!> @brief Module containing subroutines for generating 1-D and 2-D Hammersley quasi-Monte Carlo sequences. !! @details The algorithm and code for generating the 1-D Hammersley sequence was developed by John Burkardt at the Florida State University. !! Visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html" for more information. !! The algorithm and code for generating the 2-D Hammersley sequence was developed by L. Carbajal at the Oak Ridge National Lab. MODULE korc_hammersley_generator use korc_types IMPLICIT NONE PUBLIC :: hammersley,& generate_2D_hammersley_sequence PRIVATE :: hammersley_inverse,& hammersley_sequence,& r8mat_print,& r8mat_print_some,& timestamp,& prime CONTAINS !> @brief Subroutine for generating a 2-D Hammersley sequence. !! @details This subroutine uses the algorithm for generating a 1-D Hammersley sequence. !! Each MPI process in KORC generates a (different) subset of pairs (X,Y) of a 2-D Hammersley sequence. The total number of pairs (X,Y) !! is NMPIS*N, where NMPIS is the number of MPI processes in the simulation and N is the number of particles followed by each MPI process. !! Each subset of pairs (X,Y) has N elements. !! !! @param[in,out] X 1-D array with elements of a 2-D Hammersley sequence. !! @param[in,out] Y 1-D array with elements of a 2-D Hammersley sequence. !! @param[in] ID MPI rank of MPI process. !! @param[in] NMPIS Total number of MPI processes in the simulation. !! @param N Number of particles per MPI process. !! @param offset An offset to indicate the subroutine what subset of the 2-D Harmmersley sequence will be generated. !! @param ii Particle iterator. subroutine generate_2D_hammersley_sequence(ID,NMPIS,X,Y) REAL(rp), DIMENSION(:), INTENT(INOUT) :: X REAL(rp), DIMENSION(:), INTENT(INOUT) :: Y INTEGER, INTENT(IN) :: ID INTEGER, INTENT(IN) :: NMPIS INTEGER(4) :: N INTEGER(4) :: offset REAL(8), DIMENSION(2) :: R INTEGER(4) :: ii N = INT(SIZE(X),4) offset = (INT(ID+1_idef,4) - 1_4)*N ! write(output_unit_write,'("MPI process: ",I5," offset: ",I5)') ID, offset do ii=1_4,N call hammersley(ii+INT(offset,4),2_4,N*INT(NMPIS,4),R) X(ii) = REAL(R(1),rp) Y(ii) = REAL(R(2),rp) end do end subroutine generate_2D_hammersley_sequence !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". subroutine hammersley ( i, m, n, r ) !*****************************************************************************80 ! !! HAMMERSLEY computes an element of a Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 20 August 2016 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! John Hammersley, ! Monte Carlo methods for solving multivariable problems, ! Proceedings of the New York Academy of Science, ! Volume 86, 1960, pages 844-874. ! ! Parameters: ! ! Input, integer ( kind = 4 ) I, the index of the element of the sequence. ! 0 <= I. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the "base" for the first component. ! 1 <= N. ! ! Output, real ( kind = 8 ) R(M), the element of the sequence with index I. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) d integer ( kind = 4 ) i integer ( kind = 4 ) i1 integer ( kind = 4 ) j integer ( kind = 4 ) n ! integer ( kind = 4 ) prime real ( kind = 8 ) prime_inv(2:m) real ( kind = 8 ) r(m) integer ( kind = 4 ) t(2:m) t(2:m) = abs ( i ) ! ! Carry out the computation. ! do i1 = 2, m prime_inv(i1) = 1.0D+00 / real ( prime ( i1 - 1 ), kind = 8 ) end do r(1) = real ( mod ( i, n + 1 ), kind = 8 ) / real ( n, kind = 8 ) r(2:m) = 0.0D+00 do while ( any ( t(2:m) /= 0 ) ) do j = 2, m d = mod ( t(j), prime ( j - 1 ) ) r(j) = r(j) + real ( d, kind = 8 ) * prime_inv(j) prime_inv(j) = prime_inv(j) / real ( prime ( j - 1 ), kind = 8 ) t(j) = ( t(j) / prime ( j - 1 ) ) end do end do return end subroutine hammersley !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". subroutine hammersley_inverse ( r, m, n, i ) !*****************************************************************************80 ! !! HAMMERSLEY_INVERSE inverts an element of the Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 20 August 2016 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, real ( kind = 8 ) R(M), the I-th element of the Hammersley sequence. ! 0 <= R < 1.0 ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the "base" for the first component. ! 1 <= N. ! ! Output, integer ( kind = 4 ) I, the index of the element of the sequence. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) d integer ( kind = 4 ) i integer ( kind = 4 ) n integer ( kind = 4 ) p real ( kind = 8 ) r(m) real ( kind = 8 ) t if ( any ( r(1:m) < 0.0D+00 ) .or. any ( 1.0D+00 < r(1:m) ) ) then write ( *, '(a)' ) '' write ( *, '(a)' ) 'HAMMERSLEY_INVERSE - Fatal error!' write ( *, '(a)' ) ' 0 <= R <= 1.0 is required.' stop 1 end if if ( m < 1 ) then write ( *, '(a)' ) '' write ( *, '(a)' ) 'HAMMERSLEY_INVERSE - Fatal error!' write ( *, '(a)' ) ' 1 <= M is required.' stop 1 end if if ( n < 1 ) then write ( *, '(a)' ) '' write ( *, '(a)' ) 'HAMMERSLEY_INVERSE - Fatal error!' write ( *, '(a)' ) ' 1 <= N is required.' stop 1 end if ! ! Invert using the second component only, because working with base ! 2 is accurate. ! if ( 2 <= m ) then i = 0 t = r(2) p = 1 do while ( t /= 0.0D+00 ) t = t * 2.0D+00 d = int ( t ) i = i + d * p p = p * 2 t = mod ( t, 1.0D+00 ) end do else i = nint ( real ( n, kind = 8 ) * r(1) ) end if return end subroutine hammersley_inverse !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". 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, 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,i8)' ) ' Illegal prime index N = ', n write ( *, '(a,i8)' ) ' N should be between 1 and PRIME_MAX =', prime_max stop 1 end if return end function prime !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". subroutine hammersley_sequence ( i1, i2, m, n, r ) !*****************************************************************************80 ! !! HAMMERSLEY_SEQUENCE computes elements I1 through I2 of a Hammersley sequence. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 20 August 2016 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! John Hammersley, ! Monte Carlo methods for solving multivariable problems, ! Proceedings of the New York Academy of Science, ! Volume 86, 1960, pages 844-874. ! ! Parameters: ! ! Input, integer ( kind = 4 ) I1, I2, the indices of the first and last ! elements of the sequence. 0 <= I1, I2. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the "base" for the first component. ! 1 <= N. ! ! Output, real ( kind = 8 ) R(M,abs(I1-I2)+1), the elements of the sequence ! with indices I1 through I2. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) d integer ( kind = 4 ) i integer ( kind = 4 ) i1 integer ( kind = 4 ) i2 integer ( kind = 4 ) i3 integer ( kind = 4 ) j integer ( kind = 4 ) k integer ( kind = 4 ) l integer ( kind = 4 ) n ! integer ( kind = 4 ) prime real ( kind = 8 ) prime_inv(2:m) real ( kind = 8 ) r(m,abs(i1-i2)+1) integer ( kind = 4 ) t(2:m) if ( i1 <= i2 ) then i3 = +1 else i3 = -1 end if l = abs ( i2 - i1 ) + 1 r(1:m,1:l) = 0.0D+00 k = 0 do i = i1, i2, i3 t(2:m) = i ! ! Carry out the computation. ! do j = 2, m prime_inv(j) = 1.0D+00 / real ( prime ( j - 1 ), kind = 8 ) end do k = k + 1; r(1,k) = real ( mod ( i, n + 1 ), kind = 8 ) / real ( n, kind = 8 ) do while ( any ( t(2:m) /= 0 ) ) do j = 2, m d = mod ( t(j), prime ( j - 1 ) ) r(j,k) = r(j,k) + real ( d, kind = 8 ) * prime_inv(j) prime_inv(j) = prime_inv(j) / real ( prime ( j - 1 ), kind = 8 ) t(j) = ( t(j) / prime ( j - 1 ) ) end do end do end do return end subroutine hammersley_sequence !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". subroutine r8mat_print ( m, n, a, title ) !*****************************************************************************80 ! !! R8MAT_PRINT prints an R8MAT. ! ! Discussion: ! ! An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M]. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 12 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, the number of rows in A. ! ! Input, integer ( kind = 4 ) N, the number of columns in A. ! ! Input, real ( kind = 8 ) A(M,N), the matrix. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n real ( kind = 8 ) a(m,n) character ( len = * ) title call r8mat_print_some ( m, n, a, 1, 1, m, n, title ) return end subroutine r8mat_print !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". subroutine r8mat_print_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! R8MAT_PRINT_SOME prints some of an R8MAT. ! ! Discussion: ! ! An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M]. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 10 September 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input, real ( kind = 8 ) A(M,N), an M by N matrix to be printed. ! ! Input, integer ( kind = 4 ) ILO, JLO, the first row and column to print. ! ! Input, integer ( kind = 4 ) IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer ( kind = 4 ), parameter :: incx = 5 integer ( kind = 4 ) m integer ( kind = 4 ) n real ( kind = 8 ) a(m,n) character ( len = 14 ) ctemp(incx) integer ( kind = 4 ) i integer ( kind = 4 ) i2hi integer ( kind = 4 ) i2lo integer ( kind = 4 ) ihi integer ( kind = 4 ) ilo integer ( kind = 4 ) inc integer ( kind = 4 ) j integer ( kind = 4 ) j2 integer ( kind = 4 ) j2hi integer ( kind = 4 ) j2lo integer ( kind = 4 ) jhi integer ( kind = 4 ) jlo character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) if ( m <= 0 .or. n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' (None)' return end if do j2lo = max ( jlo, 1 ), min ( jhi, n ), incx j2hi = j2lo + incx - 1 j2hi = min ( j2hi, n ) j2hi = min ( j2hi, jhi ) inc = j2hi + 1 - j2lo write ( *, '(a)' ) ' ' do j = j2lo, j2hi j2 = j + 1 - j2lo write ( ctemp(j2), '(i8,6x)' ) j end do write ( *, '('' Col '',5a14)' ) ctemp(1:inc) write ( *, '(a)' ) ' Row' write ( *, '(a)' ) ' ' i2lo = max ( ilo, 1 ) i2hi = min ( ihi, m ) do i = i2lo, i2hi do j2 = 1, inc j = j2lo - 1 + j2 if ( a(i,j) == real ( int ( a(i,j) ), kind = 8 ) ) then write ( ctemp(j2), '(f8.0,6x)' ) a(i,j) else write ( ctemp(j2), '(g14.6)' ) a(i,j) end if end do write ( *, '(i5,a,5a14)' ) i, ':', ( ctemp(j), j = 1, inc ) end do end do return end subroutine r8mat_print_some !> @brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". 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: ! ! 18 May 2013 ! ! 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 timestamp END MODULE korc_hammersley_generator