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 represents an interpolator over the last step during an
32 * ODE integration for the 6th order Luther integrator.
33 *
34 * <p>This interpolator computes dense output inside the last
35 * step computed. The interpolation equation is consistent with the
36 * integration scheme.</p>
37 *
38 * @see LutherFieldIntegrator
39 * @param <T> the type of the field elements
40 */
41
42 class LutherFieldStateInterpolator<T extends CalculusFieldElement<T>>
43 extends RungeKuttaFieldStateInterpolator<T> {
44
45 /** -49 - 49 q. */
46 private final T c5a;
47
48 /** 392 + 287 q. */
49 private final T c5b;
50
51 /** -637 - 357 q. */
52 private final T c5c;
53
54 /** 833 + 343 q. */
55 private final T c5d;
56
57 /** -49 + 49 q. */
58 private final T c6a;
59
60 /** -392 - 287 q. */
61 private final T c6b;
62
63 /** -637 + 357 q. */
64 private final T c6c;
65
66 /** 833 - 343 q. */
67 private final T c6d;
68
69 /** 49 + 49 q. */
70 private final T d5a;
71
72 /** -1372 - 847 q. */
73 private final T d5b;
74
75 /** 2254 + 1029 q */
76 private final T d5c;
77
78 /** 49 - 49 q. */
79 private final T d6a;
80
81 /** -1372 + 847 q. */
82 private final T d6b;
83
84 /** 2254 - 1029 q */
85 private final T d6c;
86
87 /** Simple constructor.
88 * @param field field to which the time and state vector elements belong
89 * @param forward integration direction indicator
90 * @param yDotK slopes at the intermediate points
91 * @param globalPreviousState start of the global step
92 * @param globalCurrentState end of the global step
93 * @param softPreviousState start of the restricted step
94 * @param softCurrentState end of the restricted step
95 * @param mapper equations mapper for the all equations
96 */
97 LutherFieldStateInterpolator(final Field<T> field, final boolean forward,
98 final T[][] yDotK,
99 final FieldODEStateAndDerivative<T> globalPreviousState,
100 final FieldODEStateAndDerivative<T> globalCurrentState,
101 final FieldODEStateAndDerivative<T> softPreviousState,
102 final FieldODEStateAndDerivative<T> softCurrentState,
103 final FieldEquationsMapper<T> mapper) {
104 super(field, forward, yDotK,
105 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
106 mapper);
107 final T q = field.getZero().add(21).sqrt();
108 c5a = q.multiply( -49).add( -49);
109 c5b = q.multiply( 287).add( 392);
110 c5c = q.multiply( -357).add( -637);
111 c5d = q.multiply( 343).add( 833);
112 c6a = q.multiply( 49).add( -49);
113 c6b = q.multiply( -287).add( 392);
114 c6c = q.multiply( 357).add( -637);
115 c6d = q.multiply( -343).add( 833);
116 d5a = q.multiply( 49).add( 49);
117 d5b = q.multiply( -847).add(-1372);
118 d5c = q.multiply( 1029).add( 2254);
119 d6a = q.multiply( -49).add( 49);
120 d6b = q.multiply( 847).add(-1372);
121 d6c = q.multiply(-1029).add( 2254);
122 }
123
124 /** {@inheritDoc} */
125 @Override
126 protected LutherFieldStateInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
127 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
128 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
129 final FieldODEStateAndDerivative<T> newSoftPreviousState,
130 final FieldODEStateAndDerivative<T> newSoftCurrentState,
131 final FieldEquationsMapper<T> newMapper) {
132 return new LutherFieldStateInterpolator<T>(newField, newForward, newYDotK,
133 newGlobalPreviousState, newGlobalCurrentState,
134 newSoftPreviousState, newSoftCurrentState,
135 newMapper);
136 }
137
138 /** {@inheritDoc} */
139 @SuppressWarnings("unchecked")
140 @Override
141 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
142 final T time, final T theta,
143 final T thetaH, final T oneMinusThetaH) {
144
145 // the coefficients below have been computed by solving the
146 // order conditions from a theorem from Butcher (1963), using
147 // the method explained in Folkmar Bornemann paper "Runge-Kutta
148 // Methods, Trees, and Maple", Center of Mathematical Sciences, Munich
149 // University of Technology, February 9, 2001
150 //<http://wwwzenger.informatik.tu-muenchen.de/selcuk/sjam012101.html>
151
152 // the method is implemented in the rkcheck tool
153 // <https://www.spaceroots.org/software/rkcheck/index.html>.
154 // Running it for order 5 gives the following order conditions
155 // for an interpolator:
156 // order 1 conditions
157 // \sum_{i=1}^{i=s}\left(b_{i} \right) =1
158 // order 2 conditions
159 // \sum_{i=1}^{i=s}\left(b_{i} c_{i}\right) = \frac{\theta}{2}
160 // order 3 conditions
161 // \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{2}}{6}
162 // \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{2}\right) = \frac{\theta^{2}}{3}
163 // order 4 conditions
164 // \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{3}}{24}
165 // \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{2} \right)}\right) = \frac{\theta^{3}}{12}
166 // \sum_{i=2}^{i=s}\left(b_{i} c_{i}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{3}}{8}
167 // \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{3}\right) = \frac{\theta^{3}}{4}
168 // order 5 conditions
169 // \sum_{i=4}^{i=s}\left(b_{i} \sum_{j=3}^{j=i-1}{\left(a_{i,j} \sum_{k=2}^{k=j-1}{\left(a_{j,k} \sum_{l=1}^{l=k-1}{\left(a_{k,l} c_{l} \right)} \right)} \right)}\right) = \frac{\theta^{4}}{120}
170 // \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k}^{2} \right)} \right)}\right) = \frac{\theta^{4}}{60}
171 // \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} c_{j}\sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{4}}{40}
172 // \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{3} \right)}\right) = \frac{\theta^{4}}{20}
173 // \sum_{i=3}^{i=s}\left(b_{i} c_{i}\sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{4}}{30}
174 // \sum_{i=2}^{i=s}\left(b_{i} c_{i}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{2} \right)}\right) = \frac{\theta^{4}}{15}
175 // \sum_{i=2}^{i=s}\left(b_{i} \left(\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)} \right)^{2}\right) = \frac{\theta^{4}}{20}
176 // \sum_{i=2}^{i=s}\left(b_{i} c_{i}^{2}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{4}}{10}
177 // \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{4}\right) = \frac{\theta^{4}}{5}
178
179 // The a_{j,k} and c_{k} are given by the integrator Butcher arrays. What remains to solve
180 // are the b_i for the interpolator. They are found by solving the above equations.
181 // For a given interpolator, some equations are redundant, so in our case when we select
182 // all equations from order 1 to 4, we still don't have enough independent equations
183 // to solve from b_1 to b_7. We need to also select one equation from order 5. Here,
184 // we selected the last equation. It appears this choice implied at least the last 3 equations
185 // are fulfilled, but some of the former ones are not, so the resulting interpolator is order 5.
186 // At the end, we get the b_i as polynomials in theta.
187
188 final T coeffDot1 = theta.multiply(theta.multiply(theta.multiply(theta.multiply( 21 ).add( -47 )).add( 36 )).add( -54 / 5.0)).add(1);
189 final T coeffDot2 = time.getField().getZero();
190 final T coeffDot3 = theta.multiply(theta.multiply(theta.multiply(theta.multiply( 112 ).add(-608 / 3.0)).add( 320 / 3.0 )).add(-208 / 15.0));
191 final T coeffDot4 = theta.multiply(theta.multiply(theta.multiply(theta.multiply( -567 / 5.0).add( 972 / 5.0)).add( -486 / 5.0 )).add( 324 / 25.0));
192 final T coeffDot5 = theta.multiply(theta.multiply(theta.multiply(theta.multiply(c5a.divide(5)).add(c5b.divide(15))).add(c5c.divide(30))).add(c5d.divide(150)));
193 final T coeffDot6 = theta.multiply(theta.multiply(theta.multiply(theta.multiply(c6a.divide(5)).add(c6b.divide(15))).add(c6c.divide(30))).add(c6d.divide(150)));
194 final T coeffDot7 = theta.multiply(theta.multiply(theta.multiply( 3.0 ).add( -3 )).add( 3 / 5.0));
195 final T[] interpolatedState;
196 final T[] interpolatedDerivatives;
197
198 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
199
200 final T s = thetaH;
201 final T coeff1 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply( 21 / 5.0).add( -47 / 4.0)).add( 12 )).add( -27 / 5.0)).add(1));
202 final T coeff2 = time.getField().getZero();
203 final T coeff3 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply( 112 / 5.0).add(-152 / 3.0)).add( 320 / 9.0 )).add(-104 / 15.0)));
204 final T coeff4 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(-567 / 25.0).add( 243 / 5.0)).add( -162 / 5.0 )).add( 162 / 25.0)));
205 final T coeff5 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(c5a.divide(25)).add(c5b.divide(60))).add(c5c.divide(90))).add(c5d.divide(300))));
206 final T coeff6 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(c6a.divide(25)).add(c6b.divide(60))).add(c6c.divide(90))).add(c6d.divide(300))));
207 final T coeff7 = s.multiply(theta.multiply(theta.multiply(theta.multiply( 3 / 4.0 ).add( -1 )).add( 3 / 10.0)));
208 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4, coeff5, coeff6, coeff7);
209 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4, coeffDot5, coeffDot6, coeffDot7);
210 } else {
211
212 final T s = oneMinusThetaH;
213 final T coeff1 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply( -21 / 5.0).add( 151 / 20.0)).add( -89 / 20.0)).add( 19 / 20.0)).add(- 1 / 20.0));
214 final T coeff2 = time.getField().getZero();
215 final T coeff3 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(-112 / 5.0).add( 424 / 15.0)).add( -328 / 45.0)).add( -16 / 45.0)).add(-16 / 45.0));
216 final T coeff4 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply( 567 / 25.0).add( -648 / 25.0)).add( 162 / 25.0))));
217 final T coeff5 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(d5a.divide(25)).add(d5b.divide(300))).add(d5c.divide(900))).add( -49 / 180.0)).add(-49 / 180.0));
218 final T coeff6 = s.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(d6a.divide(25)).add(d6b.divide(300))).add(d6c.divide(900))).add( -49 / 180.0)).add(-49 / 180.0));
219 final T coeff7 = s.multiply( theta.multiply(theta.multiply(theta.multiply( -3 / 4.0 ).add( 1 / 4.0)).add( -1 / 20.0)).add( -1 / 20.0));
220 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4, coeff5, coeff6, coeff7);
221 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4, coeffDot5, coeffDot6, coeffDot7);
222 }
223
224 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
225
226 }
227
228 }