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 3/8 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/8) [ (1 - 7 theta + 8 theta^2) y'_1 35 * + 3 (1 + theta - 4 theta^2) y'_2 36 * + 3 (1 + theta) y'_3 37 * + (1 + theta + 4 theta^2) y'_4 38 * ] 39 * </pre> 40 * 41 * where theta belongs to [0 ; 1] and where y'_1 to y'_4 are the four 42 * evaluations of the derivatives already computed during the 43 * step.</p> 44 * 45 * @see ThreeEighthesIntegrator 46 * @version $Revision: 782432 $ $Date: 2009-06-07 15:08:26 -0400 (Sun, 07 Jun 2009) $ 47 * @since 1.2 48 */ 49 50 class ThreeEighthesStepInterpolator 51 extends RungeKuttaStepInterpolator { 52 53 /** Simple constructor. 54 * This constructor builds an instance that is not usable yet, the 55 * {@link AbstractStepInterpolator#reinitialize} method should be called 56 * before using the instance in order to initialize the internal arrays. This 57 * constructor is used only in order to delay the initialization in 58 * some cases. The {@link RungeKuttaIntegrator} class uses the 59 * prototyping design pattern to create the step interpolators by 60 * cloning an uninitialized model and latter initializing the copy. 61 */ 62 public ThreeEighthesStepInterpolator() { 63 } 64 65 /** Copy constructor. 66 * @param interpolator interpolator to copy from. The copy is a deep 67 * copy: its arrays are separated from the original arrays of the 68 * instance 69 */ 70 public ThreeEighthesStepInterpolator(final ThreeEighthesStepInterpolator interpolator) { 71 super(interpolator); 72 } 73 74 /** {@inheritDoc} */ 75 @Override 76 protected StepInterpolator doCopy() { 77 return new ThreeEighthesStepInterpolator(this); 78 } 79 80 81 /** {@inheritDoc} */ 82 @Override 83 protected void computeInterpolatedStateAndDerivatives(final double theta, 84 final double oneMinusThetaH) 85 throws DerivativeException { 86 87 final double fourTheta2 = 4 * theta * theta; 88 final double s = oneMinusThetaH / 8.0; 89 final double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2); 90 final double coeff2 = 3 * s * (1 + theta - fourTheta2); 91 final double coeff3 = 3 * s * (1 + theta); 92 final double coeff4 = s * (1 + theta + fourTheta2); 93 final double coeffDot3 = 0.75 * theta; 94 final double coeffDot1 = coeffDot3 * (4 * theta - 5) + 1; 95 final double coeffDot2 = coeffDot3 * (5 - 6 * theta); 96 final double coeffDot4 = coeffDot3 * (2 * theta - 1); 97 98 for (int i = 0; i < interpolatedState.length; ++i) { 99 final double yDot1 = yDotK[0][i]; 100 final double yDot2 = yDotK[1][i]; 101 final double yDot3 = yDotK[2][i]; 102 final double yDot4 = yDotK[3][i]; 103 interpolatedState[i] = 104 currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4; 105 interpolatedDerivatives[i] = 106 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4; 107 108 } 109 110 } 111 112 /** Serializable version identifier */ 113 private static final long serialVersionUID = -3345024435978721931L; 114 115 }