import numpy as np
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def SIEVE_PRIMES(x):
return x and x[:1] + SIEVE_PRIMES([n for n in x if n % x[0]])
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def decompose_to_primes(max_prime):
"""Decompose number into the primes"""
for prime in SIEVE_PRIMES(list(range(2, max_prime))):
if prime * prime > max_prime:
break
while max_prime % prime == 0:
yield prime
max_prime //= prime
if max_prime > 1:
yield max_prime
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def decompose_array(shape, psize, bbox):
"""Calculate list of product(psize) subarrays of arr, along with their
left and right edges
"""
return split_array(bbox[:, 0], bbox[:, 1], shape, psize)
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def evaluate_domain_decomposition(n_d, pieces, ldom):
"""Evaluate longest to shortest edge ratio
BEWARE: lot's of magic here"""
eff_dim = (n_d > 1).sum()
exp = float(eff_dim - 1) / float(eff_dim)
ideal_bsize = eff_dim * pieces ** (1.0 / eff_dim) * np.prod(n_d) ** exp
mask = np.where(n_d > 1)
nd_arr = np.array(n_d, dtype=np.float64)[mask]
bsize = int(np.sum(ldom[mask] / nd_arr * np.prod(nd_arr)))
load_balance = float(np.prod(n_d)) / (
float(pieces) * np.prod((n_d - 1) // ldom + 1)
)
# 0.25 is magic number
quality = load_balance / (1 + 0.25 * (bsize / ideal_bsize - 1.0))
# \todo add a factor that estimates lower cost when x-direction is
# not chopped too much
# \deprecated estimate these magic numbers
quality *= 1.0 - (0.001 * ldom[0] + 0.0001 * ldom[1]) / pieces
if np.any(ldom > n_d):
quality = 0
return quality
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def factorize_number(pieces):
"""Return array consisting of prime, its power and number of different
decompositions in three dimensions for this prime
"""
factors = list(decompose_to_primes(pieces))
temp = np.bincount(factors)
return np.array(
[
(prime, temp[prime], (temp[prime] + 1) * (temp[prime] + 2) // 2)
for prime in np.unique(factors)
],
dtype="int64",
)
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def get_psize(n_d, pieces):
"""Calculate the best division of array into px*py*pz subarrays.
The goal is to minimize the ratio of longest to shortest edge
to minimize the amount of inter-process communication.
"""
fac = factorize_number(pieces)
nfactors = len(fac[:, 2])
best = 0.0
p_size = np.ones(3, dtype=np.int64)
if pieces == 1:
return p_size
while np.all(fac[:, 2] > 0):
ldom = np.ones(3, dtype=np.int64)
for nfac in range(nfactors):
i = int(np.sqrt(0.25 + 2 * (fac[nfac, 2] - 1)) - 0.5)
k = fac[nfac, 2] - (1 + i * (i + 1) // 2)
i = fac[nfac, 1] - i
j = fac[nfac, 1] - (i + k)
ldom *= fac[nfac, 0] ** np.array([i, j, k])
quality = evaluate_domain_decomposition(n_d, pieces, ldom)
if quality > best:
best = quality
p_size = ldom
# search for next unique combination
for j in range(nfactors):
if fac[j, 2] > 1:
fac[j, 2] -= 1
break
else:
if j < nfactors - 1:
fac[j, 2] = int((fac[j, 1] + 1) * (fac[j, 1] + 2) / 2)
else:
fac[:, 2] = 0 # no more combinations to try
return p_size
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def split_array(gle, gre, shape, psize):
"""Split array into px*py*pz subarrays."""
n_d = np.array(shape, dtype=np.int64)
dds = (gre - gle) / shape
left_edges = []
right_edges = []
shapes = []
slices = []
for i in range(psize[0]):
for j in range(psize[1]):
for k in range(psize[2]):
piece = np.array((i, j, k), dtype=np.int64)
lei = n_d * piece // psize
rei = n_d * (piece + np.ones(3, dtype=np.int64)) // psize
lle = gle + lei * dds
lre = gle + rei * dds
left_edges.append(lle)
right_edges.append(lre)
shapes.append(rei - lei)
slices.append(np.s_[lei[0] : rei[0], lei[1] : rei[1], lei[2] : rei[2]])
return left_edges, right_edges, shapes, slices