132 lines
3.9 KiB
Java
132 lines
3.9 KiB
Java
package Misc;
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import java.util.Scanner;
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/*
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* Wikipedia link : https://en.wikipedia.org/wiki/Invertible_matrix
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*
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* Here we use gauss elimination method to find the inverse of a given matrix.
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* To understand gauss elimination method to find inverse of a matrix: https://www.sangakoo.com/en/unit/inverse-matrix-method-of-gaussian-elimination
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*
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* We can also find the inverse of a matrix
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*/
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public class InverseOfMatrix
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{
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public static void main(String argv[])
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{
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Scanner input = new Scanner(System.in);
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System.out.println("Enter the matrix size (Square matrix only): ");
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int n = input.nextInt();
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double a[][]= new double[n][n];
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System.out.println("Enter the elements of matrix: ");
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for(int i=0; i<n; i++)
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for(int j=0; j<n; j++)
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a[i][j] = input.nextDouble();
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double d[][] = invert(a);
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System.out.println();
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System.out.println("The inverse is: ");
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for (int i=0; i<n; ++i)
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{
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for (int j=0; j<n; ++j)
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{
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System.out.print(d[i][j]+" ");
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}
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System.out.println();
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}
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input.close();
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}
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public static double[][] invert(double a[][])
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{
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int n = a.length;
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double x[][] = new double[n][n];
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double b[][] = new double[n][n];
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int index[] = new int[n];
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for (int i=0; i<n; ++i)
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b[i][i] = 1;
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// Transform the matrix into an upper triangle
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gaussian(a, index);
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// Update the matrix b[i][j] with the ratios stored
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for (int i=0; i<n-1; ++i)
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for (int j=i+1; j<n; ++j)
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for (int k=0; k<n; ++k)
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b[index[j]][k]
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-= a[index[j]][i]*b[index[i]][k];
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// Perform backward substitutions
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for (int i=0; i<n; ++i)
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{
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x[n-1][i] = b[index[n-1]][i]/a[index[n-1]][n-1];
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for (int j=n-2; j>=0; --j)
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{
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x[j][i] = b[index[j]][i];
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for (int k=j+1; k<n; ++k)
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{
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x[j][i] -= a[index[j]][k]*x[k][i];
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}
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x[j][i] /= a[index[j]][j];
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}
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}
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return x;
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}
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// Method to carry out the partial-pivoting Gaussian
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// elimination. Here index[] stores pivoting order.
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public static void gaussian(double a[][], int index[])
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{
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int n = index.length;
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double c[] = new double[n];
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// Initialize the index
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for (int i=0; i<n; ++i)
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index[i] = i;
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// Find the rescaling factors, one from each row
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for (int i=0; i<n; ++i)
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{
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double c1 = 0;
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for (int j=0; j<n; ++j)
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{
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double c0 = Math.abs(a[i][j]);
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if (c0 > c1) c1 = c0;
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}
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c[i] = c1;
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}
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// Search the pivoting element from each column
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int k = 0;
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for (int j=0; j<n-1; ++j)
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{
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double pi1 = 0;
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for (int i=j; i<n; ++i)
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{
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double pi0 = Math.abs(a[index[i]][j]);
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pi0 /= c[index[i]];
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if (pi0 > pi1)
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{
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pi1 = pi0;
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k = i;
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}
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}
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// Interchange rows according to the pivoting order
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int itmp = index[j];
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index[j] = index[k];
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index[k] = itmp;
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for (int i=j+1; i<n; ++i)
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{
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double pj = a[index[i]][j]/a[index[j]][j];
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// Record pivoting ratios below the diagonal
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a[index[i]][j] = pj;
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// Modify other elements accordingly
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for (int l=j+1; l<n; ++l)
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a[index[i]][l] -= pj*a[index[j]][l];
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}
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}
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}
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}
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