From ca1e0ab93d81af25c22b8b7a197958346f5ec865 Mon Sep 17 00:00:00 2001
From: Stefan Sava <stefansava21@gmail.com>
Date: Sun, 21 Oct 2018 10:50:37 +0300
Subject: [PATCH] Inverse of a matrix using GaussJordan in python

---
 GaussJordan.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 GaussJordan.py

diff --git a/GaussJordan.py b/GaussJordan.py
new file mode 100644
index 0000000..a4e369d
--- /dev/null
+++ b/GaussJordan.py
@@ -0,0 +1,43 @@
+import numpy as np
+# calculate the inverse of the matrix A using Gauss-Jordan algorithm
+def GaussJordan (A):
+    (n, n) = A.shape
+    B = np.eye(n)
+
+    # Assume A has an inverse matrix
+    success = 1
+
+    if np.linalg.det(A) == 0:
+        # A cannot be reversed
+        B = np.empty(n)
+        success = 0
+        return
+
+    # merge the two matrices
+    Ae = np.concatenate((A, B.T), axis=1)
+    for i in range (0, n):
+        if Ae[i, i] == 0:
+            B = np.empty(n)
+            success = 0
+            return
+         # make the pivot position to one (as in the eye matrix)
+        Ae[i, :] = Ae[i, :] / Ae[i, i]
+
+        #form zeros above and under the main diagonal in the
+        # first half and calculate the inverse in the second half
+        for j in range(0, n):
+            if i != j:
+                Ae[j, :] = Ae[j, :] - Ae[i, :] * Ae[j, i]
+
+    #extract the inverse of matrix A from the augmented matrix
+    B = Ae[:, n : 2 * n ]
+    return (B, success)
+
+
+# example for a 4x4 matrix
+A = np.random.rand(4,4)
+(inv, success) = GaussJordan(A)
+print "The inverse using Gauss-Jordan is:"
+print inv
+print "The inverse using inv from linalg is:"
+print np.linalg.inv(A)
\ No newline at end of file