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