算法系列-----矩阵（九）-------------矩阵SVD---奇异值分解

/*************************************************************************
 *  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());
      System.out.print("A = ");
      A.print(9, 6);

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

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

}

Jama-1.0.1.jar

直接下载：

http://download.csdn.net/detail/u014737138/8025225

A = 
   1.187774   1.576314   0.637323   0.995715   1.461993
   1.836872   2.681370   1.301304   1.485940   2.327313
   3.482730   4.907988   2.185064   2.871390   4.402124
   2.713190   3.884867   1.797739   2.218906   3.435112
   3.541166   4.990545   2.281509   2.902963   4.434988
   3.644364   4.970195   2.127232   3.025903   4.523168
   2.886252   3.979685   1.736969   2.387951   3.596824
   1.958339   2.795911   1.277497   1.606028   2.483787

A = U S V^T

U = 
   0.145799  -0.378915   0.027220  -0.863638  -0.048140
   0.238540   0.531337   0.312952  -0.070249   0.052043
   0.443415   0.015206  -0.694747  -0.030124   0.506162
   0.348559   0.347829  -0.150981   0.045055  -0.116842
   0.450236   0.219763   0.492038  -0.155941   0.238693
   0.454530  -0.554452   0.202501   0.469502  -0.005552
   0.362347  -0.253695   0.128220   0.016471  -0.278724
   0.251250   0.181149  -0.310327  -0.035153  -0.768394

Sigma = 
  18.680992   0.000000   0.000000   0.000000   0.000000
   0.000000   0.292309   0.000000   0.000000   0.000000
   0.000000   0.000000   0.035702   0.000000   0.000000
   0.000000   0.000000   0.000000   0.000000   0.000000
   0.000000   0.000000   0.000000   0.000000   0.000000

V = 
   0.422356  -0.332743   0.578485  -0.413839   0.452757
   0.591529   0.311928  -0.270772  -0.522598  -0.454279
   0.264617   0.756644   0.412612   0.405020   0.152242
   0.347810  -0.434221   0.311891   0.489681  -0.594489
   0.529826  -0.175855  -0.569660   0.389615   0.460486

rank = 3
condition number = 3.3032712102739668E16
2-norm = 18.68099151701797
singular values = 
  18.680992   0.292309   0.035702   0.000000   0.000000