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Author: anserwaseem

ex8.2GaussianElimination.py

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+#Solving the system of equations for w, x, y, and z using Gauss-Elimination method.
+
+def gauss(A):
+    '''Converts a matrix into the identity
+    matrix by Gaussian elimination, with
+    the last column containing the solutions
+    for the variables'''
+    rows = len(A)#rows
+    cols = len(A[0])#columns
+    for j,rowNo in enumerate(A):
+        #diagonal term to be 1 by dividing row by diagonal term
+        if rowNo[j] != 0: #diagonal entry can't be zero
+            divisor = rowNo[j]
+        for i, term in enumerate(rowNo):
+            rowNo[i] = term / divisor
+        #add the other rows to the additive inverse for every row
+        for i in range(rows):
+            if i != j: #don't do it to row j
+                #calculate the additive inverse
+                addinv = -1*A[i][j]
+                #for every term in the ith row
+                for ind in range(cols):
+                    #add the corresponding term in the jth row multiplied by the additive inverse to the term in the ith row
+                    A[i][ind] += addinv*A[j][ind]
+    return A
+#example:
+'''
+2w- x+5y+ z=-3
+3w+2x+2y-6z=-32
+ w+3x+3y- z=-47
+5w-2z-3y+3z=49
+'''
+A = [[2,-1,5,1, -3],
+     [3,2,2,-6, -32],
+     [1,3,3,-1, -47],
+     [5,-2,-3,3, 49]]
+print(gauss(A))