levenbergmarquardtestimator.java

Apache的common math数学软件包

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package org.apache.commons.math.estimation;

import java.io.Serializable;
import java.util.Arrays;


/** 
 * This class solves a least squares problem.
 *
 * <p>This implementation <em>should</em> work even for over-determined systems
 * (i.e. systems having more variables than equations). Over-determined systems
 * are solved by ignoring the variables which have the smallest impact according
 * to their jacobian column norm. Only the rank of the matrix and some loop bounds
 * are changed to implement this. This feature has undergone only basic testing
 * for now and should still be considered experimental.</p>
 *
 * <p>The resolution engine is a simple translation of the MINPACK <a
 * href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor
 * changes. The changes include the over-determined resolution and the Q.R.
 * decomposition which has been rewritten following the algorithm described in the
 * P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle
 * appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986. The
 * redistribution policy for MINPACK is available <a
 * href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it
 * is reproduced below.</p>
 *
 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 * <tr><td>
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 *    All rights reserved
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 * modification, are permitted provided that the following conditions
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 * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran)
 * @author Burton S. Garbow (original fortran)
 * @author Kenneth E. Hillstrom (original fortran)
 * @author Jorge J. More (original fortran)

 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
 * @since 1.2
 *
 */
public class LevenbergMarquardtEstimator extends AbstractEstimator implements Serializable {

  /** 
   * Build an estimator for least squares problems.
   * <p>The default values for the algorithm settings are:
   *   <ul>
   *    <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li>
   *    <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li>
   *    <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li>
   *    <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li>
   *    <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li>
   *   </ul>
   * </p>
   */
  public LevenbergMarquardtEstimator() {

    // set up the superclass with a default  max cost evaluations setting
    setMaxCostEval(1000);

    // default values for the tuning parameters
    setInitialStepBoundFactor(100.0);
    setCostRelativeTolerance(1.0e-10);
    setParRelativeTolerance(1.0e-10);
    setOrthoTolerance(1.0e-10);

  }

  /** 
   * Set the positive input variable used in determining the initial step bound.
   * This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag*x if nonzero,
   * or else to initialStepBoundFactor itself. In most cases factor should lie
   * in the interval (0.1, 100.0). 100.0 is a generally recommended value
   * 
   * @param initialStepBoundFactor initial step bound factor
   * @see #estimate
   */
  public void setInitialStepBoundFactor(double initialStepBoundFactor) {
    this.initialStepBoundFactor = initialStepBoundFactor;
  }

  /** 
   * Set the desired relative error in the sum of squares.
   * 
   * @param costRelativeTolerance desired relative error in the sum of squares
   * @see #estimate
   */
  public void setCostRelativeTolerance(double costRelativeTolerance) {
    this.costRelativeTolerance = costRelativeTolerance;
  }

  /** 
   * Set the desired relative error in the approximate solution parameters.
   * 
   * @param parRelativeTolerance desired relative error
   * in the approximate solution parameters
   * @see #estimate
   */
  public void setParRelativeTolerance(double parRelativeTolerance) {
    this.parRelativeTolerance = parRelativeTolerance;
  }

  /** 
   * Set the desired max cosine on the orthogonality.
   * 
   * @param orthoTolerance desired max cosine on the orthogonality
   * between the function vector and the columns of the jacobian
   * @see #estimate
   */
  public void setOrthoTolerance(double orthoTolerance) {
    this.orthoTolerance = orthoTolerance;
  }

  /** 
   * Solve an estimation problem using the Levenberg-Marquardt algorithm.
   * <p>The algorithm used is a modified Levenberg-Marquardt one, based
   * on the MINPACK <a href="http://www.netlib.org/minpack/lmder.f">lmder</a>
   * routine. The algorithm settings must have been set up before this method
   * is called with the {@link #setInitialStepBoundFactor},
   * {@link #setMaxCostEval}, {@link #setCostRelativeTolerance},
   * {@link #setParRelativeTolerance} and {@link #setOrthoTolerance} methods.
   * If these methods have not been called, the default values set up by the
   * {@link #LevenbergMarquardtEstimator() constructor} will be used.</p>
   * <p>The authors of the original fortran function are:</p>
   * <ul>
   *   <li>Argonne National Laboratory. MINPACK project. March 1980</li>
   *   <li>Burton  S. Garbow</li>
   *   <li>Kenneth E. Hillstrom</li>
   *   <li>Jorge   J. More</li>
   *   </ul>
   * <p>Luc Maisonobe did the Java translation.</p>
   * 
   * @param problem estimation problem to solve
   * @exception EstimationException if convergence cannot be
   * reached with the specified algorithm settings or if there are more variables
   * than equations
   * @see #setInitialStepBoundFactor
   * @see #setCostRelativeTolerance
   * @see #setParRelativeTolerance
   * @see #setOrthoTolerance
   */
  public void estimate(EstimationProblem problem)
    throws EstimationException {

    initializeEstimate(problem);

    // arrays shared with the other private methods
    solvedCols  = Math.min(rows, cols);
    diagR       = new double[cols];
    jacNorm     = new double[cols];
    beta        = new double[cols];
    permutation = new int[cols];
    lmDir       = new double[cols];

    // local variables
    double   delta   = 0, xNorm = 0;
    double[] diag    = new double[cols];
    double[] oldX    = new double[cols];
    double[] oldRes  = new double[rows];
    double[] work1   = new double[cols];
    double[] work2   = new double[cols];
    double[] work3   = new double[cols];

    // evaluate the function at the starting point and calculate its norm
    updateResidualsAndCost();
    
    // outer loop
    lmPar = 0;
    boolean firstIteration = true;
    while (true) {

      // compute the Q.R. decomposition of the jacobian matrix
      updateJacobian();
      qrDecomposition();

      // compute Qt.res
      qTy(residuals);

      // now we don't need Q anymore,
      // so let jacobian contain the R matrix with its diagonal elements
      for (int k = 0; k < solvedCols; ++k) {
        int pk = permutation[k];
        jacobian[k * cols + pk] = diagR[pk];
      }

      if (firstIteration) {

        // scale the variables according to the norms of the columns
        // of the initial jacobian
        xNorm = 0;
        for (int k = 0; k < cols; ++k) {
          double dk = jacNorm[k];
          if (dk == 0) {
            dk = 1.0;
          }
          double xk = dk * parameters[k].getEstimate();
          xNorm  += xk * xk;
          diag[k] = dk;
        }
        xNorm = Math.sqrt(xNorm);
        
        // initialize the step bound delta
        delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);
 
      }

      // check orthogonality between function vector and jacobian columns
      double maxCosine = 0;
      if (cost != 0) {
        for (int j = 0; j < solvedCols; ++j) {
          int    pj = permutation[j];
          double s  = jacNorm[pj];
          if (s != 0) {
            double sum = 0;
            for (int i = 0, index = pj; i <= j; ++i, index += cols) {
              sum += jacobian[index] * residuals[i];
            }
            maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));
          }
        }
      }
      if (maxCosine <= orthoTolerance) {
        return;
      }

      // rescale if necessary
      for (int j = 0; j < cols; ++j) {
        diag[j] = Math.max(diag[j], jacNorm[j]);
      }

      // inner loop