You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@commons.apache.org by lu...@apache.org on 2009/03/15 20:11:06 UTC
svn commit: r754727 [1/3] - in /commons/proper/math/trunk/src:
java/org/apache/commons/math/optimization/
java/org/apache/commons/math/optimization/general/
test/org/apache/commons/math/optimization/general/
Author: luc
Date: Sun Mar 15 19:11:02 2009
New Revision: 754727
URL: http://svn.apache.org/viewvc?rev=754727&view=rev
Log:
adapted old Levenberg-Marquardt estimator to new top level optimizers API
Added:
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java (with props)
commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizerTest.java
- copied, changed from r753644, commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/LevenbergMarquardtEstimatorTest.java
Removed:
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractEstimator.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/EstimatedParameter.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/EstimationProblem.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/Estimator.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/GaussNewtonEstimator.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtEstimator.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/SimpleEstimationProblem.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/WeightedMeasurement.java
commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/EstimatedParameterTest.java
commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/LevenbergMarquardtEstimatorTest.java
commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/WeightedMeasurementTest.java
Modified:
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java
commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java
commons/proper/math/trunk/src/test/org/apache/commons/math/optimization/general/MinpackTest.java
Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java?rev=754727&r1=754726&r2=754727&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java (original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/VectorialDifferentiableOptimizer.java Sun Mar 15 19:11:02 2009
@@ -60,7 +60,17 @@
* </p>
* @return number of evaluations of the objective function
*/
- int getEvaluations();
+ int getEvaluations();
+
+ /** Get the number of evaluations of the objective function jacobian .
+ * <p>
+ * The number of evaluation correspond to the last call to the
+ * {@link #optimize(ObjectiveFunction, GoalType, double[]) optimize}
+ * method. It is 0 if the method has not been called yet.
+ * </p>
+ * @return number of evaluations of the objective function jacobian
+ */
+ int getJacobianEvaluations();
/** Set the convergence checker.
* @param checker object to use to check for convergence
Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java?rev=754727&r1=754726&r2=754727&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java (original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/AbstractLeastSquaresOptimizer.java Sun Mar 15 19:11:02 2009
@@ -30,8 +30,8 @@
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
- * Base class for implementing estimators.
- * <p>This base class handles the boilerplates methods associated to thresholds
+ * Base class for implementing least squares optimizers.
+ * <p>This base class handles the boilerplate methods associated to thresholds
* settings, jacobian and error estimation.</p>
* @version $Revision$ $Date$
* @since 1.2
@@ -61,8 +61,8 @@
* Jacobian matrix.
* <p>This matrix is in canonical form just after the calls to
* {@link #updateJacobian()}, but may be modified by the solver
- * in the derived class (the {@link LevenbergMarquardtEstimator
- * Levenberg-Marquardt estimator} does this).</p>
+ * in the derived class (the {@link LevenbergMarquardtOptimizer
+ * Levenberg-Marquardt optimizer} does this).</p>
*/
protected double[][] jacobian;
@@ -87,6 +87,9 @@
/** Current objective function value. */
protected double[] objective;
+ /** Current residuals. */
+ protected double[] residuals;
+
/** Cost value (square root of the sum of the residuals). */
protected double cost;
@@ -115,6 +118,11 @@
}
/** {@inheritDoc} */
+ public int getJacobianEvaluations() {
+ return jacobianEvaluations;
+ }
+
+ /** {@inheritDoc} */
public void setConvergenceChecker(VectorialConvergenceChecker checker) {
this.checker = checker;
}
@@ -175,7 +183,8 @@
}
cost = 0;
for (int i = 0, index = 0; i < rows; i++, index += cols) {
- final double residual = objective[i] - target[i];
+ final double residual = target[i] - objective[i];
+ residuals[i] = residual;
cost += weights[i] * residual * residual;
}
cost = Math.sqrt(cost);
@@ -186,7 +195,7 @@
* Get the Root Mean Square value.
* Get the Root Mean Square value, i.e. the root of the arithmetic
* mean of the square of all weighted residuals. This is related to the
- * criterion that is minimized by the estimator as follows: if
+ * criterion that is minimized by the optimizer as follows: if
* <em>c</em> if the criterion, and <em>n</em> is the number of
* measurements, then the RMS is <em>sqrt (c/n)</em>.
*
@@ -195,7 +204,7 @@
public double getRMS() {
double criterion = 0;
for (int i = 0; i < rows; ++i) {
- final double residual = objective[i] - target[i];
+ final double residual = residuals[i];
criterion += weights[i] * residual * residual;
}
return Math.sqrt(criterion / rows);
@@ -208,14 +217,14 @@
public double getChiSquare() {
double chiSquare = 0;
for (int i = 0; i < rows; ++i) {
- final double residual = objective[i] - target[i];
+ final double residual = residuals[i];
chiSquare += residual * residual / weights[i];
}
return chiSquare;
}
/**
- * Get the covariance matrix of unbound estimated parameters.
+ * Get the covariance matrix of optimized parameters.
* @return covariance matrix
* @exception ObjectiveException if the function jacobian cannot
* be evaluated
@@ -231,12 +240,10 @@
// compute transpose(J).J, avoiding building big intermediate matrices
double[][] jTj = new double[cols][cols];
for (int i = 0; i < cols; ++i) {
- final double[] ji = jacobian[i];
for (int j = i; j < cols; ++j) {
- final double[] jj = jacobian[j];
double sum = 0;
for (int k = 0; k < rows; ++k) {
- sum += ji[k] * jj[k];
+ sum += jacobian[k][i] * jacobian[k][j];
}
jTj[i][j] = sum;
jTj[j][i] = sum;
@@ -255,9 +262,9 @@
}
/**
- * Guess the errors in unbound estimated parameters.
+ * Guess the errors in optimized parameters.
* <p>Guessing is covariance-based, it only gives rough order of magnitude.</p>
- * @return errors in estimated parameters
+ * @return errors in optimized parameters
* @exception ObjectiveException if the function jacobian cannot b evaluated
* @exception OptimizationException if the covariances matrix cannot be computed
* or the number of degrees of freedom is not positive (number of measurements
@@ -299,6 +306,7 @@
this.target = target;
this.weights = weights;
this.variables = startPoint.clone();
+ this.residuals = new double[target.length];
// arrays shared with the other private methods
rows = target.length;
Added: commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java?rev=754727&view=auto
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java (added)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java Sun Mar 15 19:11:02 2009
@@ -0,0 +1,838 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.optimization.general;
+
+import java.util.Arrays;
+
+import org.apache.commons.math.optimization.ObjectiveException;
+import org.apache.commons.math.optimization.OptimizationException;
+import org.apache.commons.math.optimization.VectorialPointValuePair;
+
+
+/**
+ * This class solves a least squares problem using the Levenberg-Marquardt algorithm.
+ *
+ * <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.</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 numérique matricielle
+ * appliquée à l'art de l'ingénieur</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>
+ * Minpack Copyright Notice (1999) University of Chicago.
+ * All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ * <li>Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ * copyright notice, this list of conditions and the following
+ * disclaimer in the documentation and/or other materials provided
+ * with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ * must include the following acknowledgment:
+ * <code>This product includes software developed by the University of
+ * Chicago, as Operator of Argonne National Laboratory.</code>
+ * Alternately, this acknowledgment may appear in the software itself,
+ * if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ * BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+
+ * @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 $Revision$ $Date$
+ * @since 2.0
+ *
+ */
+public class LevenbergMarquardtOptimizer extends AbstractLeastSquaresOptimizer {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = 8851282236194244323L;
+
+ /** Number of solved variables. */
+ private int solvedCols;
+
+ /** Diagonal elements of the R matrix in the Q.R. decomposition. */
+ private double[] diagR;
+
+ /** Norms of the columns of the jacobian matrix. */
+ private double[] jacNorm;
+
+ /** Coefficients of the Householder transforms vectors. */
+ private double[] beta;
+
+ /** Columns permutation array. */
+ private int[] permutation;
+
+ /** Rank of the jacobian matrix. */
+ private int rank;
+
+ /** Levenberg-Marquardt parameter. */
+ private double lmPar;
+
+ /** Parameters evolution direction associated with lmPar. */
+ private double[] lmDir;
+
+ /** Positive input variable used in determining the initial step bound. */
+ private double initialStepBoundFactor;
+
+ /** Desired relative error in the sum of squares. */
+ private double costRelativeTolerance;
+
+ /** Desired relative error in the approximate solution parameters. */
+ private double parRelativeTolerance;
+
+ /** Desired max cosine on the orthogonality between the function vector
+ * and the columns of the jacobian. */
+ private double orthoTolerance;
+
+ /**
+ * Build an optimizer 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 LevenbergMarquardtOptimizer() {
+
+ // set up the superclass with a default max cost evaluations setting
+ setMaxEvaluations(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
+ */
+ 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
+ */
+ 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
+ */
+ 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
+ */
+ public void setOrthoTolerance(double orthoTolerance) {
+ this.orthoTolerance = orthoTolerance;
+ }
+
+ /** {@inheritDoc} */
+ protected VectorialPointValuePair doOptimize()
+ throws ObjectiveException, OptimizationException, IllegalArgumentException {
+
+ // 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][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 * variables[k];
+ 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; i <= j; ++i) {
+ sum += jacobian[i][pj] * residuals[i];
+ }
+ maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));
+ }
+ }
+ }
+ if (maxCosine <= orthoTolerance) {
+ // convergence has been reached
+ return new VectorialPointValuePair(variables, objective);
+ }
+
+ // rescale if necessary
+ for (int j = 0; j < cols; ++j) {
+ diag[j] = Math.max(diag[j], jacNorm[j]);
+ }
+
+ // inner loop
+ for (double ratio = 0; ratio < 1.0e-4;) {
+
+ // save the state
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ oldX[pj] = variables[pj];
+ }
+ double previousCost = cost;
+ double[] tmpVec = residuals;
+ residuals = oldRes;
+ oldRes = tmpVec;
+
+ // determine the Levenberg-Marquardt parameter
+ determineLMParameter(oldRes, delta, diag, work1, work2, work3);
+
+ // compute the new point and the norm of the evolution direction
+ double lmNorm = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ lmDir[pj] = -lmDir[pj];
+ variables[pj] = oldX[pj] + lmDir[pj];
+ double s = diag[pj] * lmDir[pj];
+ lmNorm += s * s;
+ }
+ lmNorm = Math.sqrt(lmNorm);
+
+ // on the first iteration, adjust the initial step bound.
+ if (firstIteration) {
+ delta = Math.min(delta, lmNorm);
+ }
+
+ // evaluate the function at x + p and calculate its norm
+ updateResidualsAndCost();
+
+ // compute the scaled actual reduction
+ double actRed = -1.0;
+ if (0.1 * cost < previousCost) {
+ double r = cost / previousCost;
+ actRed = 1.0 - r * r;
+ }
+
+ // compute the scaled predicted reduction
+ // and the scaled directional derivative
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ double dirJ = lmDir[pj];
+ work1[j] = 0;
+ for (int i = 0; i <= j; ++i) {
+ work1[i] += jacobian[i][pj] * dirJ;
+ }
+ }
+ double coeff1 = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ coeff1 += work1[j] * work1[j];
+ }
+ double pc2 = previousCost * previousCost;
+ coeff1 = coeff1 / pc2;
+ double coeff2 = lmPar * lmNorm * lmNorm / pc2;
+ double preRed = coeff1 + 2 * coeff2;
+ double dirDer = -(coeff1 + coeff2);
+
+ // ratio of the actual to the predicted reduction
+ ratio = (preRed == 0) ? 0 : (actRed / preRed);
+
+ // update the step bound
+ if (ratio <= 0.25) {
+ double tmp =
+ (actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;
+ if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {
+ tmp = 0.1;
+ }
+ delta = tmp * Math.min(delta, 10.0 * lmNorm);
+ lmPar /= tmp;
+ } else if ((lmPar == 0) || (ratio >= 0.75)) {
+ delta = 2 * lmNorm;
+ lmPar *= 0.5;
+ }
+
+ // test for successful iteration.
+ if (ratio >= 1.0e-4) {
+ // successful iteration, update the norm
+ firstIteration = false;
+ xNorm = 0;
+ for (int k = 0; k < cols; ++k) {
+ double xK = diag[k] * variables[k];
+ xNorm += xK * xK;
+ }
+ xNorm = Math.sqrt(xNorm);
+ } else {
+ // failed iteration, reset the previous values
+ cost = previousCost;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ variables[pj] = oldX[pj];
+ }
+ tmpVec = residuals;
+ residuals = oldRes;
+ oldRes = tmpVec;
+ }
+
+ // tests for convergence.
+ if (((Math.abs(actRed) <= costRelativeTolerance) &&
+ (preRed <= costRelativeTolerance) &&
+ (ratio <= 2.0)) ||
+ (delta <= parRelativeTolerance * xNorm)) {
+ return new VectorialPointValuePair(variables, objective);
+ }
+
+ // tests for termination and stringent tolerances
+ // (2.2204e-16 is the machine epsilon for IEEE754)
+ if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
+ throw new OptimizationException("cost relative tolerance is too small ({0})," +
+ " no further reduction in the" +
+ " sum of squares is possible",
+ costRelativeTolerance);
+ } else if (delta <= 2.2204e-16 * xNorm) {
+ throw new OptimizationException("parameters relative tolerance is too small" +
+ " ({0}), no further improvement in" +
+ " the approximate solution is possible",
+ parRelativeTolerance);
+ } else if (maxCosine <= 2.2204e-16) {
+ throw new OptimizationException("orthogonality tolerance is too small ({0})," +
+ " solution is orthogonal to the jacobian",
+ orthoTolerance);
+ }
+
+ }
+
+ }
+
+ }
+
+ /**
+ * Determine the Levenberg-Marquardt parameter.
+ * <p>This implementation is a translation in Java of the MINPACK
+ * <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a>
+ * routine.</p>
+ * <p>This method sets the lmPar and lmDir attributes.</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 qy array containing qTy
+ * @param delta upper bound on the euclidean norm of diagR * lmDir
+ * @param diag diagonal matrix
+ * @param work1 work array
+ * @param work2 work array
+ * @param work3 work array
+ */
+ private void determineLMParameter(double[] qy, double delta, double[] diag,
+ double[] work1, double[] work2, double[] work3) {
+
+ // compute and store in x the gauss-newton direction, if the
+ // jacobian is rank-deficient, obtain a least squares solution
+ for (int j = 0; j < rank; ++j) {
+ lmDir[permutation[j]] = qy[j];
+ }
+ for (int j = rank; j < cols; ++j) {
+ lmDir[permutation[j]] = 0;
+ }
+ for (int k = rank - 1; k >= 0; --k) {
+ int pk = permutation[k];
+ double ypk = lmDir[pk] / diagR[pk];
+ for (int i = 0; i < k; ++i) {
+ lmDir[permutation[i]] -= ypk * jacobian[i][pk];
+ }
+ lmDir[pk] = ypk;
+ }
+
+ // evaluate the function at the origin, and test
+ // for acceptance of the Gauss-Newton direction
+ double dxNorm = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ double s = diag[pj] * lmDir[pj];
+ work1[pj] = s;
+ dxNorm += s * s;
+ }
+ dxNorm = Math.sqrt(dxNorm);
+ double fp = dxNorm - delta;
+ if (fp <= 0.1 * delta) {
+ lmPar = 0;
+ return;
+ }
+
+ // if the jacobian is not rank deficient, the Newton step provides
+ // a lower bound, parl, for the zero of the function,
+ // otherwise set this bound to zero
+ double sum2, parl = 0;
+ if (rank == solvedCols) {
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ work1[pj] *= diag[pj] / dxNorm;
+ }
+ sum2 = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ double sum = 0;
+ for (int i = 0; i < j; ++i) {
+ sum += jacobian[i][pj] * work1[permutation[i]];
+ }
+ double s = (work1[pj] - sum) / diagR[pj];
+ work1[pj] = s;
+ sum2 += s * s;
+ }
+ parl = fp / (delta * sum2);
+ }
+
+ // calculate an upper bound, paru, for the zero of the function
+ sum2 = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ double sum = 0;
+ for (int i = 0; i <= j; ++i) {
+ sum += jacobian[i][pj] * qy[i];
+ }
+ sum /= diag[pj];
+ sum2 += sum * sum;
+ }
+ double gNorm = Math.sqrt(sum2);
+ double paru = gNorm / delta;
+ if (paru == 0) {
+ // 2.2251e-308 is the smallest positive real for IEE754
+ paru = 2.2251e-308 / Math.min(delta, 0.1);
+ }
+
+ // if the input par lies outside of the interval (parl,paru),
+ // set par to the closer endpoint
+ lmPar = Math.min(paru, Math.max(lmPar, parl));
+ if (lmPar == 0) {
+ lmPar = gNorm / dxNorm;
+ }
+
+ for (int countdown = 10; countdown >= 0; --countdown) {
+
+ // evaluate the function at the current value of lmPar
+ if (lmPar == 0) {
+ lmPar = Math.max(2.2251e-308, 0.001 * paru);
+ }
+ double sPar = Math.sqrt(lmPar);
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ work1[pj] = sPar * diag[pj];
+ }
+ determineLMDirection(qy, work1, work2, work3);
+
+ dxNorm = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ double s = diag[pj] * lmDir[pj];
+ work3[pj] = s;
+ dxNorm += s * s;
+ }
+ dxNorm = Math.sqrt(dxNorm);
+ double previousFP = fp;
+ fp = dxNorm - delta;
+
+ // if the function is small enough, accept the current value
+ // of lmPar, also test for the exceptional cases where parl is zero
+ if ((Math.abs(fp) <= 0.1 * delta) ||
+ ((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {
+ return;
+ }
+
+ // compute the Newton correction
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ work1[pj] = work3[pj] * diag[pj] / dxNorm;
+ }
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ work1[pj] /= work2[j];
+ double tmp = work1[pj];
+ for (int i = j + 1; i < solvedCols; ++i) {
+ work1[permutation[i]] -= jacobian[i][pj] * tmp;
+ }
+ }
+ sum2 = 0;
+ for (int j = 0; j < solvedCols; ++j) {
+ double s = work1[permutation[j]];
+ sum2 += s * s;
+ }
+ double correction = fp / (delta * sum2);
+
+ // depending on the sign of the function, update parl or paru.
+ if (fp > 0) {
+ parl = Math.max(parl, lmPar);
+ } else if (fp < 0) {
+ paru = Math.min(paru, lmPar);
+ }
+
+ // compute an improved estimate for lmPar
+ lmPar = Math.max(parl, lmPar + correction);
+
+ }
+ }
+
+ /**
+ * Solve a*x = b and d*x = 0 in the least squares sense.
+ * <p>This implementation is a translation in Java of the MINPACK
+ * <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a>
+ * routine.</p>
+ * <p>This method sets the lmDir and lmDiag attributes.</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 qy array containing qTy
+ * @param diag diagonal matrix
+ * @param lmDiag diagonal elements associated with lmDir
+ * @param work work array
+ */
+ private void determineLMDirection(double[] qy, double[] diag,
+ double[] lmDiag, double[] work) {
+
+ // copy R and Qty to preserve input and initialize s
+ // in particular, save the diagonal elements of R in lmDir
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ for (int i = j + 1; i < solvedCols; ++i) {
+ jacobian[i][pj] = jacobian[j][permutation[i]];
+ }
+ lmDir[j] = diagR[pj];
+ work[j] = qy[j];
+ }
+
+ // eliminate the diagonal matrix d using a Givens rotation
+ for (int j = 0; j < solvedCols; ++j) {
+
+ // prepare the row of d to be eliminated, locating the
+ // diagonal element using p from the Q.R. factorization
+ int pj = permutation[j];
+ double dpj = diag[pj];
+ if (dpj != 0) {
+ Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);
+ }
+ lmDiag[j] = dpj;
+
+ // the transformations to eliminate the row of d
+ // modify only a single element of Qty
+ // beyond the first n, which is initially zero.
+ double qtbpj = 0;
+ for (int k = j; k < solvedCols; ++k) {
+ int pk = permutation[k];
+
+ // determine a Givens rotation which eliminates the
+ // appropriate element in the current row of d
+ if (lmDiag[k] != 0) {
+
+ double sin, cos;
+ double rkk = jacobian[k][pk];
+ if (Math.abs(rkk) < Math.abs(lmDiag[k])) {
+ double cotan = rkk / lmDiag[k];
+ sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);
+ cos = sin * cotan;
+ } else {
+ double tan = lmDiag[k] / rkk;
+ cos = 1.0 / Math.sqrt(1.0 + tan * tan);
+ sin = cos * tan;
+ }
+
+ // compute the modified diagonal element of R and
+ // the modified element of (Qty,0)
+ jacobian[k][pk] = cos * rkk + sin * lmDiag[k];
+ double temp = cos * work[k] + sin * qtbpj;
+ qtbpj = -sin * work[k] + cos * qtbpj;
+ work[k] = temp;
+
+ // accumulate the tranformation in the row of s
+ for (int i = k + 1; i < solvedCols; ++i) {
+ double rik = jacobian[i][pk];
+ temp = cos * rik + sin * lmDiag[i];
+ lmDiag[i] = -sin * rik + cos * lmDiag[i];
+ jacobian[i][pk] = temp;
+ }
+
+ }
+ }
+
+ // store the diagonal element of s and restore
+ // the corresponding diagonal element of R
+ lmDiag[j] = jacobian[j][permutation[j]];
+ jacobian[j][permutation[j]] = lmDir[j];
+
+ }
+
+ // solve the triangular system for z, if the system is
+ // singular, then obtain a least squares solution
+ int nSing = solvedCols;
+ for (int j = 0; j < solvedCols; ++j) {
+ if ((lmDiag[j] == 0) && (nSing == solvedCols)) {
+ nSing = j;
+ }
+ if (nSing < solvedCols) {
+ work[j] = 0;
+ }
+ }
+ if (nSing > 0) {
+ for (int j = nSing - 1; j >= 0; --j) {
+ int pj = permutation[j];
+ double sum = 0;
+ for (int i = j + 1; i < nSing; ++i) {
+ sum += jacobian[i][pj] * work[i];
+ }
+ work[j] = (work[j] - sum) / lmDiag[j];
+ }
+ }
+
+ // permute the components of z back to components of lmDir
+ for (int j = 0; j < lmDir.length; ++j) {
+ lmDir[permutation[j]] = work[j];
+ }
+
+ }
+
+ /**
+ * Decompose a matrix A as A.P = Q.R using Householder transforms.
+ * <p>As suggested in the P. Lascaux and R. Theodor book
+ * <i>Analyse numérique matricielle appliquée à
+ * l'art de l'ingénieur</i> (Masson, 1986), instead of representing
+ * the Householder transforms with u<sub>k</sub> unit vectors such that:
+ * <pre>
+ * H<sub>k</sub> = I - 2u<sub>k</sub>.u<sub>k</sub><sup>t</sup>
+ * </pre>
+ * we use <sub>k</sub> non-unit vectors such that:
+ * <pre>
+ * H<sub>k</sub> = I - beta<sub>k</sub>v<sub>k</sub>.v<sub>k</sub><sup>t</sup>
+ * </pre>
+ * where v<sub>k</sub> = a<sub>k</sub> - alpha<sub>k</sub> e<sub>k</sub>.
+ * The beta<sub>k</sub> coefficients are provided upon exit as recomputing
+ * them from the v<sub>k</sub> vectors would be costly.</p>
+ * <p>This decomposition handles rank deficient cases since the tranformations
+ * are performed in non-increasing columns norms order thanks to columns
+ * pivoting. The diagonal elements of the R matrix are therefore also in
+ * non-increasing absolute values order.</p>
+ * @exception OptimizationException if the decomposition cannot be performed
+ */
+ private void qrDecomposition() throws OptimizationException {
+
+ // initializations
+ for (int k = 0; k < cols; ++k) {
+ permutation[k] = k;
+ double norm2 = 0;
+ for (int i = 0; i < jacobian.length; ++i) {
+ double akk = jacobian[i][k];
+ norm2 += akk * akk;
+ }
+ jacNorm[k] = Math.sqrt(norm2);
+ }
+
+ // transform the matrix column after column
+ for (int k = 0; k < cols; ++k) {
+
+ // select the column with the greatest norm on active components
+ int nextColumn = -1;
+ double ak2 = Double.NEGATIVE_INFINITY;
+ for (int i = k; i < cols; ++i) {
+ double norm2 = 0;
+ for (int j = k; j < jacobian.length; ++j) {
+ double aki = jacobian[j][permutation[i]];
+ norm2 += aki * aki;
+ }
+ if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
+ throw new OptimizationException(
+ "unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",
+ rows, cols);
+ }
+ if (norm2 > ak2) {
+ nextColumn = i;
+ ak2 = norm2;
+ }
+ }
+ if (ak2 == 0) {
+ rank = k;
+ return;
+ }
+ int pk = permutation[nextColumn];
+ permutation[nextColumn] = permutation[k];
+ permutation[k] = pk;
+
+ // choose alpha such that Hk.u = alpha ek
+ double akk = jacobian[k][pk];
+ double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);
+ double betak = 1.0 / (ak2 - akk * alpha);
+ beta[pk] = betak;
+
+ // transform the current column
+ diagR[pk] = alpha;
+ jacobian[k][pk] -= alpha;
+
+ // transform the remaining columns
+ for (int dk = cols - 1 - k; dk > 0; --dk) {
+ double gamma = 0;
+ for (int j = k; j < jacobian.length; ++j) {
+ gamma += jacobian[j][pk] * jacobian[j][permutation[k + dk]];
+ }
+ gamma *= betak;
+ for (int j = k; j < jacobian.length; ++j) {
+ jacobian[j][permutation[k + dk]] -= gamma * jacobian[j][pk];
+ }
+ }
+
+ }
+
+ rank = solvedCols;
+
+ }
+
+ /**
+ * Compute the product Qt.y for some Q.R. decomposition.
+ *
+ * @param y vector to multiply (will be overwritten with the result)
+ */
+ private void qTy(double[] y) {
+ for (int k = 0; k < cols; ++k) {
+ int pk = permutation[k];
+ double gamma = 0;
+ for (int i = k; i < rows; ++i) {
+ gamma += jacobian[i][pk] * y[i];
+ }
+ gamma *= beta[pk];
+ for (int i = k; i < rows; ++i) {
+ y[i] -= gamma * jacobian[i][pk];
+ }
+ }
+ }
+
+}
Propchange: commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange: commons/proper/math/trunk/src/java/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.java
------------------------------------------------------------------------------
svn:keywords = Author Date Id Revision