subroutine ch_cap ( c ) !*****************************************************************************80 ! !! ch_cap() capitalizes a single character. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 July 1998 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character C, the character to capitalize. ! implicit none character c integer itemp itemp = ichar ( c ) if ( 97 <= itemp .and. itemp <= 122 ) then c = char ( itemp - 32 ) end if return end function ch_eqi ( c1, c2 ) !*****************************************************************************80 ! !! CH_EQI is a case insensitive comparison of two characters for equality. ! ! Example: ! ! CH_EQI ( 'A', 'a' ) is .TRUE. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 July 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C1, C2, the characters to compare. ! ! Output, logical CH_EQI, the result of the comparison. ! implicit none logical ch_eqi character c1 character c1_cap character c2 character c2_cap c1_cap = c1 c2_cap = c2 call ch_cap ( c1_cap ) call ch_cap ( c2_cap ) if ( c1_cap == c2_cap ) then ch_eqi = .true. else ch_eqi = .false. end if return end subroutine ch_to_digit ( c, digit ) !*****************************************************************************80 ! !! CH_TO_DIGIT returns the integer value of a base 10 digit. ! ! Example: ! ! C DIGIT ! --- ----- ! '0' 0 ! '1' 1 ! ... ... ! '9' 9 ! ' ' 0 ! 'X' -1 ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 04 August 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C, the decimal digit, '0' through '9' or blank ! are legal. ! ! Output, integer DIGIT, the corresponding integer value. ! If C was 'illegal', then DIGIT is -1. ! implicit none character c integer digit if ( lge ( c, '0' ) .and. lle ( c, '9' ) ) then digit = ichar ( c ) - 48 else if ( c == ' ' ) then digit = 0 else digit = -1 end if return end subroutine cvt ( dim_num, n, batch, init, sample, sample_num, it_max, & it_fixed, seed, r, it_num, it_diff, energy ) !*****************************************************************************80 ! !! CVT computes a Centroidal Voronoi Tessellation. ! ! Discussion: ! ! This routine carries out the CVT iteration. ! ! It initializes the CVT generators, unless the user indicates that ! this has already been done. ! ! It sets a flag INITIALIZE that indicates whether the random number ! generator needs to be initialized. ! ! It decides whether to use a new seed on each iteration, or to ! reuse a seed value. ! ! It then repeatedly calls a routine that takes another step ! of the iteration. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 23 June 2005 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Qiang Du, Vance Faber, Max Gunzburger, ! Centroidal Voronoi Tessellations: Applications and Algorithms, ! SIAM Review, Volume 41, 1999, pages 637-676. ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer N, the number of Voronoi cells. ! ! Input, integer 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. ! BATCH must be at least 1. ! ! Input, integer INIT, specifies how the points are to be ! initialized. ! -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; ! 3, 'USER', call "user" routine; ! 4, points are already initialized on input. ! ! Input, integer 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; ! 3, 'USER', call "user" routine. ! ! Input, integer SAMPLE_NUM, the number of sample points. ! ! Input, integer IT_MAX, the maximum number of iterations. ! ! Input, integer IT_FIXED, the maximum number of iterations to ! take with a fixed set of sample points. ! ! Input/output, integer SEED, the current random number seed. ! ! Input/output, real ( kind = rk ) R(DIM_NUM,N), the approximate CVT points. ! If INIT = 4 on input, then it is assumed that these values have been ! initialized. On output, the CVT iteration has been applied to improve ! the value of the points. ! ! Output, integer IT_NUM, the number of iterations taken. ! Generally, this will be equal to IT_MAX, unless the iteration tolerance was ! satisfied early. ! ! Output, real ( kind = rk ) IT_DIFF, the L2 norm of the difference ! between the iterates. ! ! Output, real ( kind = rk ) ENERGY, the discrete "energy", divided ! by the number of sample points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer dim_num integer n integer batch logical, parameter :: DEBUG = .true. real ( kind = rk ) energy integer init logical initialize real ( kind = rk ) it_diff integer it_fixed integer it_max integer it_num real ( kind = rk ) r(dim_num,n) integer sample integer sample_num integer seed integer seed_base integer seed_init if ( batch < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CVT - Fatal error!' write ( *, '(a)' ) ' The input value BATCH < 1.' stop end if if ( seed <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CVT - Fatal error!' write ( *, '(a)' ) ' The input value SEED <= 0.' stop end if if ( DEBUG ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Step SEED L2-Change Energy' write ( *, '(a)' ) ' ' end if it_num = 0 it_diff = 0.0D+00 energy = 0.0D+00 seed_init = seed ! ! Initialize the data unless the user has already done that. ! if ( init /= 4 ) then initialize = .true. call cvt_sample ( dim_num, n, n, init, initialize, seed, r ) end if ! ! NOTE THIS IS NEW:... ! call cvt_energy ( dim_num, n, batch, sample, initialize, sample_num, & seed, r, energy ) if ( DEBUG ) then write ( *, '(2x,i4,2x,i12,2x,14x,2x,g14.6)' ) & it_num, seed_init, energy end if ! ! If the initialization and sampling steps use the same random number ! scheme, then the sampling scheme does not have to be initialized. ! if ( init == sample ) then initialize = .false. else initialize = .true. end if ! ! Carry out the iteration. ! do while ( it_num < it_max ) ! ! If it's time to update the seed, save its current value ! as the starting value for all iterations in this cycle. ! If it's not time to update the seed, restore it to its initial ! value for this cycle. ! if ( mod ( it_num, it_fixed ) == 0 ) then seed_base = seed else seed = seed_base end if it_num = it_num + 1 seed_init = seed call cvt_iterate ( dim_num, n, batch, sample, initialize, sample_num, & seed, r, it_diff, energy ) initialize = .false. if ( DEBUG ) then write ( *, '(2x,i4,2x,i12,2x,g14.6,2x,g14.6)' ) & it_num, seed_init, it_diff, energy end if end do return end subroutine cvt_energy ( dim_num, 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 MIT license. ! ! Modified: ! ! 02 December 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer N, the number of generators. ! ! Input, integer BATCH, the maximum number of sample points ! to generate at one time. ! ! Input, integer 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; ! 3, 'USER', call "user" routine. ! ! Input, logical INITIALIZE, is TRUE if the pseudorandom process should be ! reinitialized. ! ! Input, integer SAMPLE_NUM, the number of sample points to use. ! ! Input/output, integer SEED, a seed for the random ! number generator. ! ! Input, real ( kind = rk ) R(DIM_NUM,N), the coordinates of the points. ! ! Output, real ( kind = rk ) ENERGY, the estimated CVT energy. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer batch integer dim_num integer n real ( kind = rk ) energy integer get integer have logical initialize integer j integer nearest(batch) real ( kind = rk ) r(dim_num,n) real ( kind = rk ) s(dim_num,batch) integer sample integer sample_num integer seed have = 0 energy = 0.0D+00 do while ( have < sample_num ) get = min ( sample_num - have, batch ) call cvt_sample ( dim_num, sample_num, get, sample, initialize, seed, s ) have = have + get call find_closest ( dim_num, n, get, s, r, nearest ) do j = 1, get energy = energy & + sum ( ( s(1:dim_num,j) - r(1:dim_num,nearest(j)) )**2 ) end do end do energy = energy / real ( sample_num, kind = rk ) return end subroutine cvt_iterate ( dim_num, n, batch, sample, initialize, sample_num, & seed, r, it_diff, energy ) !*****************************************************************************80 ! !! CVT_ITERATE takes one step of the CVT iteration. ! ! Discussion: ! ! The routine is given a set of points, called "generators", which ! define a tessellation of the region into Voronoi cells. Each point ! defines a cell. Each cell, in turn, has a centroid, but it is ! unlikely that the centroid and the generator coincide. ! ! Each time this CVT iteration is carried out, an attempt is made ! to modify the generators in such a way that they are closer and ! closer to being the centroids of the Voronoi cells they generate. ! ! A large number of sample points are generated, and the nearest generator ! is determined. A count is kept of how many points were nearest to each ! generator. Once the sampling is completed, the location of all the ! generators is adjusted. This step should decrease the discrepancy ! between the generators and the centroids. ! ! The centroidal Voronoi tessellation minimizes the "energy", ! defined to be the integral, over the region, of the square of ! the distance between each point in the region and its nearest generator. ! The sampling technique supplies a discrete estimate of this ! energy. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 September 2004 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Qiang Du, Vance Faber, Max Gunzburger, ! Centroidal Voronoi Tessellations: Applications and Algorithms, ! SIAM Review, Volume 41, 1999, pages 637-676. ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer N, the number of points to generate. ! ! Input, integer 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. ! BATCH must be at least 1. ! ! Input, integer 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; ! 3, 'USER', call "user" routine. ! ! Input, logical INITIALIZE, is TRUE if the random number generator ! should be initialized, because this is the first call to it. ! ! Input, integer SAMPLE_NUM, the number of sample points. ! ! Input/output, integer SEED, the random number seed. ! ! Input/output, real ( kind = rk ) R(DIM_NUM,N), the Voronoi ! cell generators. On output, these have been modified ! ! Output, real ( kind = rk ) IT_DIFF, the L2 norm of the difference ! between the iterates. ! ! Output, real ( kind = rk ) ENERGY, the discrete "energy", divided ! by the number of sample points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer batch integer dim_num integer n integer sample_num integer count(n) real ( kind = rk ) energy integer get integer have logical initialize real ( kind = rk ) it_diff integer j integer nearest(batch) real ( kind = rk ) r(dim_num,n) real ( kind = rk ) r2(dim_num,n) real ( kind = rk ) s(dim_num,batch) integer sample integer seed ! ! Take each generator as the first sample point for its region. ! This can slightly slow the convergence, but it simplifies the ! algorithm by guaranteeing that no region is completely missed ! by the sampling. ! energy = 0.0D+00 r2(1:dim_num,1:n) = r(1:dim_num,1:n) count(1:n) = 1 ! ! Generate the sampling points S in batches. ! have = 0 do while ( have < sample_num ) get = min ( sample_num - have, batch ) call cvt_sample ( dim_num, sample_num, get, sample, initialize, seed, s ) initialize = .false. have = have + get ! ! Find the index N of the nearest cell generator to each sample point S. ! call find_closest ( dim_num, n, get, s, r, nearest ) ! ! Add S to the centroid associated with generator N. ! do j = 1, get r2(1:dim_num,nearest(j)) = r2(1:dim_num,nearest(j)) + s(1:dim_num,j) energy = energy + sum ( ( r(1:dim_num,nearest(j)) - s(1:dim_num,j) )**2 ) count(nearest(j)) = count(nearest(j)) + 1 end do end do ! ! Estimate the centroids. ! do j = 1, n r2(1:dim_num,j) = r2(1:dim_num,j) / real ( count(j), kind = rk ) end do ! ! Determine the sum of the distances between the old generators ! and the estimated centroids. ! it_diff = 0.0D+00 do j = 1, n it_diff = it_diff + sqrt ( sum ( ( r2(1:dim_num,j) - r(1:dim_num,j) )**2 ) ) end do ! ! Replace the generators by the centroids. ! r(1:dim_num,1:n) = r2(1:dim_num,1:n) ! ! Normalize the discrete energy estimate. ! energy = energy / real ( sample_num, kind = rk ) return end subroutine cvt_sample ( dim_num, n, n_now, sample, initialize, seed, r ) !*****************************************************************************80 ! !! CVT_SAMPLE returns sample points. ! ! Discussion: ! ! N sample points are to be taken from the region, of spatial ! dimension DIM_NUM. In most cases, this region is a unit box. ! ! 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 MIT license. ! ! Modified: ! ! 23 June 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer N, the number of sample points to be generated. ! ! Input, integer N_NOW, the number of sample points to be ! generated on this call. N_NOW must be at least 1. ! ! Input, integer 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; ! 3, 'USER', from the "user" routine. ! ! Input, logical INITIALIZE, is TRUE if the pseudorandom process should be ! reinitialized. ! ! Input/output, integer SEED, the random number seed. ! ! Output, real ( kind = rk ) R(DIM_NUM,N_NOW), the sample points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer dim_num integer n_now real ( kind = rk ) exponent integer, allocatable, dimension ( : ) :: halton_base integer, allocatable, dimension ( : ) :: halton_leap integer, allocatable, dimension ( : ) :: halton_seed integer halton_step integer i logical initialize integer j integer n integer ngrid integer prime real ( kind = rk ) r(dim_num,n_now) integer rank integer rank_max integer sample integer seed integer, 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:dim_num,1:n_now) ) seed = seed + n_now * dim_num else if ( sample == 0 ) then call random_number ( harvest = r(1:dim_num,1:n_now ) ) else if ( sample == 1 ) then allocate ( halton_seed(1:dim_num) ) allocate ( halton_leap(1:dim_num) ) allocate ( halton_base(1:dim_num) ) halton_step = seed halton_seed(1:dim_num) = 0 halton_leap(1:dim_num) = 1 do i = 1, dim_num halton_base(i) = prime ( i ) end do call i4_to_halton_sequence ( dim_num, n_now, halton_step, halton_seed, & halton_leap, halton_base, r(1:dim_num,1:n_now) ) deallocate ( halton_seed ) deallocate ( halton_leap ) deallocate ( halton_base ) seed = seed + n_now else if ( sample == 2 ) then allocate ( tuple(1:dim_num) ) exponent = 1.0D+00 / real ( dim_num, kind = rk ) ngrid = int ( ( real ( n, kind = rk ) ) ** exponent ) rank_max = ngrid**dim_num if ( rank_max < n ) then ngrid = ngrid + 1 rank_max = ngrid**dim_num end if if ( initialize ) then rank = -1 call tuple_next_fast ( ngrid, dim_num, rank, tuple ) end if rank = mod ( seed, rank_max ) do j = 1, n_now call tuple_next_fast ( ngrid, dim_num, rank, tuple ) rank = rank + 1 rank = mod ( rank, rank_max ) r(1:dim_num,j) = real ( 2 * tuple(1:dim_num) - 1, kind = rk ) & / real ( 2 * ngrid, kind = rk ) end do seed = seed + n_now deallocate ( tuple ) else if ( sample == 3 ) then call user ( dim_num, n_now, r ) 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 data_read ( file_in_name, dim_num, n, r, success ) !*****************************************************************************80 ! !! DATA_READ reads generator coordinate data from a file. ! ! Discussion: ! ! The file is assumed to contain one record per line. ! ! Records beginning with the '#' character are comments, and are ignored. ! Blank lines are also ignored. ! ! Each line that is not ignored is assumed to contain exactly (or at least) ! M real numbers, representing the coordinates of a point. ! ! There are assumed to be exactly (or at least) N such records. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 25 July 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) FILE_IN_NAME, the name of the input file. ! ! Input, integer DIM_NUM, the number of spatial dimensions. ! ! Input, integer N, the number of points. The program ! will stop reading data once N values have been read. ! ! Output, real ( kind = rk ) R(DIM_NUM,N), the point coordinates. ! ! Output, logical SUCCESS, is TRUE if the data was read properly. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer dim_num integer n character ( len = * ) file_in_name integer file_in_unit integer i integer ierror integer ios character ( len = 255 ) line real ( kind = rk ) r(dim_num,n) logical success real ( kind = rk ) x(dim_num) success = .true. call get_unit ( file_in_unit ) open ( unit = file_in_unit, file = file_in_name, status = 'old', & iostat = ios ) if ( ios /= 0 ) then success = .false. write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'DATA_READ - Fatal error!' write ( *, '(a)' ) ' Could not open the input file: ' // & trim ( file_in_name ) return end if i = 0 do while ( i < n ) read ( file_in_unit, '(a)', iostat = ios ) line if ( ios /= 0 ) then success = .false. return end if if ( line(1:1) == '#' .or. len_trim ( line ) == 0 ) then cycle end if call s_to_r8vec ( line, dim_num, x, ierror ) if ( ierror /= 0 ) then cycle end if i = i + 1 r(1:dim_num,i) = x(1:dim_num) end do close ( unit = file_in_unit ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'DATA_READ:' write ( *, '(a,i6)' ) ' Read coordinate data from file.' return end subroutine find_closest ( dim_num, 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 MIT license. ! ! Modified: ! ! 02 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer N, the number of cell generators. ! ! Input, integer SAMPLE_NUM, the number of sample points. ! ! Input, real ( kind = rk ) S(DIM_NUM,SAMPLE_NUM), the points to be checked. ! ! Input, real ( kind = rk ) R(DIM_NUM,N), the cell generators. ! ! Output, integer NEAREST(SAMPLE_NUM), the index of the nearest ! cell generators. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer dim_num integer n integer sample_num real ( kind = rk ) dist_sq_min real ( kind = rk ) dist_sq integer jr integer js integer nearest(sample_num) real ( kind = rk ) r(dim_num,n) real ( kind = rk ) s(dim_num,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:dim_num,jr) - s(1:dim_num,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_seed ( seed ) !*****************************************************************************80 ! !! GET_SEED returns a seed for the random number generator. ! ! Discussion: ! ! The seed depends on the current time, and ought to be (slightly) ! different every millisecond. Once the seed is obtained, a random ! number generator should be called a few times to further process ! the seed. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 02 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer SEED, a pseudorandom seed value. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer seed real ( kind = rk ) temp character ( len = 10 ) time character ( len = 8 ) today integer values(8) character ( len = 5 ) zone call date_and_time ( today, time, zone, values ) temp = 0.0D+00 temp = temp + real ( values(2) - 1, kind = rk ) / 11.0D+00 temp = temp + real ( values(3) - 1, kind = rk ) / 30.0D+00 temp = temp + real ( values(5), kind = rk ) / 23.0D+00 temp = temp + real ( values(6), kind = rk ) / 59.0D+00 temp = temp + real ( values(7), kind = rk ) / 59.0D+00 temp = temp + real ( values(8), kind = rk ) / 999.0D+00 temp = temp / 6.0D+00 do while ( temp <= 0.0D+00 ) temp = temp + 1.0D+00 end do do while ( 1.0D+00 < temp ) temp = temp - 1.0D+00 end do seed = int ( real ( huge ( 1 ), kind = rk ) * temp ) ! ! Never use a seed of 0 or maximum integer. ! if ( seed == 0 ) then seed = 1 end if if ( seed == huge ( 1 ) ) then seed = seed - 1 end if 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 MIT license. ! ! Modified: ! ! 18 September 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer IUNIT, the free unit number. ! implicit none integer i integer ios integer 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 ( dim_num, leap ) !*****************************************************************************80 ! !! HALHAM_LEAP_CHECK checks LEAP for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer LEAP(DIM_NUM), the leap vector. ! ! Output, logical, HALHAM_LEAP_CHECK, true if LEAP is legal. ! implicit none integer dim_num logical halham_leap_check integer leap(dim_num) if ( any ( leap(1:dim_num) < 1 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_LEAP_CHECK - Fatal error!' write ( *, '(a)' ) ' Some entry of LEAP < 1!' write ( *, '(a)' ) ' ' call i4vec_transpose_print ( dim_num, 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 MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the spatial dimension. ! ! Output, logical HALHAM_N_CHECK, true if N is legal. ! implicit none logical halham_n_check integer 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_dim_num_check ( dim_num ) !*****************************************************************************80 ! !! HALHAM_DIM_NUM_CHECK checks DIM_NUM for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Output, logical HALHAM_DIM_NUM_CHECK, true if DIM_NUM is legal. ! implicit none logical halham_dim_num_check integer dim_num if ( dim_num < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_DIM_NUM_CHECK - Fatal error!' write ( *, '(a)' ) ' DIM_NUM < 1.' write ( *, '(a,i12)' ) ' DIM_NUM = ', dim_num halham_dim_num_check = .false. else halham_dim_num_check = .true. end if return end function halham_seed_check ( dim_num, seed ) !*****************************************************************************80 ! !! HALHAM_SEED_CHECK checks SEED for a Halton or Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer SEED(DIM_NUM), the seed vector. ! ! Output, logical, HALHAM_SEED_CHECK, true if SEED is legal. ! implicit none integer dim_num logical halham_seed_check integer seed(dim_num) if ( any ( seed(1:dim_num) < 0 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'HALHAM_SEED_CHECK - Fatal error!' write ( *, '(a)' ) ' Some entry of SEED < 0!' write ( *, '(a)' ) ' ' call i4vec_transpose_print ( dim_num, 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 MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer STEP, the index of the subsequence element. ! ! Output, logical HALHAM_STEP_CHECK, true if STEP is legal. ! implicit none logical halham_step_check integer 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 ( dim_num, base ) !*****************************************************************************80 ! !! HALTON_BASE_CHECK checks BASE for a Halton sequence. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer DIM_NUM, the spatial dimension. ! ! Input, integer BASE(DIM_NUM), the bases. ! ! Output, logical, HALTON_BASE_CHECK, true if BASE is legal. ! implicit none integer dim_num integer base(dim_num) logical halton_base_check if ( any ( base(1:dim_num) <= 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 ( dim_num, base, 'BASE: ' ) halton_base_check = .false. else halton_base_check = .true. end if return end subroutine i4_to_halton_sequence ( dim_num, n, step, seed, leap, base, r ) !*****************************************************************************80 ! !! I4_TO_HALTON_SEQUENCE computes N elements of a leaped Halton subsequence. ! ! Discussion: ! ! The DIM_NUM-dimensional Halton sequence is really DIM_NUM 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:DIM_NUM) + STEP * LEAP(1:DIM_NUM) ! ! of the original Halton sequence. ! ! Licensing: ! ! This code is distributed under the MIT 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 DIM_NUM, the spatial dimension. ! 1 <= DIM_NUM is required. ! ! Input, integer N, the number of elements of the sequence. ! ! Input, integer STEP, the index of the subsequence element. ! 0 <= STEP is required. ! ! Input, integer SEED(DIM_NUM), the Halton sequence index ! corresponding to STEP = 0. ! ! Input, integer LEAP(DIM_NUM), the succesive jumps in the ! Halton sequence. ! ! Input, integer BASE(DIM_NUM), the Halton bases. ! ! Output, real ( kind = rk ) R(DIM_NUM,N), the next N elements of the ! leaped Halton subsequence, beginning with element STEP. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer dim_num integer n integer base(dim_num) real ( kind = rk ) base_inv integer digit(n) logical halham_leap_check logical halham_n_check logical halham_dim_num_check logical halham_seed_check logical halham_step_check logical halton_base_check integer i integer j integer leap(dim_num) real ( kind = rk ) r(dim_num,n) integer seed(dim_num) integer seed2(n) integer step ! ! Check the input. ! if ( .not. halham_dim_num_check ( dim_num ) ) 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 ( dim_num, seed ) ) then stop end if if ( .not. halham_leap_check ( dim_num, leap ) ) then stop end if if ( .not. halton_base_check ( dim_num, base ) ) then stop end if ! ! Calculate the data. ! r(1:dim_num,1:n) = 0.0D+00 do i = 1, dim_num do j = 1, n seed2(j) = seed(i) + ( step + j - 1 ) * leap(i) end do base_inv = real ( 1.0D+00, kind = rk ) / real ( base(i), kind = rk ) 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 = rk ) * base_inv base_inv = base_inv / real ( base(i), kind = rk ) 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 integer vector "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 MIT license. ! ! Modified: ! ! 03 July 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the number of components of the vector. ! ! Input, integer A(N), the vector to be printed. ! ! Input, character ( len = * ) TITLE, a title to be printed first. ! TITLE may be blank. ! implicit none integer n integer a(n) integer ihi integer ilo character ( len = 11 ) string character ( len = * ) title integer 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 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 MIT 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 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 PRIME, the N-th prime. If N is out of range, ! PRIME is returned as -1. ! implicit none integer, parameter :: prime_max = 1600 integer, save :: icall = 0 integer n integer, save, dimension ( prime_max ) :: npvec integer 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 subroutine r8mat_transpose_print ( m, n, a, title ) !*****************************************************************************80 ! !! R8MAT_TRANSPOSE_PRINT prints a real matrix, transposed. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, real ( kind = rk ) A(M,N), an M by N matrix to be printed. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n real ( kind = rk ) a(m,n) character ( len = * ) title call r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title ) return end subroutine r8mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! R8MAT_TRANSPOSE_PRINT_SOME prints some of a real matrix, transposed. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, real ( kind = rk ) A(M,N), an M by N matrix to be printed. ! ! Input, integer ILO, JLO, the first row and column to print. ! ! Input, integer IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: incx = 5 integer m integer n real ( kind = rk ) a(m,n) character ( len = 14 ) ctemp(incx) integer i integer i2 integer i2hi integer i2lo integer ihi integer ilo integer inc integer j integer j2hi integer j2lo integer jhi integer jlo character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) do i2lo = max ( ilo, 1 ), min ( ihi, m ), incx i2hi = i2lo + incx - 1 i2hi = min ( i2hi, m ) i2hi = min ( i2hi, ihi ) inc = i2hi + 1 - i2lo write ( *, '(a)' ) ' ' do i = i2lo, i2hi i2 = i + 1 - i2lo write ( ctemp(i2), '(i7,7x)') i end do write ( *, '('' Row '',5a14)' ) ctemp(1:inc) write ( *, '(a)' ) ' Col' j2lo = max ( jlo, 1 ) j2hi = min ( jhi, n ) do j = j2lo, j2hi do i2 = 1, inc i = i2lo - 1 + i2 write ( ctemp(i2), '(g14.6)' ) a(i,j) end do write ( *, '(i5,1x,5a14)' ) j, ( ctemp(i), i = 1, inc ) end do end do return end subroutine r8mat_write ( output_filename, m, n, table ) !*****************************************************************************80 ! !! R8MAT_WRITE writes an R8MAT file. ! ! Discussion: ! ! An R8MAT is an array of R8 values. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 31 May 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) OUTPUT_FILENAME, the output file name. ! ! Input, integer M, the spatial dimension. ! ! Input, integer N, the number of points. ! ! Input, real ( kind = rk ) TABLE(M,N), the table data. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer j character ( len = * ) output_filename integer output_status integer output_unit character ( len = 30 ) string real ( kind = rk ) table(m,n) ! ! Open the file. ! call get_unit ( output_unit ) open ( unit = output_unit, file = output_filename, & status = 'replace', iostat = output_status ) if ( output_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_WRITE - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the output file "' // & trim ( output_filename ) // '" on unit ', output_unit output_unit = -1 stop end if ! ! Create a format string. ! ! For less precision in the output file, try: ! ! '(', m, 'g', 14, '.', 6, ')' ! if ( 0 < m .and. 0 < n ) then write ( string, '(a1,i8,a1,i8,a1,i8,a1)' ) '(', m, 'g', 24, '.', 16, ')' ! ! Write the data. ! do j = 1, n write ( output_unit, string ) table(1:m,j) end do end if ! ! Close the file. ! close ( unit = output_unit ) return end subroutine s_cap ( s ) !*****************************************************************************80 ! !! S_CAP replaces any lowercase letters by uppercase ones in a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character ( len = * ) S, the string to be transformed. ! implicit none character c integer i integer nchar character ( len = * ) s nchar = len_trim ( s ) do i = 1, nchar c = s(i:i) call ch_cap ( c ) s(i:i) = c end do 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 MIT 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 i integer len1 integer len2 integer 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 s_to_i4 ( s, ival, ierror, last ) !*****************************************************************************80 ! !! S_TO_I4 reads an integer value from a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, a string to be examined. ! ! Output, integer IVAL, the integer value read from the string. ! If the string is blank, then IVAL will be returned 0. ! ! Output, integer IERROR, an error flag. ! 0, no error. ! 1, an error occurred. ! ! Output, integer LAST, the last character of S used. ! implicit none character c integer i integer ierror integer isgn integer istate integer ival integer last character ( len = * ) s ierror = 0 istate = 0 isgn = 1 ival = 0 do i = 1, len_trim ( s ) c = s(i:i) ! ! Haven't read anything. ! if ( istate == 0 ) then if ( c == ' ' ) then else if ( c == '-' ) then istate = 1 isgn = -1 else if ( c == '+' ) then istate = 1 isgn = + 1 else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read the sign, expecting digits. ! else if ( istate == 1 ) then if ( c == ' ' ) then else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read at least one digit, expecting more. ! else if ( istate == 2 ) then if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then ival = 10 * ival + ichar ( c ) - ichar ( '0' ) else ival = isgn * ival last = i - 1 return end if end if end do ! ! If we read all the characters in the string, see if we're OK. ! if ( istate == 2 ) then ival = isgn * ival last = len_trim ( s ) else ierror = 1 last = 0 end if return end subroutine s_to_r8 ( s, r, ierror, lchar ) !*****************************************************************************80 ! !! S_TO_R8 reads an R8 from a string. ! ! Discussion: ! ! This routine will read as many characters as possible until it reaches ! the end of the string, or encounters a character which cannot be ! part of the real number. ! ! Legal input is: ! ! 1 blanks, ! 2 '+' or '-' sign, ! 2.5 spaces ! 3 integer part, ! 4 decimal point, ! 5 fraction part, ! 6 'E' or 'e' or 'D' or 'd', exponent marker, ! 7 exponent sign, ! 8 exponent integer part, ! 9 exponent decimal point, ! 10 exponent fraction part, ! 11 blanks, ! 12 final comma or semicolon. ! ! with most quantities optional. ! ! Example: ! ! S R ! ! '1' 1.0 ! ' 1 ' 1.0 ! '1A' 1.0 ! '12,34,56' 12.0 ! ' 34 7' 34.0 ! '-1E2ABCD' -100.0 ! '-1X2ABCD' -1.0 ! ' 2E-1' 0.2 ! '23.45' 23.45 ! '-4.2E+2' -420.0 ! '17d2' 1700.0 ! '-14e-2' -0.14 ! 'e2' 100.0 ! '-12.73e-9.23' -12.73 * 10.0^(-9.23) ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 February 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string containing the ! data to be read. Reading will begin at position 1 and ! terminate at the end of the string, or when no more ! characters can be read to form a legal real. Blanks, ! commas, or other nonnumeric data will, in particular, ! cause the conversion to halt. ! ! Output, real ( kind = rk ) R, the real value that was read from the string. ! ! Output, integer IERROR, error flag. ! 0, no errors occurred. ! 1, 2, 6 or 7, the input number was garbled. The ! value of IERROR is the last type of input successfully ! read. For instance, 1 means initial blanks, 2 means ! a plus or minus sign, and so on. ! ! Output, integer LCHAR, the number of characters read from ! the string to form the number, including any terminating ! characters such as a trailing comma or blanks. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) logical ch_eqi character c integer ierror integer ihave integer isgn integer iterm integer jbot integer jsgn integer jtop integer lchar integer nchar integer ndig real ( kind = rk ) r real ( kind = rk ) rbot real ( kind = rk ) rexp real ( kind = rk ) rtop character ( len = * ) s character, parameter :: TAB = char ( 9 ) nchar = len_trim ( s ) ierror = 0 r = 0.0 lchar = - 1 isgn = 1 rtop = 0.0 rbot = 1.0 jsgn = 1 jtop = 0 jbot = 1 ihave = 1 iterm = 0 do lchar = lchar + 1 c = s(lchar+1:lchar+1) ! ! Blank or TAB character. ! if ( c == ' ' .or. c == TAB ) then if ( ihave == 2 ) then else if ( ihave == 6 .or. ihave == 7 ) then iterm = 1 else if ( 1 < ihave ) then ihave = 11 end if ! ! Comma. ! else if ( c == ',' .or. c == ';' ) then if ( ihave /= 1 ) then iterm = 1 ihave = 12 lchar = lchar + 1 end if ! ! Minus sign. ! else if ( c == '-' ) then if ( ihave == 1 ) then ihave = 2 isgn = - 1 else if ( ihave == 6 ) then ihave = 7 jsgn = - 1 else iterm = 1 end if ! ! Plus sign. ! else if ( c == '+' ) then if ( ihave == 1 ) then ihave = 2 else if ( ihave == 6 ) then ihave = 7 else iterm = 1 end if ! ! Decimal point. ! else if ( c == '.' ) then if ( ihave < 4 ) then ihave = 4 else if ( 6 <= ihave .and. ihave <= 8 ) then ihave = 9 else iterm = 1 end if ! ! Exponent marker. ! else if ( ch_eqi ( c, 'E' ) .or. ch_eqi ( c, 'D' ) ) then if ( ihave < 6 ) then ihave = 6 else iterm = 1 end if ! ! Digit. ! else if ( ihave < 11 .and. lge ( c, '0' ) .and. lle ( c, '9' ) ) then if ( ihave <= 2 ) then ihave = 3 else if ( ihave == 4 ) then ihave = 5 else if ( ihave == 6 .or. ihave == 7 ) then ihave = 8 else if ( ihave == 9 ) then ihave = 10 end if call ch_to_digit ( c, ndig ) if ( ihave == 3 ) then rtop = real ( 10.0, kind = rk ) * rtop + real ( ndig, kind = rk ) else if ( ihave == 5 ) then rtop = real ( 10.0, kind = rk ) * rtop + real ( ndig, kind = rk ) rbot = real ( 10.0, kind = rk ) * rbot else if ( ihave == 8 ) then jtop = 10 * jtop + ndig else if ( ihave == 10 ) then jtop = 10 * jtop + ndig jbot = 10 * jbot end if ! ! Anything else is regarded as a terminator. ! else iterm = 1 end if ! ! If we haven't seen a terminator, and we haven't examined the ! entire string, go get the next character. ! if ( iterm == 1 .or. nchar <= lchar+1 ) then exit end if end do ! ! If we haven't seen a terminator, and we have examined the ! entire string, then we're done, and LCHAR is equal to NCHAR. ! if ( iterm /= 1 .and. lchar+1 == nchar ) then lchar = nchar end if ! ! Number seems to have terminated. Have we got a legal number? ! Not if we terminated in states 1, 2, 6 or 7! ! if ( ihave == 1 .or. ihave == 2 .or. ihave == 6 .or. ihave == 7 ) then ierror = ihave return end if ! ! Number seems OK. Form it. ! if ( jtop == 0 ) then rexp = 1.0 else if ( jbot == 1 ) then rexp = real ( 10.0, kind = rk ) ** ( jsgn * jtop ) else rexp = jsgn * jtop rexp = rexp / jbot rexp = real ( 10.0, kind = rk ) ** rexp end if end if r = isgn * rexp * rtop / rbot return end subroutine s_to_r8vec ( s, n, rvec, ierror ) !*****************************************************************************80 ! !! S_TO_R8VEC reads an R8VEC from a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 February 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer N, the number of values expected. ! ! Output, real ( kind = rk ) RVEC(N), the values read from the string. ! ! Output, integer IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n integer i integer ierror integer ilo integer lchar real ( kind = rk ) rvec(n) character ( len = * ) s i = 0 ilo = 1 do while ( i < n ) i = i + 1 call s_to_r8 ( s(ilo:), rvec(i), ierror, lchar ) if ( ierror /= 0 ) then ierror = -i exit end if ilo = ilo + lchar end do 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 ! implicit none 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 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 MIT license. ! ! Modified: ! ! 11 August 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, the maximum entry in any component. ! M must be greater than 0. ! ! Input, integer N, the number of components. ! N must be greater than 0. ! ! Input, integer 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 X(N), the next tuple, or a dummy value if ! initialization has just been done. ! implicit none integer n integer, save, allocatable, dimension ( : ) :: base integer i integer m integer rank integer 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