/*
 * 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.ode;

/**
 * This class is used in the junit tests for the ODE integrators.
 * 
 * <p>
 * This specific problem is the following differential equation :
 * 
 * <pre>
 *    y' = t^3 - t y
 * </pre>
 * 
 * with the initial condition y (0) = 0. The solution of this equation is the
 * following function :
 * 
 * <pre>
 *   y (t) = t^2 + 2 (exp (- t^2 / 2) - 1)
 * </pre>
 * </p>
 * 
 */
public class TestProblem2 extends TestProblemAbstract {

	/** Serializable version identifier. */
	private static final long serialVersionUID = 8330741783213512366L;

	/** theoretical state */
	private double[] y;

	/**
	 * Simple constructor.
	 */
	public TestProblem2() {
		super();
		double[] y0 = { 0.0 };
		setInitialConditions(0.0, y0);
		setFinalConditions(1.0);
		double[] errorScale = { 1.0 };
		setErrorScale(errorScale);
		y = new double[y0.length];
	}

	/**
	 * Copy constructor.
	 * 
	 * @param problem
	 *            problem to copy
	 */
	public TestProblem2(TestProblem2 problem) {
		super(problem);
		y = problem.y.clone();
	}

	/** {@inheritDoc} */
	public TestProblem2 copy() {
		return new TestProblem2(this);
	}

	@Override
	public void doComputeDerivatives(double t, double[] y, double[] yDot) {

		// compute the derivatives
		for (int i = 0; i < n; ++i)
			yDot[i] = t * (t * t - y[i]);

	}

	@Override
	public double[] computeTheoreticalState(double t) {
		double t2 = t * t;
		double c = t2 + 2 * (Math.exp(-0.5 * t2) - 1);
		for (int i = 0; i < n; ++i) {
			y[i] = c;
		}
		return y;
	}

}
