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 second order
32 * Runge-Kutta integrator.
33 *
34 * <p>This interpolator computes 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>) + θ h [(1 - θ) y'<sub>1</sub> + θ y'<sub>2</sub>]
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) + (1-θ) h [θ y'<sub>1</sub> - (1+θ) y'<sub>2</sub>]
43 * </li>
44 * </ul>
45 *
46 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
47 * evaluations of the derivatives already computed during the
48 * step.</p>
49 *
50 * @see MidpointFieldIntegrator
51 * @param <T> the type of the field elements
52 */
53
54 class MidpointFieldStateInterpolator<T extends CalculusFieldElement<T>>
55 extends RungeKuttaFieldStateInterpolator<T> {
56
57 /** Simple constructor.
58 * @param field field to which the time and state vector elements belong
59 * @param forward integration direction indicator
60 * @param yDotK slopes at the intermediate points
61 * @param globalPreviousState start of the global step
62 * @param globalCurrentState end of the global step
63 * @param softPreviousState start of the restricted step
64 * @param softCurrentState end of the restricted step
65 * @param mapper equations mapper for the all equations
66 */
67 MidpointFieldStateInterpolator(final Field<T> field, final boolean forward,
68 final T[][] yDotK,
69 final FieldODEStateAndDerivative<T> globalPreviousState,
70 final FieldODEStateAndDerivative<T> globalCurrentState,
71 final FieldODEStateAndDerivative<T> softPreviousState,
72 final FieldODEStateAndDerivative<T> softCurrentState,
73 final FieldEquationsMapper<T> mapper) {
74 super(field, forward, yDotK,
75 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
76 mapper);
77 }
78
79 /** {@inheritDoc} */
80 @Override
81 protected MidpointFieldStateInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
82 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
83 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
84 final FieldODEStateAndDerivative<T> newSoftPreviousState,
85 final FieldODEStateAndDerivative<T> newSoftCurrentState,
86 final FieldEquationsMapper<T> newMapper) {
87 return new MidpointFieldStateInterpolator<T>(newField, newForward, newYDotK,
88 newGlobalPreviousState, newGlobalCurrentState,
89 newSoftPreviousState, newSoftCurrentState,
90 newMapper);
91 }
92
93 /** {@inheritDoc} */
94 @SuppressWarnings("unchecked")
95 @Override
96 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
97 final T time, final T theta,
98 final T thetaH, final T oneMinusThetaH) {
99
100 final T coeffDot2 = theta.multiply(2);
101 final T coeffDot1 = time.getField().getOne().subtract(coeffDot2);
102 final T[] interpolatedState;
103 final T[] interpolatedDerivatives;
104
105 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
106 final T coeff1 = theta.multiply(oneMinusThetaH);
107 final T coeff2 = theta.multiply(thetaH);
108 interpolatedState = previousStateLinearCombination(coeff1, coeff2);
109 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
110 } else {
111 final T coeff1 = oneMinusThetaH.multiply(theta);
112 final T coeff2 = oneMinusThetaH.multiply(theta.add(1)).negate();
113 interpolatedState = currentStateLinearCombination(coeff1, coeff2);
114 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
115 }
116
117 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
118
119 }
120
121 }