singularvaluedecomposition.java

Weka

/*
 * This software is a cooperative product of The MathWorks and the National
 * Institute of Standards and Technology (NIST) which has been released to the
 * public domain. Neither The MathWorks nor NIST assumes any responsibility
 * whatsoever for its use by other parties, and makes no guarantees, expressed
 * or implied, about its quality, reliability, or any other characteristic.
 */

/*
 * SingularValueDecomposition.java
 * Copyright (C) 1999 The Mathworks and NIST
 *
 */

package weka.core.matrix;

import java.io.Serializable;

/** 
 * Singular Value Decomposition.
 * <P>
 * For an m-by-n matrix A with m &gt;= n, the singular value decomposition is an
 * m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n
 * orthogonal matrix V so that A = U*S*V'.
 * <P>
 * The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] &gt;=
 * sigma[1] &gt;= ... &gt;= sigma[n-1].
 * <P>
 * The singular value decompostion always exists, so the constructor will never
 * fail.  The matrix condition number and the effective numerical rank can be
 * computed from this decomposition.
 * <p/>
 * Adapted from the <a href="http://math.nist.gov/javanumerics/jama/" target="_blank">JAMA</a> package.
 *
 * @author The Mathworks and NIST 
 * @author Fracpete (fracpete at waikato dot ac dot nz)
 * @version $Revision: 1.4 $
 */
public class SingularValueDecomposition 
  implements Serializable {

  /** for serialization */
  private static final long serialVersionUID = -8738089610999867951L;
  
  /** 
   * Arrays for internal storage of U and V.
   * @serial internal storage of U.
   * @serial internal storage of V.
   */
  private double[][] U, V;

  /** 
   * Array for internal storage of singular values.
   * @serial internal storage of singular values.
   */
  private double[] s;

  /** 
   * Row and column dimensions.
   * @serial row dimension.
   * @serial column dimension.
   */
  private int m, n;

  /** 
   * Construct the singular value decomposition
   * @param Arg    Rectangular matrix
   */
  public SingularValueDecomposition(Matrix Arg) {

    // Derived from LINPACK code.
    // Initialize.
    double[][] A = Arg.getArrayCopy();
    m = Arg.getRowDimension();
    n = Arg.getColumnDimension();

    /* Apparently the failing cases are only a proper subset of (m<n), 
	 so let's not throw error.  Correct fix to come later?
    if (m<n) {
	  throw new IllegalArgumentException("Jama SVD only works for m >= n"); }
    */

    int nu = Math.min(m,n);
    s = new double [Math.min(m+1,n)];
    U = new double [m][nu];
    V = new double [n][n];
    double[] e = new double [n];
    double[] work = new double [m];
    boolean wantu = true;
    boolean wantv = true;

    // Reduce A to bidiagonal form, storing the diagonal elements
    // in s and the super-diagonal elements in e.

    int nct = Math.min(m-1,n);
    int nrt = Math.max(0,Math.min(n-2,m));
    for (int k = 0; k < Math.max(nct,nrt); k++) {
      if (k < nct) {

        // Compute the transformation for the k-th column and
        // place the k-th diagonal in s[k].
        // Compute 2-norm of k-th column without under/overflow.
        s[k] = 0;
        for (int i = k; i < m; i++) {
          s[k] = Maths.hypot(s[k],A[i][k]);
        }
        if (s[k] != 0.0) {
          if (A[k][k] < 0.0) {
            s[k] = -s[k];
          }
          for (int i = k; i < m; i++) {
            A[i][k] /= s[k];
          }
          A[k][k] += 1.0;
        }
        s[k] = -s[k];
      }
      for (int j = k+1; j < n; j++) {
        if ((k < nct) & (s[k] != 0.0))  {

          // Apply the transformation.

          double t = 0;
          for (int i = k; i < m; i++) {
            t += A[i][k]*A[i][j];
          }
          t = -t/A[k][k];
          for (int i = k; i < m; i++) {
            A[i][j] += t*A[i][k];
          }
        }

        // Place the k-th row of A into e for the
        // subsequent calculation of the row transformation.

        e[j] = A[k][j];
      }
      if (wantu & (k < nct)) {

        // Place the transformation in U for subsequent back
        // multiplication.

        for (int i = k; i < m; i++) {
          U[i][k] = A[i][k];
        }
      }
      if (k < nrt) {

        // Compute the k-th row transformation and place the
        // k-th super-diagonal in e[k].
        // Compute 2-norm without under/overflow.
        e[k] = 0;
        for (int i = k+1; i < n; i++) {
          e[k] = Maths.hypot(e[k],e[i]);
        }
        if (e[k] != 0.0) {
          if (e[k+1] < 0.0) {
            e[k] = -e[k];
          }
          for (int i = k+1; i < n; i++) {
            e[i] /= e[k];
          }
          e[k+1] += 1.0;
        }
        e[k] = -e[k];
        if ((k+1 < m) & (e[k] != 0.0)) {

          // Apply the transformation.

          for (int i = k+1; i < m; i++) {
            work[i] = 0.0;
          }
          for (int j = k+1; j < n; j++) {
            for (int i = k+1; i < m; i++) {
              work[i] += e[j]*A[i][j];
            }
          }
          for (int j = k+1; j < n; j++) {
            double t = -e[j]/e[k+1];
            for (int i = k+1; i < m; i++) {
              A[i][j] += t*work[i];
            }
          }
        }
        if (wantv) {

          // Place the transformation in V for subsequent
          // back multiplication.

          for (int i = k+1; i < n; i++) {
            V[i][k] = e[i];
          }
        }
      }
    }

    // Set up the final bidiagonal matrix or order p.

    int p = Math.min(n,m+1);
    if (nct < n) {
      s[nct] = A[nct][nct];
    }
    if (m < p) {
      s[p-1] = 0.0;
    }
    if (nrt+1 < p) {
      e[nrt] = A[nrt][p-1];
    }
    e[p-1] = 0.0;

    // If required, generate U.

    if (wantu) {
      for (int j = nct; j < nu; j++) {
        for (int i = 0; i < m; i++) {
          U[i][j] = 0.0;
        }
        U[j][j] = 1.0;
      }
      for (int k = nct-1; k >= 0; k--) {
        if (s[k] != 0.0) {
          for (int j = k+1; j < nu; j++) {
            double t = 0;
            for (int i = k; i < m; i++) {
              t += U[i][k]*U[i][j];
            }
            t = -t/U[k][k];
            for (int i = k; i < m; i++) {
              U[i][j] += t*U[i][k];
            }
          }
          for (int i = k; i < m; i++ ) {
            U[i][k] = -U[i][k];
          }
          U[k][k] = 1.0 + U[k][k];
          for (int i = 0; i < k-1; i++) {
            U[i][k] = 0.0;
          }
        } else {
          for (int i = 0; i < m; i++) {
            U[i][k] = 0.0;
          }
          U[k][k] = 1.0;
        }
      }
    }

    // If required, generate V.

    if (wantv) {
      for (int k = n-1; k >= 0; k--) {
        if ((k < nrt) & (e[k] != 0.0)) {
          for (int j = k+1; j < nu; j++) {
            double t = 0;
            for (int i = k+1; i < n; i++) {
              t += V[i][k]*V[i][j];
            }
            t = -t/V[k+1][k];
            for (int i = k+1; i < n; i++) {
              V[i][j] += t*V[i][k];
            }
          }
        }
        for (int i = 0; i < n; i++) {
          V[i][k] = 0.0;
        }
        V[k][k] = 1.0;
      }
    }

    // Main iteration loop for the singular values.

    int pp = p-1;
    int iter = 0;
    double eps = Math.pow(2.0,-52.0);
    double tiny = Math.pow(2.0,-966.0);
    while (p > 0) {
      int k,kase;

      // Here is where a test for too many iterations would go.

      // This section of the program inspects for