/usr/share/pyshared/brian/utils/approximatecomparisons.py is in python-brian 1.4.1-2.
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# Copyright ENS, INRIA, CNRS
# Contributors: Romain Brette (brette@di.ens.fr) and Dan Goodman (goodman@di.ens.fr)
#
# Brian is a computer program whose purpose is to simulate models
# of biological neural networks.
#
# This software is governed by the CeCILL license under French law and
# abiding by the rules of distribution of free software. You can use,
# modify and/ or redistribute the software under the terms of the CeCILL
# license as circulated by CEA, CNRS and INRIA at the following URL
# "http://www.cecill.info".
#
# As a counterpart to the access to the source code and rights to copy,
# modify and redistribute granted by the license, users are provided only
# with a limited warranty and the software's author, the holder of the
# economic rights, and the successive licensors have only limited
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# software by the user in light of its specific status of free software,
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"""Util to test if two floating point numbers are equal
Use these functions for very precise tests of equality:
-- is_equal(x,y), for x=y
-- is_less_than_or_equal(x,y), for x<=y
-- is_greater_than_or_equal(x,y), for x>=y
Use these functions for less precise tests (for example, if you have done some operations on two varaibles):
-- is_approx_equal(x,y), for x=y
-- is_approx_less_than_or_equal(x,y), for x<=y
-- is_approx_greater_than_or_equal(x,y), for x>=y
The underlying mechanism is that the more precise version tests for equality using machine epsilon
precision, that is, x=y if abs(x-y)<abs(x)*epsilon where epsilon is the smallest value such that
1+epsilon>epsilon. The less precise mechanism simply uses 100*epsilon instead of epsilon.
Use this function for testing if you want to specify an absolute tolerance:
-- is_within_absolute_tolerance(x,y[,absolutetolerance])
The default tolerance is the sqrt of epsilon, or about 1e-8 for a 64 bit float
Note also that you can use the numpy function:
-- allclose(a, b, rtol = 1e-5, atol = 1e-8)
Where rtol is the relative tolerance, and atol is the absolute tolerance which comes into
play when the numbers are very close to zero.
Warning: none of these functions can be guaranteed to work in the way you might
expect them to. Errors can accumulate to the point where even 100*epsilon is an inappropriate test
for approximate equality.
"""
import math
# This finds the 'machine epsilon' for the current hardware float type, the
# smallest value of epsilon so that 1+epsilon>1
epsilon = 1.
while 1. + epsilon > 1.:
epsilon /= 2
epsilon *= 2.
# Result for 32 bit float should be: 1.1929093e-7
# For 64 bit float should be: 2.220446049250313e-16
# This value can be used for more approximate testing
approxepsilon = epsilon * 10000
# This value is the default tolerance for medium sized numbers (used in the units class)
defaultabsolutetolerance = math.sqrt(epsilon) # 1.4901161193847656e-008 on 64 bit system
def is_equal(x, y):
if x == y: return True
return abs(x - y) < abs(x) * epsilon
def is_less_than_or_equal(x, y):
return x < y or is_equal(x, y)
def is_greater_than_or_equal(x, y):
return x > y or is_equal(x, y)
def is_approx_equal(x, y):
if x == y: return True
return abs(x - y) < abs(x) * approxepsilon
def is_approx_less_than_or_equal(x, y):
return x < y or is_approx_equal(x, y)
def is_approx_greater_than_or_equal(x, y):
return x > y or is_approx_equal(x, y)
def is_within_absolute_tolerance(x, y, absolutetolerance=defaultabsolutetolerance):
return float(abs(x - y)) < absolutetolerance
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