1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 18 package org.apache.commons.math.ode.nonstiff; 19 20 import org.apache.commons.math.ode.DerivativeException; 21 import org.apache.commons.math.ode.sampling.AbstractStepInterpolator; 22 import org.apache.commons.math.ode.sampling.StepInterpolator; 23 24 /** 25 * This class implements a step interpolator for the Gill fourth 26 * order Runge-Kutta integrator. 27 * 28 * <p>This interpolator allows to compute dense output inside the last 29 * step computed. The interpolation equation is consistent with the 30 * integration scheme : 31 * 32 * <pre> 33 * y(t_n + theta h) = y (t_n + h) 34 * - (1 - theta) (h/6) [ (1 - theta) (1 - 4 theta) y'_1 35 * + (1 - theta) (1 + 2 theta) ((2-q) y'_2 + (2+q) y'_3) 36 * + (1 + theta + 4 theta^2) y'_4 37 * ] 38 * </pre> 39 * where theta belongs to [0 ; 1], q = sqrt(2) and where y'_1 to y'_4 40 * are the four evaluations of the derivatives already computed during 41 * the step.</p> 42 * 43 * @see GillIntegrator 44 * @version $Revision: 782432 $ $Date: 2009-06-07 15:08:26 -0400 (Sun, 07 Jun 2009) $ 45 * @since 1.2 46 */ 47 48 class GillStepInterpolator 49 extends RungeKuttaStepInterpolator { 50 51 /** Simple constructor. 52 * This constructor builds an instance that is not usable yet, the 53 * {@link AbstractStepInterpolator#reinitialize} method should be called 54 * before using the instance in order to initialize the internal arrays. This 55 * constructor is used only in order to delay the initialization in 56 * some cases. The {@link RungeKuttaIntegrator} class uses the 57 * prototyping design pattern to create the step interpolators by 58 * cloning an uninitialized model and latter initializing the copy. 59 */ 60 public GillStepInterpolator() { 61 } 62 63 /** Copy constructor. 64 * @param interpolator interpolator to copy from. The copy is a deep 65 * copy: its arrays are separated from the original arrays of the 66 * instance 67 */ 68 public GillStepInterpolator(final GillStepInterpolator interpolator) { 69 super(interpolator); 70 } 71 72 /** {@inheritDoc} */ 73 @Override 74 protected StepInterpolator doCopy() { 75 return new GillStepInterpolator(this); 76 } 77 78 79 /** {@inheritDoc} */ 80 @Override 81 protected void computeInterpolatedStateAndDerivatives(final double theta, 82 final double oneMinusThetaH) 83 throws DerivativeException { 84 85 final double twoTheta = 2 * theta; 86 final double fourTheta = 4 * theta; 87 final double s = oneMinusThetaH / 6.0; 88 final double oMt = 1 - theta; 89 final double soMt = s * oMt; 90 final double c23 = soMt * (1 + twoTheta); 91 final double coeff1 = soMt * (1 - fourTheta); 92 final double coeff2 = c23 * tMq; 93 final double coeff3 = c23 * tPq; 94 final double coeff4 = s * (1 + theta * (1 + fourTheta)); 95 final double coeffDot1 = theta * (twoTheta - 3) + 1; 96 final double cDot23 = theta * oMt; 97 final double coeffDot2 = cDot23 * tMq; 98 final double coeffDot3 = cDot23 * tPq; 99 final double coeffDot4 = theta * (twoTheta - 1); 100 101 for (int i = 0; i < interpolatedState.length; ++i) { 102 final double yDot1 = yDotK[0][i]; 103 final double yDot2 = yDotK[1][i]; 104 final double yDot3 = yDotK[2][i]; 105 final double yDot4 = yDotK[3][i]; 106 interpolatedState[i] = 107 currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4; 108 interpolatedDerivatives[i] = 109 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4; 110 } 111 112 } 113 114 /** First Gill coefficient. */ 115 private static final double tMq = 2 - Math.sqrt(2.0); 116 117 /** Second Gill coefficient. */ 118 private static final double tPq = 2 + Math.sqrt(2.0); 119 120 /** Serializable version identifier */ 121 private static final long serialVersionUID = -107804074496313322L; 122 123 }