/*
 * 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.polynomials;

import java.util.Arrays;
import junit.framework.TestCase;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.analysis.UnivariateRealFunction;

/**
 * Tests the PolynomialSplineFunction implementation.
 *
 * @version $Revision$
 */
public class PolynomialSplineFunctionTest extends TestCase {

	/** Error tolerance for tests */
	protected double tolerance = 1.0e-12;

	/**
	 * Quadratic polynomials used in tests:
	 * 
	 * x^2 + x [-1, 0) x^2 + x + 2 [0, 1) x^2 + x + 4 [1, 2)
	 * 
	 * Defined so that evaluation using PolynomialSplineFunction evaluation
	 * algorithm agrees at knot point boundaries.
	 */
	protected PolynomialFunction[] polynomials = { new PolynomialFunction(new double[] { 0d, 1d, 1d }),
			new PolynomialFunction(new double[] { 2d, 1d, 1d }), new PolynomialFunction(new double[] { 4d, 1d, 1d }) };

	/** Knot points */
	protected double[] knots = { -1, 0, 1, 2 };

	/** Derivative of test polynomials -- 2x + 1 */
	protected PolynomialFunction dp = new PolynomialFunction(new double[] { 1d, 2d });

	public void testConstructor() {
		PolynomialSplineFunction spline = new PolynomialSplineFunction(knots, polynomials);
		assertTrue(Arrays.equals(knots, spline.getKnots()));
		assertEquals(1d, spline.getPolynomials()[0].getCoefficients()[2], 0);
		assertEquals(3, spline.getN());

		try { // too few knots
			new PolynomialSplineFunction(new double[] { 0 }, polynomials);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}

		try { // too many knots
			new PolynomialSplineFunction(new double[] { 0, 1, 2, 3, 4 }, polynomials);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}

		try { // knots not increasing
			new PolynomialSplineFunction(new double[] { 0, 1, 3, 2 }, polynomials);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}
	}

	public void testValues() throws Exception {
		PolynomialSplineFunction spline = new PolynomialSplineFunction(knots, polynomials);
		UnivariateRealFunction dSpline = spline.derivative();

		/**
		 * interior points -- spline value at x should equal p(x - knot) where
		 * knot is the largest knot point less than or equal to x and p is the
		 * polynomial defined over the knot segment to which x belongs.
		 */
		double x = -1;
		int index = 0;
		for (int i = 0; i < 10; i++) {
			x += 0.25;
			index = findKnot(knots, x);
			assertEquals("spline function evaluation failed for x=" + x, polynomials[index].value(x - knots[index]),
					spline.value(x), tolerance);
			assertEquals("spline derivative evaluation failed for x=" + x, dp.value(x - knots[index]), dSpline.value(x),
					tolerance);
		}

		// knot points -- centering should zero arguments
		for (int i = 0; i < 3; i++) {
			assertEquals("spline function evaluation failed for knot=" + knots[i], polynomials[i].value(0),
					spline.value(knots[i]), tolerance);
			assertEquals("spline function evaluation failed for knot=" + knots[i], dp.value(0), dSpline.value(knots[i]),
					tolerance);
		}

		try { // outside of domain -- under min
			x = spline.value(-1.5);
			fail("Expecting IllegalArgumentException");
		} catch (FunctionEvaluationException ex) {
			// expected
		}

		try { // outside of domain -- over max
			x = spline.value(2.5);
			fail("Expecting IllegalArgumentException");
		} catch (FunctionEvaluationException ex) {
			// expected
		}
	}

	/**
	 * Do linear search to find largest knot point less than or equal to x.
	 * Implementation does binary search.
	 */
	protected int findKnot(double[] knots, double x) {
		if (x < knots[0] || x >= knots[knots.length - 1]) {
			throw new IllegalArgumentException("x is out of range");
		}
		for (int i = 0; i < knots.length; i++) {
			if (knots[i] > x) {
				return i - 1;
			}
		}
		throw new IllegalArgumentException("x is out of range");
	}
}
