FieldMidPointIntegratorTest

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 *      https://www.apache.org/licenses/LICENSE-2.0
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/*
 * This is not the original file distributed by the Apache Software Foundation
 * It has been modified by the Hipparchus project
 */
package org.hipparchus.analysis.integration;

import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.Binary64;
import org.hipparchus.util.Binary64Field;
import org.hipparchus.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test case for midpoint integrator.
 * <p>
 * Test runs show that for a default relative accuracy of 1E-6, it generally
 * takes 10 to 15 iterations for the integral to converge.
 *
 */
public final class FieldMidPointIntegratorTest {

    /**
     * Test of integrator for the sine function.
     */
    @Test
    public void testLowAccuracy() {
        CalculusFieldUnivariateFunction<Binary64> f =
                        t -> t.subtract(1).multiply(t.subtract(0.5)).multiply(t).multiply(t.add(0.5)).multiply(t.add(1));
        FieldUnivariateIntegrator<Binary64> integrator = new FieldMidPointIntegrator<>(Binary64Field.getInstance(), 0.01, 1.0e-10, 2, 4);

        Binary64 min = new Binary64(-10);
        Binary64 max =  new Binary64(-9);
        double expected = -3697001.0 / 48.0;
        double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        double result = integrator.integrate(Integer.MAX_VALUE, f, min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

    }

    /**
     * Test of integrator for the sine function.
     */
    @Test
    public void testSinFunction() {
        FieldUnivariateIntegrator<Binary64> integrator = new FieldMidPointIntegrator<>(Binary64Field.getInstance());

        Binary64 min = new Binary64(0);
        Binary64 max = new Binary64(FastMath.PI);
        double expected = 2;
        double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        double result = integrator.integrate(Integer.MAX_VALUE, x -> x.sin(), min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

        min = new Binary64(-FastMath.PI/3);
        max = new Binary64(0);
        expected = -0.5;
        tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        result = integrator.integrate(Integer.MAX_VALUE, x -> x.sin(), min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

    }

    /**
     * Test of integrator for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        CalculusFieldUnivariateFunction<Binary64> f =
                        t -> t.subtract(1).multiply(t.subtract(0.5)).multiply(t).multiply(t.add(0.5)).multiply(t.add(1));
        FieldUnivariateIntegrator<Binary64> integrator = new FieldMidPointIntegrator<>(Binary64Field.getInstance());

        Binary64 min = new Binary64(0);
        Binary64 max = new Binary64(1);
        double expected = -1.0 / 48;
        double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        double result = integrator.integrate(Integer.MAX_VALUE, f, min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

        min = new Binary64(0);
        max = new Binary64(0.5);
        expected = 11.0 / 768;
        tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        result = integrator.integrate(Integer.MAX_VALUE, f, min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

        min = new Binary64(-1);
        max = new Binary64(4);
        expected = 2048 / 3.0 - 78 + 1.0 / 48;
        tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
        result = integrator.integrate(Integer.MAX_VALUE, f, min, max).getReal();
        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
        Assert.assertEquals(expected, result, tolerance);

    }

    /**
     * Test of parameters for the integrator.
     */
    @Test
    public void testParameters() {

        try {
            // bad interval
            new FieldMidPointIntegrator<>(Binary64Field.getInstance()).integrate(1000, x -> x.sin(),
                                                                                  new Binary64(1), new Binary64(-1));
            Assert.fail("Expecting MathIllegalArgumentException - bad interval");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            // bad iteration limits
            new FieldMidPointIntegrator<>(Binary64Field.getInstance(), 5, 4);
            Assert.fail("Expecting MathIllegalArgumentException - bad iteration limits");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            // bad iteration limits
            new FieldMidPointIntegrator<>(Binary64Field.getInstance(), 10, 99);
            Assert.fail("Expecting MathIllegalArgumentException - bad iteration limits");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
    }
}