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Posted to commits@commons.apache.org by er...@apache.org on 2012/12/12 15:11:04 UTC
svn commit: r1420684 [8/15] - in /commons/proper/math/trunk/src:
main/java/org/apache/commons/math3/exception/
main/java/org/apache/commons/math3/exception/util/
main/java/org/apache/commons/math3/fitting/
main/java/org/apache/commons/math3/optim/ main...
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,939 @@
+/*
+ * 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.math3.optim.nonlinear.vector.jacobian;
+
+import java.util.Arrays;
+import org.apache.commons.math3.exception.ConvergenceException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.optim.PointVectorValuePair;
+import org.apache.commons.math3.optim.ConvergenceChecker;
+import org.apache.commons.math3.linear.RealMatrix;
+import org.apache.commons.math3.util.Precision;
+import org.apache.commons.math3.util.FastMath;
+
+
+/**
+ * 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 point than equations). Over-determined systems
+ * are solved by ignoring the point 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, the use of
+ * inherited convergence checker 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.</p>
+ * <p>The authors of the original fortran version are:
+ * <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>
+ * 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>
+ *
+ * @version $Id: LevenbergMarquardtOptimizer.java 1416643 2012-12-03 19:37:14Z tn $
+ * @since 2.0
+ */
+public class LevenbergMarquardtOptimizer
+ extends AbstractLeastSquaresOptimizer {
+ /** Number of solved point. */
+ 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 final double initialStepBoundFactor;
+ /** Desired relative error in the sum of squares. */
+ private final double costRelativeTolerance;
+ /** Desired relative error in the approximate solution parameters. */
+ private final double parRelativeTolerance;
+ /** Desired max cosine on the orthogonality between the function vector
+ * and the columns of the jacobian. */
+ private final double orthoTolerance;
+ /** Threshold for QR ranking. */
+ private final double qrRankingThreshold;
+ /** Weighted residuals. */
+ private double[] weightedResidual;
+ /** Weighted Jacobian. */
+ private double[][] weightedJacobian;
+
+ /**
+ * Build an optimizer for least squares problems with default values
+ * for all the tuning parameters (see the {@link
+ * #LevenbergMarquardtOptimizer(double,double,double,double,double)
+ * other contructor}.
+ * The default values for the algorithm settings are:
+ * <ul>
+ * <li>Initial step bound factor: 100</li>
+ * <li>Cost relative tolerance: 1e-10</li>
+ * <li>Parameters relative tolerance: 1e-10</li>
+ * <li>Orthogonality tolerance: 1e-10</li>
+ * <li>QR ranking threshold: {@link Precision#SAFE_MIN}</li>
+ * </ul>
+ */
+ public LevenbergMarquardtOptimizer() {
+ this(100, 1e-10, 1e-10, 1e-10, Precision.SAFE_MIN);
+ }
+
+ /**
+ * Constructor that allows the specification of a custom convergence
+ * checker.
+ * Note that all the usual convergence checks will be <em>disabled</em>.
+ * The default values for the algorithm settings are:
+ * <ul>
+ * <li>Initial step bound factor: 100</li>
+ * <li>Cost relative tolerance: 1e-10</li>
+ * <li>Parameters relative tolerance: 1e-10</li>
+ * <li>Orthogonality tolerance: 1e-10</li>
+ * <li>QR ranking threshold: {@link Precision#SAFE_MIN}</li>
+ * </ul>
+ *
+ * @param checker Convergence checker.
+ */
+ public LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker) {
+ this(100, checker, 1e-10, 1e-10, 1e-10, Precision.SAFE_MIN);
+ }
+
+ /**
+ * Constructor that allows the specification of a custom convergence
+ * checker, in addition to the standard ones.
+ *
+ * @param initialStepBoundFactor Positive input variable used in
+ * determining the initial step bound. This bound is set to the
+ * product of initialStepBoundFactor and the euclidean norm of
+ * {@code diag * x} if non-zero, or else to {@code initialStepBoundFactor}
+ * itself. In most cases factor should lie in the interval
+ * {@code (0.1, 100.0)}. {@code 100} is a generally recommended value.
+ * @param checker Convergence checker.
+ * @param costRelativeTolerance Desired relative error in the sum of
+ * squares.
+ * @param parRelativeTolerance Desired relative error in the approximate
+ * solution parameters.
+ * @param orthoTolerance Desired max cosine on the orthogonality between
+ * the function vector and the columns of the Jacobian.
+ * @param threshold Desired threshold for QR ranking. If the squared norm
+ * of a column vector is smaller or equal to this threshold during QR
+ * decomposition, it is considered to be a zero vector and hence the rank
+ * of the matrix is reduced.
+ */
+ public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
+ ConvergenceChecker<PointVectorValuePair> checker,
+ double costRelativeTolerance,
+ double parRelativeTolerance,
+ double orthoTolerance,
+ double threshold) {
+ super(checker);
+ this.initialStepBoundFactor = initialStepBoundFactor;
+ this.costRelativeTolerance = costRelativeTolerance;
+ this.parRelativeTolerance = parRelativeTolerance;
+ this.orthoTolerance = orthoTolerance;
+ this.qrRankingThreshold = threshold;
+ }
+
+ /**
+ * Build an optimizer for least squares problems with default values
+ * for some of the tuning parameters (see the {@link
+ * #LevenbergMarquardtOptimizer(double,double,double,double,double)
+ * other contructor}.
+ * The default values for the algorithm settings are:
+ * <ul>
+ * <li>Initial step bound factor}: 100</li>
+ * <li>QR ranking threshold}: {@link Precision#SAFE_MIN}</li>
+ * </ul>
+ *
+ * @param costRelativeTolerance Desired relative error in the sum of
+ * squares.
+ * @param parRelativeTolerance Desired relative error in the approximate
+ * solution parameters.
+ * @param orthoTolerance Desired max cosine on the orthogonality between
+ * the function vector and the columns of the Jacobian.
+ */
+ public LevenbergMarquardtOptimizer(double costRelativeTolerance,
+ double parRelativeTolerance,
+ double orthoTolerance) {
+ this(100,
+ costRelativeTolerance, parRelativeTolerance, orthoTolerance,
+ Precision.SAFE_MIN);
+ }
+
+ /**
+ * The arguments control the behaviour of the default convergence checking
+ * procedure.
+ * Additional criteria can defined through the setting of a {@link
+ * ConvergenceChecker}.
+ *
+ * @param initialStepBoundFactor Positive input variable used in
+ * determining the initial step bound. This bound is set to the
+ * product of initialStepBoundFactor and the euclidean norm of
+ * {@code diag * x} if non-zero, or else to {@code initialStepBoundFactor}
+ * itself. In most cases factor should lie in the interval
+ * {@code (0.1, 100.0)}. {@code 100} is a generally recommended value.
+ * @param costRelativeTolerance Desired relative error in the sum of
+ * squares.
+ * @param parRelativeTolerance Desired relative error in the approximate
+ * solution parameters.
+ * @param orthoTolerance Desired max cosine on the orthogonality between
+ * the function vector and the columns of the Jacobian.
+ * @param threshold Desired threshold for QR ranking. If the squared norm
+ * of a column vector is smaller or equal to this threshold during QR
+ * decomposition, it is considered to be a zero vector and hence the rank
+ * of the matrix is reduced.
+ */
+ public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
+ double costRelativeTolerance,
+ double parRelativeTolerance,
+ double orthoTolerance,
+ double threshold) {
+ super(null); // No custom convergence criterion.
+ this.initialStepBoundFactor = initialStepBoundFactor;
+ this.costRelativeTolerance = costRelativeTolerance;
+ this.parRelativeTolerance = parRelativeTolerance;
+ this.orthoTolerance = orthoTolerance;
+ this.qrRankingThreshold = threshold;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected PointVectorValuePair doOptimize() {
+ final int nR = getTarget().length; // Number of observed data.
+ final double[] currentPoint = getStartPoint();
+ final int nC = currentPoint.length; // Number of parameters.
+
+ // arrays shared with the other private methods
+ solvedCols = FastMath.min(nR, nC);
+ diagR = new double[nC];
+ jacNorm = new double[nC];
+ beta = new double[nC];
+ permutation = new int[nC];
+ lmDir = new double[nC];
+
+ // local point
+ double delta = 0;
+ double xNorm = 0;
+ double[] diag = new double[nC];
+ double[] oldX = new double[nC];
+ double[] oldRes = new double[nR];
+ double[] oldObj = new double[nR];
+ double[] qtf = new double[nR];
+ double[] work1 = new double[nC];
+ double[] work2 = new double[nC];
+ double[] work3 = new double[nC];
+
+ final RealMatrix weightMatrixSqrt = getWeightSquareRoot();
+
+ // Evaluate the function at the starting point and calculate its norm.
+ double[] currentObjective = computeObjectiveValue(currentPoint);
+ double[] currentResiduals = computeResiduals(currentObjective);
+ PointVectorValuePair current = new PointVectorValuePair(currentPoint, currentObjective);
+ double currentCost = computeCost(currentResiduals);
+
+ // Outer loop.
+ lmPar = 0;
+ boolean firstIteration = true;
+ int iter = 0;
+ final ConvergenceChecker<PointVectorValuePair> checker = getConvergenceChecker();
+ while (true) {
+ ++iter;
+ final PointVectorValuePair previous = current;
+
+ // QR decomposition of the jacobian matrix
+ qrDecomposition(computeWeightedJacobian(currentPoint));
+
+ weightedResidual = weightMatrixSqrt.operate(currentResiduals);
+ for (int i = 0; i < nR; i++) {
+ qtf[i] = weightedResidual[i];
+ }
+
+ // compute Qt.res
+ qTy(qtf);
+
+ // 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];
+ weightedJacobian[k][pk] = diagR[pk];
+ }
+
+ if (firstIteration) {
+ // scale the point according to the norms of the columns
+ // of the initial jacobian
+ xNorm = 0;
+ for (int k = 0; k < nC; ++k) {
+ double dk = jacNorm[k];
+ if (dk == 0) {
+ dk = 1.0;
+ }
+ double xk = dk * currentPoint[k];
+ xNorm += xk * xk;
+ diag[k] = dk;
+ }
+ xNorm = FastMath.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 (currentCost != 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 += weightedJacobian[i][pj] * qtf[i];
+ }
+ maxCosine = FastMath.max(maxCosine, FastMath.abs(sum) / (s * currentCost));
+ }
+ }
+ }
+ if (maxCosine <= orthoTolerance) {
+ // Convergence has been reached.
+ setCost(currentCost);
+ return current;
+ }
+
+ // rescale if necessary
+ for (int j = 0; j < nC; ++j) {
+ diag[j] = FastMath.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] = currentPoint[pj];
+ }
+ final double previousCost = currentCost;
+ double[] tmpVec = weightedResidual;
+ weightedResidual = oldRes;
+ oldRes = tmpVec;
+ tmpVec = currentObjective;
+ currentObjective = oldObj;
+ oldObj = tmpVec;
+
+ // determine the Levenberg-Marquardt parameter
+ determineLMParameter(qtf, 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];
+ currentPoint[pj] = oldX[pj] + lmDir[pj];
+ double s = diag[pj] * lmDir[pj];
+ lmNorm += s * s;
+ }
+ lmNorm = FastMath.sqrt(lmNorm);
+ // on the first iteration, adjust the initial step bound.
+ if (firstIteration) {
+ delta = FastMath.min(delta, lmNorm);
+ }
+
+ // Evaluate the function at x + p and calculate its norm.
+ currentObjective = computeObjectiveValue(currentPoint);
+ currentResiduals = computeResiduals(currentObjective);
+ current = new PointVectorValuePair(currentPoint, currentObjective);
+ currentCost = computeCost(currentResiduals);
+
+ // compute the scaled actual reduction
+ double actRed = -1.0;
+ if (0.1 * currentCost < previousCost) {
+ double r = currentCost / 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] += weightedJacobian[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 * currentCost >= previousCost) || (tmp < 0.1)) {
+ tmp = 0.1;
+ }
+ delta = tmp * FastMath.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 < nC; ++k) {
+ double xK = diag[k] * currentPoint[k];
+ xNorm += xK * xK;
+ }
+ xNorm = FastMath.sqrt(xNorm);
+
+ // tests for convergence.
+ if (checker != null) {
+ // we use the vectorial convergence checker
+ if (checker.converged(iter, previous, current)) {
+ setCost(currentCost);
+ return current;
+ }
+ }
+ } else {
+ // failed iteration, reset the previous values
+ currentCost = previousCost;
+ for (int j = 0; j < solvedCols; ++j) {
+ int pj = permutation[j];
+ currentPoint[pj] = oldX[pj];
+ }
+ tmpVec = weightedResidual;
+ weightedResidual = oldRes;
+ oldRes = tmpVec;
+ tmpVec = currentObjective;
+ currentObjective = oldObj;
+ oldObj = tmpVec;
+ // Reset "current" to previous values.
+ current = new PointVectorValuePair(currentPoint, currentObjective);
+ }
+
+ // Default convergence criteria.
+ if ((FastMath.abs(actRed) <= costRelativeTolerance &&
+ preRed <= costRelativeTolerance &&
+ ratio <= 2.0) ||
+ delta <= parRelativeTolerance * xNorm) {
+ setCost(currentCost);
+ return current;
+ }
+
+ // tests for termination and stringent tolerances
+ // (2.2204e-16 is the machine epsilon for IEEE754)
+ if ((FastMath.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
+ throw new ConvergenceException(LocalizedFormats.TOO_SMALL_COST_RELATIVE_TOLERANCE,
+ costRelativeTolerance);
+ } else if (delta <= 2.2204e-16 * xNorm) {
+ throw new ConvergenceException(LocalizedFormats.TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE,
+ parRelativeTolerance);
+ } else if (maxCosine <= 2.2204e-16) {
+ throw new ConvergenceException(LocalizedFormats.TOO_SMALL_ORTHOGONALITY_TOLERANCE,
+ 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) {
+ final int nC = weightedJacobian[0].length;
+
+ // 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 < nC; ++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 * weightedJacobian[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 = FastMath.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;
+ double 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 += weightedJacobian[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 += weightedJacobian[i][pj] * qy[i];
+ }
+ sum /= diag[pj];
+ sum2 += sum * sum;
+ }
+ double gNorm = FastMath.sqrt(sum2);
+ double paru = gNorm / delta;
+ if (paru == 0) {
+ // 2.2251e-308 is the smallest positive real for IEE754
+ paru = 2.2251e-308 / FastMath.min(delta, 0.1);
+ }
+
+ // if the input par lies outside of the interval (parl,paru),
+ // set par to the closer endpoint
+ lmPar = FastMath.min(paru, FastMath.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 = FastMath.max(2.2251e-308, 0.001 * paru);
+ }
+ double sPar = FastMath.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 = FastMath.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 ((FastMath.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]] -= weightedJacobian[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 = FastMath.max(parl, lmPar);
+ } else if (fp < 0) {
+ paru = FastMath.min(paru, lmPar);
+ }
+
+ // compute an improved estimate for lmPar
+ lmPar = FastMath.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) {
+ weightedJacobian[i][pj] = weightedJacobian[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) {
+
+ final double sin;
+ final double cos;
+ double rkk = weightedJacobian[k][pk];
+ if (FastMath.abs(rkk) < FastMath.abs(lmDiag[k])) {
+ final double cotan = rkk / lmDiag[k];
+ sin = 1.0 / FastMath.sqrt(1.0 + cotan * cotan);
+ cos = sin * cotan;
+ } else {
+ final double tan = lmDiag[k] / rkk;
+ cos = 1.0 / FastMath.sqrt(1.0 + tan * tan);
+ sin = cos * tan;
+ }
+
+ // compute the modified diagonal element of R and
+ // the modified element of (Qty,0)
+ weightedJacobian[k][pk] = cos * rkk + sin * lmDiag[k];
+ final 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 = weightedJacobian[i][pk];
+ final double temp2 = cos * rik + sin * lmDiag[i];
+ lmDiag[i] = -sin * rik + cos * lmDiag[i];
+ weightedJacobian[i][pk] = temp2;
+ }
+ }
+ }
+
+ // store the diagonal element of s and restore
+ // the corresponding diagonal element of R
+ lmDiag[j] = weightedJacobian[j][permutation[j]];
+ weightedJacobian[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 += weightedJacobian[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>
+ *
+ * @param jacobian Weighted Jacobian matrix at the current point.
+ * @exception ConvergenceException if the decomposition cannot be performed
+ */
+ private void qrDecomposition(RealMatrix jacobian) throws ConvergenceException {
+ // Code in this class assumes that the weighted Jacobian is -(W^(1/2) J),
+ // hence the multiplication by -1.
+ weightedJacobian = jacobian.scalarMultiply(-1).getData();
+
+ final int nR = weightedJacobian.length;
+ final int nC = weightedJacobian[0].length;
+
+ // initializations
+ for (int k = 0; k < nC; ++k) {
+ permutation[k] = k;
+ double norm2 = 0;
+ for (int i = 0; i < nR; ++i) {
+ double akk = weightedJacobian[i][k];
+ norm2 += akk * akk;
+ }
+ jacNorm[k] = FastMath.sqrt(norm2);
+ }
+
+ // transform the matrix column after column
+ for (int k = 0; k < nC; ++k) {
+
+ // select the column with the greatest norm on active components
+ int nextColumn = -1;
+ double ak2 = Double.NEGATIVE_INFINITY;
+ for (int i = k; i < nC; ++i) {
+ double norm2 = 0;
+ for (int j = k; j < nR; ++j) {
+ double aki = weightedJacobian[j][permutation[i]];
+ norm2 += aki * aki;
+ }
+ if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
+ throw new ConvergenceException(LocalizedFormats.UNABLE_TO_PERFORM_QR_DECOMPOSITION_ON_JACOBIAN,
+ nR, nC);
+ }
+ if (norm2 > ak2) {
+ nextColumn = i;
+ ak2 = norm2;
+ }
+ }
+ if (ak2 <= qrRankingThreshold) {
+ rank = k;
+ return;
+ }
+ int pk = permutation[nextColumn];
+ permutation[nextColumn] = permutation[k];
+ permutation[k] = pk;
+
+ // choose alpha such that Hk.u = alpha ek
+ double akk = weightedJacobian[k][pk];
+ double alpha = (akk > 0) ? -FastMath.sqrt(ak2) : FastMath.sqrt(ak2);
+ double betak = 1.0 / (ak2 - akk * alpha);
+ beta[pk] = betak;
+
+ // transform the current column
+ diagR[pk] = alpha;
+ weightedJacobian[k][pk] -= alpha;
+
+ // transform the remaining columns
+ for (int dk = nC - 1 - k; dk > 0; --dk) {
+ double gamma = 0;
+ for (int j = k; j < nR; ++j) {
+ gamma += weightedJacobian[j][pk] * weightedJacobian[j][permutation[k + dk]];
+ }
+ gamma *= betak;
+ for (int j = k; j < nR; ++j) {
+ weightedJacobian[j][permutation[k + dk]] -= gamma * weightedJacobian[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) {
+ final int nR = weightedJacobian.length;
+ final int nC = weightedJacobian[0].length;
+
+ for (int k = 0; k < nC; ++k) {
+ int pk = permutation[k];
+ double gamma = 0;
+ for (int i = k; i < nR; ++i) {
+ gamma += weightedJacobian[i][pk] * y[i];
+ }
+ gamma *= beta[pk];
+ for (int i = k; i < nR; ++i) {
+ y[i] -= gamma * weightedJacobian[i][pk];
+ }
+ }
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
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URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/package-info.java?rev=1420684&view=auto
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--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/package-info.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/package-info.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,21 @@
+/*
+ * 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.math3.optim.nonlinear.vector.jacobian;
+
+/**
+ * This package provides optimization algorithms that require derivatives.
+ */
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/package-info.java
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Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/package-info.java
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--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/package-info.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/package-info.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,21 @@
+/*
+ * 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.math3.optim.nonlinear.vector;
+
+/**
+ * Algorithms for optimizing a vector function.
+ */
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/nonlinear/vector/package-info.java
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--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/package-info.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/package-info.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,73 @@
+/*
+ * 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.math3.optim;
+
+/**
+ * <p>
+ * Generally, optimizers are algorithms that will either
+ * {@link GoalType#MINIMIZE minimize} or {@link GoalType#MAXIMIZE maximize}
+ * a scalar function, called the {@link ObjectiveFunction <em>objective
+ * function</em>}.
+ * <br/>
+ * For some scalar objective functions the gradient can be computed (analytically
+ * or numerically). Algorithms that use this knowledge are defined in the
+ * {@link org.apache.commons.math3.optim.nonlinear.scalar.gradient} package.
+ * The algorithms that do not need this additional information are located in
+ * the {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv} package.
+ * </p>
+ *
+ * <p>
+ * Some problems are solved more efficiently by algorithms that, instead of an
+ * objective function, need access to a
+ * {@link org.apache.commons.math3.optim.nonlinear.vector.ModelFunction
+ * <em>model function</em>}: such a model predicts a set of values which the
+ * algorithm tries to match with a set of given
+ * {@link org.apache.commons.math3.optim.nonlinear.vector.Target target values}.
+ * Those algorithms are located in the
+ * {@link org.apache.commons.math3.optim.nonlinear.vector} package.
+ * <br/>
+ * Algorithms that also require the
+ * {@link org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian
+ * Jacobian matrix of the model} are located in the
+ * {@link org.apache.commons.math3.optim.nonlinear.vector.jacobian} package.
+ * <br/>
+ * The {@link org.apache.commons.math3.optim.nonlinear.vector.jacobian.AbstractLeastSquaresOptimizer
+ * non-linear least-squares optimizers} are a specialization of the the latter,
+ * that minimize the distance (called <em>cost</em> or <em>χ<sup>2</sup></em>)
+ * between model and observations.
+ * <br/>
+ * For cases where the Jacobian cannot be provided, a utility class will
+ * {@link org.apache.commons.math3.optim.nonlinear.scalar.LeastSquaresConverter
+ * convert} a (vector) model into a (scalar) objective function.
+ * </p>
+ *
+ * <p>
+ * This package provides common functionality for the optimization algorithms.
+ * Abstract classes ({@link BaseOptimizer} and {@link BaseMultivariateOptimizer})
+ * define boiler-plate code for storing {@link MaxEval evaluations} and
+ * {@link MaxIter iterations} counters and a user-defined
+ * {@link ConvergenceChecker convergence checker}.
+ * </p>
+ *
+ * <p>
+ * For each of the optimizer types, there is a special implementation that
+ * wraps an optimizer instance and provides a "multi-start" feature: it calls
+ * the underlying optimizer several times with different starting points and
+ * returns the best optimum found, or all optima if so desired.
+ * This could be useful to avoid being trapped in a local extremum.
+ * </p>
+ */
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/package-info.java
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--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,287 @@
+/*
+ * 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.math3.optim.univariate;
+
+import org.apache.commons.math3.util.Incrementor;
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.TooManyEvaluationsException;
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.analysis.UnivariateFunction;
+import org.apache.commons.math3.optim.GoalType;
+
+/**
+ * Provide an interval that brackets a local optimum of a function.
+ * This code is based on a Python implementation (from <em>SciPy</em>,
+ * module {@code optimize.py} v0.5).
+ *
+ * @version $Id: BracketFinder.java 1413186 2012-11-24 13:47:59Z erans $
+ * @since 2.2
+ */
+public class BracketFinder {
+ /** Tolerance to avoid division by zero. */
+ private static final double EPS_MIN = 1e-21;
+ /**
+ * Golden section.
+ */
+ private static final double GOLD = 1.618034;
+ /**
+ * Factor for expanding the interval.
+ */
+ private final double growLimit;
+ /**
+ * Counter for function evaluations.
+ */
+ private final Incrementor evaluations = new Incrementor();
+ /**
+ * Lower bound of the bracket.
+ */
+ private double lo;
+ /**
+ * Higher bound of the bracket.
+ */
+ private double hi;
+ /**
+ * Point inside the bracket.
+ */
+ private double mid;
+ /**
+ * Function value at {@link #lo}.
+ */
+ private double fLo;
+ /**
+ * Function value at {@link #hi}.
+ */
+ private double fHi;
+ /**
+ * Function value at {@link #mid}.
+ */
+ private double fMid;
+
+ /**
+ * Constructor with default values {@code 100, 50} (see the
+ * {@link #BracketFinder(double,int) other constructor}).
+ */
+ public BracketFinder() {
+ this(100, 50);
+ }
+
+ /**
+ * Create a bracketing interval finder.
+ *
+ * @param growLimit Expanding factor.
+ * @param maxEvaluations Maximum number of evaluations allowed for finding
+ * a bracketing interval.
+ */
+ public BracketFinder(double growLimit,
+ int maxEvaluations) {
+ if (growLimit <= 0) {
+ throw new NotStrictlyPositiveException(growLimit);
+ }
+ if (maxEvaluations <= 0) {
+ throw new NotStrictlyPositiveException(maxEvaluations);
+ }
+
+ this.growLimit = growLimit;
+ evaluations.setMaximalCount(maxEvaluations);
+ }
+
+ /**
+ * Search new points that bracket a local optimum of the function.
+ *
+ * @param func Function whose optimum should be bracketed.
+ * @param goal {@link GoalType Goal type}.
+ * @param xA Initial point.
+ * @param xB Initial point.
+ * @throws TooManyEvaluationsException if the maximum number of evaluations
+ * is exceeded.
+ */
+ public void search(UnivariateFunction func, GoalType goal, double xA, double xB) {
+ evaluations.resetCount();
+ final boolean isMinim = goal == GoalType.MINIMIZE;
+
+ double fA = eval(func, xA);
+ double fB = eval(func, xB);
+ if (isMinim ?
+ fA < fB :
+ fA > fB) {
+
+ double tmp = xA;
+ xA = xB;
+ xB = tmp;
+
+ tmp = fA;
+ fA = fB;
+ fB = tmp;
+ }
+
+ double xC = xB + GOLD * (xB - xA);
+ double fC = eval(func, xC);
+
+ while (isMinim ? fC < fB : fC > fB) {
+ double tmp1 = (xB - xA) * (fB - fC);
+ double tmp2 = (xB - xC) * (fB - fA);
+
+ double val = tmp2 - tmp1;
+ double denom = Math.abs(val) < EPS_MIN ? 2 * EPS_MIN : 2 * val;
+
+ double w = xB - ((xB - xC) * tmp2 - (xB - xA) * tmp1) / denom;
+ double wLim = xB + growLimit * (xC - xB);
+
+ double fW;
+ if ((w - xC) * (xB - w) > 0) {
+ fW = eval(func, w);
+ if (isMinim ?
+ fW < fC :
+ fW > fC) {
+ xA = xB;
+ xB = w;
+ fA = fB;
+ fB = fW;
+ break;
+ } else if (isMinim ?
+ fW > fB :
+ fW < fB) {
+ xC = w;
+ fC = fW;
+ break;
+ }
+ w = xC + GOLD * (xC - xB);
+ fW = eval(func, w);
+ } else if ((w - wLim) * (wLim - xC) >= 0) {
+ w = wLim;
+ fW = eval(func, w);
+ } else if ((w - wLim) * (xC - w) > 0) {
+ fW = eval(func, w);
+ if (isMinim ?
+ fW < fC :
+ fW > fC) {
+ xB = xC;
+ xC = w;
+ w = xC + GOLD * (xC - xB);
+ fB = fC;
+ fC =fW;
+ fW = eval(func, w);
+ }
+ } else {
+ w = xC + GOLD * (xC - xB);
+ fW = eval(func, w);
+ }
+
+ xA = xB;
+ fA = fB;
+ xB = xC;
+ fB = fC;
+ xC = w;
+ fC = fW;
+ }
+
+ lo = xA;
+ fLo = fA;
+ mid = xB;
+ fMid = fB;
+ hi = xC;
+ fHi = fC;
+
+ if (lo > hi) {
+ double tmp = lo;
+ lo = hi;
+ hi = tmp;
+
+ tmp = fLo;
+ fLo = fHi;
+ fHi = tmp;
+ }
+ }
+
+ /**
+ * @return the number of evalutations.
+ */
+ public int getMaxEvaluations() {
+ return evaluations.getMaximalCount();
+ }
+
+ /**
+ * @return the number of evalutations.
+ */
+ public int getEvaluations() {
+ return evaluations.getCount();
+ }
+
+ /**
+ * @return the lower bound of the bracket.
+ * @see #getFLo()
+ */
+ public double getLo() {
+ return lo;
+ }
+
+ /**
+ * Get function value at {@link #getLo()}.
+ * @return function value at {@link #getLo()}
+ */
+ public double getFLo() {
+ return fLo;
+ }
+
+ /**
+ * @return the higher bound of the bracket.
+ * @see #getFHi()
+ */
+ public double getHi() {
+ return hi;
+ }
+
+ /**
+ * Get function value at {@link #getHi()}.
+ * @return function value at {@link #getHi()}
+ */
+ public double getFHi() {
+ return fHi;
+ }
+
+ /**
+ * @return a point in the middle of the bracket.
+ * @see #getFMid()
+ */
+ public double getMid() {
+ return mid;
+ }
+
+ /**
+ * Get function value at {@link #getMid()}.
+ * @return function value at {@link #getMid()}
+ */
+ public double getFMid() {
+ return fMid;
+ }
+
+ /**
+ * @param f Function.
+ * @param x Argument.
+ * @return {@code f(x)}
+ * @throws TooManyEvaluationsException if the maximal number of evaluations is
+ * exceeded.
+ */
+ private double eval(UnivariateFunction f, double x) {
+ try {
+ evaluations.incrementCount();
+ } catch (MaxCountExceededException e) {
+ throw new TooManyEvaluationsException(e.getMax());
+ }
+ return f.value(x);
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java
------------------------------------------------------------------------------
svn:eol-style = native
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BrentOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BrentOptimizer.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BrentOptimizer.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BrentOptimizer.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,317 @@
+/*
+ * 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.math3.optim.univariate;
+
+import org.apache.commons.math3.util.Precision;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.optim.ConvergenceChecker;
+import org.apache.commons.math3.optim.GoalType;
+
+/**
+ * For a function defined on some interval {@code (lo, hi)}, this class
+ * finds an approximation {@code x} to the point at which the function
+ * attains its minimum.
+ * It implements Richard Brent's algorithm (from his book "Algorithms for
+ * Minimization without Derivatives", p. 79) for finding minima of real
+ * univariate functions.
+ * <br/>
+ * This code is an adaptation, partly based on the Python code from SciPy
+ * (module "optimize.py" v0.5); the original algorithm is also modified
+ * <ul>
+ * <li>to use an initial guess provided by the user,</li>
+ * <li>to ensure that the best point encountered is the one returned.</li>
+ * </ul>
+ *
+ * @version $Id: BrentOptimizer.java 1416643 2012-12-03 19:37:14Z tn $
+ * @since 2.0
+ */
+public class BrentOptimizer extends UnivariateOptimizer {
+ /**
+ * Golden section.
+ */
+ private static final double GOLDEN_SECTION = 0.5 * (3 - FastMath.sqrt(5));
+ /**
+ * Minimum relative tolerance.
+ */
+ private static final double MIN_RELATIVE_TOLERANCE = 2 * FastMath.ulp(1d);
+ /**
+ * Relative threshold.
+ */
+ private final double relativeThreshold;
+ /**
+ * Absolute threshold.
+ */
+ private final double absoluteThreshold;
+
+ /**
+ * The arguments are used implement the original stopping criterion
+ * of Brent's algorithm.
+ * {@code abs} and {@code rel} define a tolerance
+ * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than
+ * <em>2 macheps</em> and preferably not much less than <em>sqrt(macheps)</em>,
+ * where <em>macheps</em> is the relative machine precision. {@code abs} must
+ * be positive.
+ *
+ * @param rel Relative threshold.
+ * @param abs Absolute threshold.
+ * @param checker Additional, user-defined, convergence checking
+ * procedure.
+ * @throws NotStrictlyPositiveException if {@code abs <= 0}.
+ * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
+ */
+ public BrentOptimizer(double rel,
+ double abs,
+ ConvergenceChecker<UnivariatePointValuePair> checker) {
+ super(checker);
+
+ if (rel < MIN_RELATIVE_TOLERANCE) {
+ throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
+ }
+ if (abs <= 0) {
+ throw new NotStrictlyPositiveException(abs);
+ }
+
+ relativeThreshold = rel;
+ absoluteThreshold = abs;
+ }
+
+ /**
+ * The arguments are used for implementing the original stopping criterion
+ * of Brent's algorithm.
+ * {@code abs} and {@code rel} define a tolerance
+ * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than
+ * <em>2 macheps</em> and preferably not much less than <em>sqrt(macheps)</em>,
+ * where <em>macheps</em> is the relative machine precision. {@code abs} must
+ * be positive.
+ *
+ * @param rel Relative threshold.
+ * @param abs Absolute threshold.
+ * @throws NotStrictlyPositiveException if {@code abs <= 0}.
+ * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
+ */
+ public BrentOptimizer(double rel,
+ double abs) {
+ this(rel, abs, null);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected UnivariatePointValuePair doOptimize() {
+ final boolean isMinim = getGoalType() == GoalType.MINIMIZE;
+ final double lo = getMin();
+ final double mid = getStartValue();
+ final double hi = getMax();
+
+ // Optional additional convergence criteria.
+ final ConvergenceChecker<UnivariatePointValuePair> checker
+ = getConvergenceChecker();
+
+ double a;
+ double b;
+ if (lo < hi) {
+ a = lo;
+ b = hi;
+ } else {
+ a = hi;
+ b = lo;
+ }
+
+ double x = mid;
+ double v = x;
+ double w = x;
+ double d = 0;
+ double e = 0;
+ double fx = computeObjectiveValue(x);
+ if (!isMinim) {
+ fx = -fx;
+ }
+ double fv = fx;
+ double fw = fx;
+
+ UnivariatePointValuePair previous = null;
+ UnivariatePointValuePair current
+ = new UnivariatePointValuePair(x, isMinim ? fx : -fx);
+ // Best point encountered so far (which is the initial guess).
+ UnivariatePointValuePair best = current;
+
+ int iter = 0;
+ while (true) {
+ final double m = 0.5 * (a + b);
+ final double tol1 = relativeThreshold * FastMath.abs(x) + absoluteThreshold;
+ final double tol2 = 2 * tol1;
+
+ // Default stopping criterion.
+ final boolean stop = FastMath.abs(x - m) <= tol2 - 0.5 * (b - a);
+ if (!stop) {
+ double p = 0;
+ double q = 0;
+ double r = 0;
+ double u = 0;
+
+ if (FastMath.abs(e) > tol1) { // Fit parabola.
+ r = (x - w) * (fx - fv);
+ q = (x - v) * (fx - fw);
+ p = (x - v) * q - (x - w) * r;
+ q = 2 * (q - r);
+
+ if (q > 0) {
+ p = -p;
+ } else {
+ q = -q;
+ }
+
+ r = e;
+ e = d;
+
+ if (p > q * (a - x) &&
+ p < q * (b - x) &&
+ FastMath.abs(p) < FastMath.abs(0.5 * q * r)) {
+ // Parabolic interpolation step.
+ d = p / q;
+ u = x + d;
+
+ // f must not be evaluated too close to a or b.
+ if (u - a < tol2 || b - u < tol2) {
+ if (x <= m) {
+ d = tol1;
+ } else {
+ d = -tol1;
+ }
+ }
+ } else {
+ // Golden section step.
+ if (x < m) {
+ e = b - x;
+ } else {
+ e = a - x;
+ }
+ d = GOLDEN_SECTION * e;
+ }
+ } else {
+ // Golden section step.
+ if (x < m) {
+ e = b - x;
+ } else {
+ e = a - x;
+ }
+ d = GOLDEN_SECTION * e;
+ }
+
+ // Update by at least "tol1".
+ if (FastMath.abs(d) < tol1) {
+ if (d >= 0) {
+ u = x + tol1;
+ } else {
+ u = x - tol1;
+ }
+ } else {
+ u = x + d;
+ }
+
+ double fu = computeObjectiveValue(u);
+ if (!isMinim) {
+ fu = -fu;
+ }
+
+ // User-defined convergence checker.
+ previous = current;
+ current = new UnivariatePointValuePair(u, isMinim ? fu : -fu);
+ best = best(best,
+ best(previous,
+ current,
+ isMinim),
+ isMinim);
+
+ if (checker != null) {
+ if (checker.converged(iter, previous, current)) {
+ return best;
+ }
+ }
+
+ // Update a, b, v, w and x.
+ if (fu <= fx) {
+ if (u < x) {
+ b = x;
+ } else {
+ a = x;
+ }
+ v = w;
+ fv = fw;
+ w = x;
+ fw = fx;
+ x = u;
+ fx = fu;
+ } else {
+ if (u < x) {
+ a = u;
+ } else {
+ b = u;
+ }
+ if (fu <= fw ||
+ Precision.equals(w, x)) {
+ v = w;
+ fv = fw;
+ w = u;
+ fw = fu;
+ } else if (fu <= fv ||
+ Precision.equals(v, x) ||
+ Precision.equals(v, w)) {
+ v = u;
+ fv = fu;
+ }
+ }
+ } else { // Default termination (Brent's criterion).
+ return best(best,
+ best(previous,
+ current,
+ isMinim),
+ isMinim);
+ }
+ ++iter;
+ }
+ }
+
+ /**
+ * Selects the best of two points.
+ *
+ * @param a Point and value.
+ * @param b Point and value.
+ * @param isMinim {@code true} if the selected point must be the one with
+ * the lowest value.
+ * @return the best point, or {@code null} if {@code a} and {@code b} are
+ * both {@code null}. When {@code a} and {@code b} have the same function
+ * value, {@code a} is returned.
+ */
+ private UnivariatePointValuePair best(UnivariatePointValuePair a,
+ UnivariatePointValuePair b,
+ boolean isMinim) {
+ if (a == null) {
+ return b;
+ }
+ if (b == null) {
+ return a;
+ }
+
+ if (isMinim) {
+ return a.getValue() <= b.getValue() ? a : b;
+ } else {
+ return a.getValue() >= b.getValue() ? a : b;
+ }
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/BrentOptimizer.java
------------------------------------------------------------------------------
svn:eol-style = native
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/MultiStartUnivariateOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/MultiStartUnivariateOptimizer.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/MultiStartUnivariateOptimizer.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/MultiStartUnivariateOptimizer.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,235 @@
+/*
+ * 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.math3.optim.univariate;
+
+import java.util.Arrays;
+import java.util.Comparator;
+import org.apache.commons.math3.exception.MathIllegalStateException;
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.NullArgumentException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.optim.MaxEval;
+import org.apache.commons.math3.optim.GoalType;
+import org.apache.commons.math3.optim.OptimizationData;
+
+/**
+ * Special implementation of the {@link UnivariateOptimizer} interface
+ * adding multi-start features to an existing optimizer.
+ * <br/>
+ * This class wraps an optimizer in order to use it several times in
+ * turn with different starting points (trying to avoid being trapped
+ * in a local extremum when looking for a global one).
+ *
+ * @version $Id$
+ * @since 3.0
+ */
+public class MultiStartUnivariateOptimizer
+ extends UnivariateOptimizer {
+ /** Underlying classical optimizer. */
+ private final UnivariateOptimizer optimizer;
+ /** Number of evaluations already performed for all starts. */
+ private int totalEvaluations;
+ /** Number of starts to go. */
+ private int starts;
+ /** Random generator for multi-start. */
+ private RandomGenerator generator;
+ /** Found optima. */
+ private UnivariatePointValuePair[] optima;
+ /** Optimization data. */
+ private OptimizationData[] optimData;
+ /**
+ * Location in {@link #optimData} where the updated maximum
+ * number of evaluations will be stored.
+ */
+ private int maxEvalIndex = -1;
+ /**
+ * Location in {@link #optimData} where the updated start value
+ * will be stored.
+ */
+ private int searchIntervalIndex = -1;
+
+ /**
+ * Create a multi-start optimizer from a single-start optimizer.
+ *
+ * @param optimizer Single-start optimizer to wrap.
+ * @param starts Number of starts to perform. If {@code starts == 1},
+ * the {@code optimize} methods will return the same solution as
+ * {@code optimizer} would.
+ * @param generator Random generator to use for restarts.
+ * @throws NullArgumentException if {@code optimizer} or {@code generator}
+ * is {@code null}.
+ * @throws NotStrictlyPositiveException if {@code starts < 1}.
+ */
+ public MultiStartUnivariateOptimizer(final UnivariateOptimizer optimizer,
+ final int starts,
+ final RandomGenerator generator) {
+ super(optimizer.getConvergenceChecker());
+
+ if (optimizer == null ||
+ generator == null) {
+ throw new NullArgumentException();
+ }
+ if (starts < 1) {
+ throw new NotStrictlyPositiveException(starts);
+ }
+
+ this.optimizer = optimizer;
+ this.starts = starts;
+ this.generator = generator;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public int getEvaluations() {
+ return totalEvaluations;
+ }
+
+ /**
+ * Gets all the optima found during the last call to {@code optimize}.
+ * The optimizer stores all the optima found during a set of
+ * restarts. The {@code optimize} method returns the best point only.
+ * This method returns all the points found at the end of each starts,
+ * including the best one already returned by the {@code optimize} method.
+ * <br/>
+ * The returned array as one element for each start as specified
+ * in the constructor. It is ordered with the results from the
+ * runs that did converge first, sorted from best to worst
+ * objective value (i.e in ascending order if minimizing and in
+ * descending order if maximizing), followed by {@code null} elements
+ * corresponding to the runs that did not converge. This means all
+ * elements will be {@code null} if the {@code optimize} method did throw
+ * an exception.
+ * This also means that if the first element is not {@code null}, it is
+ * the best point found across all starts.
+ *
+ * @return an array containing the optima.
+ * @throws MathIllegalStateException if {@link #optimize(OptimizationData[])
+ * optimize} has not been called.
+ */
+ public UnivariatePointValuePair[] getOptima() {
+ if (optima == null) {
+ throw new MathIllegalStateException(LocalizedFormats.NO_OPTIMUM_COMPUTED_YET);
+ }
+ return optima.clone();
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * @throws MathIllegalStateException if {@code optData} does not contain an
+ * instance of {@link MaxEval} or {@link SearchInterval}.
+ */
+ @Override
+ public UnivariatePointValuePair optimize(OptimizationData... optData) {
+ // Store arguments in order to pass them to the internal optimizer.
+ optimData = optData;
+ // Set up base class and perform computations.
+ return super.optimize(optData);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected UnivariatePointValuePair doOptimize() {
+ // Remove all instances of "MaxEval" and "SearchInterval" from the
+ // array that will be passed to the internal optimizer.
+ // The former is to enforce smaller numbers of allowed evaluations
+ // (according to how many have been used up already), and the latter
+ // to impose a different start value for each start.
+ for (int i = 0; i < optimData.length; i++) {
+ if (optimData[i] instanceof MaxEval) {
+ optimData[i] = null;
+ maxEvalIndex = i;
+ continue;
+ }
+ if (optimData[i] instanceof SearchInterval) {
+ optimData[i] = null;
+ searchIntervalIndex = i;
+ continue;
+ }
+ }
+ if (maxEvalIndex == -1) {
+ throw new MathIllegalStateException();
+ }
+ if (searchIntervalIndex == -1) {
+ throw new MathIllegalStateException();
+ }
+
+ RuntimeException lastException = null;
+ optima = new UnivariatePointValuePair[starts];
+ totalEvaluations = 0;
+
+ final int maxEval = getMaxEvaluations();
+ final double min = getMin();
+ final double max = getMax();
+ final double startValue = getStartValue();
+
+ // Multi-start loop.
+ for (int i = 0; i < starts; i++) {
+ // CHECKSTYLE: stop IllegalCatch
+ try {
+ // Decrease number of allowed evaluations.
+ optimData[maxEvalIndex] = new MaxEval(maxEval - totalEvaluations);
+ // New start value.
+ final double s = (i == 0) ?
+ startValue :
+ min + generator.nextDouble() * (max - min);
+ optimData[searchIntervalIndex] = new SearchInterval(min, max, s);
+ // Optimize.
+ optima[i] = optimizer.optimize(optimData);
+ } catch (RuntimeException mue) {
+ lastException = mue;
+ optima[i] = null;
+ }
+ // CHECKSTYLE: resume IllegalCatch
+
+ totalEvaluations += optimizer.getEvaluations();
+ }
+
+ sortPairs(getGoalType());
+
+ if (optima[0] == null) {
+ throw lastException; // Cannot be null if starts >= 1.
+ }
+
+ // Return the point with the best objective function value.
+ return optima[0];
+ }
+
+ /**
+ * Sort the optima from best to worst, followed by {@code null} elements.
+ *
+ * @param goal Goal type.
+ */
+ private void sortPairs(final GoalType goal) {
+ Arrays.sort(optima, new Comparator<UnivariatePointValuePair>() {
+ public int compare(final UnivariatePointValuePair o1,
+ final UnivariatePointValuePair o2) {
+ if (o1 == null) {
+ return (o2 == null) ? 0 : 1;
+ } else if (o2 == null) {
+ return -1;
+ }
+ final double v1 = o1.getValue();
+ final double v2 = o2.getValue();
+ return (goal == GoalType.MINIMIZE) ?
+ Double.compare(v1, v2) : Double.compare(v2, v1);
+ }
+ });
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/MultiStartUnivariateOptimizer.java
------------------------------------------------------------------------------
svn:eol-style = native
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/SearchInterval.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/SearchInterval.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/SearchInterval.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/SearchInterval.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,96 @@
+/*
+ * 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.math3.optim.univariate;
+
+import org.apache.commons.math3.optim.OptimizationData;
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.OutOfRangeException;
+
+/**
+ * Search interval and (optional) start value.
+ * <br/>
+ * Immutable class.
+ *
+ * @version $Id$
+ * @since 3.1
+ */
+public class SearchInterval implements OptimizationData {
+ /** Lower bound. */
+ private final double lower;
+ /** Upper bound. */
+ private final double upper;
+ /** Start value. */
+ private final double start;
+
+ /**
+ * @param lo Lower bound.
+ * @param hi Upper bound.
+ * @param init Start value.
+ * @throws NumberIsTooLargeException if {@code lo >= hi}.
+ * @throws OutOfRangeException if {@code init < lo} or {@code init > hi}.
+ */
+ public SearchInterval(double lo,
+ double hi,
+ double init) {
+ if (lo >= hi) {
+ throw new NumberIsTooLargeException(lo, hi, false);
+ }
+ if (init < lo ||
+ init > hi) {
+ throw new OutOfRangeException(init, lo, hi);
+ }
+
+ lower = lo;
+ upper = hi;
+ start = init;
+ }
+
+ /**
+ * @param lo Lower bound.
+ * @param hi Upper bound.
+ * @throws NumberIsTooLargeException if {@code lo >= hi}.
+ */
+ public SearchInterval(double lo,
+ double hi) {
+ this(lo, hi, 0.5 * (lo + hi));
+ }
+
+ /**
+ * Gets the lower bound.
+ *
+ * @return the lower bound.
+ */
+ public double getMin() {
+ return lower;
+ }
+ /**
+ * Gets the upper bound.
+ *
+ * @return the upper bound.
+ */
+ public double getMax() {
+ return upper;
+ }
+ /**
+ * Gets the start value.
+ *
+ * @return the start value.
+ */
+ public double getStartValue() {
+ return start;
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/optim/univariate/SearchInterval.java
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