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Java example source code file (LaguerreSolverTest.java)

This example Java source code file (LaguerreSolverTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

complex, expecting, laguerresolver, laguerresolvertest, nobracketingexception, numberistoolargeexception, polynomialfunction, test, toomanyevaluationsexception

The LaguerreSolverTest.java Java example source code

/*
 * 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.analysis.solvers;

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.complex.Complex;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.TestUtils;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for Laguerre solver.
 * <p>
 * Laguerre's method is very efficient in solving polynomials. Test runs
 * show that for a default absolute accuracy of 1E-6, it generally takes
 * less than 5 iterations to find one root, provided solveAll() is not
 * invoked, and 15 to 20 iterations to find all roots for quintic function.
 *
 */
public final class LaguerreSolverTest {
    /**
     * Test of solver for the linear function.
     */
    @Test
    public void testLinearFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = 4x - 1
        double coefficients[] = { -1.0, 4.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = 0.0; max = 1.0; expected = 0.25;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);
    }

    /**
     * Test of solver for the quadratic function.
     */
    @Test
    public void testQuadraticFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = 2x^2 + 5x - 3 = (x+3)(2x-1)
        double coefficients[] = { -3.0, 5.0, 2.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = 0.0; max = 2.0; expected = 0.5;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);

        min = -4.0; max = -1.0; expected = -3.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);
    }

    /**
     * Test of solver for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = x^5 - x^4 - 12x^3 + x^2 - x - 12 = (x+1)(x+3)(x-4)(x^2-x+1)
        double coefficients[] = { -12.0, -1.0, 1.0, -12.0, -1.0, 1.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = -2.0; max = 2.0; expected = -1.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);

        min = -5.0; max = -2.5; expected = -3.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);

        min = 3.0; max = 6.0; expected = 4.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
        result = solver.solve(100, f, min, max);
        Assert.assertEquals(expected, result, tolerance);
    }

    /**
     * Test of solver for the quintic function using
     * {@link LaguerreSolver#solveAllComplex(double[],double) solveAllComplex}.
     */
    @Test
    public void testQuinticFunction2() {
        // p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
        final double[] coefficients = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
        final LaguerreSolver solver = new LaguerreSolver();
        final Complex[] result = solver.solveAllComplex(coefficients, 0);

        for (Complex expected : new Complex[] { new Complex(0, -2),
                                                new Complex(0, 2),
                                                new Complex(0.5, 0.5 * FastMath.sqrt(3)),
                                                new Complex(-1, 0),
                                                new Complex(0.5, -0.5 * FastMath.sqrt(3.0)) }) {
            final double tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                                                  FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
            TestUtils.assertContains(result, expected, tolerance);
        }
    }

    /**
     * Test of parameters for the solver.
     */
    @Test
    public void testParameters() {
        double coefficients[] = { -3.0, 5.0, 2.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        try {
            // bad interval
            solver.solve(100, f, 1, -1);
            Assert.fail("Expecting NumberIsTooLargeException - bad interval");
        } catch (NumberIsTooLargeException ex) {
            // expected
        }
        try {
            // no bracketing
            solver.solve(100, f, 2, 3);
            Assert.fail("Expecting NoBracketingException - no bracketing");
        } catch (NoBracketingException ex) {
            // expected
        }
    }

    @Test(expected=org.apache.commons.math3.exception.NoDataException.class)
    public void testEmptyCoefficients() {
        double coefficients[] = {};
        LaguerreSolver solver = new LaguerreSolver();
        solver.solveComplex(coefficients, 0);
    }

    @Test(expected=org.apache.commons.math3.exception.NullArgumentException.class)
    public void testNullCoefficients() {
        LaguerreSolver solver = new LaguerreSolver();
        solver.solveComplex(null, 0);
    }

    @Test
    public void testTooManyEvaluations() {
        double coefficients[] = {1, 0, 0, 1}; // x^3 + 1 (cube roots of unity)
        final double tol = 1e-12;
        LaguerreSolver solver = new LaguerreSolver(tol);

        // No evaluations limit -> solveAllComplex should get all roots
        Complex [] expected = {new Complex(0.5, FastMath.sqrt(3) / 2),
            new Complex(-1, 0), new Complex(0.5, -FastMath.sqrt(3) / 2)};
        Complex [] roots = solver.solveAllComplex(coefficients, 0);

        for (Complex expectedRoot : expected) {
            final double tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                         FastMath.abs(expectedRoot.abs() * solver.getRelativeAccuracy()));
            TestUtils.assertContains(roots, expectedRoot, tolerance);
        }

        // Iterations limit too low -> throw TME
        try {
            solver.solveAllComplex(coefficients, 1000, 2);
            Assert.fail("Expecting TooManyEvaluationsException");
        } catch (TooManyEvaluationsException ex) {
            // expected
        }

    }
}

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