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106 lines
2.2 KiB
106 lines
2.2 KiB
# Copyright (c) 2005-2010 Zooko Wilcox-O'Hearn
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# This file is part of pyutil; see README.rst for licensing terms.
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"""
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A few commonly needed functions.
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"""
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import math
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def div_ceil(n, d):
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"""
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The smallest integer k such that k*d >= n.
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"""
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return (n/d) + (n%d != 0)
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def next_multiple(n, k):
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"""
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The smallest multiple of k which is >= n. Note that if n is 0 then the
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answer is 0.
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"""
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return div_ceil(n, k) * k
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def pad_size(n, k):
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"""
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The smallest number that has to be added to n to equal a multiple of k.
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"""
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if n%k:
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return k - n%k
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else:
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return 0
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def is_power_of_k(n, k):
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return k**int(math.log(n, k) + 0.5) == n
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def next_power_of_k(n, k):
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p = 1
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while p < n:
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p *= k
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return p
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def ave(l):
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return sum(l) / len(l)
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def log_ceil(n, b):
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"""
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The smallest integer k such that b^k >= n.
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log_ceil(n, 2) is the number of bits needed to store any of n values, e.g.
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the number of bits needed to store any of 128 possible values is 7.
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"""
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p = 1
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k = 0
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while p < n:
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p *= b
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k += 1
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return k
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def log_floor(n, b):
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"""
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The largest integer k such that b^k <= n.
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"""
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p = 1
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k = 0
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while p <= n:
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p *= b
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k += 1
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return k - 1
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def linear_fit_slope(ps):
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"""
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Single-independent-variable linear regression -- least squares method.
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At least, I *think* this function computes that answer. I no longer
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remember where I learned this trick and at the moment I can't prove to
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myself that this is correct.
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@param ps a sequence of tuples of (x, y)
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"""
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avex = ave([x for (x, y) in ps])
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avey = ave([y for (x, y) in ps])
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sxy = sum([ (x - avex) * (y - avey) for (x, y) in ps ])
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sxx = sum([ (x - avex) ** 2 for (x, y) in ps ])
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if sxx == 0:
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return None
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return sxy / sxx
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def permute(l):
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"""
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Return all possible permutations of l.
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@type l: sequence
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@rtype a set of sequences
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"""
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if len(l) == 1:
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return [l,]
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res = []
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for i in range(len(l)):
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l2 = list(l[:])
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x = l2.pop(i)
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for l3 in permute(l2):
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l3.append(x)
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res.append(l3)
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return res
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