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.math.ode; 019 020 /** This class converts second order differential equations to first 021 * order ones. 022 * 023 * <p>This class is a wrapper around a {@link 024 * SecondOrderDifferentialEquations} which allow to use a {@link 025 * FirstOrderIntegrator} to integrate it.</p> 026 * 027 * <p>The transformation is done by changing the n dimension state 028 * vector to a 2n dimension vector, where the first n components are 029 * the initial state variables and the n last components are their 030 * first time derivative. The first time derivative of this state 031 * vector then really contains both the first and second time 032 * derivative of the initial state vector, which can be handled by the 033 * underlying second order equations set.</p> 034 * 035 * <p>One should be aware that the data is duplicated during the 036 * transformation process and that for each call to {@link 037 * #computeDerivatives computeDerivatives}, this wrapper does copy 4n 038 * scalars : 2n before the call to {@link 039 * SecondOrderDifferentialEquations#computeSecondDerivatives 040 * computeSecondDerivatives} in order to dispatch the y state vector 041 * into z and zDot, and 2n after the call to gather zDot and zDDot 042 * into yDot. Since the underlying problem by itself perhaps also 043 * needs to copy data and dispatch the arrays into domain objects, 044 * this has an impact on both memory and CPU usage. The only way to 045 * avoid this duplication is to perform the transformation at the 046 * problem level, i.e. to implement the problem as a first order one 047 * and then avoid using this class.</p> 048 * 049 * @see FirstOrderIntegrator 050 * @see FirstOrderDifferentialEquations 051 * @see SecondOrderDifferentialEquations 052 * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $ 053 * @since 1.2 054 */ 055 056 public 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 public int getDimension() { 091 return 2 * dimension; 092 } 093 094 /** Get the current time derivative of the state vector. 095 * @param t current value of the independent <I>time</I> variable 096 * @param y array containing the current value of the state vector 097 * @param yDot placeholder array where to put the time derivative of the state vector 098 * @throws DerivativeException this exception is propagated to the caller if the 099 * underlying user function triggers one 100 */ 101 public void computeDerivatives(final double t, final double[] y, final double[] yDot) 102 throws DerivativeException { 103 104 // split the state vector in two 105 System.arraycopy(y, 0, z, 0, dimension); 106 System.arraycopy(y, dimension, zDot, 0, dimension); 107 108 // apply the underlying equations set 109 equations.computeSecondDerivatives(t, z, zDot, zDDot); 110 111 // build the result state derivative 112 System.arraycopy(zDot, 0, yDot, 0, dimension); 113 System.arraycopy(zDDot, 0, yDot, dimension, dimension); 114 115 } 116 117 }