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 * 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 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22
23 package org.hipparchus.ode.nonstiff;
24
25 import org.hipparchus.CalculusFieldElement;
26 import org.hipparchus.Field;
27 import org.hipparchus.ode.FieldEquationsMapper;
28 import org.hipparchus.ode.FieldODEStateAndDerivative;
29
30 /**
31 * This class implements a step interpolator for the Gill fourth
32 * order Runge-Kutta integrator.
33 *
34 * <p>This interpolator allows to compute dense output inside the last
35 * step computed. The interpolation equation is consistent with the
36 * integration scheme :</p>
37 * <ul>
38 * <li>Using reference point at step start:<br>
39 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
40 * + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
41 * + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
42 * + ( - 3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
43 * ]
44 * </li>
45 * <li>Using reference point at step start:<br>
46 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
47 * - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
48 * + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
49 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
50 * ]
51 * </li>
52 * </ul>
53 * <p>where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
54 * are the four evaluations of the derivatives already computed during
55 * the step.</p>
56 *
57 * @see GillFieldIntegrator
58 * @param <T> the type of the field elements
59 */
60
61 class GillFieldStateInterpolator<T extends CalculusFieldElement<T>>
62 extends RungeKuttaFieldStateInterpolator<T> {
63
64 /** First Gill coefficient. */
65 private final T one_minus_inv_sqrt_2;
66
67 /** Second Gill coefficient. */
68 private final T one_plus_inv_sqrt_2;
69
70 /** Simple constructor.
71 * @param field field to which the time and state vector elements belong
72 * @param forward integration direction indicator
73 * @param yDotK slopes at the intermediate points
74 * @param globalPreviousState start of the global step
75 * @param globalCurrentState end of the global step
76 * @param softPreviousState start of the restricted step
77 * @param softCurrentState end of the restricted step
78 * @param mapper equations mapper for the all equations
79 */
80 GillFieldStateInterpolator(final Field<T> field, final boolean forward,
81 final T[][] yDotK,
82 final FieldODEStateAndDerivative<T> globalPreviousState,
83 final FieldODEStateAndDerivative<T> globalCurrentState,
84 final FieldODEStateAndDerivative<T> softPreviousState,
85 final FieldODEStateAndDerivative<T> softCurrentState,
86 final FieldEquationsMapper<T> mapper) {
87 super(field, forward, yDotK,
88 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
89 mapper);
90 final T sqrt = field.getZero().add(0.5).sqrt();
91 one_minus_inv_sqrt_2 = field.getOne().subtract(sqrt);
92 one_plus_inv_sqrt_2 = field.getOne().add(sqrt);
93 }
94
95 /** {@inheritDoc} */
96 @Override
97 protected GillFieldStateInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
98 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
99 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
100 final FieldODEStateAndDerivative<T> newSoftPreviousState,
101 final FieldODEStateAndDerivative<T> newSoftCurrentState,
102 final FieldEquationsMapper<T> newMapper) {
103 return new GillFieldStateInterpolator<T>(newField, newForward, newYDotK,
104 newGlobalPreviousState, newGlobalCurrentState,
105 newSoftPreviousState, newSoftCurrentState,
106 newMapper);
107 }
108
109 /** {@inheritDoc} */
110 @SuppressWarnings("unchecked")
111 @Override
112 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
113 final T time, final T theta,
114 final T thetaH, final T oneMinusThetaH) {
115
116 final T one = time.getField().getOne();
117 final T twoTheta = theta.multiply(2);
118 final T fourTheta2 = twoTheta.multiply(twoTheta);
119 final T coeffDot1 = theta.multiply(twoTheta.subtract(3)).add(1);
120 final T cDot23 = twoTheta.multiply(one.subtract(theta));
121 final T coeffDot2 = cDot23.multiply(one_minus_inv_sqrt_2);
122 final T coeffDot3 = cDot23.multiply(one_plus_inv_sqrt_2);
123 final T coeffDot4 = theta.multiply(twoTheta.subtract(1));
124 final T[] interpolatedState;
125 final T[] interpolatedDerivatives;
126
127 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
128 final T s = thetaH.divide(6.0);
129 final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
130 final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).add(6));
131 final T coeff2 = c23.multiply(one_minus_inv_sqrt_2);
132 final T coeff3 = c23.multiply(one_plus_inv_sqrt_2);
133 final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
134 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
135 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
136 } else {
137 final T s = oneMinusThetaH.divide(-6.0);
138 final T c23 = s.multiply(twoTheta.add(2).subtract(fourTheta2));
139 final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(5)).add(1));
140 final T coeff2 = c23.multiply(one_minus_inv_sqrt_2);
141 final T coeff3 = c23.multiply(one_plus_inv_sqrt_2);
142 final T coeff4 = s.multiply(fourTheta2.add(theta).add(1));
143 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
144 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
145 }
146
147 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
148
149 }
150
151 }