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* 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,
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* See the License for the specific language governing permissions and
* limitations under the License.
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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.complex.Complex;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.TestUtils;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case 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
}
}
}