From fde73f129bf86ce9759cee616d8663f7d85806f5 Mon Sep 17 00:00:00 2001
From: sushant-sinha <sinhasushant04@gmail.com>
Date: Sat, 2 Oct 2021 01:44:25 +0530
Subject: [PATCH 1/2] Matrix Inversion

---
 Java/inverse of a matrix.java | 138 ++++++++++++++++++++++++++++++++++
 1 file changed, 138 insertions(+)
 create mode 100644 Java/inverse of a matrix.java

diff --git a/Java/inverse of a matrix.java b/Java/inverse of a matrix.java
new file mode 100644
index 00000000..e018048c
--- /dev/null
+++ b/Java/inverse of a matrix.java	
@@ -0,0 +1,138 @@
+// inverse of a matrix using Gauss Jordan Method
+
+import java.util.Scanner;
+ 
+public class matInv{
+
+    public static void main(String argv[]){
+
+        Scanner sc = new Scanner(System.in);
+
+        // get the dimensions of the matrix
+
+        System.out.println("Enter the size of square matrix ( 'n' of an 'nxn' matrix): ");
+
+        int n = sc.nextInt();
+
+        double a[][]= new double[n][n];
+
+        System.out.println("\nStart entering the elements sequentially: ");
+
+        // populate the matrix
+
+        for(int i=0; i<n; i++)
+            for(int j=0; j<n; j++)
+                a[i][j] = sc.nextDouble();
+ 
+        // call for inverting the matrix and storing the returned output in matrix 'd'
+        double ans[][] = matrixInversion(a);
+ 
+        System.out.println("\nInverse of the given "+n+"x"+n+" matrix is: ");
+        
+        for (int i=0; i<n; ++i){
+
+            for (int j=0; j<n; ++j){
+                System.out.print(ans[i][j]+"  ");
+            }
+
+            System.out.println();
+        }
+    }   
+ 
+    public static double[][] matrixInversion(double a[][]){
+
+        int n = a.length;
+
+        double x[][] = new double[n][n];
+        double b[][] = new double[n][n];
+
+        int index[] = new int[n];
+
+        for (int i=0; i<n; ++i){
+            b[i][i] = 1;
+        }
+ 
+        // matrix is coverted to an upper triangle matrix ( all elements are zeroes below the diagonal)
+        gaussian(a, index);
+ 
+        // update the matrix
+
+        for (int i=0; i<n-1; ++i)
+            for (int j=i+1; j<n; ++j)
+                for (int k=0; k<n; ++k)
+                    b[index[j]][k]-= a[index[j]][i]*b[index[i]][k];
+ 
+        // back substitution
+
+        for (int i=0; i<n; ++i) {
+
+            x[n-1][i] = b[index[n-1]][i]/a[index[n-1]][n-1];
+            
+            for (int j=n-2; j>=0; --j){
+
+                x[j][i] = b[index[j]][i];
+
+                for (int k=j+1; k<n; ++k){
+                    x[j][i] -= a[index[j]][k]*x[k][i];
+                }
+
+                x[j][i] /= a[index[j]][j];
+            }
+        }
+
+        return x;
+    }
+
+    public static void gaussian(double a[][], int index[]){
+
+        int n = index.length;
+        double c[] = new double[n];
+ 
+        for (int i=0; i<n; ++i) 
+            index[i] = i;
+ 
+        for (int i=0; i<n; ++i){
+
+            double c1 = 0;
+            
+            for (int j=0; j<n; ++j){
+
+                double c0 = Math.abs(a[i][j]);
+                if (c0 > c1) c1 = c0;
+            }
+
+            c[i] = c1;
+        }
+
+        int k = 0;
+
+        for (int j=0; j<n-1; ++j){
+
+            double pi1 = 0;
+
+            for (int i=j; i<n; ++i){
+
+                double pi0 = Math.abs(a[index[i]][j]);
+                pi0 /= c[index[i]];
+
+                if (pi0 > pi1){
+                    pi1 = pi0;
+                    k = i;
+                }
+            }
+ 
+            int itmp = index[j];
+            index[j] = index[k];
+            index[k] = itmp;
+            for (int i=j+1; i<n; ++i){
+
+                double pj = a[index[i]][j]/a[index[j]][j];
+ 
+                a[index[i]][j] = pj;
+ 
+                for (int l=j+1; l<n; ++l)
+                    a[index[i]][l] -= pj*a[index[j]][l];
+            }
+        }
+    }
+}
\ No newline at end of file

From e94d3381d0907b943b6d9253f6ae8fd0d3425076 Mon Sep 17 00:00:00 2001
From: sushant-sinha <sinhasushant04@gmail.com>
Date: Sat, 2 Oct 2021 01:48:04 +0530
Subject: [PATCH 2/2] Matrix Inversion 1

---
 Java/inverse of a matrix.java | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Java/inverse of a matrix.java b/Java/inverse of a matrix.java
index e018048c..163ffd0e 100644
--- a/Java/inverse of a matrix.java	
+++ b/Java/inverse of a matrix.java	
@@ -1,5 +1,3 @@
-// inverse of a matrix using Gauss Jordan Method
-
 import java.util.Scanner;
  
 public class matInv{
@@ -94,7 +92,7 @@ public static void gaussian(double a[][], int index[]){
         for (int i=0; i<n; ++i){
 
             double c1 = 0;
-            
+
             for (int j=0; j<n; ++j){
 
                 double c0 = Math.abs(a[i][j]);