Examples of org.apache.commons.math3.analysis.integration.UnivariateIntegrator.integrate()

Package org.apache.commons.math3.analysis.integration

Class org.apache.commons.math3.analysis.integration.UnivariateIntegrator

Examples of org.apache.commons.math3.analysis.integration.UnivariateIntegrator.integrate()

org.apache.commons.math3.analysis.integration.UnivariateIntegrator.integrate()
Integrate the function in the given interval. @param maxEval Maximum number of evaluations. @param f the integrand function @param min the min bound for the interval @param max the upper bound for the interval @return the value of integral @throws TooManyEvaluationsException if the maximum number of functionevaluations is exceeded. @throws MaxCountExceededException if the maximum iteration count is exceededor the integrator detects convergence problems otherwise @throws MathIllegalArgumentException if min > max or the endpoints do notsatisfy the requirements specified by the integrator @throws NullArgumentException if {@code f} is {@code null}.

        integ.addStepHandler(new StepNormalizer(0.5, this, mode, bounds));
        double[] y   = {0.0};
        double start = reverse ? getEnd()   : getStart();
        double end   = reverse ? getStart() : getEnd();
        output       = new ArrayList<Double>();
        integ.integrate(this, start, y, end, y);
        double[] actual = new double[output.size()];
        for(int i = 0; i < actual.length; i++) {
            actual[i] = output.get(i);
        }
        Assert.assertArrayEquals(expected, actual, 1e-5);

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        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;
        double[] y = {2.0, 2.0, 2.0, 4.0, 2.0, 7.0, 15.0};
        return integrator.integrate(new Ode(), t0, y, tEnd, y);
    }


    private static class Ode implements FirstOrderDifferentialEquations {
        public int getDimension() {
            return 7;

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                for (int l = 0; l < functions.length; ++l) {
                    integ.addEventHandler(functions[l],
                                          Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
                }
                Assert.assertEquals(functions.length, integ.getEventHandlers().size());
                double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                                                  pb.getFinalTime(), new double[pb.getDimension()]);
                if (functions.length == 0) {
                    Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
                }

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        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        Assert.assertTrue(handler.getLastError() < 9.0e-17);
        Assert.assertTrue(handler.getMaximalValueError() < 4.0e-15);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        Assert.assertTrue(handler.getLastError() > 0.00002);
        Assert.assertTrue(handler.getMaximalValueError() > 0.001);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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        double step = FastMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        Assert.assertTrue(handler.getLastError() < 3.0e-13);
        Assert.assertTrue(handler.getMaximalValueError() < 5.0e-13);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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        final TestProblem3 pb  = new TestProblem3(0.9);
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        integ.addStepHandler(new KeplerHandler(pb));
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);
    }


    private static class KeplerHandler implements StepHandler {

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                }
            }
            public void init(double t0, double[] y0, double t) {
            }
        });
        integ.integrate(new FirstOrderDifferentialEquations() {
            public void computeDerivatives(double t, double[] y, double[] dot) {
                dot[0] = 1.0;
            }
            public int getDimension() {
                return 1;

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    double convergence = 1.0e-8 * maxStep;
    for (int l = 0; l < functions.length; ++l) {
      integ.addEventHandler(functions[l], Double.POSITIVE_INFINITY, convergence, 1000);
    }
    Assert.assertEquals(functions.length, integ.getEventHandlers().size());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    Assert.assertEquals(0, handler.getMaximalValueError(), 2.1e-7);
    Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);

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    FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                scalAbsoluteTolerance,
                                                                scalRelativeTolerance);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    Assert.assertEquals(integ.getEvaluations(), pb.getCalls());
    Assert.assertTrue(pb.getCalls() < 3300);

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