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From t.@apache.org
Subject [1/5] [math] Remove deprecated classes in optim package.
Date Sat, 11 Apr 2015 14:06:06 GMT
Repository: commons-math
Updated Branches:
  refs/heads/master 8a7645356 -> e31fde875


http://git-wip-us.apache.org/repos/asf/commons-math/blob/0737cf82/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
b/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
deleted file mode 100644
index b0a2ca3..0000000
--- a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizer.java
+++ /dev/null
@@ -1,962 +0,0 @@
-/*
- * 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.math4.optim.nonlinear.vector.jacobian;
-
-import java.util.Arrays;
-
-import org.apache.commons.math4.exception.ConvergenceException;
-import org.apache.commons.math4.exception.MathUnsupportedOperationException;
-import org.apache.commons.math4.exception.util.LocalizedFormats;
-import org.apache.commons.math4.linear.RealMatrix;
-import org.apache.commons.math4.optim.ConvergenceChecker;
-import org.apache.commons.math4.optim.PointVectorValuePair;
-import org.apache.commons.math4.util.FastMath;
-import org.apache.commons.math4.util.Precision;
-
-
-/**
- * This class solves a least-squares problem using the Levenberg-Marquardt
- * algorithm.
- * <br/>
- * Constraints are not supported: the call to
- * {@link #optimize(OptimizationData[]) optimize} will throw
- * {@link MathUnsupportedOperationException} if bounds are passed to it.
- *
- * <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 num&eacute;rique matricielle
- * appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</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>
- *
- * @since 2.0
- * @deprecated All classes and interfaces in this package are deprecated.
- * The optimizers that were provided here were moved to the
- * {@link org.apache.commons.math4.fitting.leastsquares} package
- * (cf. MATH-1008).
- */
-@Deprecated
-public class LevenbergMarquardtOptimizer
-    extends AbstractLeastSquaresOptimizer {
-    /** Twice the "epsilon machine". */
-    private static final double TWO_EPS = 2 * Precision.EPSILON;
-    /** 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() {
-        checkParameters();
-
-        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;
-        final ConvergenceChecker<PointVectorValuePair> checker = getConvergenceChecker();
-        while (true) {
-            incrementIterationCount();
-
-            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 /= 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 && checker.converged(getIterations(), 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
-                if (FastMath.abs(actRed) <= TWO_EPS &&
-                    preRed <= TWO_EPS &&
-                    ratio <= 2.0) {
-                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_COST_RELATIVE_TOLERANCE,
-                                                   costRelativeTolerance);
-                } else if (delta <= TWO_EPS * xNorm) {
-                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE,
-                                                   parRelativeTolerance);
-                } else if (maxCosine <= TWO_EPS) {
-                    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) {
-            paru = Precision.SAFE_MIN / 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(Precision.SAFE_MIN, 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 num&eacute;rique matricielle appliqu&eacute;e &agrave;
-     * l'art de l'ing&eacute;nieur</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];
-            }
-        }
-    }
-
-    /**
-     * @throws MathUnsupportedOperationException if bounds were passed to the
-     * {@link #optimize(OptimizationData[]) optimize} method.
-     */
-    private void checkParameters() {
-        if (getLowerBound() != null ||
-            getUpperBound() != null) {
-            throw new MathUnsupportedOperationException(LocalizedFormats.CONSTRAINT);
-        }
-    }
-}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/0737cf82/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/package-info.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/package-info.java
b/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/package-info.java
deleted file mode 100644
index ab06a53..0000000
--- a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/jacobian/package-info.java
+++ /dev/null
@@ -1,26 +0,0 @@
-/*
- * 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.
- */
-
-/**
- * This package provides optimization algorithms that require derivatives.
- *
- * @deprecated All classes and interfaces in this package are deprecated.
- * The optimizers that were provided here were moved to the
- * {@link org.apache.commons.math4.fitting.leastsquares} package
- * (cf. MATH-1008).
- */
-package org.apache.commons.math4.optim.nonlinear.vector.jacobian;

http://git-wip-us.apache.org/repos/asf/commons-math/blob/0737cf82/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/package-info.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/package-info.java
b/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/package-info.java
deleted file mode 100644
index 91ac3ff..0000000
--- a/src/main/java/org/apache/commons/math4/optim/nonlinear/vector/package-info.java
+++ /dev/null
@@ -1,26 +0,0 @@
-/*
- * 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.
- */
-
-/**
- * Algorithms for optimizing a vector function.
- *
- * @deprecated All classes and interfaces in this package are deprecated.
- * The optimizers that were provided here were moved to the
- * {@link org.apache.commons.math4.fitting.leastsquares} package
- * (cf. MATH-1008).
- */
-package org.apache.commons.math4.optim.nonlinear.vector;

http://git-wip-us.apache.org/repos/asf/commons-math/blob/0737cf82/src/main/java/org/apache/commons/math4/optim/univariate/MultiStartUnivariateOptimizer.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/optim/univariate/MultiStartUnivariateOptimizer.java
b/src/main/java/org/apache/commons/math4/optim/univariate/MultiStartUnivariateOptimizer.java
index cbfa268..c8a59e9 100644
--- a/src/main/java/org/apache/commons/math4/optim/univariate/MultiStartUnivariateOptimizer.java
+++ b/src/main/java/org/apache/commons/math4/optim/univariate/MultiStartUnivariateOptimizer.java
@@ -45,9 +45,9 @@ public class MultiStartUnivariateOptimizer
     /** Number of evaluations already performed for all starts. */
     private int totalEvaluations;
     /** Number of starts to go. */
-    private int starts;
+    private final int starts;
     /** Random generator for multi-start. */
-    private RandomGenerator generator;
+    private final RandomGenerator generator;
     /** Found optima. */
     private UnivariatePointValuePair[] optima;
     /** Optimization data. */
@@ -211,6 +211,7 @@ public class MultiStartUnivariateOptimizer
      */
     private void sortPairs(final GoalType goal) {
         Arrays.sort(optima, new Comparator<UnivariatePointValuePair>() {
+                @Override
                 public int compare(final UnivariatePointValuePair o1,
                                    final UnivariatePointValuePair o2) {
                     if (o1 == null) {


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