program main !*****************************************************************************80 ! !! cvt_box() demonstrates a CVT calculation with points forced to the boundary. ! ! Discussion: ! ! This code essentially carries out a standard CVT iteration, but ! at the end of every iteration, the CVT generators are modified ! by replacing points that are near the boundary by their projections ! on the boundary. The goal is to get a set of points with the ! good distribution properties of a CVT, but which also "mesh" the ! boundary. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 December 2004 ! ! Author: ! ! Lili Ju ! ! Local parameters: ! ! Local, real ( kind = 8 ) AV_POINTS(2,N), used to store the running ! total and then average of the sample points closest to each ! generator. ! ! Local, integer ( kind = 4 ) COUNT(2,N), counts the number of sample points ! that were nearest to each generator. ! ! Local, real ( kind = 8 ) GENERATOR(2,N), the coordinates of the ! CVT generators. ! ! Local, integer ( kind = 4 ) IT_MAX, the number of CVT iterations to ! carry out. (the user specifies this.) ! ! Local, integer ( kind = 4 ) N, the number of generators (the user ! specifies this). ! ! Local, integer ( kind = 4 ) NPP, the number of subintervals into which the ! perimeter of the box is to be divided, as part of the projection ! scheme that sends some interior points to the boundary. ! ! Local, integer ( kind = 4 ) SAMPLE_NUM, the total number of sampling ! points to generate on one CVT iteration. (The user specifies this.) ! ! Local, integer ( kind = 4 ) SEED, a seed for the random number generator. ! implicit none real ( kind = 8 ), allocatable, dimension ( :, : ) :: av_points integer ( kind = 4 ) batch integer ( kind = 4 ), allocatable, dimension ( : ) :: count logical, parameter :: DEBUG = .true. real ( kind = 8 ) :: energy real ( kind = 8 ) :: energy2 real ( kind = 8 ), allocatable, dimension ( :, : ) :: generator integer ( kind = 4 ) init character ( len = 255 ) init_string logical initialize integer ( kind = 4 ) ios real ( kind = 8 ) it_diff integer ( kind = 4 ) it_fixed integer ( kind = 4 ) it_max integer ( kind = 4 ) it_num integer ( kind = 4 ) j integer ( kind = 4 ) n integer ( kind = 4 ) ndim integer ( kind = 4 ) nearest(1) integer ( kind = 4 ) npp real ( kind = 8 ), allocatable, dimension ( : ) :: s logical s_eqi integer ( kind = 4 ) sample integer ( kind = 4 ) sample_num character ( len = 255 ) sample_string integer ( kind = 4 ) seed integer ( kind = 4 ) seed_init integer ( kind = 4 ) seed_iter call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box:' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Generate a constrained CVT dataset.' ! ! Get some input from the user. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' NDIM is the spatial dimension.' write ( *, '(a)' ) ' (Try ''2'' if you have no preference.)' write ( *, '(a)' ) ' (Any value less than 1 terminates execution.)' read ( *, * ) ndim write ( *, '(a,i12)' ) ' User input NDIM = ', ndim if ( ndim < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i6)' ) ' The input value of NDIM = ', ndim write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' N is the number of points to generate.' write ( *, '(a)' ) ' (Try ''100'' if you have no preference.)' write ( *, '(a)' ) ' (Any value less than 1 terminates execution.)' read ( *, * ) n write ( *, '(a,i12)' ) ' User input N = ', n if ( n < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i6)' ) ' The input value of N = ', n write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' NPP is the number of sample points used to' write ( *, '(a)' ) ' check the boundary.' write ( *, '(a)' ) ' (Try ''1000'' if you have no preference.)' write ( *, '(a)' ) ' (Any value less than 1 terminates execution.)' read ( *, * ) npp write ( *, '(a,i12)' ) ' User input NPP = ', npp if ( n < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i6)' ) ' The input value of N = ', n write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter SEED, a seed for the random number generator:' write ( *, '(a)' ) ' (Try ''123456789'' if you do not have a preference.)' write ( *, '(a)' ) ' (Any negative value terminates execution).' read ( *, *, iostat = ios ) seed if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box - Warning!' write ( *, '(a)' ) ' Terminating abnormally because of an I/O error' write ( *, '(a)' ) ' while expecting input for SEED.' stop end if write ( *, '(a,i12)' ) ' User input SEED = ', seed seed_init = seed write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' INIT is the method of initializing the data:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' file read data from a file;' write ( *, '(a)' ) ' GRID by picking points from a grid;' write ( *, '(a)' ) ' HALTON from a Halton sequence;' write ( *, '(a)' ) ' RANDOM using FORTRAN RANDOM function;' write ( *, '(a)' ) ' UNIFORM using a simple uniform RNG;' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' (Try ''RANDOM'' if you do not have a preference.)' write ( *, '(a)' ) ' (A blank value terminates execution).' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter INIT:' read ( *, '(a)', iostat = ios ) init_string if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box - Warning!' write ( *, '(a)' ) ' Terminating abnormally because of an I/O error' write ( *, '(a)' ) ' while expecting input for INIT.' stop end if write ( *, '(a)' ) ' User input INIT = "' // trim ( init_string ) // '".' if ( s_eqi ( init_string(1:6), 'RANDOM' ) ) then init = -1 else if ( s_eqi ( init_string(1:7), 'UNIFORM' ) ) then init = 0 else if ( s_eqi ( init_string(1:6), 'HALTON' ) ) then init = 1 else if ( s_eqi ( init_string(1:4), 'GRID' ) ) then init = 2 else if ( 0 < len_trim ( init_string ) ) then init = 3 else write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a)' ) ' The input value of INIT ' write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if if ( len_trim ( init_string ) <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a)' ) ' The input value of INIT ' write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' User input INIT = "' // trim ( init_string ) // '".' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' IT_MAX is the maximum number of iterations.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' An iteration carries out the following steps:' write ( *, '(a)' ) ' * the Voronoi region associated with each' write ( *, '(a)' ) ' generator is estimated by sampling;' write ( *, '(a)' ) ' * the centroid of each Voronoi region is estimated.' write ( *, '(a)' ) ' * the generator is replaced by the centroid.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' If "enough" sampling points are used,' write ( *, '(a)' ) ' and "enough" iterations are taken, this process' write ( *, '(a)' ) ' will converge.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' (Try ''50'' if you have no preference.)' write ( *, '(a)' ) ' (A negative value terminates execution).' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter IT_MAX: ' read ( *, * ) it_max write ( *, '(a,i12)' ) ' User input IT_MAX = ', it_max if ( it_max < 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i12)' ) ' The input value of IT_MAX = ', it_max write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' IT_FIXED is the number of consecutive iterations' write ( *, '(a)' ) ' to take with a fixed set of sample points.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Setting IT_FIXED to 1 means a new set of sample' write ( *, '(a)' ) ' points is generated on every iterative step;' write ( *, '(a)' ) ' Setting IT_FIXED equal to IT_MAX means a single set' write ( *, '(a)' ) ' of sample points is used for the entire iteration.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Any value between 1 and IT_MAX is reasonable.' write ( *, '(a)' ) ' ' write ( *, '(a,i6,a)' ) ' (Try ', it_max, & ' if you do not have a preference.)' write ( *, '(a)' ) ' (A 0 or negative value terminates execution).' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter IT_FIXED:' read ( *, *, iostat = ios ) it_fixed if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box - Warning!' write ( *, '(a)' ) ' Terminating abnormally because of an I/O error' write ( *, '(a)' ) ' while expecting input for IT_FIXED.' stop end if write ( *, '(a,i6)' ) ' User input IT_FIXED = ', it_fixed if ( it_fixed <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i12)' ) ' The input value of IT_FIXED = ', it_fixed write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' SAMPLE is the method of sampling the region:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' GRID by picking points from a grid;' write ( *, '(a)' ) ' HALTON from a Halton sequence;' write ( *, '(a)' ) ' RANDOM using FORTRAN RANDOM function;' write ( *, '(a)' ) ' UNIFORM using a simple uniform RNG;' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' (Try ''RANDOM'' if you do not have a preference.)' write ( *, '(a)' ) ' (A blank value terminates execution).' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter SAMPLE:' read ( *, '(a)', iostat = ios ) sample_string if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box - Warning!' write ( *, '(a)' ) ' Terminating abnormally because of an I/O error' write ( *, '(a)' ) ' while expecting input for SAMPLE.' stop end if write ( *, '(a)' ) ' User input SAMPLE = "' // trim ( sample_string ) & // '".' if ( len_trim ( sample_string ) <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a)' ) ' The input value of SAMPLE ' write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if if ( s_eqi ( sample_string(1:6), 'RANDOM' ) ) then sample = -1 else if ( s_eqi ( sample_string(1:7), 'UNIFORM' ) ) then sample = 0 else if ( s_eqi ( sample_string(1:6), 'HALTON' ) ) then sample = 1 else if ( s_eqi ( sample_string(1:4), 'GRID' ) ) then sample = 2 else sample = 3 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a)' ) ' The input value of SAMPLE ' write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' SAMPLE_NUM is the number of sample points.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The Voronoi regions will be explored by generating' write ( *, '(a)' ) ' SAMPLE_NUM points. For each sample point, the' write ( *, '(a)' ) ' nearest generator is found. Using more points' write ( *, '(a)' ) ' gives a better estimate of these regions.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' SAMPLE_NUM should be much larger than N, the' write ( *, '(a)' ) ' number of generators. ' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' (Try ''10000'' if you have no preference.) ' write ( *, '(a)' ) ' (A zero or negative value terminates execution.)' write ( *, '(a)' ) ' ' read ( *, * ) sample_num write ( *, '(a,i12)' ) ' User input SAMPLE_NUM = ', sample_num if ( sample_num <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box' write ( *, '(a,i12)' ) ' The input value of SAMPLE_NUM = ', sample_num write ( *, '(a)' ) ' is interpreted as a request for termination.' write ( *, '(a)' ) ' Normal end of execution.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' BATCH is the number of sample points to create' write ( *, '(a)' ) ' at one time.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' BATCH should be between 1 and SAMPLE_NUM.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' It is FASTER to set BATCH to SAMPLE_NUM;' write ( *, '(a)' ) ' setting BATCH to 1 requires the least memory.' write ( *, '(a)' ) ' ' write ( *, '(a,i12,a)' ) ' (Try ', min ( sample_num, 1000 ), & ' if you do not have a preference.)' write ( *, '(a)' ) ' (A zero or negative value terminates execution.)' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Enter BATCH:' read ( *, *, iostat = ios ) batch if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box - Warning!' write ( *, '(a)' ) ' Terminating abnormally because of an I/O error' write ( *, '(a)' ) ' while expecting input for SAMPLE_NUM.' stop end if write ( *, '(a,i12)' ) ' User input BATCH = ', batch ! ! Allocate space. ! allocate ( av_points(2,n) ) allocate ( count(n) ) allocate ( generator(ndim,n) ) allocate ( s(ndim) ) if ( DEBUG ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Energy Energy after' write ( *, '(a)' ) ' Iteration Seed of CVT projection' write ( *, '(a)' ) ' ' end if ! ! Initialize the generators by randomly sampling the region. ! seed_iter = seed_init seed = seed_iter initialize = .true. call cvt_sample ( ndim, n, n, init, initialize, seed, generator ) if ( sample == init ) then initialize = .false. else initialize = .true. end if seed = seed_iter call cvt_energy ( ndim, n, batch, sample, initialize, sample_num, seed, & generator, energy ) initialize = .false. ! ! Project points to the boundary. ! call mpb ( ndim, n, generator, npp ) seed = seed_iter it_num = 0 it_diff = 0.0D+00 call cvt_energy ( ndim, n, batch, sample, initialize, sample_num, seed, & generator, energy2 ) write ( *, '(2x,i6,2x,i12,2x,g14.6,2x,g14.6)' ) & it_num, seed_iter, energy, energy2 call cvt_write ( ndim, n, batch, seed_init, seed, init_string, it_max, & it_fixed, it_num, it_diff, energy2, sample_string, sample_num, generator, & 'initial.txt' ) call points_eps ( 'initial.eps', ndim, n, generator, 'Initial generators' ) ! ! Start the iteration. ! do it_num = 1, it_max ! ! Sample the region. ! seed_iter = seed av_points(1:ndim,1:n) = 0.0D+00 count(1:n) = 0 do j = 1, sample_num call cvt_sample ( ndim, sample_num, 1, sample, initialize, seed, s ) call find_closest ( ndim, n, 1, s, generator, nearest ) av_points(1:ndim,nearest(1)) = av_points(1:ndim,nearest(1)) & + s(1:ndim) count(nearest(1)) = count(nearest(1)) + 1 end do ! ! Replace the generators by the average of the sample points. ! do j = 1, n if ( count(j) /= 0 ) then generator(1:ndim,j) = av_points(1:ndim,j) / real ( count(j), kind = 8 ) end if end do seed = seed_iter call cvt_energy ( ndim, n, batch, sample, initialize, sample_num, seed, & generator, energy ) ! ! Apply Lili's projection method. ! In this case, the energy is changed, so it must be recalculated. ! call mpb ( ndim, n, generator, npp ) seed = seed_iter call cvt_energy ( ndim, n, batch, sample, initialize, sample_num, seed, & generator, energy2 ) write ( *, '(2x,i6,2x,i12,2x,g14.6,2x,g14.6)' ) & it_num, seed_iter, energy, energy2 end do ! ! Write out the final points. ! call cvt_write ( ndim, n, batch, seed_init, seed, init_string, it_max, & it_fixed, it_num, it_diff, energy2, sample_string, sample_num, generator, & 'final.txt' ) call points_eps ( 'final.eps', ndim, n, generator, 'Final generators' ) ! ! Free memory. ! deallocate ( av_points ) deallocate ( count ) deallocate ( generator ) deallocate ( s ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'cvt_box:' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop end subroutine ch_cap ( c ) !*****************************************************************************80 ! !! CH_CAP capitalizes a single character. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 19 July 1998 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character C, the character to capitalize. ! implicit none character c integer ( kind = 4 ) itemp itemp = ichar ( c ) if ( 97 <= itemp .and. itemp <= 122 ) then c = char ( itemp - 32 ) end if return end subroutine cvt_energy ( ndim, n, batch, sample, initialize, sample_num, & seed, r, energy ) !*****************************************************************************80 ! !! CVT_ENERGY computes the CVT energy of a dataset. ! ! Discussion: ! ! For a given number of generators, a CVT is a minimizer (or at least ! a local minimizer) of the CVT energy. During a CVT iteration, ! it should generally be the case that the CVT energy decreases from ! step to step, and that perturbations or adjustments of an ! approximate CVT will almost always have higher CVT energy. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 02 December 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of generators. ! ! Input, integer ( kind = 4 ) BATCH, the maximum number of sample points to ! generate at one time. ! ! Input, integer ( kind = 4 ) SAMPLE, specifies how the sampling is done. ! -1, 'RANDOM', using FORTRAN RANDOM function; ! 0, 'UNIFORM', using a simple uniform RNG; ! 1, 'HALTON', from a Halton sequence; ! 2, 'GRID', points from a grid; ! ! Input, logical INITIALIZE, is TRUE if the pseudorandom process should be ! reinitialized. ! ! Input, integer ( kind = 4 ) SAMPLE_NUM, the number of sample points to use. ! ! Input/output, integer ( kind = 4 ) SEED, a seed for the random ! number generator. ! ! Input, real ( kind = 8 ) R(NDIM,N), the coordinates of the points. ! ! Output, real ( kind = 8 ) ENERGY, the estimated CVT energy. ! implicit none integer ( kind = 4 ) batch integer ( kind = 4 ) ndim integer ( kind = 4 ) n real ( kind = 8 ) energy integer ( kind = 4 ) get integer ( kind = 4 ) have logical initialize integer ( kind = 4 ) j integer ( kind = 4 ) nearest(batch) real ( kind = 8 ) r(ndim,n) real ( kind = 8 ) s(ndim,batch) integer ( kind = 4 ) sample integer ( kind = 4 ) sample_num integer ( kind = 4 ) seed have = 0 energy = 0.0D+00 do while ( have < sample_num ) get = min ( sample_num - have, batch ) call cvt_sample ( ndim, sample_num, get, sample, initialize, seed, s ) have = have + get call find_closest ( ndim, n, get, s, r, nearest ) do j = 1, get energy = energy & + sum ( ( s(1:ndim,j) - r(1:ndim,nearest(j)) )**2 ) end do end do energy = energy / real ( sample_num, kind = 8 ) return end subroutine cvt_sample ( ndim, n, n_now, sample, initialize, seed, r ) !****************************************************************************** ! !! CVT_SAMPLE returns sample points. ! ! Discussion: ! ! N sample points are to be taken from the unit box of dimension NDIM. ! ! These sample points are usually created by a pseudorandom process ! for which the points are essentially indexed by a quantity called ! SEED. To get N sample points, we generate values with indices ! SEED through SEED+N-1. ! ! It may not be practical to generate all the sample points in a ! single call. For that reason, the routine allows the user to ! request a total of N points, but to require that only N_NOW be ! generated now (on this call). ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of sample points to be generated. ! ! Input, integer ( kind = 4 ) N_NOW, the number of sample points to be ! generated on this call. N_NOW must be at least 1. ! ! Input, integer ( kind = 4 ) SAMPLE, specifies how the sampling is done. ! -1, 'RANDOM', using FORTRAN RANDOM function; ! 0, 'UNIFORM', using a simple uniform RNG; ! 1, 'HALTON', from a Halton sequence; ! 2, 'GRID', points from a grid; ! ! Input, logical INITIALIZE, is TRUE if the pseudorandom process should be ! reinitialized. ! ! Input/output, integer ( kind = 4 ) SEED, the random number seed. ! ! Output, real ( kind = 8 ) R(NDIM,N_NOW), the sample points. ! implicit none integer ( kind = 4 ) ndim integer ( kind = 4 ) n_now real ( kind = 8 ) exponent integer ( kind = 4 ), allocatable, dimension ( : ) :: halton_base integer ( kind = 4 ), allocatable, dimension ( : ) :: halton_leap integer ( kind = 4 ), allocatable, dimension ( : ) :: halton_seed integer ( kind = 4 ) halton_step integer ( kind = 4 ) i logical initialize integer ( kind = 4 ) j integer ( kind = 4 ) n integer ( kind = 4 ) ngrid integer ( kind = 4 ) prime real ( kind = 8 ) :: r(ndim,n_now) integer ( kind = 4 ) rank integer ( kind = 4 ) rank_max integer ( kind = 4 ) sample integer ( kind = 4 ) seed integer ( kind = 4 ), allocatable, dimension ( : ) :: tuple if ( n_now < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CVT_SAMPLE - Fatal error!' write ( *, '(a)' ) ' N_NOW < 1.' stop end if if ( sample == -1 ) then call random_number ( harvest = r(1:ndim,1:n_now) ) seed = seed + n_now * ndim else if ( sample == 0 ) then call random_number ( harvest = r(1:ndim,1:n_now) ) else if ( sample == 1 ) then allocate ( halton_seed(1:ndim) ) allocate ( halton_leap(1:ndim) ) allocate ( halton_base(1:ndim) ) halton_step = seed halton_seed(1:ndim) = 0 halton_leap(1:ndim) = 1 do i = 1, ndim halton_base(i) = prime ( i ) end do call i4_to_halton_sequence ( ndim, n_now, halton_step, halton_seed, & halton_leap, halton_base, r(1:ndim,1:n_now) ) deallocate ( halton_seed ) deallocate ( halton_leap ) deallocate ( halton_base ) seed = seed + n_now else if ( sample == 2 ) then allocate ( tuple(1:ndim) ) exponent = real ( 1.0, kind = 8 ) / real ( ndim, kind = 8 ) ngrid = int ( ( real ( n, kind = 8 ) )**exponent ) rank_max = ngrid**ndim if ( rank_max < n ) then ngrid = ngrid + 1 rank_max = ngrid**ndim end if if ( initialize ) then rank = -1 call tuple_next_fast ( ngrid, ndim, rank, tuple ) end if rank = mod ( seed, rank_max ) do j = 1, n_now call tuple_next_fast ( ngrid, ndim, rank, tuple ) rank = rank + 1 rank = mod ( rank, rank_max ) r(1:ndim,j) = real ( 2 * tuple(1:ndim) - 1, kind = 8 ) & / real ( 2 * ngrid, kind = 8 ) end do seed = seed + n_now deallocate ( tuple ) else write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CVT_SAMPLE - Fatal error!' write ( *, '(a,i6,a)' ) ' The value of SAMPLE = ', sample, ' is illegal.' stop end if return end subroutine cvt_write ( ndim, n, batch, seed_init, seed, init_string, it_max, & it_fixed, it_num, it_diff, energy, sample_string, sample_num, r, & file_out_name ) !*****************************************************************************80 ! !! CVT_WRITE writes a CVT dataset to a file. ! ! Discussion: ! ! The initial lines of the file are comments, which begin with a ! '#' character. ! ! Thereafter, each line of the file contains the NDIM-dimensional ! components of the next entry of the dataset. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 17 November 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Input, integer ( kind = 4 ) BATCH, sets the maximum number of sample points ! generated at one time. It is inefficient to generate the sample ! points 1 at a time, but memory intensive to generate them all ! at once. You might set BATCH to min ( SAMPLE_NUM, 10000 ), for instance. ! ! Input, integer ( kind = 4 ) SEED_INIT, the initial random number seed. ! ! Input, integer ( kind = 4 ) SEED, the current random number seed. ! ! Input, character ( len = * ) INIT_STRING, specifies how the initial ! generators are chosen: ! filename, by reading data from a file; ! 'GRID', picking points from a grid; ! 'HALTON', from a Halton sequence; ! 'RANDOM', using FORTRAN RANDOM function; ! 'UNIFORM', using a simple uniform RNG; ! ! Input, integer ( kind = 4 ) IT_MAX, the maximum number of iterations ! allowed. ! ! Input, integer ( kind = 4 ) IT_FIXED, the number of iterations to take ! with a fixed set of sample points. ! ! Input, integer ( kind = 4 ) IT_NUM, the actual number of iterations taken. ! ! Input, real ( kind = 8 ) IT_DIFF, the L2 norm of the change ! in the CVT coordinates on the last iteration. ! ! Input, real ( kind = 8 ) ENERGY, the discrete "energy", divided ! by the number of sample points. ! ! Input, character ( len = * ) SAMPLE_STRING, specifies how the ! region is sampled: ! 'GRID', picking points from a grid; ! 'HALTON', from a Halton sequence; ! 'RANDOM', using FORTRAN RANDOM function; ! 'UNIFORM', using a simple uniform RNG; ! ! Input, integer ( kind = 4 ) SAMPLE_NUM, the number of sampling points used ! on each iteration. ! ! Input, real ( kind = 8 ) R(NDIM,N), the points. ! ! Input, character ( len = * ) FILE_OUT_NAME, the name of ! the output file. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) ndim integer ( kind = 4 ) batch real ( kind = 8 ) energy character ( len = * ) file_out_name integer ( kind = 4 ) file_out_unit character ( len = * ) init_string integer ( kind = 4 ) ios real ( kind = 8 ) it_diff integer ( kind = 4 ) it_fixed integer ( kind = 4 ) it_max integer ( kind = 4 ) it_num integer ( kind = 4 ) j real ( kind = 8 ) r(ndim,n) character ( len = * ) sample_string integer ( kind = 4 ) sample_num integer ( kind = 4 ) seed integer ( kind = 4 ) seed_init character ( len = 40 ) string call get_unit ( file_out_unit ) open ( unit = file_out_unit, file = file_out_name, & status = 'replace', iostat = ios ) if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CVT_WRITE - Fatal error!' write ( *, '(a)' ) ' Could not open the output file.' stop end if write ( file_out_unit, '(a)' ) '# ' // trim ( file_out_name ) write ( file_out_unit, '(a)' ) '# created by routine CVT_WRITE.F90' write ( file_out_unit, '(a)' ) '#' write ( file_out_unit, '(a,i12)' ) '# Spatial dimension NDIM = ', ndim write ( file_out_unit, '(a,i12)' ) '# Number of points N = ', n write ( file_out_unit, '(a,i12)' ) '# Initial SEED_INIT = ', & seed_init write ( file_out_unit, '(a,i12)' ) '# Current SEED = ', seed write ( file_out_unit, '(a)' ) '# INIT = "' & // trim ( init_string ) // '".' write ( file_out_unit, '(a,i12)' ) '# Max iterations IT_MAX = ', it_max write ( file_out_unit, '(a,i12)' ) '# IT_FIXED (fixed samples) = ', & it_fixed write ( file_out_unit, '(a,i12)' ) '# Iterations IT_NUM = ', it_num write ( file_out_unit, '(a,g14.6)' ) '# Difference IT_DIFF = ', it_diff write ( file_out_unit, '(a,g14.6)' ) '# CVT ENERGY = ', energy write ( file_out_unit, '(a)' ) '# SAMPLE = "' & // trim ( sample_string ) // '".' write ( file_out_unit, '(a,i12)' ) '# Samples SAMPLE_NUM = ', & sample_num write ( file_out_unit, '(a,i12)' ) '# Sampling BATCH size = ', batch write ( file_out_unit, '(a,g14.6)' ) '# EPSILON (unit roundoff) = ', & epsilon ( r(1,1) ) write ( file_out_unit, '(a)' ) '#' write ( string, '(a,i3,a)' ) '(', ndim, 'f10.6)' do j = 1, n write ( file_out_unit, string ) r(1:ndim,j) end do close ( unit = file_out_unit ) return end subroutine find_closest ( ndim, n, sample_num, s, r, nearest ) !*****************************************************************************80 ! !! FIND_CLOSEST finds the nearest R point to each S point. ! ! Discussion: ! ! This routine finds the closest Voronoi cell generator by checking every ! one. For problems with many cells, this process can take the bulk ! of the CPU time. Other approaches, which group the cell generators into ! bins, can run faster by a large factor. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 02 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of cell generators. ! ! Input, integer ( kind = 4 ) SAMPLE_NUM, the number of sample points. ! ! Input, real ( kind = 8 ) S(NDIM,SAMPLE_NUM), the points to be checked. ! ! Input, real ( kind = 8 ) R(NDIM,N), the cell generators. ! ! Output, integer ( kind = 4 ) NEAREST(SAMPLE_NUM), the index of the nearest ! cell generators. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) ndim integer ( kind = 4 ) sample_num real ( kind = 8 ) dist_sq_min real ( kind = 8 ) dist_sq integer ( kind = 4 ) jr integer ( kind = 4 ) js integer ( kind = 4 ) nearest(sample_num) real ( kind = 8 ) r(ndim,n) real ( kind = 8 ) s(ndim,sample_num) do js = 1, sample_num dist_sq_min = huge ( dist_sq_min ) nearest(js) = -1 do jr = 1, n dist_sq = sum ( ( r(1:ndim,jr) - s(1:ndim,js) )**2 ) if ( dist_sq < dist_sq_min ) then dist_sq_min = dist_sq nearest(js) = jr end if end do end do return end subroutine get_unit ( iunit ) !*****************************************************************************80 ! !! GET_UNIT returns a free FORTRAN unit number. ! ! Discussion: ! ! A "free" FORTRAN unit number is an integer between 1 and 99 which ! is not currently associated with an I/O device. A free FORTRAN unit ! number is needed in order to open a file with the OPEN command. ! ! If IUNIT = 0, then no free FORTRAN unit could be found, although ! all 99 units were checked (except for units 5, 6 and 9, which ! are commonly reserved for console I/O). ! ! Otherwise, IUNIT is an integer between 1 and 99, representing a ! free FORTRAN unit. Note that GET_UNIT assumes that units 5 and 6 ! are special, and will never return those values. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 18 September 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer ( kind = 4 ) IUNIT, the free unit number. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ) ios integer ( kind = 4 ) iunit logical lopen iunit = 0 do i = 1, 99 if ( i /= 5 .and. i /= 6 .and. i /= 9 ) then inquire ( unit = i, opened = lopen, iostat = ios ) if ( ios == 0 ) then if ( .not. lopen ) then iunit = i return end if end if end if end do return end function halham_leap_check ( ndim, leap ) !*****************************************************************************80 ! !! HALHAM_LEAP_CHECK checks LEAP for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) LEAP(NDIM), the leap vector. ! ! Output, logical, HALHAM_LEAP_CHECK, true if LEAP is legal. ! implicit none integer ( kind = 4 ) ndim logical halham_leap_check integer ( kind = 4 ) leap(ndim) if ( any ( leap(1:ndim) < 1 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_LEAP_CHECK - Fatal error!' write ( *, '(a)' ) ' Some entry of LEAP < 1!' write ( *, '(a)' ) ' ' call i4vec_transpose_print ( ndim, leap, 'LEAP: ' ) halham_leap_check = .false. else halham_leap_check = .true. end if return end function halham_n_check ( n ) !*****************************************************************************80 ! !! HALHAM_N_CHECK checks N for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the spatial dimension. ! ! Output, logical HALHAM_N_CHECK, true if N is legal. ! implicit none logical halham_n_check integer ( kind = 4 ) n if ( n < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_N_CHECK - Fatal error!' write ( *, '(a)' ) ' N < 1.' write ( *, '(a,i12)' ) ' N = ', n halham_n_check = .false. else halham_n_check = .true. end if return end function halham_ndim_check ( ndim ) !*****************************************************************************80 ! !! HALHAM_NDIM_CHECK checks NDIM for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Output, logical HALHAM_NDIM_CHECK, true if NDIM is legal. ! implicit none logical halham_ndim_check integer ( kind = 4 ) ndim if ( ndim < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_NDIM_CHECK - Fatal error!' write ( *, '(a)' ) ' NDIM < 1.' write ( *, '(a,i12)' ) ' NDIM = ', ndim halham_ndim_check = .false. else halham_ndim_check = .true. end if return end function halham_seed_check ( ndim, seed ) !*****************************************************************************80 ! !! HALHAM_SEED_CHECK checks SEED for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) SEED(NDIM), the seed vector. ! ! Output, logical, HALHAM_SEED_CHECK, true if SEED is legal. ! implicit none integer ( kind = 4 ) ndim logical halham_seed_check integer ( kind = 4 ) seed(ndim) if ( any ( seed(1:ndim) < 0 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_SEED_CHECK - Fatal error!' write ( *, '(a)' ) ' Some entry of SEED < 0!' write ( *, '(a)' ) ' ' call i4vec_transpose_print ( ndim, seed, 'SEED: ' ) halham_seed_check = .false. else halham_seed_check = .true. end if return end function halham_step_check ( step ) !*****************************************************************************80 ! !! HALHAM_STEP_CHECK checks STEP for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) STEP, the index of the subsequence element. ! ! Output, logical HALHAM_STEP_CHECK, true if STEP is legal. ! implicit none logical halham_step_check integer ( kind = 4 ) step if ( step < 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_STEP_CHECK - Fatal error!' write ( *, '(a)' ) ' STEP < 0.' write ( *, '(a,i12)' ) ' STEP = ', step halham_step_check = .false. else halham_step_check = .true. end if return end function halton_base_check ( ndim, base ) !*****************************************************************************80 ! !! HALTON_BASE_CHECK checks BASE for a Halton sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) BASE(NDIM), the bases. ! ! Output, logical, HALTON_BASE_CHECK, true if BASE is legal. ! implicit none integer ( kind = 4 ) ndim integer ( kind = 4 ) base(ndim) logical halton_base_check if ( any ( base(1:ndim) <= 1 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALTON_BASE_CHECK - Fatal error!' write ( *, '(a)' ) ' Some entry of BASE is <= 1!' write ( *, '(a)' ) ' ' call i4vec_transpose_print ( ndim, base, 'BASE: ' ) halton_base_check = .false. else halton_base_check = .true. end if return end subroutine i4_to_halton_sequence ( ndim, n, step, seed, leap, base, r ) !*****************************************************************************80 ! !! I4_TO_HALTON_SEQUENCE computes N elements of a leaped Halton subsequence. ! ! Discussion: ! ! The NDIM-dimensional Halton sequence is really NDIM separate ! sequences, each generated by a particular base. ! ! This routine selects elements of a "leaped" subsequence of the ! Halton sequence. The subsequence elements are indexed by a ! quantity called STEP, which starts at 0. The STEP-th subsequence ! element is simply element ! ! SEED(1:NDIM) + STEP * LEAP(1:NDIM) ! ! of the original Halton sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! J H Halton, ! On the efficiency of certain quasi-random sequences of points ! in evaluating multi-dimensional integrals, ! Numerische Mathematik, ! Volume 2, 1960, pages 84-90. ! ! J H Halton and G B Smith, ! Algorithm 247: Radical-Inverse Quasi-Random Point Sequence, ! Communications of the ACM, ! Volume 7, 1964, pages 701-702. ! ! Ladislav Kocis and William Whiten, ! Computational Investigations of Low-Discrepancy Sequences, ! ACM Transactions on Mathematical Software, ! Volume 23, Number 2, 1997, pages 266-294. ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! 1 <= NDIM is required. ! ! Input, integer ( kind = 4 ) N, the number of elements of the sequence. ! ! Input, integer ( kind = 4 ) STEP, the index of the subsequence element. ! 0 <= STEP is required. ! ! Input, integer ( kind = 4 ) SEED(NDIM), the Halton sequence index ! corresponding to STEP = 0. ! ! Input, integer ( kind = 4 ) LEAP(NDIM), the succesive jumps in the ! Halton sequence. ! ! Input, integer ( kind = 4 ) BASE(NDIM), the Halton bases. ! ! Output, real ( kind = 8 ) R(NDIM,N), the next N elements of the ! leaped Halton subsequence, beginning with element STEP. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) ndim integer ( kind = 4 ) base(ndim) real ( kind = 8 ) base_inv integer ( kind = 4 ) digit(n) logical halham_leap_check logical halham_n_check logical halham_ndim_check logical halham_seed_check logical halham_step_check logical halton_base_check integer ( kind = 4 ) i integer ( kind = 4 ) j integer ( kind = 4 ) leap(ndim) real ( kind = 8 ) r(ndim,n) integer ( kind = 4 ) seed(ndim) integer ( kind = 4 ) seed2(n) integer ( kind = 4 ) step ! ! Check the input. ! if ( .not. halham_ndim_check ( ndim ) ) then stop end if if ( .not. halham_n_check ( n ) ) then stop end if if ( .not. halham_step_check ( step ) ) then stop end if if ( .not. halham_seed_check ( ndim, seed ) ) then stop end if if ( .not. halham_leap_check ( ndim, leap ) ) then stop end if if ( .not. halton_base_check ( ndim, base ) ) then stop end if ! ! Calculate the data. ! r(1:ndim,1:n) = 0.0D+00 do i = 1, ndim do j = 1, n seed2(j) = seed(i) + ( step + j - 1 ) * leap(i) end do base_inv = real ( 1.0D+00, kind = 8 ) / real ( base(i), kind = 8 ) do while ( any ( seed2(1:n) /= 0 ) ) digit(1:n) = mod ( seed2(1:n), base(i) ) r(i,1:n) = r(i,1:n) + real ( digit(1:n), kind = 8 ) * base_inv base_inv = base_inv / real ( base(i), kind = 8 ) seed2(1:n) = seed2(1:n) / base(i) end do end do return end subroutine i4vec_transpose_print ( n, a, title ) !*****************************************************************************80 ! !! I4VEC_TRANSPOSE_PRINT prints an I4VEC "transposed". ! ! Example: ! ! A = (/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 /) ! TITLE = 'My vector: ' ! ! My vector: 1 2 3 4 5 ! 6 7 8 9 10 ! 11 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 03 July 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the number of components of the vector. ! ! Input, integer ( kind = 4 ) A(N), the vector to be printed. ! ! Input, character ( len = * ) TITLE, a title to be printed first. ! TITLE may be blank. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) a(n) integer ( kind = 4 ) ihi integer ( kind = 4 ) ilo character ( len = 11 ) string character ( len = * ) title integer ( kind = 4 ) title_len if ( 0 < len_trim ( title ) ) then title_len = len ( title ) write ( string, '(a,i3,a)' ) '(', title_len, 'x,5i12)' do ilo = 1, n, 5 ihi = min ( ilo + 5 - 1, n ) if ( ilo == 1 ) then write ( *, '(a, 5i12)' ) title, a(ilo:ihi) else write ( *, string ) a(ilo:ihi) end if end do else do ilo = 1, n, 5 ihi = min ( ilo + 5 - 1, n ) write ( *, '(5i12)' ) a(ilo:ihi) end do end if return end subroutine mpb ( ndim, n, generator, npp ) !*****************************************************************************80 ! !! MPB projects generators onto the boundary of the region. ! ! Discussion: ! ! The number NPP sets the number of subintervals into which we subdivide ! the boundary. It does NOT specify how many points will be pulled onto ! the boundary. The reason for this is that, after the first boundary ! subinterval has had a generator pulled into it, on every subsequent ! subinterval the nearest generator is likely to be the one in the ! previous subinterval! Unless an interior generator is closer than ! some small distance, this process will simply drag some unfortunate ! generator onto the boundary, and then around from interval to interval ! for a considerable time. ! ! The algorithm could be changed, if desired, so that points snapped ! to the boundary are guaranteed not to move, at least not twice in ! one application of this routine! ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 June 2004 ! ! Author: ! ! Lili Ju ! ! Parameters: ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of generators. ! ! Input/output, real ( kind = 8 ) GENERATOR(NDIM,N), the coordinates of ! the generators. On output, some generators will have been moved. ! ! Input, integer ( kind = 4 ) NPP, the number of subintervals into which the ! perimeter is divided. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) ndim real ( kind = 8 ) dx real ( kind = 8 ) dy real ( kind = 8 ) generator(ndim,n) real ( kind = 8 ) hh integer ( kind = 4 ) i integer ( kind = 4 ) nearest(1) integer ( kind = 4 ) npp real ( kind = 8 ) u real ( kind = 8 ) sample(ndim) dx = 1.0D+00 dy = 1.0D+00 ! ! HH is the length of an individual segment of the perimeter of the region. ! ! U is set in such a way that on step I, it measures the distance from ! the lower left corner of the box to the midpoint of the I-th subinterval ! on the perimeter of the box. ! hh = 2.0D+00 * ( dx + dy ) / real ( npp, kind = 8 ) u = -0.5D+00 * hh do i = 1, npp u = u + hh ! ! The portion of the bottom perimeter from (0,0) to (1,0). ! if ( u < dx ) then sample(1:2) = (/ u, 0.0D+00 /) call find_closest ( ndim, n, 1, sample, generator, nearest ) generator(2,nearest(1)) = 0.0D+00 ! ! The portion of the right perimeter from (1,0) to (1,1). ! else if ( dx < u .and. u < dx + dy ) then sample(1:2) = (/ 1.0D+00, ( u - dx ) /) call find_closest ( ndim, n, 1, sample, generator, nearest ) generator(1,nearest(1)) = 1.0D+00 ! ! The portion of the top perimeter from (1,1) to (0,1). ! else if ( dx + dy < u .and. u < dx + dy + dx ) then sample(1:2) = (/ 1.0D+00 - ( u - dx - dy ), 1.0D+00 /) call find_closest ( ndim, n, 1, sample, generator, nearest ) generator(2,nearest(1)) = 1.0D+00 ! ! The portion of the left perimeter from (0,1) to (0,0). ! else if ( dx + dy + dx < u ) then sample(1:2) = (/ 0.0D+00, 1.0D+00 - ( u - dx - dy - dx ) /) call find_closest ( ndim, n, 1, sample, generator, nearest ) generator(1,nearest(1)) = 0.0D+00 end if end do return end subroutine points_eps ( file_name, ndim, node_num, node_xy, title ) !*****************************************************************************80 ! !! POINTS_EPS creates an EPS file image of a set of points. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) FILE_NAME, the name of the file to create. ! ! Input, integer ( kind = 4 ) NDIM, the spatial dimension. ! ! Input, integer ( kind = 4 ) NODE_NUM, the number of nodes. ! ! Input, real ( kind = 8 ) NODE_XY(2,NODE_NUM), the coordinates ! of the nodes. ! ! Input, character ( len = * ) TITLE, a title for the plot. ! implicit none integer ( kind = 4 ) node_num integer ( kind = 4 ) ndim integer ( kind = 4 ), parameter :: circle_size = 3 logical, parameter :: DEBUG = .false. real ( kind = 8 ) dif integer ( kind = 4 ) eps_unit integer ( kind = 4 ) eps_x integer ( kind = 4 ) eps_y character ( len = * ) file_name integer ( kind = 4 ) ios integer ( kind = 4 ) node real ( kind = 8 ) node_xy(ndim,node_num) real ( kind = 8 ) node_x_max real ( kind = 8 ) node_x_min real ( kind = 8 ) node_y_max real ( kind = 8 ) node_y_min real ( kind = 8 ) scale character ( len = * ) title ! ! Determine the range of the points. ! node_x_min = huge ( node_x_min ) node_x_max = -huge ( node_x_max ) node_y_min = huge ( node_y_min ) node_y_max = -huge ( node_y_max ) do node = 1, node_num node_x_min = min ( node_x_min, node_xy(1,node) ) node_x_max = max ( node_x_max, node_xy(1,node) ) node_y_min = min ( node_y_min, node_xy(2,node) ) node_y_max = max ( node_y_max, node_xy(2,node) ) end do if ( node_y_max - node_y_min < node_x_max - node_x_min ) then scale = node_x_max - node_x_min dif = ( node_x_max - node_x_min ) - ( node_y_max - node_y_min ) node_y_max = node_y_max + 0.5D+00 * dif node_y_min = node_y_min - 0.5D+00 * dif else scale = node_y_max - node_y_min dif = ( node_y_max - node_y_min ) - ( node_x_max - node_x_min ) node_x_max = node_x_max + 0.5D+00 * dif node_x_min = node_x_min - 0.5D+00 * dif end if call get_unit ( eps_unit ) open ( unit = eps_unit, file = file_name, status = 'replace', iostat = ios ) if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'POINTS_EPS - Fatal error!' write ( *, '(a)' ) ' Could not open the output EPS file.' stop end if write ( eps_unit, '(a)' ) '%!PS-Adobe-3.0 EPSF-3.0' write ( eps_unit, '(a)' ) & '%%Creator: points_eps(cvt_box.f90)' write ( eps_unit, '(a)' ) '%%Title: ' // trim ( file_name ) write ( eps_unit, '(a)' ) '%%Pages: 1' write ( eps_unit, '(a)' ) '%%BoundingBox: 36 36 576 756' write ( eps_unit, '(a)' ) '%%Document-Fonts: Times-Roman' write ( eps_unit, '(a)' ) '%%LanguageLevel: 1' write ( eps_unit, '(a)' ) '%%EndComments' write ( eps_unit, '(a)' ) '%%BeginProlog' write ( eps_unit, '(a)' ) '/inch {72 mul} def' write ( eps_unit, '(a)' ) '%%EndProlog' write ( eps_unit, '(a)' ) '%%Page: 1 1' write ( eps_unit, '(a)' ) 'save' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Set RGB line color.' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 0.9000 0.9000 0.9000 setrgbcolor' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Draw a gray border around the page.' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) 'newpath' write ( eps_unit, '(a)' ) ' 36 126 moveto' write ( eps_unit, '(a)' ) ' 576 126 lineto' write ( eps_unit, '(a)' ) ' 576 666 lineto' write ( eps_unit, '(a)' ) ' 36 666 lineto' write ( eps_unit, '(a)' ) ' 36 126 lineto' write ( eps_unit, '(a)' ) 'stroke' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Set RGB line color.' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 0.0000 0.0000 0.0000 setrgbcolor' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Label the plot:' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 0.0000 0.0000 0.0000 setrgbcolor' write ( eps_unit, '(a)' ) '/Times-Roman findfont 0.50 inch scalefont setfont' write ( eps_unit, '(a)' ) ' 36 666 moveto' write ( eps_unit, '(a)' ) '(' // trim ( title ) // ') show' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Define a clipping polygon' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 36 126 moveto' write ( eps_unit, '(a)' ) ' 576 126 lineto' write ( eps_unit, '(a)' ) ' 576 666 lineto' write ( eps_unit, '(a)' ) ' 36 666 lineto' write ( eps_unit, '(a)' ) ' 36 126 lineto' write ( eps_unit, '(a)' ) 'clip newpath' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Draw the boundary in red:' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 0.9000 0.0000 0.0000 setrgbcolor' write ( eps_unit, '(a)' ) 'newpath' write ( eps_unit, '(a)' ) ' 61 151 moveto' write ( eps_unit, '(a)' ) ' 551 151 lineto' write ( eps_unit, '(a)' ) ' 551 641 lineto' write ( eps_unit, '(a)' ) ' 61 641 lineto' write ( eps_unit, '(a)' ) ' 61 151 lineto' write ( eps_unit, '(a)' ) 'stroke' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% Draw filled dots at each node:' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) ' 0.0000 0.0000 0.9000 setrgbcolor' do node = 1, node_num eps_x = int ( & ( ( node_x_max - node_xy(1,node) ) * 61.0D+00 & + ( + node_xy(1,node) - node_x_min ) * 551.0D+00 ) & / scale ) eps_y = int ( & ( ( node_y_max - node_xy(2,node) ) * 151.0D+00 & + ( node_xy(2,node) - node_y_min ) * 641.0D+00 ) & / scale ) write ( eps_unit, '(a,i4,2x,i4,2x,i4,a)' ) & 'newpath ', eps_x, eps_y, circle_size, ' 0 360 arc closepath fill' end do write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) 'restore showpage' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '% End of page' write ( eps_unit, '(a)' ) '%' write ( eps_unit, '(a)' ) '%%Trailer' write ( eps_unit, '(a)' ) '%%EOF' close ( unit = eps_unit ) if ( DEBUG ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'POINTS_EPS:' write ( *, '(a)' ) ' An encapsulated PostScript file was created' write ( *, '(a)' ) ' containing an image of the points.' write ( *, '(a)' ) ' The file is named "' // trim ( file_name ) // '".' end if return end function prime ( n ) !*****************************************************************************80 ! !! PRIME returns any of the first PRIME_MAX prime numbers. ! ! Discussion: ! ! PRIME_MAX is 1600, and the largest prime stored is 13499. ! ! Thanks to Bart Vandewoestyne for pointing out a typo, 18 February 2005. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 18 February 2005 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Milton Abramowitz and Irene Stegun, ! Handbook of Mathematical Functions, ! US Department of Commerce, 1964, pages 870-873. ! ! Daniel Zwillinger, ! CRC Standard Mathematical Tables and Formulae, ! 30th Edition, ! CRC Press, 1996, pages 95-98. ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the index of the desired prime number. ! In general, is should be true that 0 <= N <= PRIME_MAX. ! N = -1 returns PRIME_MAX, the index of the largest prime available. ! N = 0 is legal, returning PRIME = 1. ! ! Output, integer ( kind = 4 ) PRIME, the N-th prime. If N is out of range, ! PRIME is returned as -1. ! implicit none integer ( kind = 4 ), parameter :: prime_max = 1600 integer ( kind = 4 ), save :: icall = 0 integer ( kind = 4 ) n integer ( kind = 4 ), save, dimension ( prime_max ) :: npvec integer ( kind = 4 ) prime if ( icall == 0 ) then icall = 1 npvec(1:100) = (/ & 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, & 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, & 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, & 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, & 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, & 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, & 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, & 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, & 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, & 467, 479, 487, 491, 499, 503, 509, 521, 523, 541 /) npvec(101:200) = (/ & 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, & 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, & 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, & 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, & 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, & 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, & 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, & 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, & 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, & 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223 /) npvec(201:300) = (/ & 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, & 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, & 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, & 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, & 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, & 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, & 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, & 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, & 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, & 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987 /) npvec(301:400) = (/ & 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, & 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, & 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, & 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, & 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, & 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, & 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, & 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, & 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, & 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741 /) npvec(401:500) = (/ & 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, & 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, & 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, & 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, & 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, & 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, & 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, & 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, & 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, & 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571 /) npvec(501:600) = (/ & 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, & 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, & 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, & 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, & 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, & 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, & 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, & 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, & 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, & 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409 /) npvec(601:700) = (/ & 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, & 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, & 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, & 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, & 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, & 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, & 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, & 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, & 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, & 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279 /) npvec(701:800) = (/ & 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, & 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, & 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, & 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, & 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, & 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, & 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, & 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, & 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, & 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133 /) npvec(801:900) = (/ & 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, & 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, & 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, & 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, & 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, & 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, & 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, & 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, & 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, & 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997 /) npvec(901:1000) = (/ & 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, & 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, & 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, & 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, & 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, & 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, & 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, & 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, & 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, & 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919 /) npvec(1001:1100) = (/ & 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, & 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, & 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, & 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, & 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, & 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, & 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, & 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, & 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, & 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831 /) npvec(1101:1200) = (/ & 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, & 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, & 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, & 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, & 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, & 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, & 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, & 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, & 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, & 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733 /) npvec(1201:1300) = (/ & 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, & 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, & 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973,10007, & 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099, & 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177, & 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271, & 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343, & 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459, & 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567, & 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657 /) npvec(1301:1400) = (/ & 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739, & 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859, & 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949, & 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059, & 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149, & 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251, & 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329, & 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443, & 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527, & 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657 /) npvec(1401:1500) = (/ & 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777, & 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833, & 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933, & 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011, & 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109, & 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211, & 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289, & 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401, & 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487, & 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553 /) npvec(1501:1600) = (/ & 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641, & 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739, & 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829, & 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923, & 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007, & 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109, & 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187, & 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309, & 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411, & 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499 /) end if if ( n == -1 ) then prime = prime_max else if ( n == 0 ) then prime = 1 else if ( n <= prime_max ) then prime = npvec(n) else prime = -1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'PRIME - Fatal error!' write ( *, '(a,i6)' ) ' Illegal prime index N = ', n write ( *, '(a,i6)' ) ' N should be between 1 and PRIME_MAX =', prime_max stop end if return end function s_eqi ( s1, s2 ) !*****************************************************************************80 ! !! S_EQI is a case insensitive comparison of two strings for equality. ! ! Example: ! ! S_EQI ( 'Anjana', 'ANJANA' ) is TRUE. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 14 April 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S1, S2, the strings to compare. ! ! Output, logical S_EQI, the result of the comparison. ! implicit none character c1 character c2 integer ( kind = 4 ) i integer ( kind = 4 ) len1 integer ( kind = 4 ) len2 integer ( kind = 4 ) lenc logical s_eqi character ( len = * ) s1 character ( len = * ) s2 len1 = len ( s1 ) len2 = len ( s2 ) lenc = min ( len1, len2 ) s_eqi = .false. do i = 1, lenc c1 = s1(i:i) c2 = s2(i:i) call ch_cap ( c1 ) call ch_cap ( c2 ) if ( c1 /= c2 ) then return end if end do do i = lenc + 1, len1 if ( s1(i:i) /= ' ' ) then return end if end do do i = lenc + 1, len2 if ( s2(i:i) /= ' ' ) then return end if end do s_eqi = .true. 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 GNU LGPL license. ! ! Modified: ! ! 06 August 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none character ( len = 8 ) ampm integer ( kind = 4 ) d integer ( kind = 4 ) h integer ( kind = 4 ) m integer ( kind = 4 ) mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer ( kind = 4 ) n integer ( kind = 4 ) s integer ( kind = 4 ) values(8) integer ( kind = 4 ) 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 subroutine tuple_next_fast ( m, n, rank, x ) !*****************************************************************************80 ! !! TUPLE_NEXT_FAST computes the next element of a tuple space, "fast". ! ! Discussion: ! ! The elements are N vectors. Each entry is constrained to lie ! between 1 and M. The elements are produced one at a time. ! The first element is ! (1,1,...,1) ! and the last element is ! (M,M,...,M) ! Intermediate elements are produced in lexicographic order. ! ! This code was written as a possibly faster version of TUPLE_NEXT. ! ! Example: ! ! N = 2, ! M = 3 ! ! INPUT OUTPUT ! ------- ------- ! Rank X ! ---- ---- ! -1 -1 -1 ! ! 0 1 1 ! 1 1 2 ! 2 1 3 ! 3 2 1 ! 4 2 2 ! 5 2 3 ! 6 3 1 ! 7 3 2 ! 8 3 3 ! 9 1 1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 11 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, the maximum entry in any component. ! M must be greater than 0. ! ! Input, integer ( kind = 4 ) N, the number of components. ! N must be greater than 0. ! ! Input, integer ( kind = 4 ) RANK, indicates the rank of the tuple. ! Typically, 0 <= RANK < N**M. Values of RANK greater than ! N**M are legal and meaningful; they are equivalent to the ! corresponding value mod (N**M). If RANK < 0, this indicates ! that this is the first call for the given values of (M,N). ! Initialization is done, and X is set to a dummy value. ! ! Output, integer ( kind = 4 ) X(N), the next tuple, or a dummy value if ! initialization has just been done. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ), save, allocatable, dimension ( : ) :: base integer ( kind = 4 ) i integer ( kind = 4 ) m integer ( kind = 4 ) rank integer ( kind = 4 ) x(n) if ( rank < 0 ) then if ( m <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TUPLE_NEXT_FAST - Fatal error!' write ( *, '(a)' ) ' The value M <= 0 is not allowed.' write ( *, '(a,i6)' ) ' M = ', m stop end if if ( n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TUPLE_NEXT_FAST - Fatal error!' write ( *, '(a)' ) ' The value N <= 0 is not allowed.' write ( *, '(a,i6)' ) ' N = ', n stop end if if ( allocated ( base ) ) then deallocate ( base ) end if allocate ( base(1:n) ) base(n) = 1 do i = n-1, 1, -1 base(i) = base(i+1) * m end do x(1:n) = -1 else x(1:n) = mod ( rank / base(1:n), m ) + 1 end if return end