Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 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.StepInterpolator; |
| 22 | |
| 23 | /** |
| 24 | * This class implements a step interpolator for the 3/8 fourth |
| 25 | * order Runge-Kutta integrator. |
| 26 | * |
| 27 | * <p>This interpolator allows to compute dense output inside the last |
| 28 | * step computed. The interpolation equation is consistent with the |
| 29 | * integration scheme : |
| 30 | * |
| 31 | * <pre> |
| 32 | * y(t_n + theta h) = y (t_n + h) |
| 33 | * - (1 - theta) (h/8) [ (1 - 7 theta + 8 theta^2) y'_1 |
| 34 | * + 3 (1 + theta - 4 theta^2) y'_2 |
| 35 | * + 3 (1 + theta) y'_3 |
| 36 | * + (1 + theta + 4 theta^2) y'_4 |
| 37 | * ] |
| 38 | * </pre> |
| 39 | * |
| 40 | * where theta belongs to [0 ; 1] and where y'_1 to y'_4 are the four |
| 41 | * evaluations of the derivatives already computed during the |
| 42 | * step.</p> |
| 43 | * |
| 44 | * @see ThreeEighthesIntegrator |
| 45 | * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ |
| 46 | * @since 1.2 |
| 47 | */ |
| 48 | |
| 49 | class ThreeEighthesStepInterpolator |
| 50 | extends RungeKuttaStepInterpolator { |
| 51 | |
| 52 | /** Serializable version identifier */ |
| 53 | private static final long serialVersionUID = -3345024435978721931L; |
| 54 | |
| 55 | /** Simple constructor. |
| 56 | * This constructor builds an instance that is not usable yet, the |
| 57 | * {@link |
| 58 | * org.apache.commons.math.ode.sampling.AbstractStepInterpolator#reinitialize} |
| 59 | * method should be called before using the instance in order to |
| 60 | * initialize the internal arrays. This constructor is used only |
| 61 | * in order to delay the initialization in some cases. The {@link |
| 62 | * RungeKuttaIntegrator} class uses the prototyping design pattern |
| 63 | * to create the step interpolators by cloning an uninitialized model |
| 64 | * and later initializing the copy. |
| 65 | */ |
| 66 | public ThreeEighthesStepInterpolator() { |
| 67 | } |
| 68 | |
| 69 | /** Copy constructor. |
| 70 | * @param interpolator interpolator to copy from. The copy is a deep |
| 71 | * copy: its arrays are separated from the original arrays of the |
| 72 | * instance |
| 73 | */ |
| 74 | public ThreeEighthesStepInterpolator(final ThreeEighthesStepInterpolator interpolator) { |
| 75 | super(interpolator); |
| 76 | } |
| 77 | |
| 78 | /** {@inheritDoc} */ |
| 79 | @Override |
| 80 | protected StepInterpolator doCopy() { |
| 81 | return new ThreeEighthesStepInterpolator(this); |
| 82 | } |
| 83 | |
| 84 | |
| 85 | /** {@inheritDoc} */ |
| 86 | @Override |
| 87 | protected void computeInterpolatedStateAndDerivatives(final double theta, |
| 88 | final double oneMinusThetaH) |
| 89 | throws DerivativeException { |
| 90 | |
| 91 | final double fourTheta2 = 4 * theta * theta; |
| 92 | final double s = oneMinusThetaH / 8.0; |
| 93 | final double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2); |
| 94 | final double coeff2 = 3 * s * (1 + theta - fourTheta2); |
| 95 | final double coeff3 = 3 * s * (1 + theta); |
| 96 | final double coeff4 = s * (1 + theta + fourTheta2); |
| 97 | final double coeffDot3 = 0.75 * theta; |
| 98 | final double coeffDot1 = coeffDot3 * (4 * theta - 5) + 1; |
| 99 | final double coeffDot2 = coeffDot3 * (5 - 6 * theta); |
| 100 | final double coeffDot4 = coeffDot3 * (2 * theta - 1); |
| 101 | |
| 102 | for (int i = 0; i < interpolatedState.length; ++i) { |
| 103 | final double yDot1 = yDotK[0][i]; |
| 104 | final double yDot2 = yDotK[1][i]; |
| 105 | final double yDot3 = yDotK[2][i]; |
| 106 | final double yDot4 = yDotK[3][i]; |
| 107 | interpolatedState[i] = |
| 108 | currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4; |
| 109 | interpolatedDerivatives[i] = |
| 110 | coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4; |
| 111 | |
| 112 | } |
| 113 | |
| 114 | } |
| 115 | |
| 116 | } |