/******************************************************************************
 *  Compilation:  javac -classpath .:jama.jar SVD.java
 *  Execution:    java  -classpath .:jama.jar SVD
 *  Dependencies: jama.jar
 *
 *  Test client for computing singular values of a matrix.
 *
 *       http://math.nist.gov/javanumerics/jama/
 *       http://math.nist.gov/javanumerics/jama/Jama-1.0.1.jar
 *
 ******************************************************************************/

import Jama.Matrix;
import Jama.SingularValueDecomposition;

public class SVD {
   public static void main(String[] args) {

      // create M-by-N matrix that doesn't have full rank
      int M = 8, N = 5;
      Matrix B = Matrix.random(5, 3);
      Matrix A = Matrix.random(M, N).times(B).times(B.transpose());
      StdOut.print("A = ");
      A.print(9, 6);

      // compute the singular vallue decomposition
      StdOut.println("A = U S V^T");
      StdOut.println();
      SingularValueDecomposition s = A.svd();
      StdOut.print("U = ");
      Matrix U = s.getU();
      U.print(9, 6);
      StdOut.print("Sigma = ");
      Matrix S = s.getS();
      S.print(9, 6);
      StdOut.print("V = ");
      Matrix V = s.getV();
      V.print(9, 6);
      StdOut.println("rank = " + s.rank());
      StdOut.println("condition number = " + s.cond());
      StdOut.println("2-norm = " + s.norm2());

      // print out singular values
      StdOut.print("singular values = ");
      Matrix svalues = new Matrix(s.getSingularValues(), 1);
      svalues.print(9, 6);
   }

}