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Author: Sachwin-Kohli

Maths/Gaussian.java

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+/**
+ * \file
+ * \brief [Gaussian elimination
+ * method](https://en.wikipedia.org/wiki/Gaussian_elimination)
+ */
+import java.util.*;
+
+/** Main function */
+public class Gaussian {
+
+  public static void main(String[] args) {
+
+
+    int mat_size, i, j, step;
+    Scanner sc = new Scanner(System.in);
+    
+    System.out.println("Matrix Size : ");
+    mat_size = sc.nextInt();
+
+    double [][] mat = new double[mat_size+1][mat_size+1];
+    double [][] x = new double[mat_size][mat_size+1];
+
+    System.out.println("Enter value of the matrix");
+    System.out.println(' ');
+    for (i = 0; i < mat_size; i++) {
+        for (j = 0; j <= mat_size; j++) {
+            mat[i][j] = sc.nextInt();
+        }
+    }
+
+    // perform Gaussian elimination
+    for (step = 0; step < mat_size - 1; step++) {
+        for (i = step; i < mat_size - 1; i++) {
+            double a = (mat[i + 1][step] / mat[step][step]);
+
+            for (j = step; j <= mat_size; j++)
+                mat[i + 1][j] = mat[i + 1][j] - (a * mat[step][j]);
+        }
+    }
+    
+     System.out.println("Matrix using Gaussian Elimination method: ");
+     System.out.println(" ");
+    for (i = 0; i < mat_size; i++) {
+        for (j = 0; j <= mat_size; j++) {
+            x[i][j] = mat[i][j];
+            System.out.print(mat[i][j] + " ");
+        }
+        System.out.println();
+    }
+    System.out.println( "Value of the Gaussian Elimination method: ");
+    System.out.println(" ");
+    
+    for (i = mat_size - 1; i >= 0; i--) {
+        double sum = 0;
+        for (j = mat_size - 1; j > i; j--) {
+            x[i][j] = x[j][j] * x[i][j];
+            sum = x[i][j] + sum;
+        }
+        if (x[i][i] == 0){
+            x[i][i] = 0;
+        }
+        else{
+            x[i][i] = (x[i][mat_size] - sum) / (x[i][i]);
+        }
+        System.out.print("x" + i + "=" + x[i][i]);
+        System.out.println(" ");
+    }
+
+}
+}