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.math4.legacy.ode.nonstiff;
19
20 import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator;
21 import org.apache.commons.math4.core.jdkmath.JdkMath;
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 * where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
47 * are the four evaluations of the derivatives already computed during
48 * the step.
49 *
50 * @see GillIntegrator
51 * @since 1.2
52 */
53
54 class GillStepInterpolator
55 extends RungeKuttaStepInterpolator {
56
57 /** First Gill coefficient. */
58 private static final double ONE_MINUS_INV_SQRT_2 = 1 - JdkMath.sqrt(0.5);
59
60 /** Second Gill coefficient. */
61 private static final double ONE_PLUS_INV_SQRT_2 = 1 + JdkMath.sqrt(0.5);
62
63 /** Serializable version identifier. */
64 private static final long serialVersionUID = 20111120L;
65
66 /** Simple constructor.
67 * This constructor builds an instance that is not usable yet, the
68 * {@link
69 * org.apache.commons.math4.legacy.ode.sampling.AbstractStepInterpolator#reinitialize}
70 * method should be called before using the instance in order to
71 * initialize the internal arrays. This constructor is used only
72 * in order to delay the initialization in some cases. The {@link
73 * RungeKuttaIntegrator} class uses the prototyping design pattern
74 * to create the step interpolators by cloning an uninitialized model
75 * and later initializing the copy.
76 */
77 // CHECKSTYLE: stop RedundantModifier
78 // the public modifier here is needed for serialization
79 public GillStepInterpolator() {
80 }
81 // CHECKSTYLE: resume RedundantModifier
82
83 /** Copy constructor.
84 * @param interpolator interpolator to copy from. The copy is a deep
85 * copy: its arrays are separated from the original arrays of the
86 * instance
87 */
88 GillStepInterpolator(final GillStepInterpolator interpolator) {
89 super(interpolator);
90 }
91
92 /** {@inheritDoc} */
93 @Override
94 protected StepInterpolator doCopy() {
95 return new GillStepInterpolator(this);
96 }
97
98
99 /** {@inheritDoc} */
100 @Override
101 protected void computeInterpolatedStateAndDerivatives(final double theta,
102 final double oneMinusThetaH) {
103
104 final double twoTheta = 2 * theta;
105 final double fourTheta2 = twoTheta * twoTheta;
106 final double coeffDot1 = theta * (twoTheta - 3) + 1;
107 final double cDot23 = twoTheta * (1 - theta);
108 final double coeffDot2 = cDot23 * ONE_MINUS_INV_SQRT_2;
109 final double coeffDot3 = cDot23 * ONE_PLUS_INV_SQRT_2;
110 final double coeffDot4 = theta * (twoTheta - 1);
111
112 if (previousState != null && theta <= 0.5) {
113 final double s = theta * h / 6.0;
114 final double c23 = s * (6 * theta - fourTheta2);
115 final double coeff1 = s * (6 - 9 * theta + fourTheta2);
116 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
117 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
118 final double coeff4 = s * (-3 * theta + fourTheta2);
119 for (int i = 0; i < interpolatedState.length; ++i) {
120 final double yDot1 = yDotK[0][i];
121 final double yDot2 = yDotK[1][i];
122 final double yDot3 = yDotK[2][i];
123 final double yDot4 = yDotK[3][i];
124 interpolatedState[i] =
125 previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4;
126 interpolatedDerivatives[i] =
127 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
128 }
129 } else {
130 final double s = oneMinusThetaH / 6.0;
131 final double c23 = s * (2 + twoTheta - fourTheta2);
132 final double coeff1 = s * (1 - 5 * theta + fourTheta2);
133 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
134 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
135 final double coeff4 = s * (1 + theta + fourTheta2);
136 for (int i = 0; i < interpolatedState.length; ++i) {
137 final double yDot1 = yDotK[0][i];
138 final double yDot2 = yDotK[1][i];
139 final double yDot3 = yDotK[2][i];
140 final double yDot4 = yDotK[3][i];
141 interpolatedState[i] =
142 currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
143 interpolatedDerivatives[i] =
144 coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
145 }
146 }
147 }
148 }