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 the 3/8 fourth
25 * order Runge-Kutta integrator.
26 *
27 * <p>This interpolator allows to compute 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>)
33 * + θ (h/8) [ (8 - 15 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
34 * + 3 * (15 θ - 12 θ<sup>2</sup>) y'<sub>2</sub>
35 * + 3 θ y'<sub>3</sub>
36 * + (-3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
37 * ]
38 * </li>
39 * <li>Using reference point at step end:<br>
40 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
41 * - (1 - θ) (h/8) [(1 - 7 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
42 * + 3 (1 + θ - 4 θ<sup>2</sup>) y'<sub>2</sub>
43 * + 3 (1 + θ) y'<sub>3</sub>
44 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
45 * ]
46 * </li>
47 * </ul>
48 *
49 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> are the four
50 * evaluations of the derivatives already computed during the
51 * step.</p>
52 *
53 * @see ThreeEighthesIntegrator
54 */
55
56 class ThreeEighthesStateInterpolator
57 extends RungeKuttaStateInterpolator {
58
59 /** Serializable version identifier. */
60 private static final long serialVersionUID = 20160328L;
61
62 /** Simple constructor.
63 * @param forward integration direction indicator
64 * @param yDotK slopes at the intermediate points
65 * @param globalPreviousState start of the global step
66 * @param globalCurrentState end of the global step
67 * @param softPreviousState start of the restricted step
68 * @param softCurrentState end of the restricted step
69 * @param mapper equations mapper for the all equations
70 */
71 ThreeEighthesStateInterpolator(final boolean forward,
72 final double[][] yDotK,
73 final ODEStateAndDerivative globalPreviousState,
74 final ODEStateAndDerivative globalCurrentState,
75 final ODEStateAndDerivative softPreviousState,
76 final ODEStateAndDerivative softCurrentState,
77 final EquationsMapper mapper) {
78 super(forward, yDotK,
79 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
80 mapper);
81 }
82
83 /** {@inheritDoc} */
84 @Override
85 protected ThreeEighthesStateInterpolator create(final boolean newForward, final double[][] newYDotK,
86 final ODEStateAndDerivative newGlobalPreviousState,
87 final ODEStateAndDerivative newGlobalCurrentState,
88 final ODEStateAndDerivative newSoftPreviousState,
89 final ODEStateAndDerivative newSoftCurrentState,
90 final EquationsMapper newMapper) {
91 return new ThreeEighthesStateInterpolator(newForward, newYDotK,
92 newGlobalPreviousState, newGlobalCurrentState,
93 newSoftPreviousState, newSoftCurrentState,
94 newMapper);
95 }
96
97 /** {@inheritDoc} */
98 @Override
99 protected ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
100 final double time, final double theta,
101 final double thetaH, final double oneMinusThetaH) {
102
103 final double coeffDot3 = 0.75 * theta;
104 final double coeffDot1 = coeffDot3 * (4 * theta - 5) + 1;
105 final double coeffDot2 = coeffDot3 * (5 - 6 * theta);
106 final double coeffDot4 = coeffDot3 * (2 * theta - 1);
107 final double[] interpolatedState;
108 final double[] interpolatedDerivatives;
109
110 if (getGlobalPreviousState() != null && theta <= 0.5) {
111 final double s = thetaH / 8.0;
112 final double fourTheta2 = 4 * theta * theta;
113 final double coeff1 = s * (8 - 15 * theta + 2 * fourTheta2);
114 final double coeff2 = 3 * s * (5 * theta - fourTheta2);
115 final double coeff3 = 3 * s * theta;
116 final double coeff4 = s * (-3 * theta + fourTheta2);
117 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
118 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
119 } else {
120 final double s = oneMinusThetaH / -8.0;
121 final double fourTheta2 = 4 * theta * theta;
122 final double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2);
123 final double coeff2 = 3 * s * (1 + theta - fourTheta2);
124 final double coeff3 = 3 * s * (1 + theta);
125 final double coeff4 = s * (1 + theta + fourTheta2);
126 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
127 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
128 }
129
130 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
131
132 }
133
134 }