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 second order
27 * Runge-Kutta integrator.
28 *
29 * <p>This interpolator computes 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>) + θ h [(1 - θ) y'<sub>1</sub> + θ y'<sub>2</sub>]
35 * </li>
36 * <li>Using reference point at step end:<br>
37 * 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>]
38 * </li>
39 * </ul>
40 *
41 * where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
42 * evaluations of the derivatives already computed during the
43 * step.</p>
44 *
45 * @see MidpointFieldIntegrator
46 * @param <T> the type of the field elements
47 * @since 3.6
48 */
49
50 class MidpointFieldStepInterpolator<T extends RealFieldElement<T>>
51 extends RungeKuttaFieldStepInterpolator<T> {
52
53 /** Simple constructor.
54 * @param field field to which the time and state vector elements belong
55 * @param forward integration direction indicator
56 * @param yDotK slopes at the intermediate points
57 * @param globalPreviousState start of the global step
58 * @param globalCurrentState end of the global step
59 * @param softPreviousState start of the restricted step
60 * @param softCurrentState end of the restricted step
61 * @param mapper equations mapper for the all equations
62 */
63 MidpointFieldStepInterpolator(final Field<T> field, final boolean forward,
64 final T[][] yDotK,
65 final FieldODEStateAndDerivative<T> globalPreviousState,
66 final FieldODEStateAndDerivative<T> globalCurrentState,
67 final FieldODEStateAndDerivative<T> softPreviousState,
68 final FieldODEStateAndDerivative<T> softCurrentState,
69 final FieldEquationsMapper<T> mapper) {
70 super(field, forward, yDotK,
71 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
72 mapper);
73 }
74
75 /** {@inheritDoc} */
76 @Override
77 protected MidpointFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
78 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
79 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
80 final FieldODEStateAndDerivative<T> newSoftPreviousState,
81 final FieldODEStateAndDerivative<T> newSoftCurrentState,
82 final FieldEquationsMapper<T> newMapper) {
83 return new MidpointFieldStepInterpolator<>(newField, newForward, newYDotK,
84 newGlobalPreviousState, newGlobalCurrentState,
85 newSoftPreviousState, newSoftCurrentState,
86 newMapper);
87 }
88
89 /** {@inheritDoc} */
90 @SuppressWarnings("unchecked")
91 @Override
92 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
93 final T time, final T theta,
94 final T thetaH, final T oneMinusThetaH) {
95
96 final T coeffDot2 = theta.multiply(2);
97 final T coeffDot1 = time.getField().getOne().subtract(coeffDot2);
98 final T[] interpolatedState;
99 final T[] interpolatedDerivatives;
100
101 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
102 final T coeff1 = theta.multiply(oneMinusThetaH);
103 final T coeff2 = theta.multiply(thetaH);
104 interpolatedState = previousStateLinearCombination(coeff1, coeff2);
105 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
106 } else {
107 final T coeff1 = oneMinusThetaH.multiply(theta);
108 final T coeff2 = oneMinusThetaH.multiply(theta.add(1)).negate();
109 interpolatedState = currentStateLinearCombination(coeff1, coeff2);
110 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
111 }
112
113 return new FieldODEStateAndDerivative<>(time, interpolatedState, interpolatedDerivatives);
114 }
115 }