Java Matrix Invert invert(double a[][])

Description

invert

License

Open Source License

Declaration

public static double[][] invert(double a[][]) 

Method Source Code

//package com.java2s;
//License from project: Open Source License 

public class Main {
    public static double[][] invert(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;// ww  w.jav a 2s.  c  o m
        }

        // Transform the matrix into an upper triangle
        gaussian(a, index);

        // Update the matrix b[i][j] with the ratios stored
        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];
                }
            }
        }

        // Perform backward substitutions
        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];

        // Initialize the index
        for (int i = 0; i < n; ++i) {
            index[i] = i;
        }

        // Find the rescaling factors, one from each row
        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;
        }

        // Search the pivoting element from each column
        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;
                }
            }

            // Interchange rows according to the pivoting order
            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];

                // Record pivoting ratios below the diagonal
                a[index[i]][j] = pj;

                // Modify other elements accordingly
                for (int l = j + 1; l < n; ++l) {
                    a[index[i]][l] -= pj * a[index[j]][l];
                }
            }
        }
    }
}

Related

1. invert(final int[][] input)
2. invert(float[] mat)
3. invert2x2(final double[][] src, final double[][] dest)
4. invert3x3(float[] mat)