Return-Path: X-Original-To: apmail-commons-commits-archive@minotaur.apache.org Delivered-To: apmail-commons-commits-archive@minotaur.apache.org Received: from mail.apache.org (hermes.apache.org [140.211.11.3]) by minotaur.apache.org (Postfix) with SMTP id 600BCDF14 for ; Wed, 12 Dec 2012 14:12:22 +0000 (UTC) Received: (qmail 75247 invoked by uid 500); 12 Dec 2012 14:12:22 -0000 Delivered-To: apmail-commons-commits-archive@commons.apache.org Received: (qmail 75167 invoked by uid 500); 12 Dec 2012 14:12:22 -0000 Mailing-List: contact commits-help@commons.apache.org; run by ezmlm Precedence: bulk List-Help: List-Unsubscribe: List-Post: List-Id: Reply-To: dev@commons.apache.org Delivered-To: mailing list commits@commons.apache.org Received: (qmail 75159 invoked by uid 99); 12 Dec 2012 14:12:21 -0000 Received: from athena.apache.org (HELO athena.apache.org) (140.211.11.136) by apache.org (qpsmtpd/0.29) with ESMTP; Wed, 12 Dec 2012 14:12:21 +0000 X-ASF-Spam-Status: No, hits=-1999.0 required=5.0 tests=ALL_TRUSTED,FRT_OFFER2 X-Spam-Check-By: apache.org Received: from [140.211.11.4] (HELO eris.apache.org) (140.211.11.4) by apache.org (qpsmtpd/0.29) with ESMTP; Wed, 12 Dec 2012 14:12:18 +0000 Received: from eris.apache.org (localhost [127.0.0.1]) by eris.apache.org (Postfix) with ESMTP id 1C15B2388C7E; Wed, 12 Dec 2012 14:11:25 +0000 (UTC) Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Subject: svn commit: r1420684 [13/15] - 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/ mai... Date: Wed, 12 Dec 2012 14:11:04 -0000 To: commits@commons.apache.org From: erans@apache.org X-Mailer: svnmailer-1.0.8-patched Message-Id: <20121212141125.1C15B2388C7E@eris.apache.org> X-Virus-Checked: Checked by ClamAV on apache.org Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTestValidation.java URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTestValidation.java?rev=1420684&view=auto ============================================================================== --- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTestValidation.java (added) +++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTestValidation.java Wed Dec 12 14:10:38 2012 @@ -0,0 +1,334 @@ +/* + * 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 java.util.List; +import java.util.ArrayList; +import java.awt.geom.Point2D; +import org.apache.commons.math3.optim.PointVectorValuePair; +import org.apache.commons.math3.optim.InitialGuess; +import org.apache.commons.math3.optim.MaxEval; +import org.apache.commons.math3.optim.nonlinear.vector.Target; +import org.apache.commons.math3.optim.nonlinear.vector.Weight; +import org.apache.commons.math3.stat.descriptive.SummaryStatistics; +import org.apache.commons.math3.stat.descriptive.StatisticalSummary; +import org.apache.commons.math3.util.FastMath; +import org.junit.Test; +import org.junit.Assert; + +/** + * This class demonstrates the main functionality of the + * {@link AbstractLeastSquaresOptimizer}, common to the + * optimizer implementations in package + * {@link org.apache.commons.math3.optimization.general}. + *
+ * Not enabled by default, as the class name does not end with "Test". + *
+ * Invoke by running + * 

+ *  mvn test -Dtest=AbstractLeastSquaresOptimizerTestValidation
+ *
+ * or by running + * 

+ *  mvn test -Dtest=AbstractLeastSquaresOptimizerTestValidation -DargLine="-DmcRuns=1234 -server"
+ *
+ */ +public class AbstractLeastSquaresOptimizerTestValidation { + private static final int MONTE_CARLO_RUNS = Integer.parseInt(System.getProperty("mcRuns", + "100")); + + /** + * Using a Monte-Carlo procedure, this test checks the error estimations + * as provided by the square-root of the diagonal elements of the + * covariance matrix. + *
+ * The test generates sets of observations, each sampled from + * a Gaussian distribution. + *
+ * The optimization problem solved is defined in class + * {@link StraightLineProblem}. + *
+ * The output (on stdout) will be a table summarizing the distribution + * of parameters generated by the Monte-Carlo process and by the direct + * estimation provided by the diagonal elements of the covariance matrix. + */ + @Test + public void testParametersErrorMonteCarloObservations() { + // Error on the observations. + final double yError = 15; + + // True values of the parameters. + final double slope = 123.456; + final double offset = -98.765; + + // Samples generator. + final RandomStraightLinePointGenerator lineGenerator + = new RandomStraightLinePointGenerator(slope, offset, + yError, + -1e3, 1e4, + 138577L); + + // Number of observations. + final int numObs = 100; // XXX Should be a command-line option. + // number of parameters. + final int numParams = 2; + + // Parameters found for each of Monte-Carlo run. + final SummaryStatistics[] paramsFoundByDirectSolution = new SummaryStatistics[numParams]; + // Sigma estimations (square-root of the diagonal elements of the + // covariance matrix), for each Monte-Carlo run. + final SummaryStatistics[] sigmaEstimate = new SummaryStatistics[numParams]; + + // Initialize statistics accumulators. + for (int i = 0; i < numParams; i++) { + paramsFoundByDirectSolution[i] = new SummaryStatistics(); + sigmaEstimate[i] = new SummaryStatistics(); + } + + // Dummy optimizer (to compute the covariance matrix). + final AbstractLeastSquaresOptimizer optim = new DummyOptimizer(); + final double[] init = { slope, offset }; + + // Monte-Carlo (generates many sets of observations). + final int mcRepeat = MONTE_CARLO_RUNS; + int mcCount = 0; + while (mcCount < mcRepeat) { + // Observations. + final Point2D.Double[] obs = lineGenerator.generate(numObs); + + final StraightLineProblem problem = new StraightLineProblem(yError); + for (int i = 0; i < numObs; i++) { + final Point2D.Double p = obs[i]; + problem.addPoint(p.x, p.y); + } + + // Direct solution (using simple regression). + final double[] regress = problem.solve(); + + // Estimation of the standard deviation (diagonal elements of the + // covariance matrix). + final PointVectorValuePair optimum + = optim.optimize(new MaxEval(Integer.MAX_VALUE), + problem.getModelFunction(), + problem.getModelFunctionJacobian(), + new Target(problem.target()), + new Weight(problem.weight()), + new InitialGuess(init)); + final double[] sigma = optim.computeSigma(optimum.getPoint(), 1e-14); + + // Accumulate statistics. + for (int i = 0; i < numParams; i++) { + paramsFoundByDirectSolution[i].addValue(regress[i]); + sigmaEstimate[i].addValue(sigma[i]); + } + + // Next Monte-Carlo. + ++mcCount; + } + + // Print statistics. + final String line = "--------------------------------------------------------------"; + System.out.println(" True value Mean Std deviation"); + for (int i = 0; i < numParams; i++) { + System.out.println(line); + System.out.println("Parameter #" + i); + + StatisticalSummary s = paramsFoundByDirectSolution[i].getSummary(); + System.out.printf(" %+.6e %+.6e %+.6e\n", + init[i], + s.getMean(), + s.getStandardDeviation()); + + s = sigmaEstimate[i].getSummary(); + System.out.printf("sigma: %+.6e (%+.6e)\n", + s.getMean(), + s.getStandardDeviation()); + } + System.out.println(line); + + // Check the error estimation. + for (int i = 0; i < numParams; i++) { + Assert.assertEquals(paramsFoundByDirectSolution[i].getSummary().getStandardDeviation(), + sigmaEstimate[i].getSummary().getMean(), + 8e-2); + } + } + + /** + * In this test, the set of observations is fixed. + * Using a Monte-Carlo procedure, it generates sets of parameters, + * and determine the parameter change that will result in the + * normalized chi-square becoming larger by one than the value from + * the best fit solution. + *
+ * The optimization problem solved is defined in class + * {@link StraightLineProblem}. + *
+ * The output (on stdout) will be a list of lines containing: + *
    + *
  • slope of the straight line,
    • + *
  • intercept of the straight line,
    • + *
  • chi-square of the solution defined by the above two values.
    • + *
+ * The output is separated into two blocks (with a blank line between + * them); the first block will contain all parameter sets for which + * {@code chi2 < chi2_b + 1} + * and the second block, all sets for which + * {@code chi2 >= chi2_b + 1} + * where {@code chi2_b} is the lowest chi-square (corresponding to the + * best solution). + */ + @Test + public void testParametersErrorMonteCarloParameters() { + // Error on the observations. + final double yError = 15; + + // True values of the parameters. + final double slope = 123.456; + final double offset = -98.765; + + // Samples generator. + final RandomStraightLinePointGenerator lineGenerator + = new RandomStraightLinePointGenerator(slope, offset, + yError, + -1e3, 1e4, + 13839013L); + + // Number of observations. + final int numObs = 10; + // number of parameters. + final int numParams = 2; + + // Create a single set of observations. + final Point2D.Double[] obs = lineGenerator.generate(numObs); + + final StraightLineProblem problem = new StraightLineProblem(yError); + for (int i = 0; i < numObs; i++) { + final Point2D.Double p = obs[i]; + problem.addPoint(p.x, p.y); + } + + // Direct solution (using simple regression). + final double[] regress = problem.solve(); + + // Dummy optimizer (to compute the chi-square). + final AbstractLeastSquaresOptimizer optim = new DummyOptimizer(); + final double[] init = { slope, offset }; + // Get chi-square of the best parameters set for the given set of + // observations. + final double bestChi2N = getChi2N(optim, problem, regress); + final double[] sigma = optim.computeSigma(regress, 1e-14); + + // Monte-Carlo (generates a grid of parameters). + final int mcRepeat = MONTE_CARLO_RUNS; + final int gridSize = (int) FastMath.sqrt(mcRepeat); + + // Parameters found for each of Monte-Carlo run. + // Index 0 = slope + // Index 1 = offset + // Index 2 = normalized chi2 + final List paramsAndChi2 = new ArrayList(gridSize * gridSize); + + final double slopeRange = 10 * sigma[0]; + final double offsetRange = 10 * sigma[1]; + final double minSlope = slope - 0.5 * slopeRange; + final double minOffset = offset - 0.5 * offsetRange; + final double deltaSlope = slopeRange/ gridSize; + final double deltaOffset = offsetRange / gridSize; + for (int i = 0; i < gridSize; i++) { + final double s = minSlope + i * deltaSlope; + for (int j = 0; j < gridSize; j++) { + final double o = minOffset + j * deltaOffset; + final double chi2N = getChi2N(optim, problem, new double[] {s, o}); + + paramsAndChi2.add(new double[] {s, o, chi2N}); + } + } + + // Output (for use with "gnuplot"). + + // Some info. + + // For plotting separately sets of parameters that have a large chi2. + final double chi2NPlusOne = bestChi2N + 1; + int numLarger = 0; + + final String lineFmt = "%+.10e %+.10e %.8e\n"; + + // Point with smallest chi-square. + System.out.printf(lineFmt, regress[0], regress[1], bestChi2N); + System.out.println(); // Empty line. + + // Points within the confidence interval. + for (double[] d : paramsAndChi2) { + if (d[2] <= chi2NPlusOne) { + System.out.printf(lineFmt, d[0], d[1], d[2]); + } + } + System.out.println(); // Empty line. + + // Points outside the confidence interval. + for (double[] d : paramsAndChi2) { + if (d[2] > chi2NPlusOne) { + ++numLarger; + System.out.printf(lineFmt, d[0], d[1], d[2]); + } + } + System.out.println(); // Empty line. + + System.out.println("# sigma=" + Arrays.toString(sigma)); + System.out.println("# " + numLarger + " sets filtered out"); + } + + /** + * @return the normalized chi-square. + */ + private double getChi2N(AbstractLeastSquaresOptimizer optim, + StraightLineProblem problem, + double[] params) { + final double[] t = problem.target(); + final double[] w = problem.weight(); + + optim.optimize(new MaxEval(Integer.MAX_VALUE), + problem.getModelFunction(), + problem.getModelFunctionJacobian(), + new Target(t), + new Weight(w), + new InitialGuess(params)); + + return optim.getChiSquare() / (t.length - params.length); + } +} + +/** + * A dummy optimizer. + * Used for computing the covariance matrix. + */ +class DummyOptimizer extends AbstractLeastSquaresOptimizer { + public DummyOptimizer() { + super(null); + } + + /** + * This method does nothing and returns a dummy value. + */ + @Override + public PointVectorValuePair doOptimize() { + final double[] params = getStartPoint(); + final double[] res = computeResiduals(computeObjectiveValue(params)); + setCost(computeCost(res)); + return new PointVectorValuePair(params, null); + } +} Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTestValidation.java ------------------------------------------------------------------------------ svn:eol-style = native Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleProblem.java URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleProblem.java?rev=1420684&view=auto ============================================================================== --- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleProblem.java (added) +++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleProblem.java Wed Dec 12 14:10:38 2012 @@ -0,0 +1,177 @@ +/* + * 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.ArrayList; +import org.apache.commons.math3.analysis.MultivariateVectorFunction; +import org.apache.commons.math3.analysis.MultivariateMatrixFunction; +import org.apache.commons.math3.util.MathUtils; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian; + +/** + * Class that models a circle. + * The parameters of problem are: + *
    + *
  • the x-coordinate of the circle center,
    • + *
  • the y-coordinate of the circle center,
    • + *
  • the radius of the circle.
    • + *
+ * The model functions are: + *
    + *
  • for each triplet (cx, cy, r), the (x, y) coordinates of a point on the + * corresponding circle.
    • + *
+ */ +class CircleProblem { + /** Cloud of points assumed to be fitted by a circle. */ + private final ArrayList points; + /** Error on the x-coordinate of the points. */ + private final double xSigma; + /** Error on the y-coordinate of the points. */ + private final double ySigma; + /** Number of points on the circumference (when searching which + model point is closest to a given "observation". */ + private final int resolution; + + /** + * @param xError Assumed error for the x-coordinate of the circle points. + * @param yError Assumed error for the y-coordinate of the circle points. + * @param searchResolution Number of points to try when searching the one + * that is closest to a given "observed" point. + */ + public CircleProblem(double xError, + double yError, + int searchResolution) { + points = new ArrayList(); + xSigma = xError; + ySigma = yError; + resolution = searchResolution; + } + + /** + * @param xError Assumed error for the x-coordinate of the circle points. + * @param yError Assumed error for the y-coordinate of the circle points. + */ + public CircleProblem(double xError, + double yError) { + this(xError, yError, 500); + } + + public void addPoint(double px, double py) { + points.add(new double[] { px, py }); + } + + public double[] target() { + final double[] t = new double[points.size() * 2]; + for (int i = 0; i < points.size(); i++) { + final double[] p = points.get(i); + final int index = i * 2; + t[index] = p[0]; + t[index + 1] = p[1]; + } + + return t; + } + + public double[] weight() { + final double wX = 1 / (xSigma * xSigma); + final double wY = 1 / (ySigma * ySigma); + final double[] w = new double[points.size() * 2]; + for (int i = 0; i < points.size(); i++) { + final int index = i * 2; + w[index] = wX; + w[index + 1] = wY; + } + + return w; + } + + public ModelFunction getModelFunction() { + return new ModelFunction(new MultivariateVectorFunction() { + public double[] value(double[] params) { + final double cx = params[0]; + final double cy = params[1]; + final double r = params[2]; + + final double[] model = new double[points.size() * 2]; + + final double deltaTheta = MathUtils.TWO_PI / resolution; + for (int i = 0; i < points.size(); i++) { + final double[] p = points.get(i); + final double px = p[0]; + final double py = p[1]; + + double bestX = 0; + double bestY = 0; + double dMin = Double.POSITIVE_INFINITY; + + // Find the angle for which the circle passes closest to the + // current point (using a resolution of 100 points along the + // circumference). + for (double theta = 0; theta <= MathUtils.TWO_PI; theta += deltaTheta) { + final double currentX = cx + r * FastMath.cos(theta); + final double currentY = cy + r * FastMath.sin(theta); + final double dX = currentX - px; + final double dY = currentY - py; + final double d = dX * dX + dY * dY; + if (d < dMin) { + dMin = d; + bestX = currentX; + bestY = currentY; + } + } + + final int index = i * 2; + model[index] = bestX; + model[index + 1] = bestY; + } + + return model; + } + }); + } + + public ModelFunctionJacobian getModelFunctionJacobian() { + return new ModelFunctionJacobian(new MultivariateMatrixFunction() { + public double[][] value(double[] point) { + return jacobian(point); + } + }); + } + + private double[][] jacobian(double[] params) { + final double[][] jacobian = new double[points.size() * 2][3]; + + for (int i = 0; i < points.size(); i++) { + final int index = i * 2; + // Partial derivative wrt x-coordinate of center. + jacobian[index][0] = 1; + jacobian[index + 1][0] = 0; + // Partial derivative wrt y-coordinate of center. + jacobian[index][1] = 0; + jacobian[index + 1][1] = 1; + // Partial derivative wrt radius. + final double[] p = points.get(i); + jacobian[index][2] = (p[0] - params[0]) / params[2]; + jacobian[index + 1][2] = (p[1] - params[1]) / params[2]; + } + + return jacobian; + } +} Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleProblem.java ------------------------------------------------------------------------------ svn:eol-style = native Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleVectorial.java URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleVectorial.java?rev=1420684&view=auto ============================================================================== --- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleVectorial.java (added) +++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleVectorial.java Wed Dec 12 14:10:38 2012 @@ -0,0 +1,97 @@ +/* + * 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.ArrayList; +import org.apache.commons.math3.analysis.MultivariateVectorFunction; +import org.apache.commons.math3.analysis.MultivariateMatrixFunction; +import org.apache.commons.math3.geometry.euclidean.twod.Vector2D; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian; + +/** + * Class used in the tests. + */ +class CircleVectorial { + private ArrayList points; + + public CircleVectorial() { + points = new ArrayList(); + } + + public void addPoint(double px, double py) { + points.add(new Vector2D(px, py)); + } + + public int getN() { + return points.size(); + } + + public double getRadius(Vector2D center) { + double r = 0; + for (Vector2D point : points) { + r += point.distance(center); + } + return r / points.size(); + } + + public ModelFunction getModelFunction() { + return new ModelFunction(new MultivariateVectorFunction() { + public double[] value(double[] params) { + Vector2D center = new Vector2D(params[0], params[1]); + double radius = getRadius(center); + double[] residuals = new double[points.size()]; + for (int i = 0; i < residuals.length; i++) { + residuals[i] = points.get(i).distance(center) - radius; + } + + return residuals; + } + }); + } + + public ModelFunctionJacobian getModelFunctionJacobian() { + return new ModelFunctionJacobian(new MultivariateMatrixFunction() { + public double[][] value(double[] params) { + final int n = points.size(); + final Vector2D center = new Vector2D(params[0], params[1]); + + double dRdX = 0; + double dRdY = 0; + for (Vector2D pk : points) { + double dk = pk.distance(center); + dRdX += (center.getX() - pk.getX()) / dk; + dRdY += (center.getY() - pk.getY()) / dk; + } + dRdX /= n; + dRdY /= n; + + // Jacobian of the radius residuals. + double[][] jacobian = new double[n][2]; + for (int i = 0; i < n; i++) { + final Vector2D pi = points.get(i); + final double di = pi.distance(center); + jacobian[i][0] = (center.getX() - pi.getX()) / di - dRdX; + jacobian[i][1] = (center.getY() - pi.getY()) / di - dRdY; + } + + return jacobian; + } + }); + } +} Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/CircleVectorial.java ------------------------------------------------------------------------------ svn:eol-style = native Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/GaussNewtonOptimizerTest.java URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/GaussNewtonOptimizerTest.java?rev=1420684&view=auto ============================================================================== --- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/GaussNewtonOptimizerTest.java (added) +++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/GaussNewtonOptimizerTest.java Wed Dec 12 14:10:38 2012 @@ -0,0 +1,159 @@ +/* + * 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.io.IOException; +import org.apache.commons.math3.exception.ConvergenceException; +import org.apache.commons.math3.exception.TooManyEvaluationsException; +import org.apache.commons.math3.optim.SimpleVectorValueChecker; +import org.apache.commons.math3.optim.InitialGuess; +import org.apache.commons.math3.optim.MaxEval; +import org.apache.commons.math3.optim.nonlinear.vector.Target; +import org.apache.commons.math3.optim.nonlinear.vector.Weight; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian; +import org.junit.Test; + +/** + *

Some of the unit tests are re-implementations of the MINPACK file17 and file22 test files. + * The redistribution policy for MINPACK is available here, for + * convenience, it is reproduced below.

+ + * + * + * + *
+ * Minpack Copyright Notice (1999) University of Chicago. + * All rights reserved + *
+ * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + *
    + *
  1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer.
    2. + *
  2. 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.
    3. + *
  3. The end-user documentation included with the redistribution, if any, + * must include the following acknowledgment: + * This product includes software developed by the University of + * Chicago, as Operator of Argonne National Laboratory. + * Alternately, this acknowledgment may appear in the software itself, + * if and wherever such third-party acknowledgments normally appear.
    4. + *
  4. 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.
    5. + *
  5. 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.
    6. + *
    + + * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests) + * @author Burton S. Garbow (original fortran minpack tests) + * @author Kenneth E. Hillstrom (original fortran minpack tests) + * @author Jorge J. More (original fortran minpack tests) + * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation) + */ +public class GaussNewtonOptimizerTest + extends AbstractLeastSquaresOptimizerAbstractTest { + + @Override + public AbstractLeastSquaresOptimizer createOptimizer() { + return new GaussNewtonOptimizer(new SimpleVectorValueChecker(1.0e-6, 1.0e-6)); + } + + @Override + @Test(expected = ConvergenceException.class) + public void testMoreEstimatedParametersSimple() { + /* + * Exception is expected with this optimizer + */ + super.testMoreEstimatedParametersSimple(); + } + + @Override + @Test(expected=ConvergenceException.class) + public void testMoreEstimatedParametersUnsorted() { + /* + * Exception is expected with this optimizer + */ + super.testMoreEstimatedParametersUnsorted(); + } + + @Test(expected=TooManyEvaluationsException.class) + public void testMaxEvaluations() throws Exception { + CircleVectorial circle = new CircleVectorial(); + circle.addPoint( 30.0, 68.0); + circle.addPoint( 50.0, -6.0); + circle.addPoint(110.0, -20.0); + circle.addPoint( 35.0, 15.0); + circle.addPoint( 45.0, 97.0); + + GaussNewtonOptimizer optimizer + = new GaussNewtonOptimizer(new SimpleVectorValueChecker(1e-30, 1e-30)); + + optimizer.optimize(new MaxEval(100), + circle.getModelFunction(), + circle.getModelFunctionJacobian(), + new Target(new double[] { 0, 0, 0, 0, 0 }), + new Weight(new double[] { 1, 1, 1, 1, 1 }), + new InitialGuess(new double[] { 98.680, 47.345 })); + } + + @Override + @Test(expected=ConvergenceException.class) + public void testCircleFittingBadInit() { + /* + * This test does not converge with this optimizer. + */ + super.testCircleFittingBadInit(); + } + + @Override + @Test(expected = ConvergenceException.class) + public void testHahn1() + throws IOException { + /* + * TODO This test leads to a singular problem with the Gauss-Newton + * optimizer. This should be inquired. + */ + super.testHahn1(); + } +} Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/GaussNewtonOptimizerTest.java ------------------------------------------------------------------------------ svn:eol-style = native Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizerTest.java URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizerTest.java?rev=1420684&view=auto ============================================================================== --- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizerTest.java (added) +++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizerTest.java Wed Dec 12 14:10:38 2012 @@ -0,0 +1,403 @@ +/* + * 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.io.Serializable; +import java.util.ArrayList; +import java.util.List; +import org.apache.commons.math3.optim.PointVectorValuePair; +import org.apache.commons.math3.optim.InitialGuess; +import org.apache.commons.math3.optim.MaxEval; +import org.apache.commons.math3.optim.nonlinear.vector.Target; +import org.apache.commons.math3.optim.nonlinear.vector.Weight; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction; +import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian; +import org.apache.commons.math3.analysis.MultivariateVectorFunction; +import org.apache.commons.math3.analysis.MultivariateMatrixFunction; +import org.apache.commons.math3.exception.ConvergenceException; +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.TooManyEvaluationsException; +import org.apache.commons.math3.geometry.euclidean.twod.Vector2D; +import org.apache.commons.math3.linear.SingularMatrixException; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.Precision; +import org.junit.Assert; +import org.junit.Test; +import org.junit.Ignore; + +/** + *

    Some of the unit tests are re-implementations of the MINPACK file17 and file22 test files. + * The redistribution policy for MINPACK is available here, for + * convenience, it is reproduced below.

    + + * + * + * + *
    + * Minpack Copyright Notice (1999) University of Chicago. + * All rights reserved + *
    + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + *
      + *
    1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer.
      2. + *
    2. 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.
      3. + *
    3. The end-user documentation included with the redistribution, if any, + * must include the following acknowledgment: + * This product includes software developed by the University of + * Chicago, as Operator of Argonne National Laboratory. + * Alternately, this acknowledgment may appear in the software itself, + * if and wherever such third-party acknowledgments normally appear.
      4. + *
    4. 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.
      5. + *
    5. 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.
      6. + *
      + + * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests) + * @author Burton S. Garbow (original fortran minpack tests) + * @author Kenneth E. Hillstrom (original fortran minpack tests) + * @author Jorge J. More (original fortran minpack tests) + * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation) + */ +public class LevenbergMarquardtOptimizerTest + extends AbstractLeastSquaresOptimizerAbstractTest { + @Override + public AbstractLeastSquaresOptimizer createOptimizer() { + return new LevenbergMarquardtOptimizer(); + } + + @Override + @Test(expected=SingularMatrixException.class) + public void testNonInvertible() { + /* + * Overrides the method from parent class, since the default singularity + * threshold (1e-14) does not trigger the expected exception. + */ + LinearProblem problem = new LinearProblem(new double[][] { + { 1, 2, -3 }, + { 2, 1, 3 }, + { -3, 0, -9 } + }, new double[] { 1, 1, 1 }); + + AbstractLeastSquaresOptimizer optimizer = createOptimizer(); + PointVectorValuePair optimum + = optimizer.optimize(new MaxEval(100), + problem.getModelFunction(), + problem.getModelFunctionJacobian(), + problem.getTarget(), + new Weight(new double[] { 1, 1, 1 }), + new InitialGuess(new double[] { 0, 0, 0 })); + Assert.assertTrue(FastMath.sqrt(optimizer.getTargetSize()) * optimizer.getRMS() > 0.6); + + optimizer.computeCovariances(optimum.getPoint(), 1.5e-14); + } + + @Test + public void testControlParameters() { + CircleVectorial circle = new CircleVectorial(); + circle.addPoint( 30.0, 68.0); + circle.addPoint( 50.0, -6.0); + circle.addPoint(110.0, -20.0); + circle.addPoint( 35.0, 15.0); + circle.addPoint( 45.0, 97.0); + checkEstimate(circle.getModelFunction(), + circle.getModelFunctionJacobian(), + 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false); + checkEstimate(circle.getModelFunction(), + circle.getModelFunctionJacobian(), + 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true); + checkEstimate(circle.getModelFunction(), + circle.getModelFunctionJacobian(), + 0.1, 5, 1.0e-15, 1.0e-16, 1.0e-10, true); + circle.addPoint(300, -300); + checkEstimate(circle.getModelFunction(), + circle.getModelFunctionJacobian(), + 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true); + } + + private void checkEstimate(ModelFunction problem, + ModelFunctionJacobian problemJacobian, + double initialStepBoundFactor, int maxCostEval, + double costRelativeTolerance, double parRelativeTolerance, + double orthoTolerance, boolean shouldFail) { + try { + LevenbergMarquardtOptimizer optimizer + = new LevenbergMarquardtOptimizer(initialStepBoundFactor, + costRelativeTolerance, + parRelativeTolerance, + orthoTolerance, + Precision.SAFE_MIN); + optimizer.optimize(new MaxEval(maxCostEval), + problem, + problemJacobian, + new Target(new double[] { 0, 0, 0, 0, 0 }), + new Weight(new double[] { 1, 1, 1, 1, 1 }), + new InitialGuess(new double[] { 98.680, 47.345 })); + Assert.assertTrue(!shouldFail); + } catch (DimensionMismatchException ee) { + Assert.assertTrue(shouldFail); + } catch (TooManyEvaluationsException ee) { + Assert.assertTrue(shouldFail); + } + } + + /** + * Non-linear test case: fitting of decay curve (from Chapter 8 of + * Bevington's textbook, "Data reduction and analysis for the physical sciences"). + * XXX The expected ("reference") values may not be accurate and the tolerance too + * relaxed for this test to be currently really useful (the issue is under + * investigation). + */ + @Test + public void testBevington() { + final double[][] dataPoints = { + // column 1 = times + { 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, + 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, + 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, + 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, + 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, + 765, 780, 795, 810, 825, 840, 855, 870, 885, }, + // column 2 = measured counts + { 775, 479, 380, 302, 185, 157, 137, 119, 110, 89, + 74, 61, 66, 68, 48, 54, 51, 46, 55, 29, + 28, 37, 49, 26, 35, 29, 31, 24, 25, 35, + 24, 30, 26, 28, 21, 18, 20, 27, 17, 17, + 14, 17, 24, 11, 22, 17, 12, 10, 13, 16, + 9, 9, 14, 21, 17, 13, 12, 18, 10, }, + }; + + final BevingtonProblem problem = new BevingtonProblem(); + + final int len = dataPoints[0].length; + final double[] weights = new double[len]; + for (int i = 0; i < len; i++) { + problem.addPoint(dataPoints[0][i], + dataPoints[1][i]); + + weights[i] = 1 / dataPoints[1][i]; + } + + final LevenbergMarquardtOptimizer optimizer + = new LevenbergMarquardtOptimizer(); + + final PointVectorValuePair optimum + = optimizer.optimize(new MaxEval(100), + problem.getModelFunction(), + problem.getModelFunctionJacobian(), + new Target(dataPoints[1]), + new Weight(weights), + new InitialGuess(new double[] { 10, 900, 80, 27, 225 })); + + final double[] solution = optimum.getPoint(); + final double[] expectedSolution = { 10.4, 958.3, 131.4, 33.9, 205.0 }; + + final double[][] covarMatrix = optimizer.computeCovariances(solution, 1e-14); + final double[][] expectedCovarMatrix = { + { 3.38, -3.69, 27.98, -2.34, -49.24 }, + { -3.69, 2492.26, 81.89, -69.21, -8.9 }, + { 27.98, 81.89, 468.99, -44.22, -615.44 }, + { -2.34, -69.21, -44.22, 6.39, 53.80 }, + { -49.24, -8.9, -615.44, 53.8, 929.45 } + }; + + final int numParams = expectedSolution.length; + + // Check that the computed solution is within the reference error range. + for (int i = 0; i < numParams; i++) { + final double error = FastMath.sqrt(expectedCovarMatrix[i][i]); + Assert.assertEquals("Parameter " + i, expectedSolution[i], solution[i], error); + } + + // Check that each entry of the computed covariance matrix is within 10% + // of the reference matrix entry. + for (int i = 0; i < numParams; i++) { + for (int j = 0; j < numParams; j++) { + Assert.assertEquals("Covariance matrix [" + i + "][" + j + "]", + expectedCovarMatrix[i][j], + covarMatrix[i][j], + FastMath.abs(0.1 * expectedCovarMatrix[i][j])); + } + } + } + + @Test + public void testCircleFitting2() { + final double xCenter = 123.456; + final double yCenter = 654.321; + final double xSigma = 10; + final double ySigma = 15; + final double radius = 111.111; + // The test is extremely sensitive to the seed. + final long seed = 59421061L; + final RandomCirclePointGenerator factory + = new RandomCirclePointGenerator(xCenter, yCenter, radius, + xSigma, ySigma, + seed); + final CircleProblem circle = new CircleProblem(xSigma, ySigma); + + final int numPoints = 10; + for (Vector2D p : factory.generate(numPoints)) { + circle.addPoint(p.getX(), p.getY()); + } + + // First guess for the center's coordinates and radius. + final double[] init = { 90, 659, 115 }; + + final LevenbergMarquardtOptimizer optimizer + = new LevenbergMarquardtOptimizer(); + final PointVectorValuePair optimum = optimizer.optimize(new MaxEval(100), + circle.getModelFunction(), + circle.getModelFunctionJacobian(), + new Target(circle.target()), + new Weight(circle.weight()), + new InitialGuess(init)); + + final double[] paramFound = optimum.getPoint(); + + // Retrieve errors estimation. + final double[] asymptoticStandardErrorFound = optimizer.computeSigma(paramFound, 1e-14); + + // Check that the parameters are found within the assumed error bars. + Assert.assertEquals(xCenter, paramFound[0], asymptoticStandardErrorFound[0]); + Assert.assertEquals(yCenter, paramFound[1], asymptoticStandardErrorFound[1]); + Assert.assertEquals(radius, paramFound[2], asymptoticStandardErrorFound[2]); + } + + private static class QuadraticProblem { + private List x; + private List y; + + public QuadraticProblem() { + x = new ArrayList(); + y = new ArrayList(); + } + + public void addPoint(double x, double y) { + this.x.add(x); + this.y.add(y); + } + + public ModelFunction getModelFunction() { + return new ModelFunction(new MultivariateVectorFunction() { + public double[] value(double[] variables) { + double[] values = new double[x.size()]; + for (int i = 0; i < values.length; ++i) { + values[i] = (variables[0] * x.get(i) + variables[1]) * x.get(i) + variables[2]; + } + return values; + } + }); + } + + public ModelFunctionJacobian getModelFunctionJacobian() { + return new ModelFunctionJacobian(new MultivariateMatrixFunction() { + public double[][] value(double[] params) { + double[][] jacobian = new double[x.size()][3]; + for (int i = 0; i < jacobian.length; ++i) { + jacobian[i][0] = x.get(i) * x.get(i); + jacobian[i][1] = x.get(i); + jacobian[i][2] = 1.0; + } + return jacobian; + } + }); + } + } + + private static class BevingtonProblem { + private List time; + private List count; + + public BevingtonProblem() { + time = new ArrayList(); + count = new ArrayList(); + } + + public void addPoint(double t, double c) { + time.add(t); + count.add(c); + } + + public ModelFunction getModelFunction() { + return new ModelFunction(new MultivariateVectorFunction() { + public double[] value(double[] params) { + double[] values = new double[time.size()]; + for (int i = 0; i < values.length; ++i) { + final double t = time.get(i); + values[i] = params[0] + + params[1] * Math.exp(-t / params[3]) + + params[2] * Math.exp(-t / params[4]); + } + return values; + } + }); + } + + public ModelFunctionJacobian getModelFunctionJacobian() { + return new ModelFunctionJacobian(new MultivariateMatrixFunction() { + public double[][] value(double[] params) { + double[][] jacobian = new double[time.size()][5]; + + for (int i = 0; i < jacobian.length; ++i) { + final double t = time.get(i); + jacobian[i][0] = 1; + + final double p3 = params[3]; + final double p4 = params[4]; + final double tOp3 = t / p3; + final double tOp4 = t / p4; + jacobian[i][1] = Math.exp(-tOp3); + jacobian[i][2] = Math.exp(-tOp4); + jacobian[i][3] = params[1] * Math.exp(-tOp3) * tOp3 / p3; + jacobian[i][4] = params[2] * Math.exp(-tOp4) * tOp4 / p4; + } + return jacobian; + } + }); + } + } +} Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/LevenbergMarquardtOptimizerTest.java ------------------------------------------------------------------------------ svn:eol-style = native