Examples with SingularValueDecomposition org.apache.ignite.ml.math.decompositions.SingularValueDecomposition used on opensource projects

Example 1 with SingularValueDecomposition

use of org.apache.ignite.ml.math.decompositions.SingularValueDecomposition in project ignite by apache.

the class SingularValueDecompositionExample method main.

/**
     * Executes example.
     *
     * @param args Command line arguments, none required.
     */
public static void main(String[] args) {
    System.out.println(">>> Singular value decomposition (SVD) example started.");
    // Let's compute a SVD of (l x k) matrix m. This decomposition can be thought as extension of EigenDecomposition to
    // rectangular matrices. The factorization we get is following:
    // m = u * s * v^{*}, where
    // u is a real or complex unitary matrix
    // s is a rectangular diagonal matrix with non-negative real numbers on diagonal (this numbers are singular values of m)
    // v is a real or complex unitary matrix
    // If m is real then u and v are also real.
    // Complex case is not supported for the moment.
    DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] { { 1.0d, 0.0d, 0.0d, 0.0d, 2.0d }, { 0.0d, 0.0d, 3.0d, 0.0d, 0.0d }, { 0.0d, 0.0d, 0.0d, 0.0d, 0.0d }, { 0.0d, 2.0d, 0.0d, 0.0d, 0.0d } });
    System.out.println("\n>>> Matrix m for decomposition: ");
    Tracer.showAscii(m);
    SingularValueDecomposition dec = new SingularValueDecomposition(m);
    System.out.println("\n>>> Made decomposition m = u * s * v^{*}.");
    System.out.println(">>> Matrix u is ");
    Tracer.showAscii(dec.getU());
    System.out.println(">>> Matrix s is ");
    Tracer.showAscii(dec.getS());
    System.out.println(">>> Matrix v is ");
    Tracer.showAscii(dec.getV());
    // This decomposition can in particular help with solving problem of finding x minimizing 2-norm of m x such
    // that 2-norm of x is 1. It appears that it is the right singular vector corresponding to minimal singular
    // value, which is always last.
    System.out.println("\n>>> Vector x minimizing 2-norm of m x such that 2 norm of x is 1: ");
    Tracer.showAscii(dec.getV().viewColumn(dec.getSingularValues().length - 1));
    System.out.println("\n>>> Singular value decomposition (SVD) example completed.");
}