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.core.Field;
21 import org.apache.commons.math4.legacy.core.RealFieldElement;
22 import org.apache.commons.math4.legacy.ode.FieldEquationsMapper;
23 import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
24
25 /**
26 * This class implements a step interpolator for the 3/8 fourth
27 * order Runge-Kutta integrator.
28 *
29 * <p>This interpolator allows to compute dense output inside the last
30 * step computed. The interpolation equation is consistent with the
31 * integration scheme :
32 * <ul>
33 * <li>Using reference point at step start:<br>
34 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
35 * + θ (h/8) [ (8 - 15 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
36 * + 3 * (15 θ - 12 θ<sup>2</sup>) y'<sub>2</sub>
37 * + 3 θ y'<sub>3</sub>
38 * + (-3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
39 * ]
40 * </li>
41 * <li>Using reference point at step end:<br>
42 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
43 * - (1 - θ) (h/8) [(1 - 7 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
44 * + 3 (1 + θ - 4 θ<sup>2</sup>) y'<sub>2</sub>
45 * + 3 (1 + θ) y'<sub>3</sub>
46 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
47 * ]
48 * </li>
49 * </ul>
50 *
51 * where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> are the four
52 * evaluations of the derivatives already computed during the
53 * step.
54 *
55 * @see ThreeEighthesFieldIntegrator
56 * @param <T> the type of the field elements
57 * @since 3.6
58 */
59
60 class ThreeEighthesFieldStepInterpolator<T extends RealFieldElement<T>>
61 extends RungeKuttaFieldStepInterpolator<T> {
62
63 /** Simple constructor.
64 * @param field field to which the time and state vector elements belong
65 * @param forward integration direction indicator
66 * @param yDotK slopes at the intermediate points
67 * @param globalPreviousState start of the global step
68 * @param globalCurrentState end of the global step
69 * @param softPreviousState start of the restricted step
70 * @param softCurrentState end of the restricted step
71 * @param mapper equations mapper for the all equations
72 */
73 ThreeEighthesFieldStepInterpolator(final Field<T> field, final boolean forward,
74 final T[][] yDotK,
75 final FieldODEStateAndDerivative<T> globalPreviousState,
76 final FieldODEStateAndDerivative<T> globalCurrentState,
77 final FieldODEStateAndDerivative<T> softPreviousState,
78 final FieldODEStateAndDerivative<T> softCurrentState,
79 final FieldEquationsMapper<T> mapper) {
80 super(field, forward, yDotK,
81 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
82 mapper);
83 }
84
85 /** {@inheritDoc} */
86 @Override
87 protected ThreeEighthesFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
88 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
89 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
90 final FieldODEStateAndDerivative<T> newSoftPreviousState,
91 final FieldODEStateAndDerivative<T> newSoftCurrentState,
92 final FieldEquationsMapper<T> newMapper) {
93 return new ThreeEighthesFieldStepInterpolator<>(newField, newForward, newYDotK,
94 newGlobalPreviousState, newGlobalCurrentState,
95 newSoftPreviousState, newSoftCurrentState,
96 newMapper);
97 }
98
99 /** {@inheritDoc} */
100 @SuppressWarnings("unchecked")
101 @Override
102 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
103 final T time, final T theta,
104 final T thetaH, final T oneMinusThetaH) {
105
106 final T coeffDot3 = theta.multiply(0.75);
107 final T coeffDot1 = coeffDot3.multiply(theta.multiply(4).subtract(5)).add(1);
108 final T coeffDot2 = coeffDot3.multiply(theta.multiply(-6).add(5));
109 final T coeffDot4 = coeffDot3.multiply(theta.multiply(2).subtract(1));
110 final T[] interpolatedState;
111 final T[] interpolatedDerivatives;
112
113 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
114 final T s = thetaH.divide(8);
115 final T fourTheta2 = theta.multiply(theta).multiply(4);
116 final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(15)).add(8));
117 final T coeff2 = s.multiply(theta.multiply(5).subtract(fourTheta2)).multiply(3);
118 final T coeff3 = s.multiply(theta).multiply(3);
119 final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
120 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
121 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
122 } else {
123 final T s = oneMinusThetaH.divide(-8);
124 final T fourTheta2 = theta.multiply(theta).multiply(4);
125 final T thetaPlus1 = theta.add(1);
126 final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(7)).add(1));
127 final T coeff2 = s.multiply(thetaPlus1.subtract(fourTheta2)).multiply(3);
128 final T coeff3 = s.multiply(thetaPlus1).multiply(3);
129 final T coeff4 = s.multiply(thetaPlus1.add(fourTheta2));
130 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
131 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
132 }
133
134 return new FieldODEStateAndDerivative<>(time, interpolatedState, interpolatedDerivatives);
135 }
136 }