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.math3.ode.nonstiff;
19
20 import org.apache.commons.math3.ode.sampling.StepInterpolator;
21 import org.apache.commons.math3.util.FastMath;
22
23 /**
24 * This class implements a step interpolator for the Gill 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 * <ul>
31 * <li>Using reference point at step start:<br>
32 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
33 * + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
34 * + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
35 * + ( - 3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
36 * ]
37 * </li>
38 * <li>Using reference point at step start:<br>
39 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
40 * - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
41 * + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
42 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
43 * ]
44 * </li>
45 * </ul>
46 * </p>
47 * where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
48 * are the four evaluations of the derivatives already computed during
49 * the step.</p>
50 *
51 * @see GillIntegrator
52 * @version $Id: GillStepInterpolator.java 1416643 2012-12-03 19:37:14Z tn $
53 * @since 1.2
54 */
55
56 class GillStepInterpolator
57 extends RungeKuttaStepInterpolator {
58
59 /** First Gill coefficient. */
60 private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);
61
62 /** Second Gill coefficient. */
63 private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);
64
65 /** Serializable version identifier. */
66 private static final long serialVersionUID = 20111120L;
67
68 /** Simple constructor.
69 * This constructor builds an instance that is not usable yet, the
70 * {@link
71 * org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize}
72 * method should be called before using the instance in order to
73 * initialize the internal arrays. This constructor is used only
74 * in order to delay the initialization in some cases. The {@link
75 * RungeKuttaIntegrator} class uses the prototyping design pattern
76 * to create the step interpolators by cloning an uninitialized model
77 * and later initializing the copy.
78 */
79 public GillStepInterpolator() {
80 }
81
82 /** Copy constructor.
83 * @param interpolator interpolator to copy from. The copy is a deep
84 * copy: its arrays are separated from the original arrays of the
85 * instance
86 */
87 public GillStepInterpolator(final GillStepInterpolator interpolator) {
88 super(interpolator);
89 }
90
91 /** {@inheritDoc} */
92 @Override
93 protected StepInterpolator doCopy() {
94 return new GillStepInterpolator(this);
95 }
96
97
98 /** {@inheritDoc} */
99 @Override
100 protected void computeInterpolatedStateAndDerivatives(final double theta,
101 final double oneMinusThetaH) {
102
103 final double twoTheta = 2 * theta;
104 final double fourTheta2 = twoTheta * twoTheta;
105 final double coeffDot1 = theta * (twoTheta - 3) + 1;
106 final double cDot23 = twoTheta * (1 - theta);
107 final double coeffDot2 = cDot23 * ONE_MINUS_INV_SQRT_2;
108 final double coeffDot3 = cDot23 * ONE_PLUS_INV_SQRT_2;
109 final double coeffDot4 = theta * (twoTheta - 1);
110
111 if ((previousState != null) && (theta <= 0.5)) {
112 final double s = theta * h / 6.0;
113 final double c23 = s * (6 * theta - fourTheta2);
114 final double coeff1 = s * (6 - 9 * theta + fourTheta2);
115 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
116 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
117 final double coeff4 = s * (-3 * theta + fourTheta2);
118 for (int i = 0; i < interpolatedState.length; ++i) {
119 final double yDot1 = yDotK[0][i];
120 final double yDot2 = yDotK[1][i];
121 final double yDot3 = yDotK[2][i];
122 final double yDot4 = yDotK[3][i];
123 interpolatedState[i] =
124 previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4;
125 interpolatedDerivatives[i] =
126 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
127 }
128 } else {
129 final double s = oneMinusThetaH / 6.0;
130 final double c23 = s * (2 + twoTheta - fourTheta2);
131 final double coeff1 = s * (1 - 5 * theta + fourTheta2);
132 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
133 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
134 final double coeff4 = s * (1 + theta + fourTheta2);
135 for (int i = 0; i < interpolatedState.length; ++i) {
136 final double yDot1 = yDotK[0][i];
137 final double yDot2 = yDotK[1][i];
138 final double yDot3 = yDotK[2][i];
139 final double yDot4 = yDotK[3][i];
140 interpolatedState[i] =
141 currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
142 interpolatedDerivatives[i] =
143 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
144 }
145 }
146
147 }
148
149 }