Merge pull request #11 from volf52/matrix-ops-python

2D Matrix Operations without using Numpy

Author: rawktron

recipes/Python/Matrix Operations without numpy/LICENSE

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+MIT License
+
+Copyright (c) 2017 Muhammad Arslan <rslnkrmt2552@gmail.com>
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

recipes/Python/Matrix Operations without numpy/README.md

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+Created on 2017-09-09
+
+Author : Muhammad Arslan <rslnkrmt@gmail.com>
+
+Licence : MIT
+
+2-D Matrix operations without the use of numpy module
+------------------------------------------------------------------
+
+In situations where numpy module isn't available, you can use these functions to calculate the inverse, determinant, transpose of matrix, calculate the minors of it's elements, and multiply two matrices together.
+Any advice to make these functions better will be appreciated.

recipes/Python/Matrix Operations without numpy/matrix_ops.py

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+def transpose(matrix):
+    return [[row[i] for row in matrix] for i in range(len(matrix[0]))]
+
+
+def multip(X, Y):
+    return [[sum(a*b for a, b in zip(X_row, Y_col)) for Y_col in zip(*Y)] for X_row in X]
+
+
+def getMatrixMinor(m, i, j):
+    return [row[:j] + row[j+1:] for row in (m[:i]+m[i+1:])]
+
+
+def getMatrixDeternminant(m):
+    # base case for 2x2 matrix
+    if len(m) == 2:
+        return (m[0][0]*m[1][1]-m[0][1]*m[1][0])*1.0
+
+    determinant = 0
+    for c in range(len(m)):
+        determinant += ((-1.0)**c)*m[0][c]*getMatrixDeternminant(getMatrixMinor(m, 0, c))
+    return determinant
+
+
+def getMatrixInverse(m):
+    determinant = getMatrixDeternminant(m)
+    # special case for 2x2 matrix:
+    if len(m) == 2:
+        return [[m[1][1]/determinant, -1*m[0][1]/determinant],
+                [-1*m[1][0]/determinant, m[0][0]/determinant]]
+
+    # find matrix of cofactors
+    cofactors = []
+    for r in range(len(m)):
+        cofactorRow = []
+        for c in range(len(m)):
+            minor = getMatrixMinor(m,r,c)
+            cofactorRow.append(((-1)**(r+c)) * getMatrixDeternminant(minor))
+        cofactors.append(cofactorRow)
+    cofactors = transpose(cofactors)
+    for r in range(len(cofactors)):
+        for c in range(len(cofactors)):
+            cofactors[r][c] = cofactors[r][c]/determinant
+    return cofactors