| /* |
| * 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.math4.analysis.solvers; |
| |
| import org.apache.commons.numbers.complex.Complex; |
| import org.apache.commons.math4.analysis.polynomials.PolynomialFunction; |
| import org.apache.commons.math4.analysis.solvers.LaguerreSolver; |
| import org.apache.commons.math4.exception.NoBracketingException; |
| import org.apache.commons.math4.exception.NumberIsTooLargeException; |
| import org.apache.commons.math4.util.FastMath; |
| import org.apache.commons.math4.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[] { Complex.ofCartesian(0, -2), |
| Complex.ofCartesian(0, 2), |
| Complex.ofCartesian(0.5, 0.5 * FastMath.sqrt(3)), |
| Complex.ofCartesian(-1, 0), |
| Complex.ofCartesian(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 |
| } |
| } |
| } |