/usr/share/pyshared/brian/utils/approximatecomparisons.py is in python-brian 1.3.1-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 | # ----------------------------------------------------------------------------------
# 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
# liability.
#
# In this respect, the user's attention is drawn to the risks associated
# with loading, using, modifying and/or developing or reproducing the
# software by the user in light of its specific status of free software,
# that may mean that it is complicated to manipulate, and that also
# therefore means that it is reserved for developers and experienced
# professionals having in-depth computer knowledge. Users are therefore
# encouraged to load and test the software's suitability as regards their
# requirements in conditions enabling the security of their systems and/or
# data to be ensured and, more generally, to use and operate it in the
# same conditions as regards security.
#
# The fact that you are presently reading this means that you have had
# knowledge of the CeCILL license and that you accept its terms.
# ----------------------------------------------------------------------------------
#
"""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
|