<reponame>bellaz89/pyFEL
'''
    Implementation of the Hammersley low discrepancy sequence
'''

import numba
from numba import int64, objmode
from numba.experimental import jitclass
import numpy as np
from scipy.special import erfcinv

spec = [
    ('base', int64),
    ('idx', int64)
]

@jitclass(spec)
class Hammersley(object):
    '''
        Hammersley low discrepancy sequence generator
    '''
    def __init__(self, prime_idx):
        '''
            Initialize the sequence with the nth prime number
        '''
        self.base = int64(PRIME_VECTOR[prime_idx])
        self.idx = int64(0)

    def set_idx(self, new_idx):
        '''
            Skip the sequence to 'new_idx'
        '''
        if new_idx < 0:
            self.idx = 0
        else:
            self.idx = new_idx

    def get_value(self):
        '''
            Get an element from the sequence
        '''
        xs = 0.0
        xsi = 1.0
        i1 = int64(0)
        self.idx += 1
        i2 = int64(self.idx)

        while True:
            xsi /= self.base
            i1 = int64(i2/self.base)
            xs += (i2-self.base*i1)*xsi
            i2 = i1
            if i2 <= 0:
                return xs

    def get_array(self, n):
        '''
            Get a numpy 1D array with length 'n'
        '''
        sequence = np.empty(n, dtype=np.float64)
        for i in range(n):
            sequence[i] = self.get_value()

        return sequence

    def get_normal_array(self, n):
        '''
            Get a normal distribuited 1D array with length 'n'
        '''

        x = self.get_array(n)*2.0
        y = np.zeros_like(x)

        # The JIT has to be disabled because erfcinv is not recognized
        # by Numba
        with objmode(y='double[:]'):
            y = erfcinv(x)

        return y

PRIME_VECTOR = np.array([
    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, 
  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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
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, 
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, 
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], dtype=np.int64)

'''
    Implementation of the Hammersley low discrepancy sequence
'''

import numba
from numba import int64, objmode
from numba.experimental import jitclass
import numpy as np
from scipy.special import erfcinv

spec = [
    ('base', int64),
    ('idx', int64)
]

@jitclass(spec)
class Hammersley(object):
    '''
        Hammersley low discrepancy sequence generator
    '''
    def __init__(self, prime_idx):
        '''
            Initialize the sequence with the nth prime number
        '''
        self.base = int64(PRIME_VECTOR[prime_idx])
        self.idx = int64(0)

    def set_idx(self, new_idx):
        '''
            Skip the sequence to 'new_idx'
        '''
        if new_idx < 0:
            self.idx = 0
        else:
            self.idx = new_idx

    def get_value(self):
        '''
            Get an element from the sequence
        '''
        xs = 0.0
        xsi = 1.0
        i1 = int64(0)
        self.idx += 1
        i2 = int64(self.idx)

        while True:
            xsi /= self.base
            i1 = int64(i2/self.base)
            xs += (i2-self.base*i1)*xsi
            i2 = i1
            if i2 <= 0:
                return xs

    def get_array(self, n):
        '''
            Get a numpy 1D array with length 'n'
        '''
        sequence = np.empty(n, dtype=np.float64)
        for i in range(n):
            sequence[i] = self.get_value()

        return sequence

    def get_normal_array(self, n):
        '''
            Get a normal distribuited 1D array with length 'n'
        '''

        x = self.get_array(n)*2.0
        y = np.zeros_like(x)

        # The JIT has to be disabled because erfcinv is not recognized
        # by Numba
        with objmode(y='double[:]'):
            y = erfcinv(x)

        return y

PRIME_VECTOR = np.array([
    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, 
  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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
 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, 
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, 
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, 
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], dtype=np.int64)
Implementation of the Hammersley low discrepancy sequence Hammersley low discrepancy sequence generator Initialize the sequence with the nth prime number Skip the sequence to 'new_idx' Get an element from the sequence Get a numpy 1D array with length 'n' Get a normal distribuited 1D array with length 'n' # The JIT has to be disabled because erfcinv is not recognized # by Numba