/*
 * 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.math.analysis.solvers;

import org.apache.commons.math.MathException;
import org.apache.commons.math.TestUtils;
import org.apache.commons.math.analysis.SinFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.complex.Complex;
import junit.framework.TestCase;

/**
 * Testcase 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.
 * 
 * @version $Revision$ $Date$
 */
public final class LaguerreSolverTest extends TestCase {

	/**
	 * Test deprecated APIs.
	 */
	@Deprecated
	public void testDeprecated() throws MathException {
		double min, max, expected, result, tolerance;

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

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

	/**
	 * Test of solver for the linear function.
	 */
	public void testLinearFunction() throws MathException {
		double min, max, expected, result, tolerance;

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

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

	/**
	 * Test of solver for the quadratic function.
	 */
	public void testQuadraticFunction() throws MathException {
		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);
		UnivariateRealSolver solver = new LaguerreSolver();

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

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

	/**
	 * Test of solver for the quintic function.
	 */
	public void testQuinticFunction() throws MathException {
		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);
		UnivariateRealSolver solver = new LaguerreSolver();

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

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

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

	/**
	 * Test of solver for the quintic function using solveAll().
	 */
	public void testQuinticFunction2() throws MathException {
		double initial = 0.0, tolerance;
		Complex expected, result[];

		// p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
		double coefficients[] = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
		LaguerreSolver solver = new LaguerreSolver();
		result = solver.solveAll(coefficients, initial);

		expected = new Complex(0.0, -2.0);
		tolerance = Math.max(solver.getAbsoluteAccuracy(), Math.abs(expected.abs() * solver.getRelativeAccuracy()));
		TestUtils.assertContains(result, expected, tolerance);

		expected = new Complex(0.0, 2.0);
		tolerance = Math.max(solver.getAbsoluteAccuracy(), Math.abs(expected.abs() * solver.getRelativeAccuracy()));
		TestUtils.assertContains(result, expected, tolerance);

		expected = new Complex(0.5, 0.5 * Math.sqrt(3.0));
		tolerance = Math.max(solver.getAbsoluteAccuracy(), Math.abs(expected.abs() * solver.getRelativeAccuracy()));
		TestUtils.assertContains(result, expected, tolerance);

		expected = new Complex(-1.0, 0.0);
		tolerance = Math.max(solver.getAbsoluteAccuracy(), Math.abs(expected.abs() * solver.getRelativeAccuracy()));
		TestUtils.assertContains(result, expected, tolerance);

		expected = new Complex(0.5, -0.5 * Math.sqrt(3.0));
		tolerance = Math.max(solver.getAbsoluteAccuracy(), Math.abs(expected.abs() * solver.getRelativeAccuracy()));
		TestUtils.assertContains(result, expected, tolerance);
	}

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

		try {
			// bad interval
			solver.solve(f, 1, -1);
			fail("Expecting IllegalArgumentException - bad interval");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			// no bracketing
			solver.solve(f, 2, 3);
			fail("Expecting IllegalArgumentException - no bracketing");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			// bad function
			solver.solve(new SinFunction(), -1, 1);
			fail("Expecting IllegalArgumentException - bad function");
		} catch (IllegalArgumentException ex) {
			// expected
		}
	}
}
