unit simplex in M dimensions.' ! ! Get sample points. ! seed = 123456789 call simplex01_sample ( m, n, seed, x ) write ( *, '(a)' ) '' write ( *, '(a,i6)' ) ' Number of sample points used is ', n ! ! Randomly choose exponents. ! write ( *, '(a)' ) '' write ( *, '(a)' ) ' We randomly choose the exponents.' write ( *, '(a)' ) '' write ( *, '(a)' ) ' Ex Ey Ez MC-Estimate Exact Error' write ( *, '(a)' ) '' do test = 1, test_num call i4vec_uniform_ab ( m, 0, 4, seed, e ) call monomial_value ( m, n, e, x, value ) result = simplex01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = rk ) call simplex01_monomial_integral ( m, e, exact ) error = abs ( result - exact ) write ( *, '(2x,i2,2x,i2,2x,i2,2x,g14.6,2x,g14.6,2x,e10.2)' ) & e(1:m), result, exact, error end do return end subroutine test02 ( ) !*****************************************************************************80 ! !! TEST02 compares exact and estimated integrals in 6D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 13 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 6 integer, parameter :: n = 4192 integer e(m) real ( kind = rk ) error real ( kind = rk ) exact real ( kind = rk ) result integer seed real ( kind = rk ) simplex01_volume integer test integer, parameter :: test_num = 20 real ( kind = rk ) value(n) real ( kind = rk ) x(m,n) write ( *, '(a)' ) '' write ( *, '(a)' ) 'TEST02' write ( *, '(a)' ) ' Estimate monomial integrals using Monte Carlo' write ( *, '(a)' ) ' over the interior of the unit simplex in M dimensions.' ! ! Get sample points. ! seed = 123456789 call simplex01_sample ( m, n, seed, x ) write ( *, '(a)' ) '' write ( *, '(a,i6)' ) ' Number of sample points used is ', n ! ! Randomly choose exponents. ! write ( *, '(a)' ) '' write ( *, '(a)' ) ' We randomly choose the exponents.' write ( *, '(a)' ) '' write ( *, '(a)' ) ' E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error' write ( *, '(a)' ) '' do test = 1, test_num call i4vec_uniform_ab ( m, 0, 3, seed, e ) call monomial_value ( m, n, e, x, value ) result = simplex01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = rk ) call simplex01_monomial_integral ( m, e, exact ) error = abs ( result - exact ) write ( *, '(6(2x,i2),2x,g14.6,2x,g14.6,2x,e10.2)' ) & e(1:m), result, exact, error end do return end