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 import org.hipparchus.util.FastMath;
23
24 /**
25 * This class implements a step interpolator for the Gill fourth
26 * order Runge-Kutta integrator.
27 *
28 * <p>This interpolator allows to compute dense output inside the last
29 * step computed. The interpolation equation is consistent with the
30 * integration scheme :</p>
31 * <ul>
32 * <li>Using reference point at step start:<br>
33 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
34 * + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
35 * + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) 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 start:<br>
40 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
41 * - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
42 * + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
43 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
44 * ]
45 * </li>
46 * </ul>
47 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
48 * are the four evaluations of the derivatives already computed during
49 * the step.</p>
50 *
51 * @see GillIntegrator
52 */
53
54 class GillStateInterpolator
55 extends RungeKuttaStateInterpolator {
56
57 /** First Gill coefficient. */
58 private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);
59
60 /** Second Gill coefficient. */
61 private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);
62
63 /** Serializable version identifier. */
64 private static final long serialVersionUID = 20160328L;
65
66 /** Simple constructor.
67 * @param forward integration direction indicator
68 * @param yDotK slopes at the intermediate points
69 * @param globalPreviousState start of the global step
70 * @param globalCurrentState end of the global step
71 * @param softPreviousState start of the restricted step
72 * @param softCurrentState end of the restricted step
73 * @param mapper equations mapper for the all equations
74 */
75 GillStateInterpolator(final boolean forward,
76 final double[][] yDotK,
77 final ODEStateAndDerivative globalPreviousState,
78 final ODEStateAndDerivative globalCurrentState,
79 final ODEStateAndDerivative softPreviousState,
80 final ODEStateAndDerivative softCurrentState,
81 final EquationsMapper mapper) {
82 super(forward, yDotK,
83 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
84 mapper);
85 }
86
87 /** {@inheritDoc} */
88 @Override
89 protected GillStateInterpolator create(final boolean newForward, final double[][] newYDotK,
90 final ODEStateAndDerivative newGlobalPreviousState,
91 final ODEStateAndDerivative newGlobalCurrentState,
92 final ODEStateAndDerivative newSoftPreviousState,
93 final ODEStateAndDerivative newSoftCurrentState,
94 final EquationsMapper newMapper) {
95 return new GillStateInterpolator(newForward, newYDotK,
96 newGlobalPreviousState, newGlobalCurrentState,
97 newSoftPreviousState, newSoftCurrentState,
98 newMapper);
99 }
100
101 /** {@inheritDoc} */
102 @Override
103 protected ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
104 final double time, final double theta,
105 final double thetaH, final double oneMinusThetaH) {
106
107 final double twoTheta = 2 * theta;
108 final double fourTheta2 = twoTheta * twoTheta;
109 final double coeffDot1 = theta * (twoTheta - 3) + 1;
110 final double cDot23 = twoTheta * (1 - theta);
111 final double coeffDot2 = cDot23 * ONE_MINUS_INV_SQRT_2;
112 final double coeffDot3 = cDot23 * ONE_PLUS_INV_SQRT_2;
113 final double coeffDot4 = theta * (twoTheta - 1);
114
115 final double[] interpolatedState;
116 final double[] interpolatedDerivatives;
117 if (getGlobalPreviousState() != null && theta <= 0.5) {
118 final double s = thetaH / 6.0;
119 final double c23 = s * (6 * theta - fourTheta2);
120 final double coeff1 = s * (6 - 9 * theta + fourTheta2);
121 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
122 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
123 final double coeff4 = s * (-3 * theta + fourTheta2);
124 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
125 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
126 } else {
127 final double s = oneMinusThetaH / -6.0;
128 final double c23 = s * (2 + twoTheta - fourTheta2);
129 final double coeff1 = s * (1 - 5 * theta + fourTheta2);
130 final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
131 final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
132 final double coeff4 = s * (1 + theta + fourTheta2);
133 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
134 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
135 }
136
137 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
138
139 }
140
141 }