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pypete/utilsym.py
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# Copyright (c) 2012, Peter Abeles. All Rights Reserved. | |
# | |
# Licensed under the Apache License, Version 2.0 (the "License"); | |
# you may not use this file except in compliance with the License. | |
# You may obtain a copy of the License at | |
# | |
# http://www.apache.org/licenses/LICENSE-2.0 | |
# | |
# Unless required by applicable law or agreed to in writing, software | |
# distributed under the License is distributed on an "AS IS" BASIS, | |
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
# See the License for the specific language governing permissions and | |
# limitations under the License. | |
# Utility functions for handling symbolic math and converting into Java code | |
# | |
# Works with Sage Version 5.2 | |
from numpy.core.fromnumeric import var | |
from numpy.linalg.linalg import det | |
from sage.all import * | |
def symMatrix( numRows , numCols , letter ): | |
"""Creates a matrix where each element is a unique symbol | |
""" | |
A = matrix(SR,numRows,numCols) | |
for i in range(0,numRows): | |
for j in range(0,numCols): | |
A[i,j] = var('%s%d%d' % (letter,i,j) ) | |
return A | |
def expandPower( expression ): | |
"""Expands out variables which are multiplied by an integer value | |
For example x^2 = x*x and x^4 = x*x*x*x | |
""" | |
l = expression.split('*') | |
# handle special case with a minus sign in front | |
if l[0][0] == '-': | |
l[0] = l[0][1:] | |
expression = '-' | |
else: | |
expression = '' | |
for s in l: | |
if len(s) >= 3 and s[-2] == '^': | |
var = s[:-2] | |
expanded = var | |
for i in range(int(s[-1])-1): expanded += '*'+var | |
expression += expanded + '*' | |
else: | |
expression += s + '*' | |
return expression[:-1] | |
def extractVarEq( expression , key ): | |
"""Expands the expression out and searches for all blocks of multiplication that are multiplied by the key. | |
All other blocks are discarded and the key is removed from the selected blocks | |
Example: "x*a*b + y*a*a*b - c*x*d" would output "a*b - c*d" if the key was 'x' | |
""" | |
chars = set('xyz') | |
# expand out and convert into a string | |
expression = str(expression.expand()) | |
# Make sure negative symbols are not stripped and split into multiplicative blocks | |
s = expression.replace('- ','-').split(' ') | |
# Find blocks multiplied by the key and remove the key from the string | |
if len(key) == 0: | |
var = [w for w in s if len(w) != 1 and not any( c in chars for c in w )] | |
else: | |
var = [w[:-(1+len(key))] for w in s if (w.endswith(key) and not any(c in chars for c in w[:-len(key)])) ] | |
# Expand out power | |
var = [expandPower(w) for w in var] | |
# construct a string which can be compiled | |
ret = var[0] | |
for w in var[1:]: | |
if w[0] == '-': | |
ret += ' - '+w[1:] | |
else: | |
ret += ' + '+w | |
return ret | |