1 /*
2 * Licensed to the Hipparchus project 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 Hipparchus project 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 package org.hipparchus.ode.nonstiff;
19
20 import org.hipparchus.ode.EquationsMapper;
21 import org.hipparchus.ode.ODEStateAndDerivative;
22
23 /**
24 * This class implements a step interpolator for second order
25 * Runge-Kutta integrator.
26 *
27 * <p>This interpolator computes dense output inside the last
28 * step computed. The interpolation equation is consistent with the
29 * integration scheme :</p>
30 * <ul>
31 * <li>Using reference point at step start:<br>
32 * 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>]
33 * </li>
34 * <li>Using reference point at step end:<br>
35 * 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>]
36 * </li>
37 * </ul>
38 *
39 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
40 * evaluations of the derivatives already computed during the
41 * step.</p>
42 *
43 * @see MidpointIntegrator
44 */
45
46 class MidpointStateInterpolator
47 extends RungeKuttaStateInterpolator {
48
49 /** Serializable version identifier. */
50 private static final long serialVersionUID = 20160328L;
51
52 /** Simple constructor.
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 MidpointStateInterpolator(final boolean forward,
62 final double[][] yDotK,
63 final ODEStateAndDerivative globalPreviousState,
64 final ODEStateAndDerivative globalCurrentState,
65 final ODEStateAndDerivative softPreviousState,
66 final ODEStateAndDerivative softCurrentState,
67 final EquationsMapper mapper) {
68 super(forward, yDotK,
69 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
70 mapper);
71 }
72
73 /** {@inheritDoc} */
74 @Override
75 protected MidpointStateInterpolator create(final boolean newForward, final double[][] newYDotK,
76 final ODEStateAndDerivative newGlobalPreviousState,
77 final ODEStateAndDerivative newGlobalCurrentState,
78 final ODEStateAndDerivative newSoftPreviousState,
79 final ODEStateAndDerivative newSoftCurrentState,
80 final EquationsMapper newMapper) {
81 return new MidpointStateInterpolator(newForward, newYDotK,
82 newGlobalPreviousState, newGlobalCurrentState,
83 newSoftPreviousState, newSoftCurrentState,
84 newMapper);
85 }
86
87 /** {@inheritDoc} */
88 @Override
89 protected ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
90 final double time, final double theta,
91 final double thetaH, final double oneMinusThetaH) {
92 final double coeffDot2 = 2 * theta;
93 final double coeffDot1 = 1 - coeffDot2;
94
95 final double[] interpolatedState;
96 final double[] interpolatedDerivatives;
97 if (getGlobalPreviousState() != null && theta <= 0.5) {
98
99 final double coeff1 = theta * oneMinusThetaH;
100 final double coeff2 = theta * thetaH;
101 interpolatedState = previousStateLinearCombination(coeff1, coeff2);
102 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
103 } else {
104 final double coeff1 = oneMinusThetaH * theta;
105 final double coeff2 = -oneMinusThetaH * (1.0 + theta);
106 interpolatedState = currentStateLinearCombination(coeff1, coeff2);
107 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
108 }
109
110 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
111
112 }
113
114 }