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

@Test
public void testMoreEstimatedParametersSimple() {
    LinearProblem problem = new LinearProblem(new double[][] {
            { 3.0, 2.0,  0.0, 0.0 },
            { 0.0, 1.0, -1.0, 1.0 },
            { 2.0, 0.0,  1.0, 0.0 }
    }, new double[] { 7.0, 3.0, 5.0 });

    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6));
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 7, 6, 5, 4 }));
    Assert.assertEquals(0, optimum.getValue(), 1.0e-10);

}
 

@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 testColumnsPermutation() {
    LinearProblem problem
        = new LinearProblem(new double[][] { { 1.0, -1.0 }, { 0.0, 2.0 }, { 1.0, -2.0 } },
                            new double[] { 4.0, 6.0, 1.0 });

    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6),
                                                  1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 0, 0 }));
    Assert.assertEquals(7.0, optimum.getPoint()[0], 1.0e-10);
    Assert.assertEquals(3.0, optimum.getPoint()[1], 1.0e-10);
    Assert.assertEquals(0.0, optimum.getValue(), 1.0e-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
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 );
}
 

@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=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 }));
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param fLineTol Tolerance (relative error on the objective function)
 * for the internal line search algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double fLineTol,
                    double pointTol) {
    final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                      fLineTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(init));
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }

    Assert.assertTrue(optim.getIterations() > 0);
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double pointTol) {
    final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(init));
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }
}
 

@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 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 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 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);
}
 

@Test
public void testOptimumOutsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionMappingAdapter wrapped
        = new MultivariateFunctionMappingAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper());

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[][] {
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.75 }),
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.95 }),
            wrapped.boundedToUnbounded(new double[] { 1.7, 2.90 })
        });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(wrapped.boundedToUnbounded(new double[] { 1.5, 2.25 })));
    final double[] bounded = wrapped.unboundedToBounded(optimum.getPoint());

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), bounded[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), bounded[1], 2e-7);
}
 

@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[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 });
    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6),
                                                  1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 0, 0, 0, 0, 0, 0 }));
    for (int i = 0; i < problem.target.length; ++i) {
        Assert.assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10);
    }
}
 

@Test
public void testNonInversible() {
    LinearProblem problem = new LinearProblem(new double[][] {
            {  1, 2, -3 },
            {  2, 1,  3 },
            { -3, 0, -9 }
    }, new double[] { 1, 1, 1 });
    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6),
                                                  1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 0, 0, 0 }));
    Assert.assertTrue(optimum.getValue() > 0.5);
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param fLineTol Tolerance (relative error on the objective function)
 * for the internal line search algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double fLineTol,
                    double pointTol) {
    final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                      fLineTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(init));
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }

    Assert.assertTrue(optim.getIterations() > 0);
}
 

@Test
public void testStartSimplexInsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(2.0, 2.5, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionMappingAdapter wrapped
        = new MultivariateFunctionMappingAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper());

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[][] {
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.75 }),
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.95 }),
            wrapped.boundedToUnbounded(new double[] { 1.7, 2.90 })
        });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(wrapped.boundedToUnbounded(new double[] { 1.5, 2.25 })));
    final double[] bounded = wrapped.unboundedToBounded(optimum.getPoint());

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), bounded[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), bounded[1], 2e-7);
}
 

@Test(expected=TooManyEvaluationsException.class)
public void testMaxEvaluations() throws Exception {
    CircleVectorial circle = new CircleVectorial();
    circle.addPoint( 30.0,  68.0);
    circle.addPoint( 50.0,  -6.0);
    circle.addPoint(110.0, -20.0);
    circle.addPoint( 35.0,  15.0);
    circle.addPoint( 45.0,  97.0);

    GaussNewtonOptimizer optimizer
        = new GaussNewtonOptimizer(new SimpleVectorValueChecker(1e-30, 1e-30));

    optimizer.optimize(new MaxEval(100),
                       circle.getModelFunction(),
                       circle.getModelFunctionJacobian(),
                       new Target(new double[] { 0, 0, 0, 0, 0 }),
                       new Weight(new double[] { 1, 1, 1, 1, 1 }),
                       new InitialGuess(new double[] { 98.680, 47.345 }));
}
 

@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);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

@Test
public void testStartSimplexOutsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(2.0, 2.5, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionPenaltyAdapter wrapped
          = new MultivariateFunctionPenaltyAdapter(biQuadratic,
                                                   biQuadratic.getLower(),
                                                   biQuadratic.getUpper(),
                                                   1000.0, new double[] { 100.0, 100.0 });

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { -1.5, 4.0 }));

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), optimum.getPoint()[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), optimum.getPoint()[1], 2e-7);
}
 

@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 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);
    }
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param fLineTol Tolerance (relative error on the objective function)
 * for the internal line search algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double fLineTol,
                    double pointTol) {
    final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                      fLineTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(init));
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }

    Assert.assertTrue(optim.getIterations() > 0);
}
 

@Test
public void testStartSimplexInsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(2.0, 2.5, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionMappingAdapter wrapped
        = new MultivariateFunctionMappingAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper());

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[][] {
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.75 }),
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.95 }),
            wrapped.boundedToUnbounded(new double[] { 1.7, 2.90 })
        });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(wrapped.boundedToUnbounded(new double[] { 1.5, 2.25 })));
    final double[] bounded = wrapped.unboundedToBounded(optimum.getPoint());

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), bounded[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), bounded[1], 2e-7);
}
 

@Test
public void testOneSet() {
    LinearProblem problem = new LinearProblem(new double[][] {
            {  1,  0, 0 },
            { -1,  1, 0 },
            {  0, -1, 1 }
    }, new double[] { 1, 1, 1});
    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6),
                                                  1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 0, 0, 0 }));
    Assert.assertEquals(1.0, optimum.getPoint()[0], 1.0e-10);
    Assert.assertEquals(2.0, optimum.getPoint()[1], 1.0e-10);
    Assert.assertEquals(3.0, optimum.getPoint()[2], 1.0e-10);

}
 

@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);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

@Test
public void testMoreEstimatedParametersUnsorted() {
    LinearProblem problem = new LinearProblem(new double[][] {
             { 1.0, 1.0,  0.0,  0.0, 0.0,  0.0 },
             { 0.0, 0.0,  1.0,  1.0, 1.0,  0.0 },
             { 0.0, 0.0,  0.0,  0.0, 1.0, -1.0 },
             { 0.0, 0.0, -1.0,  1.0, 0.0,  1.0 },
             { 0.0, 0.0,  0.0, -1.0, 1.0,  0.0 }
    }, new double[] { 3.0, 12.0, -1.0, 7.0, 1.0 });
    NonLinearConjugateGradientOptimizer optimizer
       = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                 new SimpleValueChecker(1e-6, 1e-6),
                                                 1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 2, 2, 2, 2, 2, 2 }));
    Assert.assertEquals(0, optimum.getValue(), 1.0e-10);
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double pointTol) {
    final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(init));
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }
}
 

@Test
public void testOptimumOutsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionMappingAdapter wrapped
        = new MultivariateFunctionMappingAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper());

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[][] {
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.75 }),
            wrapped.boundedToUnbounded(new double[] { 1.5, 2.95 }),
            wrapped.boundedToUnbounded(new double[] { 1.7, 2.90 })
        });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(wrapped.boundedToUnbounded(new double[] { 1.5, 2.25 })));
    final double[] bounded = wrapped.unboundedToBounded(optimum.getPoint());

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), bounded[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), bounded[1], 2e-7);
}