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From er...@apache.org
Subject svn commit: r1420684 [12/15] - 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 GMT
Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,228 @@
+/*
+ * 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.scalar.noderiv;
+
+import org.apache.commons.math3.analysis.MultivariateFunction;
+import org.apache.commons.math3.optim.MaxEval;
+import org.apache.commons.math3.optim.GoalType;
+import org.apache.commons.math3.optim.InitialGuess;
+import org.apache.commons.math3.optim.PointValuePair;
+import org.apache.commons.math3.optim.SimpleValueChecker;
+import org.apache.commons.math3.optim.ObjectiveFunction;
+import org.apache.commons.math3.util.FastMath;
+import org.junit.Assert;
+import org.junit.Test;
+
+public class SimplexOptimizerMultiDirectionalTest {
+    @Test
+    public void testMinimize1() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(200),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { -3, 0 }),
+                                 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6);
+        Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
+        Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13);
+        Assert.assertTrue(optimizer.getEvaluations() > 120);
+        Assert.assertTrue(optimizer.getEvaluations() < 150);
+    }
+
+    @Test
+    public void testMinimize2() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(200),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { 1, 0 }),
+                                 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
+        Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
+        Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
+        Assert.assertTrue(optimizer.getEvaluations() > 120);
+        Assert.assertTrue(optimizer.getEvaluations() < 150);
+    }
+
+    @Test
+    public void testMaximize1() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(200),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MAXIMIZE,
+                                 new InitialGuess(new double[] { -3.0, 0.0 }),
+                                 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 7e-7);
+        Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-7);
+        Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 2e-14);
+        Assert.assertTrue(optimizer.getEvaluations() > 120);
+        Assert.assertTrue(optimizer.getEvaluations() < 150);
+    }
+
+    @Test
+    public void testMaximize2() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30));
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(200),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MAXIMIZE,
+                                 new InitialGuess(new double[] { 1, 0 }),
+                                 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
+        Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
+        Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 2e-12);
+        Assert.assertTrue(optimizer.getEvaluations() > 180);
+        Assert.assertTrue(optimizer.getEvaluations() < 220);
+    }
+
+    @Test
+    public void testRosenbrock() {
+        MultivariateFunction rosenbrock
+            = new MultivariateFunction() {
+                    public double value(double[] x) {
+                        ++count;
+                        double a = x[1] - x[0] * x[0];
+                        double b = 1.0 - x[0];
+                        return 100 * a * a + b * b;
+                    }
+                };
+
+        count = 0;
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
+        PointValuePair optimum
+           = optimizer.optimize(new MaxEval(100),
+                                new ObjectiveFunction(rosenbrock),
+                                GoalType.MINIMIZE,
+                                new InitialGuess(new double[] { -1.2, 1 }),
+                                new MultiDirectionalSimplex(new double[][] {
+                                        { -1.2,  1.0 },
+                                        { 0.9, 1.2 },
+                                        {  3.5, -2.3 } }));
+
+        Assert.assertEquals(count, optimizer.getEvaluations());
+        Assert.assertTrue(optimizer.getEvaluations() > 50);
+        Assert.assertTrue(optimizer.getEvaluations() < 100);
+        Assert.assertTrue(optimum.getValue() > 1e-2);
+    }
+
+    @Test
+    public void testPowell() {
+        MultivariateFunction powell
+            = new MultivariateFunction() {
+                    public double value(double[] x) {
+                        ++count;
+                        double a = x[0] + 10 * x[1];
+                        double b = x[2] - x[3];
+                        double c = x[1] - 2 * x[2];
+                        double d = x[0] - x[3];
+                        return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
+                    }
+                };
+
+        count = 0;
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
+        PointValuePair optimum
+            = optimizer.optimize(new MaxEval(1000),
+                                 new ObjectiveFunction(powell),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { 3, -1, 0, 1 }),
+                                 new MultiDirectionalSimplex(4));
+        Assert.assertEquals(count, optimizer.getEvaluations());
+        Assert.assertTrue(optimizer.getEvaluations() > 800);
+        Assert.assertTrue(optimizer.getEvaluations() < 900);
+        Assert.assertTrue(optimum.getValue() > 1e-2);
+    }
+
+    @Test
+    public void testMath283() {
+        // fails because MultiDirectional.iterateSimplex is looping forever
+        // the while(true) should be replaced with a convergence check
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14);
+        final Gaussian2D function = new Gaussian2D(0, 0, 1);
+        PointValuePair estimate = optimizer.optimize(new MaxEval(1000),
+                                                     new ObjectiveFunction(function),
+                                                     GoalType.MAXIMIZE,
+                                                     new InitialGuess(function.getMaximumPosition()),
+                                                     new MultiDirectionalSimplex(2));
+        final double EPSILON = 1e-5;
+        final double expectedMaximum = function.getMaximum();
+        final double actualMaximum = estimate.getValue();
+        Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);
+
+        final double[] expectedPosition = function.getMaximumPosition();
+        final double[] actualPosition = estimate.getPoint();
+        Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
+        Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
+    }
+
+    private static class FourExtrema implements MultivariateFunction {
+        // The following function has 4 local extrema.
+        final double xM = -3.841947088256863675365;
+        final double yM = -1.391745200270734924416;
+        final double xP =  0.2286682237349059125691;
+        final double yP = -yM;
+        final double valueXmYm = 0.2373295333134216789769; // Local maximum.
+        final double valueXmYp = -valueXmYm; // Local minimum.
+        final double valueXpYm = -0.7290400707055187115322; // Global minimum.
+        final double valueXpYp = -valueXpYm; // Global maximum.
+
+        public double value(double[] variables) {
+            final double x = variables[0];
+            final double y = variables[1];
+            return (x == 0 || y == 0) ? 0 :
+                FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y);
+        }
+    }
+
+    private static class Gaussian2D implements MultivariateFunction {
+        private final double[] maximumPosition;
+        private final double std;
+
+        public Gaussian2D(double xOpt, double yOpt, double std) {
+            maximumPosition = new double[] { xOpt, yOpt };
+            this.std = std;
+        }
+
+        public double getMaximum() {
+            return value(maximumPosition);
+        }
+
+        public double[] getMaximumPosition() {
+            return maximumPosition.clone();
+        }
+
+        public double value(double[] point) {
+            final double x = point[0], y = point[1];
+            final double twoS2 = 2.0 * std * std;
+            return 1.0 / (twoS2 * FastMath.PI) * FastMath.exp(-(x * x + y * y) / twoS2);
+        }
+    }
+
+    private int count;
+}

Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java
------------------------------------------------------------------------------
    svn:eol-style = native

Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerNelderMeadTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerNelderMeadTest.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerNelderMeadTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/SimplexOptimizerNelderMeadTest.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,295 @@
+/*
+ * 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.scalar.noderiv;
+
+
+import org.apache.commons.math3.exception.TooManyEvaluationsException;
+import org.apache.commons.math3.analysis.MultivariateFunction;
+import org.apache.commons.math3.analysis.MultivariateVectorFunction;
+import org.apache.commons.math3.linear.Array2DRowRealMatrix;
+import org.apache.commons.math3.linear.RealMatrix;
+import org.apache.commons.math3.optim.GoalType;
+import org.apache.commons.math3.optim.InitialGuess;
+import org.apache.commons.math3.optim.MaxEval;
+import org.apache.commons.math3.optim.ObjectiveFunction;
+import org.apache.commons.math3.optim.PointValuePair;
+import org.apache.commons.math3.optim.nonlinear.scalar.LeastSquaresConverter;
+import org.apache.commons.math3.util.FastMath;
+import org.junit.Assert;
+import org.junit.Test;
+
+public class SimplexOptimizerNelderMeadTest {
+    @Test
+    public void testMinimize1() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { -3, 0 }),
+                                 new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 2e-7);
+        Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 2e-5);
+        Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 6e-12);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 90);
+    }
+
+    @Test
+    public void testMinimize2() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { 1, 0 }),
+                                 new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 5e-6);
+        Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 6e-6);
+        Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 1e-11);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 90);
+    }
+
+    @Test
+    public void testMaximize1() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MAXIMIZE,
+                                 new InitialGuess(new double[] { -3, 0 }),
+                                 new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 1e-5);
+        Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
+        Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 3e-12);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 90);
+    }
+
+    @Test
+    public void testMaximize2() {
+        SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
+        final FourExtrema fourExtrema = new FourExtrema();
+
+        final PointValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 new ObjectiveFunction(fourExtrema),
+                                 GoalType.MAXIMIZE,
+                                 new InitialGuess(new double[] { 1, 0 }),
+                                 new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
+        Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 4e-6);
+        Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 5e-6);
+        Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 7e-12);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 90);
+    }
+
+    @Test
+    public void testRosenbrock() {
+
+        Rosenbrock rosenbrock = new Rosenbrock();
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
+        PointValuePair optimum
+        = optimizer.optimize(new MaxEval(100),
+                             new ObjectiveFunction(rosenbrock),
+                             GoalType.MINIMIZE,
+                             new InitialGuess(new double[] { -1.2, 1 }),
+                                new NelderMeadSimplex(new double[][] {
+                                        { -1.2,  1 },
+                                        { 0.9, 1.2 },
+                                        {  3.5, -2.3 } }));
+
+        Assert.assertEquals(rosenbrock.getCount(), optimizer.getEvaluations());
+        Assert.assertTrue(optimizer.getEvaluations() > 40);
+        Assert.assertTrue(optimizer.getEvaluations() < 50);
+        Assert.assertTrue(optimum.getValue() < 8e-4);
+    }
+
+    @Test
+    public void testPowell() {
+        Powell powell = new Powell();
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
+        PointValuePair optimum =
+            optimizer.optimize(new MaxEval(200),
+                               new ObjectiveFunction(powell),
+                               GoalType.MINIMIZE,
+                               new InitialGuess(new double[] { 3, -1, 0, 1 }),
+                               new NelderMeadSimplex(4));
+        Assert.assertEquals(powell.getCount(), optimizer.getEvaluations());
+        Assert.assertTrue(optimizer.getEvaluations() > 110);
+        Assert.assertTrue(optimizer.getEvaluations() < 130);
+        Assert.assertTrue(optimum.getValue() < 2e-3);
+    }
+
+    @Test
+    public void testLeastSquares1() {
+        final RealMatrix factors
+            = new Array2DRowRealMatrix(new double[][] {
+                    { 1, 0 },
+                    { 0, 1 }
+                }, false);
+        LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
+                public double[] value(double[] variables) {
+                    return factors.operate(variables);
+                }
+            }, new double[] { 2.0, -3.0 });
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
+        PointValuePair optimum =
+            optimizer.optimize(new MaxEval(200),
+                               new ObjectiveFunction(ls),
+                               GoalType.MINIMIZE,
+                               new InitialGuess(new double[] { 10, 10 }),
+                               new NelderMeadSimplex(2));
+        Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5);
+        Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 80);
+        Assert.assertTrue(optimum.getValue() < 1.0e-6);
+    }
+
+    @Test
+    public void testLeastSquares2() {
+        final RealMatrix factors
+            = new Array2DRowRealMatrix(new double[][] {
+                    { 1, 0 },
+                    { 0, 1 }
+                }, false);
+        LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
+                public double[] value(double[] variables) {
+                    return factors.operate(variables);
+                }
+            }, new double[] { 2, -3 }, new double[] { 10, 0.1 });
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
+        PointValuePair optimum =
+            optimizer.optimize(new MaxEval(200),
+                               new ObjectiveFunction(ls),
+                               GoalType.MINIMIZE,
+                               new InitialGuess(new double[] { 10, 10 }),
+                               new NelderMeadSimplex(2));
+        Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
+        Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 80);
+        Assert.assertTrue(optimum.getValue() < 1e-6);
+    }
+
+    @Test
+    public void testLeastSquares3() {
+        final RealMatrix factors =
+            new Array2DRowRealMatrix(new double[][] {
+                    { 1, 0 },
+                    { 0, 1 }
+                }, false);
+        LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
+                public double[] value(double[] variables) {
+                    return factors.operate(variables);
+                }
+            }, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
+                    { 1, 1.2 }, { 1.2, 2 }
+                }));
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
+        PointValuePair optimum
+            = optimizer.optimize(new MaxEval(200),
+                                 new ObjectiveFunction(ls),
+                                 GoalType.MINIMIZE,
+                                 new InitialGuess(new double[] { 10, 10 }),
+                                 new NelderMeadSimplex(2));
+        Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
+        Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
+        Assert.assertTrue(optimizer.getEvaluations() > 60);
+        Assert.assertTrue(optimizer.getEvaluations() < 80);
+        Assert.assertTrue(optimum.getValue() < 1e-6);
+    }
+
+    @Test(expected=TooManyEvaluationsException.class)
+    public void testMaxIterations() {
+        Powell powell = new Powell();
+        SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
+        optimizer.optimize(new MaxEval(20),
+                           new ObjectiveFunction(powell),
+                           GoalType.MINIMIZE,
+                           new InitialGuess(new double[] { 3, -1, 0, 1 }),
+                           new NelderMeadSimplex(4));
+    }
+
+    private static class FourExtrema implements MultivariateFunction {
+        // The following function has 4 local extrema.
+        final double xM = -3.841947088256863675365;
+        final double yM = -1.391745200270734924416;
+        final double xP =  0.2286682237349059125691;
+        final double yP = -yM;
+        final double valueXmYm = 0.2373295333134216789769; // Local maximum.
+        final double valueXmYp = -valueXmYm; // Local minimum.
+        final double valueXpYm = -0.7290400707055187115322; // Global minimum.
+        final double valueXpYp = -valueXpYm; // Global maximum.
+
+        public double value(double[] variables) {
+            final double x = variables[0];
+            final double y = variables[1];
+            return (x == 0 || y == 0) ? 0 :
+                FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y);
+        }
+    }
+
+    private static class Rosenbrock implements MultivariateFunction {
+        private int count;
+
+        public Rosenbrock() {
+            count = 0;
+        }
+
+        public double value(double[] x) {
+            ++count;
+            double a = x[1] - x[0] * x[0];
+            double b = 1.0 - x[0];
+            return 100 * a * a + b * b;
+        }
+
+        public int getCount() {
+            return count;
+        }
+    }
+
+    private static class Powell implements MultivariateFunction {
+        private int count;
+
+        public Powell() {
+            count = 0;
+        }
+
+        public double value(double[] x) {
+            ++count;
+            double a = x[0] + 10 * x[1];
+            double b = x[2] - x[3];
+            double c = x[1] - 2 * x[2];
+            double d = x[0] - x[3];
+            return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
+        }
+
+        public int getCount() {
+            return count;
+        }
+    }
+}

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Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/MultiStartMultivariateVectorOptimizerTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/MultiStartMultivariateVectorOptimizerTest.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/MultiStartMultivariateVectorOptimizerTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/MultiStartMultivariateVectorOptimizerTest.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,205 @@
+/*
+ * 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;
+
+import org.apache.commons.math3.analysis.MultivariateVectorFunction;
+import org.apache.commons.math3.analysis.MultivariateMatrixFunction;
+import org.apache.commons.math3.exception.MathIllegalStateException;
+import org.apache.commons.math3.linear.BlockRealMatrix;
+import org.apache.commons.math3.linear.RealMatrix;
+import org.apache.commons.math3.optim.MaxEval;
+import org.apache.commons.math3.optim.InitialGuess;
+import org.apache.commons.math3.optim.PointVectorValuePair;
+import org.apache.commons.math3.optim.SimpleVectorValueChecker;
+import org.apache.commons.math3.optim.nonlinear.vector.jacobian.GaussNewtonOptimizer;
+import org.apache.commons.math3.random.GaussianRandomGenerator;
+import org.apache.commons.math3.random.JDKRandomGenerator;
+import org.apache.commons.math3.random.RandomVectorGenerator;
+import org.apache.commons.math3.random.UncorrelatedRandomVectorGenerator;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * <p>Some of the unit tests are re-implementations of the MINPACK <a
+ * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
+ * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files.
+ * The redistribution policy for MINPACK is available <a
+ * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
+ * convenience, it is reproduced below.</p>
+ *
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ *    Minpack Copyright Notice (1999) University of Chicago.
+ *    All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ *  <li>Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ *     copyright notice, this list of conditions and the following
+ *     disclaimer in the documentation and/or other materials provided
+ *     with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ *     must include the following acknowledgment:
+ *     <code>This product includes software developed by the University of
+ *           Chicago, as Operator of Argonne National Laboratory.</code>
+ *     Alternately, this acknowledgment may appear in the software itself,
+ *     if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ *     BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ *     POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+ *
+ * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran 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 MultiStartMultivariateVectorOptimizerTest {
+    @Test(expected=NullPointerException.class)
+    public void testGetOptimaBeforeOptimize() {
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
+        JacobianMultivariateVectorOptimizer underlyingOptimizer
+            = new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-6, 1e-6));
+        JDKRandomGenerator g = new JDKRandomGenerator();
+        g.setSeed(16069223052l);
+        RandomVectorGenerator generator
+            = new UncorrelatedRandomVectorGenerator(1, new GaussianRandomGenerator(g));
+        MultiStartMultivariateVectorOptimizer optimizer
+            = new MultiStartMultivariateVectorOptimizer(underlyingOptimizer, 10, generator);
+
+        optimizer.getOptima();
+    }
+
+    @Test
+    public void testTrivial() {
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
+        JacobianMultivariateVectorOptimizer underlyingOptimizer
+            = new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-6, 1e-6));
+        JDKRandomGenerator g = new JDKRandomGenerator();
+        g.setSeed(16069223052l);
+        RandomVectorGenerator generator
+            = new UncorrelatedRandomVectorGenerator(1, new GaussianRandomGenerator(g));
+        MultiStartMultivariateVectorOptimizer optimizer
+            = new MultiStartMultivariateVectorOptimizer(underlyingOptimizer, 10, generator);
+
+        PointVectorValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 problem.getModelFunction(),
+                                 problem.getModelFunctionJacobian(),
+                                 problem.getTarget(),
+                                 new Weight(new double[] { 1 }),
+                                 new InitialGuess(new double[] { 0 }));
+        Assert.assertEquals(1.5, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(3.0, optimum.getValue()[0], 1e-10);
+        PointVectorValuePair[] optima = optimizer.getOptima();
+        Assert.assertEquals(10, optima.length);
+        for (int i = 0; i < optima.length; i++) {
+            Assert.assertEquals(1.5, optima[i].getPoint()[0], 1e-10);
+            Assert.assertEquals(3.0, optima[i].getValue()[0], 1e-10);
+        }
+        Assert.assertTrue(optimizer.getEvaluations() > 20);
+        Assert.assertTrue(optimizer.getEvaluations() < 50);
+        Assert.assertEquals(100, optimizer.getMaxEvaluations());
+    }
+
+    /**
+     * Test demonstrating that the user exception is fnally thrown if none
+     * of the runs succeed.
+     */
+    @Test(expected=TestException.class)
+    public void testNoOptimum() {
+        JacobianMultivariateVectorOptimizer underlyingOptimizer
+            = new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-6, 1e-6));
+        JDKRandomGenerator g = new JDKRandomGenerator();
+        g.setSeed(12373523445l);
+        RandomVectorGenerator generator
+            = new UncorrelatedRandomVectorGenerator(1, new GaussianRandomGenerator(g));
+        MultiStartMultivariateVectorOptimizer optimizer
+            = new MultiStartMultivariateVectorOptimizer(underlyingOptimizer, 10, generator);
+        optimizer.optimize(new MaxEval(100),
+                           new Target(new double[] { 0 }),
+                           new Weight(new double[] { 1 }),
+                           new InitialGuess(new double[] { 0 }),
+                           new ModelFunction(new MultivariateVectorFunction() {
+                                   public double[] value(double[] point) {
+                                       throw new TestException();
+                                   }
+                               }));
+    }
+
+    private static class TestException extends RuntimeException {}
+
+    private static class LinearProblem {
+        private final RealMatrix factors;
+        private final double[] target;
+
+        public LinearProblem(double[][] factors,
+                             double[] target) {
+            this.factors = new BlockRealMatrix(factors);
+            this.target  = target;
+        }
+
+        public Target getTarget() {
+            return new Target(target);
+        }
+
+        public ModelFunction getModelFunction() {
+            return new ModelFunction(new MultivariateVectorFunction() {
+                    public double[] value(double[] variables) {
+                        return factors.operate(variables);
+                    }
+                });
+        }
+
+        public ModelFunctionJacobian getModelFunctionJacobian() {
+            return new ModelFunctionJacobian(new MultivariateMatrixFunction() {
+                    public double[][] value(double[] point) {
+                        return factors.getData();
+                    }
+                });
+        }
+    }
+}

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Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerAbstractTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerAbstractTest.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerAbstractTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerAbstractTest.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,617 @@
+/*
+ * 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 java.io.Serializable;
+import java.util.Arrays;
+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.NumberIsTooSmallException;
+import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
+import org.apache.commons.math3.linear.BlockRealMatrix;
+import org.apache.commons.math3.linear.RealMatrix;
+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.util.FastMath;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * <p>Some of the unit tests are re-implementations of the MINPACK <a
+ * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
+ * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files.
+ * The redistribution policy for MINPACK is available <a
+ * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
+ * convenience, it is reproduced below.</p>
+
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ *    Minpack Copyright Notice (1999) University of Chicago.
+ *    All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ *  <li>Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ *     copyright notice, this list of conditions and the following
+ *     disclaimer in the documentation and/or other materials provided
+ *     with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ *     must include the following acknowledgment:
+ *     <code>This product includes software developed by the University of
+ *           Chicago, as Operator of Argonne National Laboratory.</code>
+ *     Alternately, this acknowledgment may appear in the software itself,
+ *     if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ *     BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ *     POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+
+ * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran 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)
+ * @version $Id: AbstractLeastSquaresOptimizerAbstractTest.java 1407467 2012-11-09 14:30:49Z erans $
+ */
+public abstract class AbstractLeastSquaresOptimizerAbstractTest {
+
+    public abstract AbstractLeastSquaresOptimizer createOptimizer();
+
+    @Test
+    public void testTrivial() {
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               problem.getModelFunction(),
+                               problem.getModelFunctionJacobian(),
+                               problem.getTarget(),
+                               new Weight(new double[] { 1 }),
+                               new InitialGuess(new double[] { 0 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(1.5, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(3.0, optimum.getValue()[0], 1e-10);
+    }
+
+    @Test
+    public void testQRColumnsPermutation() {
+
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 1, -1 }, { 0, 2 }, { 1, -2 } },
+                                new double[] { 4, 6, 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 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(7, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(3, optimum.getPoint()[1], 1e-10);
+        Assert.assertEquals(4, optimum.getValue()[0], 1e-10);
+        Assert.assertEquals(6, optimum.getValue()[1], 1e-10);
+        Assert.assertEquals(1, optimum.getValue()[2], 1e-10);
+    }
+
+    @Test
+    public void testNoDependency() {
+        LinearProblem problem = new LinearProblem(new double[][] {
+                { 2, 0, 0, 0, 0, 0 },
+                { 0, 2, 0, 0, 0, 0 },
+                { 0, 0, 2, 0, 0, 0 },
+                { 0, 0, 0, 2, 0, 0 },
+                { 0, 0, 0, 0, 2, 0 },
+                { 0, 0, 0, 0, 0, 2 }
+        }, new double[] { 0, 1.1, 2.2, 3.3, 4.4, 5.5 });
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               problem.getModelFunction(),
+                               problem.getModelFunctionJacobian(),
+                               problem.getTarget(),
+                               new Weight(new double[] { 1, 1, 1, 1, 1, 1 }),
+                               new InitialGuess(new double[] { 0, 0, 0, 0, 0, 0 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        for (int i = 0; i < problem.target.length; ++i) {
+            Assert.assertEquals(0.55 * i, optimum.getPoint()[i], 1e-10);
+        }
+    }
+
+    @Test
+    public void testOneSet() {
+
+        LinearProblem problem = new LinearProblem(new double[][] {
+                {  1,  0, 0 },
+                { -1,  1, 0 },
+                {  0, -1, 1 }
+        }, 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.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(1, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(2, optimum.getPoint()[1], 1e-10);
+        Assert.assertEquals(3, optimum.getPoint()[2], 1e-10);
+    }
+
+    @Test
+    public void testTwoSets() {
+        double epsilon = 1e-7;
+        LinearProblem problem = new LinearProblem(new double[][] {
+                {  2,  1,   0,  4,       0, 0 },
+                { -4, -2,   3, -7,       0, 0 },
+                {  4,  1,  -2,  8,       0, 0 },
+                {  0, -3, -12, -1,       0, 0 },
+                {  0,  0,   0,  0, epsilon, 1 },
+                {  0,  0,   0,  0,       1, 1 }
+        }, new double[] { 2, -9, 2, 2, 1 + epsilon * epsilon, 2});
+
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               problem.getModelFunction(),
+                               problem.getModelFunctionJacobian(),
+                               problem.getTarget(),
+                               new Weight(new double[] { 1, 1, 1, 1, 1, 1 }),
+                               new InitialGuess(new double[] { 0, 0, 0, 0, 0, 0 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(3, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(4, optimum.getPoint()[1], 1e-10);
+        Assert.assertEquals(-1, optimum.getPoint()[2], 1e-10);
+        Assert.assertEquals(-2, optimum.getPoint()[3], 1e-10);
+        Assert.assertEquals(1 + epsilon, optimum.getPoint()[4], 1e-10);
+        Assert.assertEquals(1 - epsilon, optimum.getPoint()[5], 1e-10);
+    }
+
+    @Test(expected=ConvergenceException.class)
+    public void testNonInvertible() throws Exception {
+
+        LinearProblem problem = new LinearProblem(new double[][] {
+                {  1, 2, -3 },
+                {  2, 1,  3 },
+                { -3, 0, -9 }
+        }, new double[] { 1, 1, 1 });
+
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+
+        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 }));
+    }
+
+    @Test
+    public void testIllConditioned() {
+        LinearProblem problem1 = new LinearProblem(new double[][] {
+                { 10, 7,  8,  7 },
+                {  7, 5,  6,  5 },
+                {  8, 6, 10,  9 },
+                {  7, 5,  9, 10 }
+        }, new double[] { 32, 23, 33, 31 });
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum1 =
+            optimizer.optimize(new MaxEval(100),
+                               problem1.getModelFunction(),
+                               problem1.getModelFunctionJacobian(),
+                               problem1.getTarget(),
+                               new Weight(new double[] { 1, 1, 1, 1 }),
+                               new InitialGuess(new double[] { 0, 1, 2, 3 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(1, optimum1.getPoint()[0], 1e-10);
+        Assert.assertEquals(1, optimum1.getPoint()[1], 1e-10);
+        Assert.assertEquals(1, optimum1.getPoint()[2], 1e-10);
+        Assert.assertEquals(1, optimum1.getPoint()[3], 1e-10);
+
+        LinearProblem problem2 = new LinearProblem(new double[][] {
+                { 10.00, 7.00, 8.10, 7.20 },
+                {  7.08, 5.04, 6.00, 5.00 },
+                {  8.00, 5.98, 9.89, 9.00 },
+                {  6.99, 4.99, 9.00, 9.98 }
+        }, new double[] { 32, 23, 33, 31 });
+        PointVectorValuePair optimum2 =
+            optimizer.optimize(new MaxEval(100),
+                               problem2.getModelFunction(),
+                               problem2.getModelFunctionJacobian(),
+                               problem2.getTarget(), 
+                               new Weight(new double[] { 1, 1, 1, 1 }),
+                               new InitialGuess(new double[] { 0, 1, 2, 3 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(-81, optimum2.getPoint()[0], 1e-8);
+        Assert.assertEquals(137, optimum2.getPoint()[1], 1e-8);
+        Assert.assertEquals(-34, optimum2.getPoint()[2], 1e-8);
+        Assert.assertEquals( 22, optimum2.getPoint()[3], 1e-8);
+    }
+
+    @Test
+    public void testMoreEstimatedParametersSimple() {
+
+        LinearProblem problem = new LinearProblem(new double[][] {
+                { 3, 2,  0, 0 },
+                { 0, 1, -1, 1 },
+                { 2, 0,  1, 0 }
+        }, new double[] { 7, 3, 5 });
+
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        optimizer.optimize(new MaxEval(100),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           problem.getTarget(),
+                           new Weight(new double[] { 1, 1, 1 }),
+                           new InitialGuess(new double[] { 7, 6, 5, 4 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+    }
+
+    @Test
+    public void testMoreEstimatedParametersUnsorted() {
+        LinearProblem problem = new LinearProblem(new double[][] {
+                { 1, 1,  0,  0, 0,  0 },
+                { 0, 0,  1,  1, 1,  0 },
+                { 0, 0,  0,  0, 1, -1 },
+                { 0, 0, -1,  1, 0,  1 },
+                { 0, 0,  0, -1, 1,  0 }
+       }, new double[] { 3, 12, -1, 7, 1 });
+
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               problem.getModelFunction(),
+                               problem.getModelFunctionJacobian(),
+                               problem.getTarget(),
+                               new Weight(new double[] { 1, 1, 1, 1, 1 }),
+                               new InitialGuess(new double[] { 2, 2, 2, 2, 2, 2 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(3, optimum.getPointRef()[2], 1e-10);
+        Assert.assertEquals(4, optimum.getPointRef()[3], 1e-10);
+        Assert.assertEquals(5, optimum.getPointRef()[4], 1e-10);
+        Assert.assertEquals(6, optimum.getPointRef()[5], 1e-10);
+    }
+
+    @Test
+    public void testRedundantEquations() {
+        LinearProblem problem = new LinearProblem(new double[][] {
+                { 1,  1 },
+                { 1, -1 },
+                { 1,  3 }
+        }, new double[] { 3, 1, 5 });
+
+        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[] { 1, 1 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(2, optimum.getPointRef()[0], 1e-10);
+        Assert.assertEquals(1, optimum.getPointRef()[1], 1e-10);
+    }
+
+    @Test
+    public void testInconsistentEquations() {
+        LinearProblem problem = new LinearProblem(new double[][] {
+                { 1,  1 },
+                { 1, -1 },
+                { 1,  3 }
+        }, new double[] { 3, 1, 4 });
+
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        optimizer.optimize(new MaxEval(100),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           problem.getTarget(),
+                           new Weight(new double[] { 1, 1, 1 }),
+                           new InitialGuess(new double[] { 1, 1 }));
+        Assert.assertTrue(optimizer.getRMS() > 0.1);
+    }
+
+    @Test(expected=DimensionMismatchException.class)
+    public void testInconsistentSizes1() {
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } },
+                                new double[] { -1, 1 });
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               problem.getModelFunction(),
+                               problem.getModelFunctionJacobian(),
+                               problem.getTarget(),
+                               new Weight(new double[] { 1, 1 }),
+                               new InitialGuess(new double[] { 0, 0 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(-1, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(1, optimum.getPoint()[1], 1e-10);
+
+        optimizer.optimize(new MaxEval(100),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           problem.getTarget(),
+                           new Weight(new double[] { 1 }),
+                           new InitialGuess(new double[] { 0, 0 }));
+    }
+
+    @Test(expected=DimensionMismatchException.class)
+    public void testInconsistentSizes2() {
+        LinearProblem problem
+            = new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } },
+                                new double[] { -1, 1 });
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 problem.getModelFunction(),
+                                 problem.getModelFunctionJacobian(),
+                                 problem.getTarget(),
+                                 new Weight(new double[] { 1, 1 }),
+                                 new InitialGuess(new double[] { 0, 0 }));
+        Assert.assertEquals(0, optimizer.getRMS(), 1e-10);
+        Assert.assertEquals(-1, optimum.getPoint()[0], 1e-10);
+        Assert.assertEquals(1, optimum.getPoint()[1], 1e-10);
+
+        optimizer.optimize(new MaxEval(100),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           new Target(new double[] { 1 }),
+                           new Weight(new double[] { 1 }),
+                           new InitialGuess(new double[] { 0, 0 }));
+    }
+
+    @Test
+    public void testCircleFitting() {
+        CircleVectorial circle = new CircleVectorial();
+        circle.addPoint( 30,  68);
+        circle.addPoint( 50,  -6);
+        circle.addPoint(110, -20);
+        circle.addPoint( 35,  15);
+        circle.addPoint( 45,  97);
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum
+            = 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 }));
+        Assert.assertTrue(optimizer.getEvaluations() < 10);
+        double rms = optimizer.getRMS();
+        Assert.assertEquals(1.768262623567235,  FastMath.sqrt(circle.getN()) * rms,  1e-10);
+        Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]);
+        Assert.assertEquals(69.96016176931406, circle.getRadius(center), 1e-6);
+        Assert.assertEquals(96.07590211815305, center.getX(),            1e-6);
+        Assert.assertEquals(48.13516790438953, center.getY(),            1e-6);
+        double[][] cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14);
+        Assert.assertEquals(1.839, cov[0][0], 0.001);
+        Assert.assertEquals(0.731, cov[0][1], 0.001);
+        Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
+        Assert.assertEquals(0.786, cov[1][1], 0.001);
+
+        // add perfect measurements and check errors are reduced
+        double  r = circle.getRadius(center);
+        for (double d= 0; d < 2 * FastMath.PI; d += 0.01) {
+            circle.addPoint(center.getX() + r * FastMath.cos(d), center.getY() + r * FastMath.sin(d));
+        }
+        double[] target = new double[circle.getN()];
+        Arrays.fill(target, 0);
+        double[] weights = new double[circle.getN()];
+        Arrays.fill(weights, 2);
+        optimum = optimizer.optimize(new MaxEval(100),
+                                     circle.getModelFunction(),
+                                     circle.getModelFunctionJacobian(),
+                                     new Target(target),
+                                     new Weight(weights),
+                                     new InitialGuess(new double[] { 98.680, 47.345 }));
+        cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14);
+        Assert.assertEquals(0.0016, cov[0][0], 0.001);
+        Assert.assertEquals(3.2e-7, cov[0][1], 1e-9);
+        Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
+        Assert.assertEquals(0.0016, cov[1][1], 0.001);
+    }
+
+    @Test
+    public void testCircleFittingBadInit() {
+        CircleVectorial circle = new CircleVectorial();
+        double[][] points = circlePoints;
+        double[] target = new double[points.length];
+        Arrays.fill(target, 0);
+        double[] weights = new double[points.length];
+        Arrays.fill(weights, 2);
+        for (int i = 0; i < points.length; ++i) {
+            circle.addPoint(points[i][0], points[i][1]);
+        }
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 circle.getModelFunction(),
+                                 circle.getModelFunctionJacobian(),
+                                 new Target(target),
+                                 new Weight(weights),
+                                 new InitialGuess(new double[] { -12, -12 }));
+        Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]);
+        Assert.assertTrue(optimizer.getEvaluations() < 25);
+        Assert.assertEquals( 0.043, optimizer.getRMS(), 1e-3);
+        Assert.assertEquals( 0.292235,  circle.getRadius(center), 1e-6);
+        Assert.assertEquals(-0.151738,  center.getX(),            1e-6);
+        Assert.assertEquals( 0.2075001, center.getY(),            1e-6);
+    }
+
+    @Test
+    public void testCircleFittingGoodInit() {
+        CircleVectorial circle = new CircleVectorial();
+        double[][] points = circlePoints;
+        double[] target = new double[points.length];
+        Arrays.fill(target, 0);
+        double[] weights = new double[points.length];
+        Arrays.fill(weights, 2);
+        for (int i = 0; i < points.length; ++i) {
+            circle.addPoint(points[i][0], points[i][1]);
+        }
+        AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        PointVectorValuePair optimum =
+            optimizer.optimize(new MaxEval(100),
+                               circle.getModelFunction(),
+                               circle.getModelFunctionJacobian(),
+                               new Target(target),
+                               new Weight(weights),
+                               new InitialGuess(new double[] { 0, 0 }));
+        Assert.assertEquals(-0.1517383071957963, optimum.getPointRef()[0], 1e-6);
+        Assert.assertEquals(0.2074999736353867,  optimum.getPointRef()[1], 1e-6);
+        Assert.assertEquals(0.04268731682389561, optimizer.getRMS(),       1e-8);
+    }
+
+    private final double[][] circlePoints = new double[][] {
+        {-0.312967,  0.072366}, {-0.339248,  0.132965}, {-0.379780,  0.202724},
+        {-0.390426,  0.260487}, {-0.361212,  0.328325}, {-0.346039,  0.392619},
+        {-0.280579,  0.444306}, {-0.216035,  0.470009}, {-0.149127,  0.493832},
+        {-0.075133,  0.483271}, {-0.007759,  0.452680}, { 0.060071,  0.410235},
+        { 0.103037,  0.341076}, { 0.118438,  0.273884}, { 0.131293,  0.192201},
+        { 0.115869,  0.129797}, { 0.072223,  0.058396}, { 0.022884,  0.000718},
+        {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
+        {-0.278592, -0.005008}, {-0.337655,  0.056658}, {-0.385899,  0.112526},
+        {-0.405517,  0.186957}, {-0.415374,  0.262071}, {-0.387482,  0.343398},
+        {-0.347322,  0.397943}, {-0.287623,  0.458425}, {-0.223502,  0.475513},
+        {-0.135352,  0.478186}, {-0.061221,  0.483371}, { 0.003711,  0.422737},
+        { 0.065054,  0.375830}, { 0.108108,  0.297099}, { 0.123882,  0.222850},
+        { 0.117729,  0.134382}, { 0.085195,  0.056820}, { 0.029800, -0.019138},
+        {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
+        {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561,  0.014926},
+        {-0.471036,  0.074716}, {-0.488638,  0.182508}, {-0.485990,  0.254068},
+        {-0.463943,  0.338438}, {-0.406453,  0.404704}, {-0.334287,  0.466119},
+        {-0.254244,  0.503188}, {-0.161548,  0.495769}, {-0.075733,  0.495560},
+        { 0.001375,  0.434937}, { 0.082787,  0.385806}, { 0.115490,  0.323807},
+        { 0.141089,  0.223450}, { 0.138693,  0.131703}, { 0.126415,  0.049174},
+        { 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
+        {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
+        {-0.405195, -0.000895}, {-0.444937,  0.085456}, {-0.484357,  0.175597},
+        {-0.472453,  0.248681}, {-0.438580,  0.347463}, {-0.402304,  0.422428},
+        {-0.326777,  0.479438}, {-0.247797,  0.505581}, {-0.152676,  0.519380},
+        {-0.071754,  0.516264}, { 0.015942,  0.472802}, { 0.076608,  0.419077},
+        { 0.127673,  0.330264}, { 0.159951,  0.262150}, { 0.153530,  0.172681},
+        { 0.140653,  0.089229}, { 0.078666,  0.024981}, { 0.023807, -0.037022},
+        {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
+    };
+
+    public void doTestStRD(final StatisticalReferenceDataset dataset,
+                           final double errParams,
+                           final double errParamsSd) {
+        final AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        final double[] w = new double[dataset.getNumObservations()];
+        Arrays.fill(w, 1);
+
+        final double[][] data = dataset.getData();
+        final double[] initial = dataset.getStartingPoint(0);
+        final StatisticalReferenceDataset.LeastSquaresProblem problem = dataset.getLeastSquaresProblem();
+        final PointVectorValuePair optimum
+            = optimizer.optimize(new MaxEval(100),
+                                 problem.getModelFunction(),
+                                 problem.getModelFunctionJacobian(),
+                                 new Target(data[1]),
+                                 new Weight(w),
+                                 new InitialGuess(initial));
+
+        final double[] actual = optimum.getPoint();
+        for (int i = 0; i < actual.length; i++) {
+            double expected = dataset.getParameter(i);
+            double delta = FastMath.abs(errParams * expected);
+            Assert.assertEquals(dataset.getName() + ", param #" + i,
+                                expected, actual[i], delta);
+        }
+    }
+
+    @Test
+    public void testKirby2() throws IOException {
+        doTestStRD(StatisticalReferenceDatasetFactory.createKirby2(), 1E-7, 1E-7);
+    }
+
+    @Test
+    public void testHahn1() throws IOException {
+        doTestStRD(StatisticalReferenceDatasetFactory.createHahn1(), 1E-7, 1E-4);
+    }
+
+    static class LinearProblem {
+        private final RealMatrix factors;
+        private final double[] target;
+
+        public LinearProblem(double[][] factors, double[] target) {
+            this.factors = new BlockRealMatrix(factors);
+            this.target  = target;
+        }
+
+        public Target getTarget() {
+            return new Target(target);
+        }
+
+        public ModelFunction getModelFunction() {
+            return new ModelFunction(new MultivariateVectorFunction() {
+                    public double[] value(double[] params) {
+                        return factors.operate(params);
+                    }
+                });
+        }
+
+        public ModelFunctionJacobian getModelFunctionJacobian() {
+            return new ModelFunctionJacobian(new MultivariateMatrixFunction() {
+                    public double[][] value(double[] params) {
+                        return factors.getData();
+                    }
+                });
+        }
+    }
+}

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Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTest.java?rev=1420684&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTest.java Wed Dec 12 14:10:38 2012
@@ -0,0 +1,126 @@
+/*
+ * 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 java.util.Arrays;
+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.util.FastMath;
+import org.junit.Test;
+import org.junit.Assert;
+
+public class AbstractLeastSquaresOptimizerTest {
+
+    public static AbstractLeastSquaresOptimizer createOptimizer() {
+        return new AbstractLeastSquaresOptimizer(null) {
+
+            @Override
+            protected PointVectorValuePair doOptimize() {
+                final double[] params = getStartPoint();
+                final double[] res = computeResiduals(computeObjectiveValue(params));
+                setCost(computeCost(res));
+                return new PointVectorValuePair(params, null);
+            }
+        };
+    }
+
+    @Test
+    public void testGetChiSquare() throws IOException {
+        final StatisticalReferenceDataset dataset
+            = StatisticalReferenceDatasetFactory.createKirby2();
+        final AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        final double[] a = dataset.getParameters();
+        final double[] y = dataset.getData()[1];
+        final double[] w = new double[y.length];
+        Arrays.fill(w, 1.0);
+
+        StatisticalReferenceDataset.LeastSquaresProblem problem
+            = dataset.getLeastSquaresProblem();
+
+        optimizer.optimize(new MaxEval(1),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           new Target(y),
+                           new Weight(w),
+                           new InitialGuess(a));
+        final double expected = dataset.getResidualSumOfSquares();
+        final double actual = optimizer.getChiSquare();
+        Assert.assertEquals(dataset.getName(), expected, actual,
+                            1E-11 * expected);
+    }
+
+    @Test
+    public void testGetRMS() throws IOException {
+        final StatisticalReferenceDataset dataset
+            = StatisticalReferenceDatasetFactory.createKirby2();
+        final AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        final double[] a = dataset.getParameters();
+        final double[] y = dataset.getData()[1];
+        final double[] w = new double[y.length];
+        Arrays.fill(w, 1);
+
+        StatisticalReferenceDataset.LeastSquaresProblem problem
+            = dataset.getLeastSquaresProblem();
+
+        optimizer.optimize(new MaxEval(1),
+                           problem.getModelFunction(),
+                           problem.getModelFunctionJacobian(),
+                           new Target(y),
+                           new Weight(w),
+                           new InitialGuess(a));
+
+        final double expected = FastMath
+            .sqrt(dataset.getResidualSumOfSquares() /
+                  dataset.getNumObservations());
+        final double actual = optimizer.getRMS();
+        Assert.assertEquals(dataset.getName(), expected, actual,
+                            1E-11 * expected);
+    }
+
+    @Test
+    public void testComputeSigma() throws IOException {
+        final StatisticalReferenceDataset dataset
+            = StatisticalReferenceDatasetFactory.createKirby2();
+        final AbstractLeastSquaresOptimizer optimizer = createOptimizer();
+        final double[] a = dataset.getParameters();
+        final double[] y = dataset.getData()[1];
+        final double[] w = new double[y.length];
+        Arrays.fill(w, 1);
+
+        StatisticalReferenceDataset.LeastSquaresProblem problem
+            = dataset.getLeastSquaresProblem();
+
+        final PointVectorValuePair optimum
+            = optimizer.optimize(new MaxEval(1),
+                                 problem.getModelFunction(),
+                                 problem.getModelFunctionJacobian(),
+                                 new Target(y),
+                                 new Weight(w),
+                                 new InitialGuess(a));
+
+        final double[] sig = optimizer.computeSigma(optimum.getPoint(), 1e-14);
+
+        final int dof = y.length - a.length;
+        final double[] expected = dataset.getParametersStandardDeviations();
+        for (int i = 0; i < sig.length; i++) {
+            final double actual = FastMath.sqrt(optimizer.getChiSquare() / dof) * sig[i];
+            Assert.assertEquals(dataset.getName() + ", parameter #" + i,
+                                expected[i], actual, 1e-6 * expected[i]);
+        }
+    }
+}

Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/optim/nonlinear/vector/jacobian/AbstractLeastSquaresOptimizerTest.java
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