org.apache.commons.math3.optim.PointVectorValuePair Java Examples

@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);
    }
}
 

@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(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
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);
}
 

private void minpackTest(MinpackFunction function, boolean exceptionExpected) {
    LevenbergMarquardtOptimizer optimizer
        = new LevenbergMarquardtOptimizer(FastMath.sqrt(2.22044604926e-16),
                                          FastMath.sqrt(2.22044604926e-16),
                                          2.22044604926e-16);
    try {
        PointVectorValuePair optimum
            = optimizer.optimize(new MaxEval(400 * (function.getN() + 1)),
                                 function.getModelFunction(),
                                 function.getModelFunctionJacobian(),
                                 new Target(function.getTarget()),
                                 new Weight(function.getWeight()),
                                 new InitialGuess(function.getStartPoint()));
        Assert.assertFalse(exceptionExpected);
        function.checkTheoreticalMinCost(optimizer.getRMS());
        function.checkTheoreticalMinParams(optimum);
    } catch (TooManyEvaluationsException e) {
        Assert.assertTrue(exceptionExpected);
    }
}
 

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 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);
}
 

@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 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);
}
 

/**
 * @return a comparator for sorting the optima.
 */
private Comparator<PointVectorValuePair> getPairComparator() {
    return new Comparator<PointVectorValuePair>() {
        private final RealVector target = new ArrayRealVector(optimizer.getTarget(), false);
        private final RealMatrix weight = optimizer.getWeight();

        public int compare(final PointVectorValuePair o1,
                           final PointVectorValuePair o2) {
            if (o1 == null) {
                return (o2 == null) ? 0 : 1;
            } else if (o2 == null) {
                return -1;
            }
            return Double.compare(weightedResidual(o1),
                                  weightedResidual(o2));
        }

        private double weightedResidual(final PointVectorValuePair pv) {
            final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
            final RealVector r = target.subtract(v);
            return r.dotProduct(weight.operate(r));
        }
    };
}
 

@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(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 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);
}
 

@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);
}
 

/**
 * @return a comparator for sorting the optima.
 */
private Comparator<PointVectorValuePair> getPairComparator() {
    return new Comparator<PointVectorValuePair>() {
        private final RealVector target = new ArrayRealVector(optimizer.getTarget(), false);
        private final RealMatrix weight = optimizer.getWeight();

        public int compare(final PointVectorValuePair o1,
                           final PointVectorValuePair o2) {
            if (o1 == null) {
                return (o2 == null) ? 0 : 1;
            } else if (o2 == null) {
                return -1;
            }
            return Double.compare(weightedResidual(o1),
                                  weightedResidual(o2));
        }

        private double weightedResidual(final PointVectorValuePair pv) {
            final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
            final RealVector r = target.subtract(v);
            return r.dotProduct(weight.operate(r));
        }
    };
}
 

/**
 * @return a comparator for sorting the optima.
 */
private Comparator<PointVectorValuePair> getPairComparator() {
    return new Comparator<PointVectorValuePair>() {
        private final RealVector target = new ArrayRealVector(optimizer.getTarget(), false);
        private final RealMatrix weight = optimizer.getWeight();

        public int compare(final PointVectorValuePair o1,
                           final PointVectorValuePair o2) {
            if (o1 == null) {
                return (o2 == null) ? 0 : 1;
            } else if (o2 == null) {
                return -1;
            }
            return Double.compare(weightedResidual(o1),
                                  weightedResidual(o2));
        }

        private double weightedResidual(final PointVectorValuePair pv) {
            final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
            final RealVector r = target.subtract(v);
            return r.dotProduct(weight.operate(r));
        }
    };
}
 

@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 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 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 void minpackTest(MinpackFunction function, boolean exceptionExpected) {
    LevenbergMarquardtOptimizer optimizer
        = new LevenbergMarquardtOptimizer(FastMath.sqrt(2.22044604926e-16),
                                          FastMath.sqrt(2.22044604926e-16),
                                          2.22044604926e-16);
    try {
        PointVectorValuePair optimum
            = optimizer.optimize(new MaxEval(400 * (function.getN() + 1)),
                                 function.getModelFunction(),
                                 function.getModelFunctionJacobian(),
                                 new Target(function.getTarget()),
                                 new Weight(function.getWeight()),
                                 new InitialGuess(function.getStartPoint()));
        Assert.assertFalse(exceptionExpected);
        function.checkTheoreticalMinCost(optimizer.getRMS());
        function.checkTheoreticalMinParams(optimum);
    } catch (TooManyEvaluationsException e) {
        Assert.assertTrue(exceptionExpected);
    }
}
 

@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 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 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());
}
 

public void checkTheoreticalMinParams(PointVectorValuePair optimum) {
    double[] params = optimum.getPointRef();
    if (theoreticalMinParams != null) {
        for (int i = 0; i < theoreticalMinParams.length; ++i) {
            double mi = theoreticalMinParams[i];
            double vi = params[i];
            Assert.assertEquals(mi, vi, paramsAccuracy * (1.0 + FastMath.abs(mi)));
        }
    }
}
 

@Test
public void testIssue914() {
    LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
    JacobianMultivariateVectorOptimizer underlyingOptimizer =
            new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-6, 1e-6)) {
        public PointVectorValuePair optimize(OptimizationData... optData) {
            // filter out simple bounds, as they are not supported
            // by the underlying optimizer, and we don't really care for this test
            OptimizationData[] filtered = optData.clone();
            for (int i = 0; i < filtered.length; ++i) {
                if (filtered[i] instanceof SimpleBounds) {
                    filtered[i] = null;
                }
            }
            return super.optimize(filtered);
        }
    };
    JDKRandomGenerator g = new JDKRandomGenerator();
    g.setSeed(16069223052l);
    RandomVectorGenerator generator =
            new UncorrelatedRandomVectorGenerator(1, new GaussianRandomGenerator(g));
    MultiStartMultivariateVectorOptimizer optimizer =
            new MultiStartMultivariateVectorOptimizer(underlyingOptimizer, 10, generator);

    optimizer.optimize(new MaxEval(100),
                       problem.getModelFunction(),
                       problem.getModelFunctionJacobian(),
                       problem.getTarget(),
                       new Weight(new double[] { 1 }),
                       new InitialGuess(new double[] { 0 }),
                       new SimpleBounds(new double[] { -1.0e-10 }, new double[] {  1.0e-10 }));
    PointVectorValuePair[] optima = optimizer.getOptima();
    // only the first start should have succeeded
    Assert.assertEquals(1, optima.length);

}
 

public void checkTheoreticalMinParams(PointVectorValuePair optimum) {
    double[] params = optimum.getPointRef();
    if (theoreticalMinParams != null) {
        for (int i = 0; i < theoreticalMinParams.length; ++i) {
            double mi = theoreticalMinParams[i];
            double vi = params[i];
            Assert.assertEquals(mi, vi, paramsAccuracy * (1.0 + FastMath.abs(mi)));
        }
    }
}
 

/**
 * Fit a curve.
 * This method compute the coefficients of the curve that best
 * fit the sample of observed points previously given through calls
 * to the {@link #addObservedPoint(WeightedObservedPoint)
 * addObservedPoint} method.
 *
 * @param f parametric function to fit.
 * @param initialGuess first guess of the function parameters.
 * @param maxEval Maximum number of function evaluations.
 * @return the fitted parameters.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the number of allowed evaluations is exceeded.
 * @throws org.apache.commons.math3.exception.DimensionMismatchException
 * if the start point dimension is wrong.
 * @since 3.0
 */
public double[] fit(int maxEval, T f,
                    final double[] initialGuess) {
    // Prepare least squares problem.
    double[] target  = new double[observations.size()];
    double[] weights = new double[observations.size()];
    int i = 0;
    for (WeightedObservedPoint point : observations) {
        target[i]  = point.getY();
        weights[i] = point.getWeight();
        ++i;
    }

    // Input to the optimizer: the model and its Jacobian.
    final TheoreticalValuesFunction model = new TheoreticalValuesFunction(f);

    // Perform the fit.
    final PointVectorValuePair optimum
        = optimizer.optimize(new MaxEval(maxEval),
                             model.getModelFunction(),
                             model.getModelFunctionJacobian(),
                             new Target(target),
                             new Weight(weights),
                             new InitialGuess(initialGuess));
    // Extract the coefficients.
    return optimum.getPointRef();
}
 

@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
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]);
    }
}
 

@Test
public void testIssue914() {
    LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
    JacobianMultivariateVectorOptimizer underlyingOptimizer =
            new GaussNewtonOptimizer(true, new SimpleVectorValueChecker(1e-6, 1e-6)) {
        @Override
        public PointVectorValuePair optimize(OptimizationData... optData) {
            // filter out simple bounds, as they are not supported
            // by the underlying optimizer, and we don't really care for this test
            OptimizationData[] filtered = optData.clone();
            for (int i = 0; i < filtered.length; ++i) {
                if (filtered[i] instanceof SimpleBounds) {
                    filtered[i] = null;
                }
            }
            return super.optimize(filtered);
        }
    };
    JDKRandomGenerator g = new JDKRandomGenerator();
    g.setSeed(16069223052l);
    RandomVectorGenerator generator =
            new UncorrelatedRandomVectorGenerator(1, new GaussianRandomGenerator(g));
    MultiStartMultivariateVectorOptimizer optimizer =
            new MultiStartMultivariateVectorOptimizer(underlyingOptimizer, 10, generator);

    optimizer.optimize(new MaxEval(100),
                       problem.getModelFunction(),
                       problem.getModelFunctionJacobian(),
                       problem.getTarget(),
                       new Weight(new double[] { 1 }),
                       new InitialGuess(new double[] { 0 }),
                       new SimpleBounds(new double[] { -1.0e-10 }, new double[] {  1.0e-10 }));
    PointVectorValuePair[] optima = optimizer.getOptima();
    // only the first start should have succeeded
    Assert.assertEquals(1, optima.length);

}