fixed the pattern function and the memoization thereof
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Stephen Mardson McQuay
parent
08f898d83a
commit
2e7391f573
@ -2,6 +2,9 @@ import sys
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import numpy as np
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from functools import wraps
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import itertools
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import logging
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log = logging.getLogger('interp')
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@ -99,7 +102,7 @@ def get_error(phi, R, S, order = 2):
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B = [] # baker eq 9
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w = [] # baker eq 11
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p = pattern(order, len(phi), offset = -1)
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p = pattern(len(phi), order)
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log.info("pattern: %s" % p)
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for (s,q) in zip(S.verts, S.q):
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@ -183,42 +186,74 @@ def run_baker(X, R, S, order=2):
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return answer
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def _boxings(n, k):
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"""\
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source for this function:
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http://old.nabble.com/Simple-combinatorics-with-Numpy-td20086915.html
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http://old.nabble.com/Re:-Simple-combinatorics-with-Numpy-p20099736.html
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"""
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seq, i = [n] * k + [0], k
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while i:
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yield tuple(seq[i] - seq[i+1] for i in xrange(k))
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i = seq.index(0) - 1
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seq[i:k] = [seq[i] - 1] * (k-i)
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def _samples_ur(items, k, offset = 0):
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"""Returns k unordered samples (with replacement) from items."""
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n = len(items)
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for sample in _boxings(k, n):
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selections = [[items[i]]*count for i,count in enumerate(sample)]
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yield tuple([x + offset for sel in selections for x in sel])
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def memoize(f):
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"""
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I only cache on power and phicount; I figure that one should stick to a
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particular offset throughout one's codebase.
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for more information on what I'm doing here,
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please read:
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http://en.wikipedia.org/wiki/Memoize
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"""
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cache = {}
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@wraps(f)
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def memf(*x, **kargs):
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if x not in cache:
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cache[x] = f(*x, **kargs)
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return cache[x]
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return memf
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def combinations_with_replacement(iterable, r):
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"""
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What I really need for the pattern function only
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exists in python 2.7 and greater. The docs suggest
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the implementation in this function as a
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replacement.
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see: http://docs.python.org/library/itertools.html#itertools.combinations_with_replacement
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"""
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pool = tuple(iterable)
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n = len(pool)
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for indices in itertools.product(range(n), repeat=r):
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if sorted(indices) == list(indices):
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yield tuple(pool[i] for i in indices)
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@memoize
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def pattern(power, phicount, offset = 0):
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log.debug("(power = %s, phicount = %s)" % (power, phicount))
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r = []
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for i in _samples_ur(range(1, phicount + 1), power, offset):
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if not len(set(i)) == 1:
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r.append(i)
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return r
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def pattern(simplex_size, nu):
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"""
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my useful docstring
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"""
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log.debug("pattern: simplex: %d, order: %d" % (simplex_size, nu))
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return [i for i in combinations_with_replacement(xrange(simplex_size), nu) if len(set(i)) != 1]
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if __name__ == '__main__':
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print len(pattern(3, 2)), pattern(3, 2)
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print len(pattern(4, 2)), pattern(4, 2)
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print len(pattern(3, 3)), pattern(3, 3)
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print len(pattern(4, 3)), pattern(4, 3)
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print len(pattern(3, 4)), pattern(3, 4)
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print len(pattern(4, 4)), pattern(4, 4)
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print len(pattern(3, 2)), pattern(3, 2)
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print len(pattern(4, 2)), pattern(4, 2)
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print len(pattern(3, 3)), pattern(3, 3)
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print len(pattern(4, 3)), pattern(4, 3)
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print len(pattern(3, 4)), pattern(3, 4)
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print len(pattern(4, 4)), pattern(4, 4)
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print len(pattern(3, 2)), pattern(3, 2)
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print len(pattern(4, 2)), pattern(4, 2)
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print len(pattern(3, 3)), pattern(3, 3)
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print len(pattern(4, 3)), pattern(4, 3)
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print len(pattern(3, 4)), pattern(3, 4)
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print len(pattern(4, 4)), pattern(4, 4)
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print len(pattern(3, 2)), pattern(3, 2)
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print len(pattern(4, 2)), pattern(4, 2)
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print len(pattern(3, 3)), pattern(3, 3)
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print len(pattern(4, 3)), pattern(4, 3)
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print len(pattern(3, 4)), pattern(3, 4)
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print len(pattern(4, 4)), pattern(4, 4)
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@ -13,35 +13,35 @@ class Test(unittest.TestCase):
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from interp.baker import pattern
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def test_baker_eq_8(self):
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b = sorted([tuple(sorted(i)) for i in ((1,2),(2,3),(3,1))])
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p = sorted(pattern(power = 2, phicount = 3))
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b = sorted([tuple(sorted(i)) for i in ((0,1),(1,2),(2,0))])
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p = sorted(pattern(3,2))
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self.assertEqual(b,p)
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def test_baker_eq_17(self):
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b = sorted([tuple(sorted(i)) for i in ((1,2,2), (1,3,3), (2,1,1), (2,3,3), (3,1,1), (3,2,2), (1,2,3))])
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p = sorted(pattern(power = 3, phicount = 3))
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b = sorted([tuple(sorted(i)) for i in ((0,1,1), (0,2,2), (1,0,0), (1,2,2), (2,0,0), (2,1,1), (0,1,2))])
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p = sorted(pattern(3,3))
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self.assertEqual(b,p)
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def test_baker_eq_15(self):
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b = sorted([tuple(sorted(i)) for i in (
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(1,2), (1,3), (1,4),
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(2,3), (2,4), (3,4))])
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(0,1), (0,2), (0,3),
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(1,2), (1,3), (2,3))])
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p = sorted(pattern(power = 2, phicount = 4))
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p = sorted(pattern(4,2))
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self.assertEqual(b,p)
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def test_smcquay_(self):
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b = sorted([tuple(sorted(i)) for i in (
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(1,2,3), (2,3,4), (1,2,4), (1,3,4),
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(1,1,2), (1,2,2),
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(2,3,3), (2,2,3),
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(0,1,2), (1,2,3), (0,1,3), (0,2,3),
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(0,0,1), (0,1,1),
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(1,2,2), (1,1,2),
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(0,2,2), (0,0,2),
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(1,3,3), (1,1,3),
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(2,4,4), (2,2,4),
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(3,3,4), (3,4,4),
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(1,4,4), (1,1,4))])
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(2,2,3), (2,3,3),
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(0,3,3), (0,0,3))])
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p = sorted(pattern(power = 3, phicount = 4))
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p = sorted(pattern(4,3))
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self.assertEqual(b,p)
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