001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math4.ode;
019
020
021/** This class converts second order differential equations to first
022 * order ones.
023 *
024 * <p>This class is a wrapper around a {@link
025 * SecondOrderDifferentialEquations} which allow to use a {@link
026 * FirstOrderIntegrator} to integrate it.</p>
027 *
028 * <p>The transformation is done by changing the n dimension state
029 * vector to a 2n dimension vector, where the first n components are
030 * the initial state variables and the n last components are their
031 * first time derivative. The first time derivative of this state
032 * vector then really contains both the first and second time
033 * derivative of the initial state vector, which can be handled by the
034 * underlying second order equations set.</p>
035 *
036 * <p>One should be aware that the data is duplicated during the
037 * transformation process and that for each call to {@link
038 * #computeDerivatives computeDerivatives}, this wrapper does copy 4n
039 * scalars : 2n before the call to {@link
040 * SecondOrderDifferentialEquations#computeSecondDerivatives
041 * computeSecondDerivatives} in order to dispatch the y state vector
042 * into z and zDot, and 2n after the call to gather zDot and zDDot
043 * into yDot. Since the underlying problem by itself perhaps also
044 * needs to copy data and dispatch the arrays into domain objects,
045 * this has an impact on both memory and CPU usage. The only way to
046 * avoid this duplication is to perform the transformation at the
047 * problem level, i.e. to implement the problem as a first order one
048 * and then avoid using this class.</p>
049 *
050 * @see FirstOrderIntegrator
051 * @see FirstOrderDifferentialEquations
052 * @see SecondOrderDifferentialEquations
053 * @since 1.2
054 */
055
056public class FirstOrderConverter implements FirstOrderDifferentialEquations {
057
058    /** Underlying second order equations set. */
059    private final SecondOrderDifferentialEquations equations;
060
061    /** second order problem dimension. */
062    private final int dimension;
063
064    /** state vector. */
065    private final double[] z;
066
067    /** first time derivative of the state vector. */
068    private final double[] zDot;
069
070    /** second time derivative of the state vector. */
071    private final double[] zDDot;
072
073  /** Simple constructor.
074   * Build a converter around a second order equations set.
075   * @param equations second order equations set to convert
076   */
077  public FirstOrderConverter (final SecondOrderDifferentialEquations equations) {
078      this.equations = equations;
079      dimension      = equations.getDimension();
080      z              = new double[dimension];
081      zDot           = new double[dimension];
082      zDDot          = new double[dimension];
083  }
084
085  /** Get the dimension of the problem.
086   * <p>The dimension of the first order problem is twice the
087   * dimension of the underlying second order problem.</p>
088   * @return dimension of the problem
089   */
090  @Override
091public int getDimension() {
092    return 2 * dimension;
093  }
094
095  /** Get the current time derivative of the state vector.
096   * @param t current value of the independent <I>time</I> variable
097   * @param y array containing the current value of the state vector
098   * @param yDot placeholder array where to put the time derivative of the state vector
099   */
100  @Override
101public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
102
103    // split the state vector in two
104    System.arraycopy(y, 0,         z,    0, dimension);
105    System.arraycopy(y, dimension, zDot, 0, dimension);
106
107    // apply the underlying equations set
108    equations.computeSecondDerivatives(t, z, zDot, zDDot);
109
110    // build the result state derivative
111    System.arraycopy(zDot,  0, yDot, 0,         dimension);
112    System.arraycopy(zDDot, 0, yDot, dimension, dimension);
113
114  }
115
116}