program main !*****************************************************************************80 ! !! hyperball_integrals_test() tests hyperball_integrals(). ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 04 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'hyperball_integrals_test():' write ( *, '(a)' ) ' Fortran90 version' write ( *, '(a)' ) ' Test hyperball_integrals().' call test01 ( ) call test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'hyperball_integrals_test():' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine test01 ( ) !*****************************************************************************80 ! !! TEST01 uses HYPERBALL01_SAMPLE to compare exact and estimated integrals in 3D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 10 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 3 integer e(m) real ( kind = rk ) error real ( kind = rk ) exact real ( kind = rk ) hyperball01_volume integer, parameter :: n = 4192 real ( kind = rk ) result integer test integer, parameter :: test_num = 20 real ( kind = rk ), allocatable :: value(:) real ( kind = rk ), 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 ! ! Get sample points. ! allocate ( x(1:m,1:n) ) call hyperball01_sample ( m, n, x ) write ( *, '(a)' ) '' write ( *, '(a,i6)' ) ' Number of sample points used is ', n ! ! Randomly choose exponents between 0 and 8. ! write ( *, '(a)' ) '' write ( *, '(a)' ) ' If any exponent is odd, the integral is zero.' write ( *, '(a)' ) ' We will restrict this test to randomly chosen even exponents.' write ( *, '(a)' ) '' write ( *, '(a)' ) ' Ex Ey Ez MC-Estimate Exact Error' write ( *, '(a)' ) '' allocate ( value(1:n) ) do test = 1, test_num call i4vec_uniform_ab ( m, 0, 4, e ) e(1:m) = e(1:m) * 2 call monomial_value ( m, n, e, x, value ) result = hyperball01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = rk ) call hyperball01_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 deallocate ( value ) deallocate ( x ) return end subroutine test02 ( ) !*****************************************************************************80 ! !! TEST02 uses HYPERBALL01_SAMPLE to compare exact and estimated integrals in 6D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 10 January 2014 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 6 integer e(m) real ( kind = rk ) error real ( kind = rk ) exact real ( kind = rk ) hyperball01_volume integer, parameter :: n = 4192 real ( kind = rk ) result integer test integer, parameter :: test_num = 20 real ( kind = rk ), allocatable :: value(:) real ( kind = rk ), 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 ! ! Get sample points. ! allocate ( x(1:m,1:n) ) call hyperball01_sample ( m, n, x ) write ( *, '(a)' ) '' write ( *, '(a,i6)' ) ' Number of sample points used is ', n ! ! Randomly choose exponents between 0 and 8. ! write ( *, '(a)' ) '' write ( *, '(a)' ) ' If any exponent is odd, the integral is zero.' write ( *, '(a)' ) ' We will restrict this test to randomly chosen even exponents.' write ( *, '(a)' ) '' write ( *, '(a)' ) ' E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error' write ( *, '(a)' ) '' allocate ( value(1:n) ) do test = 1, test_num call i4vec_uniform_ab ( m, 0, 3, e ) e(1:m) = e(1:m) * 2 call monomial_value ( m, n, e, x, value ) result = hyperball01_volume ( m ) * sum ( value(1:n) ) & / real ( n, kind = rk ) call hyperball01_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 deallocate ( value ) deallocate ( x ) 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 ( *, '(i2.2,1x,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