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;
24
25 import java.util.ArrayList;
26 import java.util.List;
27
28 import org.hipparchus.CalculusFieldElement;
29 import org.hipparchus.exception.LocalizedCoreFormats;
30 import org.hipparchus.exception.MathIllegalArgumentException;
31 import org.hipparchus.exception.MathIllegalStateException;
32 import org.hipparchus.ode.sampling.FieldODEStepHandler;
33 import org.hipparchus.ode.sampling.FieldODEStateInterpolator;
34 import org.hipparchus.util.FastMath;
35
36 /**
37 * This class stores all information provided by an ODE integrator
38 * during the integration process and build a continuous model of the
39 * solution from this.
40 *
41 * <p>This class act as a step handler from the integrator point of
42 * view. It is called iteratively during the integration process and
43 * stores a copy of all steps information in a sorted collection for
44 * later use. Once the integration process is over, the user can use
45 * the {@link #getInterpolatedState(CalculusFieldElement) getInterpolatedState}
46 * method to retrieve this information at any time. It is important to wait
47 * for the integration to be over before attempting to call {@link
48 * #getInterpolatedState(CalculusFieldElement)} because some internal
49 * variables are set only once the last step has been handled.</p>
50 *
51 * <p>This is useful for example if the main loop of the user
52 * application should remain independent from the integration process
53 * or if one needs to mimic the behaviour of an analytical model
54 * despite a numerical model is used (i.e. one needs the ability to
55 * get the model value at any time or to navigate through the
56 * data).</p>
57 *
58 * <p>If problem modeling is done with several separate
59 * integration phases for contiguous intervals, the same
60 * FieldDenseOutputModel can be used as step handler for all
61 * integration phases as long as they are performed in order and in
62 * the same direction. As an example, one can extrapolate the
63 * trajectory of a satellite with one model (i.e. one set of
64 * differential equations) up to the beginning of a maneuver, use
65 * another more complex model including thrusters modeling and
66 * accurate attitude control during the maneuver, and revert to the
67 * first model after the end of the maneuver. If the same continuous
68 * output model handles the steps of all integration phases, the user
69 * do not need to bother when the maneuver begins or ends, he has all
70 * the data available in a transparent manner.</p>
71 *
72 * <p>One should be aware that the amount of data stored in a
73 * FieldDenseOutputModel instance can be important if the state vector
74 * is large, if the integration interval is long or if the steps are
75 * small (which can result from small tolerance settings in {@link
76 * org.hipparchus.ode.nonstiff.AdaptiveStepsizeFieldIntegrator adaptive
77 * step size integrators}).</p>
78 *
79 * @see FieldODEStepHandler
80 * @see FieldODEStateInterpolator
81 * @param <T> the type of the field elements
82 */
83
84 public class FieldDenseOutputModel<T extends CalculusFieldElement<T>>
85 implements FieldODEStepHandler<T> {
86
87 /** Initial integration time. */
88 private T initialTime;
89
90 /** Final integration time. */
91 private T finalTime;
92
93 /** Integration direction indicator. */
94 private boolean forward;
95
96 /** Current interpolator index. */
97 private int index;
98
99 /** Steps table. */
100 private List<FieldODEStateInterpolator<T>> steps;
101
102 /** Simple constructor.
103 * Build an empty continuous output model.
104 */
105 public FieldDenseOutputModel() {
106 steps = new ArrayList<>();
107 initialTime = null;
108 finalTime = null;
109 forward = true;
110 index = 0;
111 }
112
113 /** Append another model at the end of the instance.
114 * @param model model to add at the end of the instance
115 * @exception MathIllegalArgumentException if the model to append is not
116 * compatible with the instance (dimension of the state vector,
117 * propagation direction, hole between the dates)
118 * @exception MathIllegalArgumentException if the dimensions of the states or
119 * the number of secondary states do not match
120 * @exception MathIllegalStateException if the number of functions evaluations is exceeded
121 * during step finalization
122 */
123 public void append(final FieldDenseOutputModel<T> model)
124 throws MathIllegalArgumentException, MathIllegalStateException {
125
126 if (model.steps.isEmpty()) {
127 return;
128 }
129
130 if (steps.isEmpty()) {
131 initialTime = model.initialTime;
132 forward = model.forward;
133 } else {
134
135 // safety checks
136 final FieldODEStateAndDerivative<T> s1 = steps.get(0).getPreviousState();
137 final FieldODEStateAndDerivative<T> s2 = model.steps.get(0).getPreviousState();
138 checkDimensionsEquality(s1.getPrimaryStateDimension(), s2.getPrimaryStateDimension());
139 checkDimensionsEquality(s1.getNumberOfSecondaryStates(), s2.getNumberOfSecondaryStates());
140 for (int i = 0; i < s1.getNumberOfSecondaryStates(); ++i) {
141 checkDimensionsEquality(s1.getSecondaryStateDimension(i), s2.getSecondaryStateDimension(i));
142 }
143
144 if (forward ^ model.forward) {
145 throw new MathIllegalArgumentException(LocalizedODEFormats.PROPAGATION_DIRECTION_MISMATCH);
146 }
147
148 final FieldODEStateInterpolator<T> lastInterpolator = steps.get(index);
149 final T current = lastInterpolator.getCurrentState().getTime();
150 final T previous = lastInterpolator.getPreviousState().getTime();
151 final T step = current.subtract(previous);
152 final T gap = model.getInitialTime().subtract(current);
153 if (gap.abs().subtract(step.abs().multiply(1.0e-3)).getReal() > 0) {
154 throw new MathIllegalArgumentException(LocalizedODEFormats.HOLE_BETWEEN_MODELS_TIME_RANGES,
155 gap.norm());
156 }
157
158 }
159
160 steps.addAll(model.steps);
161
162 index = steps.size() - 1;
163 finalTime = (steps.get(index)).getCurrentState().getTime();
164
165 }
166
167 /** Check dimensions equality.
168 * @param d1 first dimension
169 * @param d2 second dimansion
170 * @exception MathIllegalArgumentException if dimensions do not match
171 */
172 private void checkDimensionsEquality(final int d1, final int d2)
173 throws MathIllegalArgumentException {
174 if (d1 != d2) {
175 throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
176 d2, d1);
177 }
178 }
179
180 /** {@inheritDoc} */
181 @Override
182 public void init(final FieldODEStateAndDerivative<T> initialState, final T t) {
183 initialTime = initialState.getTime();
184 finalTime = t;
185 forward = true;
186 index = 0;
187 steps.clear();
188 }
189
190 /** {@inheritDoc} */
191 @Override
192 public void handleStep(final FieldODEStateInterpolator<T> interpolator) {
193
194 if (steps.isEmpty()) {
195 initialTime = interpolator.getPreviousState().getTime();
196 forward = interpolator.isForward();
197 }
198
199 steps.add(interpolator);
200 }
201
202 /** {@inheritDoc} */
203 @Override
204 public void finish(FieldODEStateAndDerivative<T> finalState) {
205 finalTime = finalState.getTime();
206 index = steps.size() - 1;
207 }
208
209 /**
210 * Get the initial integration time.
211 * @return initial integration time
212 */
213 public T getInitialTime() {
214 return initialTime;
215 }
216
217 /**
218 * Get the final integration time.
219 * @return final integration time
220 */
221 public T getFinalTime() {
222 return finalTime;
223 }
224
225 /**
226 * Get the state at interpolated time.
227 * @param time time of the interpolated point
228 * @return state at interpolated time
229 */
230 public FieldODEStateAndDerivative<T> getInterpolatedState(final T time) {
231
232 // initialize the search with the complete steps table
233 int iMin = 0;
234 final FieldODEStateInterpolator<T> sMin = steps.get(iMin);
235 T tMin = sMin.getPreviousState().getTime().add(sMin.getCurrentState().getTime()).multiply(0.5);
236
237 int iMax = steps.size() - 1;
238 final FieldODEStateInterpolator<T> sMax = steps.get(iMax);
239 T tMax = sMax.getPreviousState().getTime().add(sMax.getCurrentState().getTime()).multiply(0.5);
240
241 // handle points outside of the integration interval
242 // or in the first and last step
243 if (locatePoint(time, sMin) <= 0) {
244 index = iMin;
245 return sMin.getInterpolatedState(time);
246 }
247 if (locatePoint(time, sMax) >= 0) {
248 index = iMax;
249 return sMax.getInterpolatedState(time);
250 }
251
252 // reduction of the table slice size
253 while (iMax - iMin > 5) {
254
255 // use the last estimated index as the splitting index
256 final FieldODEStateInterpolator<T> si = steps.get(index);
257 final int location = locatePoint(time, si);
258 if (location < 0) {
259 iMax = index;
260 tMax = si.getPreviousState().getTime().add(si.getCurrentState().getTime()).multiply(0.5);
261 } else if (location > 0) {
262 iMin = index;
263 tMin = si.getPreviousState().getTime().add(si.getCurrentState().getTime()).multiply(0.5);
264 } else {
265 // we have found the target step, no need to continue searching
266 return si.getInterpolatedState(time);
267 }
268
269 // compute a new estimate of the index in the reduced table slice
270 final int iMed = (iMin + iMax) / 2;
271 final FieldODEStateInterpolator<T> sMed = steps.get(iMed);
272 final T tMed = sMed.getPreviousState().getTime().add(sMed.getCurrentState().getTime()).multiply(0.5);
273
274 if (tMed.subtract(tMin).abs().subtract(1.0e-6).getReal() < 0 ||
275 tMax.subtract(tMed).abs().subtract(1.0e-6).getReal() < 0) {
276 // too close to the bounds, we estimate using a simple dichotomy
277 index = iMed;
278 } else {
279 // estimate the index using a reverse quadratic polynomial
280 // (reverse means we have i = P(t), thus allowing to simply
281 // compute index = P(time) rather than solving a quadratic equation)
282 final T d12 = tMax.subtract(tMed);
283 final T d23 = tMed.subtract(tMin);
284 final T d13 = tMax.subtract(tMin);
285 final T dt1 = time.subtract(tMax);
286 final T dt2 = time.subtract(tMed);
287 final T dt3 = time.subtract(tMin);
288 final T iLagrange = dt2.multiply(dt3).multiply(d23).multiply(iMax).
289 subtract(dt1.multiply(dt3).multiply(d13).multiply(iMed)).
290 add( dt1.multiply(dt2).multiply(d12).multiply(iMin)).
291 divide(d12.multiply(d23).multiply(d13));
292 index = (int) FastMath.rint(iLagrange.getReal());
293 }
294
295 // force the next size reduction to be at least one tenth
296 final int low = FastMath.max(iMin + 1, (9 * iMin + iMax) / 10);
297 final int high = FastMath.min(iMax - 1, (iMin + 9 * iMax) / 10);
298 if (index < low) {
299 index = low;
300 } else if (index > high) {
301 index = high;
302 }
303
304 }
305
306 // now the table slice is very small, we perform an iterative search
307 index = iMin;
308 while (index <= iMax && locatePoint(time, steps.get(index)) > 0) {
309 ++index;
310 }
311
312 return steps.get(index).getInterpolatedState(time);
313
314 }
315
316 /** Compare a step interval and a double.
317 * @param time point to locate
318 * @param interval step interval
319 * @return -1 if the double is before the interval, 0 if it is in
320 * the interval, and +1 if it is after the interval, according to
321 * the interval direction
322 */
323 private int locatePoint(final T time, final FieldODEStateInterpolator<T> interval) {
324 if (forward) {
325 if (time.subtract(interval.getPreviousState().getTime()).getReal() < 0) {
326 return -1;
327 } else if (time.subtract(interval.getCurrentState().getTime()).getReal() > 0) {
328 return +1;
329 } else {
330 return 0;
331 }
332 }
333 if (time.subtract(interval.getPreviousState().getTime()).getReal() > 0) {
334 return -1;
335 } else if (time.subtract(interval.getCurrentState().getTime()).getReal() < 0) {
336 return +1;
337 } else {
338 return 0;
339 }
340 }
341
342 }