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 * https://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 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22
23 package org.hipparchus.ode.nonstiff;
24
25 import org.hipparchus.CalculusFieldElement;
26 import org.hipparchus.Field;
27 import org.hipparchus.ode.FieldEquationsMapper;
28 import org.hipparchus.ode.FieldODEStateAndDerivative;
29
30 /**
31 * This class implements a step interpolator for the 3/8 fourth
32 * order Runge-Kutta integrator.
33 *
34 * <p>This interpolator allows to compute dense output inside the last
35 * step computed. The interpolation equation is consistent with the
36 * integration scheme :</p>
37 * <ul>
38 * <li>Using reference point at step start:<br>
39 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
40 * + θ (h/8) [ (8 - 15 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
41 * + 3 * (15 θ - 12 θ<sup>2</sup>) y'<sub>2</sub>
42 * + 3 θ y'<sub>3</sub>
43 * + (-3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
44 * ]
45 * </li>
46 * <li>Using reference point at step end:<br>
47 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
48 * - (1 - θ) (h/8) [(1 - 7 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
49 * + 3 (1 + θ - 4 θ<sup>2</sup>) y'<sub>2</sub>
50 * + 3 (1 + θ) y'<sub>3</sub>
51 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
52 * ]
53 * </li>
54 * </ul>
55 *
56 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> are the four
57 * evaluations of the derivatives already computed during the
58 * step.</p>
59 *
60 * @see ThreeEighthesFieldIntegrator
61 * @param <T> the type of the field elements
62 */
63
64 class ThreeEighthesFieldStateInterpolator<T extends CalculusFieldElement<T>>
65 extends RungeKuttaFieldStateInterpolator<T> {
66
67 /** Simple constructor.
68 * @param field field to which the time and state vector elements belong
69 * @param forward integration direction indicator
70 * @param yDotK slopes at the intermediate points
71 * @param globalPreviousState start of the global step
72 * @param globalCurrentState end of the global step
73 * @param softPreviousState start of the restricted step
74 * @param softCurrentState end of the restricted step
75 * @param mapper equations mapper for the all equations
76 */
77 ThreeEighthesFieldStateInterpolator(final Field<T> field, final boolean forward,
78 final T[][] yDotK,
79 final FieldODEStateAndDerivative<T> globalPreviousState,
80 final FieldODEStateAndDerivative<T> globalCurrentState,
81 final FieldODEStateAndDerivative<T> softPreviousState,
82 final FieldODEStateAndDerivative<T> softCurrentState,
83 final FieldEquationsMapper<T> mapper) {
84 super(field, forward, yDotK,
85 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
86 mapper);
87 }
88
89 /** {@inheritDoc} */
90 @Override
91 protected ThreeEighthesFieldStateInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
92 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
93 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
94 final FieldODEStateAndDerivative<T> newSoftPreviousState,
95 final FieldODEStateAndDerivative<T> newSoftCurrentState,
96 final FieldEquationsMapper<T> newMapper) {
97 return new ThreeEighthesFieldStateInterpolator<T>(newField, newForward, newYDotK,
98 newGlobalPreviousState, newGlobalCurrentState,
99 newSoftPreviousState, newSoftCurrentState,
100 newMapper);
101 }
102
103 /** {@inheritDoc} */
104 @SuppressWarnings("unchecked")
105 @Override
106 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
107 final T time, final T theta,
108 final T thetaH, final T oneMinusThetaH) {
109
110 final T coeffDot3 = theta.multiply(0.75);
111 final T coeffDot1 = coeffDot3.multiply(theta.multiply(4).subtract(5)).add(1);
112 final T coeffDot2 = coeffDot3.multiply(theta.multiply(-6).add(5));
113 final T coeffDot4 = coeffDot3.multiply(theta.multiply(2).subtract(1));
114 final T[] interpolatedState;
115 final T[] interpolatedDerivatives;
116
117 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
118 final T s = thetaH.divide(8);
119 final T fourTheta2 = theta.multiply(theta).multiply(4);
120 final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(15)).add(8));
121 final T coeff2 = s.multiply(theta.multiply(5).subtract(fourTheta2)).multiply(3);
122 final T coeff3 = s.multiply(theta).multiply(3);
123 final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
124 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
125 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
126 } else {
127 final T s = oneMinusThetaH.divide(-8);
128 final T fourTheta2 = theta.multiply(theta).multiply(4);
129 final T thetaPlus1 = theta.add(1);
130 final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(7)).add(1));
131 final T coeff2 = s.multiply(thetaPlus1.subtract(fourTheta2)).multiply(3);
132 final T coeff3 = s.multiply(thetaPlus1).multiply(3);
133 final T coeff4 = s.multiply(thetaPlus1.add(fourTheta2));
134 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
135 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
136 }
137
138 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
139
140 }
141
142 }