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    
018    package org.apache.commons.math3.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     * @version $Id: FirstOrderConverter.java 1416643 2012-12-03 19:37:14Z tn $
054     * @since 1.2
055     */
056    
057    public class FirstOrderConverter implements FirstOrderDifferentialEquations {
058    
059        /** Underlying second order equations set. */
060        private final SecondOrderDifferentialEquations equations;
061    
062        /** second order problem dimension. */
063        private final int dimension;
064    
065        /** state vector. */
066        private final double[] z;
067    
068        /** first time derivative of the state vector. */
069        private final double[] zDot;
070    
071        /** second time derivative of the state vector. */
072        private final double[] zDDot;
073    
074      /** Simple constructor.
075       * Build a converter around a second order equations set.
076       * @param equations second order equations set to convert
077       */
078      public FirstOrderConverter (final SecondOrderDifferentialEquations equations) {
079          this.equations = equations;
080          dimension      = equations.getDimension();
081          z              = new double[dimension];
082          zDot           = new double[dimension];
083          zDDot          = new double[dimension];
084      }
085    
086      /** Get the dimension of the problem.
087       * <p>The dimension of the first order problem is twice the
088       * dimension of the underlying second order problem.</p>
089       * @return dimension of the problem
090       */
091      public 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      public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
101    
102        // split the state vector in two
103        System.arraycopy(y, 0,         z,    0, dimension);
104        System.arraycopy(y, dimension, zDot, 0, dimension);
105    
106        // apply the underlying equations set
107        equations.computeSecondDerivatives(t, z, zDot, zDDot);
108    
109        // build the result state derivative
110        System.arraycopy(zDot,  0, yDot, 0,         dimension);
111        System.arraycopy(zDDot, 0, yDot, dimension, dimension);
112    
113      }
114    
115    }