Finding the pseudo-inverse of a matrix.

Here’s a Java program that finds the pseudo-inverse of a matrix:

  import Jama.Matrix;

    public class PseudoInverse {

    public static void main(String[] args) {

        double[][] data = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; // Example matrix data

        Matrix matrix = new Matrix(data);

        Matrix pseudoInverse = getPseudoInverse(matrix);

        // Print the pseudo-inverse matrix

        System.out.println("Pseudo-inverse of the matrix:");

        printMatrix(pseudoInverse);

    }

    public static Matrix getPseudoInverse(Matrix matrix) {

        int m = matrix.getRowDimension();

        int n = matrix.getColumnDimension();

        // Perform Singular Value Decomposition (SVD)

        Jama.SingularValueDecomposition svd = matrix.svd();

        // Get the singular values

        double[] singularValues = svd.getSingularValues();

      
        // Set a tolerance threshold to determine non-zero singular values

        double tolerance = Math.max(m, n) * singularValues[0] * 1e-15;

        // Invert the non-zero singular values

        for (int i = 0; i < singularValues.length; i++) {

            if (Math.abs(singularValues[i]) > tolerance) {

                singularValues[i] = 1.0 / singularValues[i];

            } else {

                singularValues[i] = 0.0;

            }
        }

        // Construct the pseudo-inverse matrix

        Matrix singularValueMatrix = Matrix.diag(singularValues);

        Matrix v = svd.getV();

        Matrix u = svd.getU();

        Matrix pseudoInverse = v.times(singularValueMatrix.transpose()).times(u.transpose());      

        return pseudoInverse;

    }

    public static void printMatrix(Matrix matrix) {

        int rows = matrix.getRowDimension();

        int cols = matrix.getColumnDimension();

        for (int i = 0; i < rows; i++) {

            for (int j = 0; j < cols; j++) {

                System.out.print(matrix.get(i, j) + " ");

            }

            System.out.println();

        }

    }

}

This program uses the `Jama` library, which provides functionality for performing matrix operations. The `getPseudoInverse` method takes a matrix as input, performs Singular Value Decomposition (SVD), and constructs the pseudo-inverse matrix based on the singular values. The `printMatrix` method is used to display the resulting pseudo-inverse matrix. In the example, the matrix `{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}` is used, but you can modify it with your desired matrix data.