sequences.py

'''
This code is from 
https://github.com/PhaethonPrime/hammersley
'''

from six import moves, iteritems

# this list of primes allows up to a size 120 vector
saved_primes = [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]

def get_phi(p, k):
    p_ = p
    k_ = k
    phi = 0
    while k_ > 0:
        a = k_ % p
        phi += float(a)/p_
        k_ = int(k_/p)
        p_ *= p
    return phi

def generate_hammersley(n_dims=2, n_points=100, primes=None):
    primes = primes if primes is not None else saved_primes
    for k in moves.range(n_points):
        points = [float(k)/n_points] + [get_phi(primes[d], k) for d in moves.range(n_dims-1)]
        yield points
        
def generate_halton(n_dims=2, n_points=100, primes=None):
    primes = primes if primes is not None else saved_primes
    for k in moves.range(n_points):
        points = [get_phi(primes[d], k) for d in moves.range(n_dims)]
        yield points