implementation of Gaussian Elimination pivoting as a numerical linear algebra algorithm

linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py

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+import sys
+import time
+
+import numpy as np
+
+matrixab = np.loadtxt("matrix.txt")
+B = np.copy(matrixab[:, matrixab.shape[1] - 1])
+
+
+def foo(matrix):
+    start = time.process_time()
+    ab = np.copy(matrix)
+    numofrows = ab.shape[0]
+    numofcolumns = ab.shape[1] - 1
+    xlst = []
+
+    """Lead element search"""
+    print("Matrix before leading coefficient search: ")
+    print(ab)
+    print(" ")
+
+    """Upper triangular matrix"""
+    for columnnum in range(numofrows):
+        for i in range(columnnum, numofcolumns):
+            if abs(ab[i][columnnum]) > abs(ab[columnnum][columnnum]):
+                ab[[columnnum, i]] = ab[[i, columnnum]]
+                if ab[columnnum, columnnum] == 0.0:
+                    sys.exit("Matrix is not correct")
+            else:
+                pass
+        if columnnum != 0:
+            for i in range(columnnum, numofrows):
+                ab[i, :] -= (
+                    ab[i, columnnum - 1]
+                    / ab[columnnum - 1, columnnum - 1]
+                    * ab[columnnum - 1, :]
+                )
+
+    print("Upper triangular matrix: ")
+    print(ab.round(3))
+    print(" ")
+
+    """Find x vector"""
+    columnnum = numofrows
+    while columnnum != 0:
+        columnnum -= 1
+        lineofx = ab[columnnum, numofrows]
+        if columnnum + 1 != numofrows:
+            for y in range(1, numofrows - columnnum):
+                lineofx += -ab[columnnum, numofrows - y] * xlst[y - 1]
+        x = lineofx / ab[columnnum, columnnum]
+        xlst.append(x)
+
+    stop = time.process_time()
+    xlst.reverse()
+    print("x vector: ")
+    print(xlst)
+    print(" ")
+    print(f"Start time: {start}, End time: {stop}")
+    print(f"Elapsed time during the whole function in seconds: {stop - start}")
+
+    return np.asarray(xlst)
+
+
+if __name__ == "__main__":
+    vectorofxalpha = foo(matrixab)
+
+"""Cond(A)"""
+modifiedb = np.copy(B)
+modifiedb[np.argmax(abs(B))] = B[np.argmax(abs(B))] / 100 * 101
+
+matrixab[:, matrixab.shape[1] - 1] = modifiedb
+print()
+print("Cond(A) check: ")
+vectorofxbeta = foo(matrixab)
+
+deltab = modifiedb - B
+deltax = vectorofxalpha - vectorofxbeta
+print(" ")
+conda = abs(np.sum(deltax) / np.sum(vectorofxalpha)) * (np.sum(B) / np.sum(deltab))
+print(f"Cond(A) =< {conda:0.6f}")
+
+
+# Example usage:
+# n_size = 3
+# a_matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=float)
+# b_vector = np.array([10, 11, 12], dtype=float)
+
+# solution = custom_gauss_elimination_pivoting(a_matrix, b_vector, n_size)
+# print("Solution:", solution)
+
+
+# URL that points to Wikipedia or another similar explanation.
+# >>>>>>URL:https://courses.engr.illinois.edu/cs357/su2013/lectures/lecture07.pdf<<<<<#

linear_algebra/src/gaussian_elimination_pivoting/matrix.txt

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+5.0 -5.0 -3.0 4.0 -11.0
+1.0 -4.0 6.0 -4.0 -10.0
+-2.0 -5.0 4.0 -5.0 -12.0
+-3.0 -3.0 5.0 -5.0 8.0