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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,
* 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.math3.ode;
/** This class converts second order differential equations to first
* order ones.
*
* This class is a wrapper around a {@link
* SecondOrderDifferentialEquations} which allow to use a {@link
* FirstOrderIntegrator} to integrate it.
*
* The transformation is done by changing the n dimension state
* vector to a 2n dimension vector, where the first n components are
* the initial state variables and the n last components are their
* first time derivative. The first time derivative of this state
* vector then really contains both the first and second time
* derivative of the initial state vector, which can be handled by the
* underlying second order equations set.
*
* One should be aware that the data is duplicated during the
* transformation process and that for each call to {@link
* #computeDerivatives computeDerivatives}, this wrapper does copy 4n
* scalars : 2n before the call to {@link
* SecondOrderDifferentialEquations#computeSecondDerivatives
* computeSecondDerivatives} in order to dispatch the y state vector
* into z and zDot, and 2n after the call to gather zDot and zDDot
* into yDot. Since the underlying problem by itself perhaps also
* needs to copy data and dispatch the arrays into domain objects,
* this has an impact on both memory and CPU usage. The only way to
* avoid this duplication is to perform the transformation at the
* problem level, i.e. to implement the problem as a first order one
* and then avoid using this class.
*
* @see FirstOrderIntegrator
* @see FirstOrderDifferentialEquations
* @see SecondOrderDifferentialEquations
* @since 1.2
*/
public class FirstOrderConverter implements FirstOrderDifferentialEquations {
/** Underlying second order equations set. */
private final SecondOrderDifferentialEquations equations;
/** second order problem dimension. */
private final int dimension;
/** state vector. */
private final double[] z;
/** first time derivative of the state vector. */
private final double[] zDot;
/** second time derivative of the state vector. */
private final double[] zDDot;
/** Simple constructor.
* Build a converter around a second order equations set.
* @param equations second order equations set to convert
*/
public FirstOrderConverter (final SecondOrderDifferentialEquations equations) {
this.equations = equations;
dimension = equations.getDimension();
z = new double[dimension];
zDot = new double[dimension];
zDDot = new double[dimension];
}
/** Get the dimension of the problem.
* The dimension of the first order problem is twice the
* dimension of the underlying second order problem.
* @return dimension of the problem
*/
public int getDimension() {
return 2 * dimension;
}
/** Get the current time derivative of the state vector.
* @param t current value of the independent time variable
* @param y array containing the current value of the state vector
* @param yDot placeholder array where to put the time derivative of the state vector
*/
public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
// split the state vector in two
System.arraycopy(y, 0, z, 0, dimension);
System.arraycopy(y, dimension, zDot, 0, dimension);
// apply the underlying equations set
equations.computeSecondDerivatives(t, z, zDot, zDDot);
// build the result state derivative
System.arraycopy(zDot, 0, yDot, 0, dimension);
System.arraycopy(zDDot, 0, yDot, dimension, dimension);
}
}