001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    
018    package org.apache.commons.math3.ode;
019    
020    import java.io.Serializable;
021    import java.util.ArrayList;
022    import java.util.List;
023    
024    import org.apache.commons.math3.exception.DimensionMismatchException;
025    import org.apache.commons.math3.exception.MathIllegalArgumentException;
026    import org.apache.commons.math3.exception.MaxCountExceededException;
027    import org.apache.commons.math3.exception.util.LocalizedFormats;
028    import org.apache.commons.math3.ode.sampling.StepHandler;
029    import org.apache.commons.math3.ode.sampling.StepInterpolator;
030    import org.apache.commons.math3.util.FastMath;
031    
032    /**
033     * This class stores all information provided by an ODE integrator
034     * during the integration process and build a continuous model of the
035     * solution from this.
036     *
037     * <p>This class act as a step handler from the integrator point of
038     * view. It is called iteratively during the integration process and
039     * stores a copy of all steps information in a sorted collection for
040     * later use. Once the integration process is over, the user can use
041     * the {@link #setInterpolatedTime setInterpolatedTime} and {@link
042     * #getInterpolatedState getInterpolatedState} to retrieve this
043     * information at any time. It is important to wait for the
044     * integration to be over before attempting to call {@link
045     * #setInterpolatedTime setInterpolatedTime} because some internal
046     * variables are set only once the last step has been handled.</p>
047     *
048     * <p>This is useful for example if the main loop of the user
049     * application should remain independent from the integration process
050     * or if one needs to mimic the behaviour of an analytical model
051     * despite a numerical model is used (i.e. one needs the ability to
052     * get the model value at any time or to navigate through the
053     * data).</p>
054     *
055     * <p>If problem modeling is done with several separate
056     * integration phases for contiguous intervals, the same
057     * ContinuousOutputModel can be used as step handler for all
058     * integration phases as long as they are performed in order and in
059     * the same direction. As an example, one can extrapolate the
060     * trajectory of a satellite with one model (i.e. one set of
061     * differential equations) up to the beginning of a maneuver, use
062     * another more complex model including thrusters modeling and
063     * accurate attitude control during the maneuver, and revert to the
064     * first model after the end of the maneuver. If the same continuous
065     * output model handles the steps of all integration phases, the user
066     * do not need to bother when the maneuver begins or ends, he has all
067     * the data available in a transparent manner.</p>
068     *
069     * <p>An important feature of this class is that it implements the
070     * <code>Serializable</code> interface. This means that the result of
071     * an integration can be serialized and reused later (if stored into a
072     * persistent medium like a filesystem or a database) or elsewhere (if
073     * sent to another application). Only the result of the integration is
074     * stored, there is no reference to the integrated problem by
075     * itself.</p>
076     *
077     * <p>One should be aware that the amount of data stored in a
078     * ContinuousOutputModel instance can be important if the state vector
079     * is large, if the integration interval is long or if the steps are
080     * small (which can result from small tolerance settings in {@link
081     * org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator adaptive
082     * step size integrators}).</p>
083     *
084     * @see StepHandler
085     * @see StepInterpolator
086     * @version $Id: ContinuousOutputModel.java 1416643 2012-12-03 19:37:14Z tn $
087     * @since 1.2
088     */
089    
090    public class ContinuousOutputModel
091      implements StepHandler, Serializable {
092    
093        /** Serializable version identifier */
094        private static final long serialVersionUID = -1417964919405031606L;
095    
096        /** Initial integration time. */
097        private double initialTime;
098    
099        /** Final integration time. */
100        private double finalTime;
101    
102        /** Integration direction indicator. */
103        private boolean forward;
104    
105        /** Current interpolator index. */
106        private int index;
107    
108        /** Steps table. */
109        private List<StepInterpolator> steps;
110    
111      /** Simple constructor.
112       * Build an empty continuous output model.
113       */
114      public ContinuousOutputModel() {
115        steps = new ArrayList<StepInterpolator>();
116        initialTime = Double.NaN;
117        finalTime   = Double.NaN;
118        forward     = true;
119        index       = 0;
120      }
121    
122      /** Append another model at the end of the instance.
123       * @param model model to add at the end of the instance
124       * @exception MathIllegalArgumentException if the model to append is not
125       * compatible with the instance (dimension of the state vector,
126       * propagation direction, hole between the dates)
127       * @exception MaxCountExceededException if the number of functions evaluations is exceeded
128       * during step finalization
129       */
130      public void append(final ContinuousOutputModel model)
131        throws MathIllegalArgumentException, MaxCountExceededException {
132    
133        if (model.steps.size() == 0) {
134          return;
135        }
136    
137        if (steps.size() == 0) {
138          initialTime = model.initialTime;
139          forward     = model.forward;
140        } else {
141    
142          if (getInterpolatedState().length != model.getInterpolatedState().length) {
143              throw new DimensionMismatchException(model.getInterpolatedState().length,
144                                                   getInterpolatedState().length);
145          }
146    
147          if (forward ^ model.forward) {
148              throw new MathIllegalArgumentException(LocalizedFormats.PROPAGATION_DIRECTION_MISMATCH);
149          }
150    
151          final StepInterpolator lastInterpolator = steps.get(index);
152          final double current  = lastInterpolator.getCurrentTime();
153          final double previous = lastInterpolator.getPreviousTime();
154          final double step = current - previous;
155          final double gap = model.getInitialTime() - current;
156          if (FastMath.abs(gap) > 1.0e-3 * FastMath.abs(step)) {
157            throw new MathIllegalArgumentException(LocalizedFormats.HOLE_BETWEEN_MODELS_TIME_RANGES,
158                                                   FastMath.abs(gap));
159          }
160    
161        }
162    
163        for (StepInterpolator interpolator : model.steps) {
164          steps.add(interpolator.copy());
165        }
166    
167        index = steps.size() - 1;
168        finalTime = (steps.get(index)).getCurrentTime();
169    
170      }
171    
172      /** {@inheritDoc} */
173      public void init(double t0, double[] y0, double t) {
174        initialTime = Double.NaN;
175        finalTime   = Double.NaN;
176        forward     = true;
177        index       = 0;
178        steps.clear();
179      }
180    
181      /** Handle the last accepted step.
182       * A copy of the information provided by the last step is stored in
183       * the instance for later use.
184       * @param interpolator interpolator for the last accepted step.
185       * @param isLast true if the step is the last one
186       * @exception MaxCountExceededException if the number of functions evaluations is exceeded
187       * during step finalization
188       */
189      public void handleStep(final StepInterpolator interpolator, final boolean isLast)
190          throws MaxCountExceededException {
191    
192        if (steps.size() == 0) {
193          initialTime = interpolator.getPreviousTime();
194          forward     = interpolator.isForward();
195        }
196    
197        steps.add(interpolator.copy());
198    
199        if (isLast) {
200          finalTime = interpolator.getCurrentTime();
201          index     = steps.size() - 1;
202        }
203    
204      }
205    
206      /**
207       * Get the initial integration time.
208       * @return initial integration time
209       */
210      public double getInitialTime() {
211        return initialTime;
212      }
213    
214      /**
215       * Get the final integration time.
216       * @return final integration time
217       */
218      public double getFinalTime() {
219        return finalTime;
220      }
221    
222      /**
223       * Get the time of the interpolated point.
224       * If {@link #setInterpolatedTime} has not been called, it returns
225       * the final integration time.
226       * @return interpolation point time
227       */
228      public double getInterpolatedTime() {
229        return steps.get(index).getInterpolatedTime();
230      }
231    
232      /** Set the time of the interpolated point.
233       * <p>This method should <strong>not</strong> be called before the
234       * integration is over because some internal variables are set only
235       * once the last step has been handled.</p>
236       * <p>Setting the time outside of the integration interval is now
237       * allowed (it was not allowed up to version 5.9 of Mantissa), but
238       * should be used with care since the accuracy of the interpolator
239       * will probably be very poor far from this interval. This allowance
240       * has been added to simplify implementation of search algorithms
241       * near the interval endpoints.</p>
242       * @param time time of the interpolated point
243       */
244      public void setInterpolatedTime(final double time) {
245    
246          // initialize the search with the complete steps table
247          int iMin = 0;
248          final StepInterpolator sMin = steps.get(iMin);
249          double tMin = 0.5 * (sMin.getPreviousTime() + sMin.getCurrentTime());
250    
251          int iMax = steps.size() - 1;
252          final StepInterpolator sMax = steps.get(iMax);
253          double tMax = 0.5 * (sMax.getPreviousTime() + sMax.getCurrentTime());
254    
255          // handle points outside of the integration interval
256          // or in the first and last step
257          if (locatePoint(time, sMin) <= 0) {
258            index = iMin;
259            sMin.setInterpolatedTime(time);
260            return;
261          }
262          if (locatePoint(time, sMax) >= 0) {
263            index = iMax;
264            sMax.setInterpolatedTime(time);
265            return;
266          }
267    
268          // reduction of the table slice size
269          while (iMax - iMin > 5) {
270    
271            // use the last estimated index as the splitting index
272            final StepInterpolator si = steps.get(index);
273            final int location = locatePoint(time, si);
274            if (location < 0) {
275              iMax = index;
276              tMax = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
277            } else if (location > 0) {
278              iMin = index;
279              tMin = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
280            } else {
281              // we have found the target step, no need to continue searching
282              si.setInterpolatedTime(time);
283              return;
284            }
285    
286            // compute a new estimate of the index in the reduced table slice
287            final int iMed = (iMin + iMax) / 2;
288            final StepInterpolator sMed = steps.get(iMed);
289            final double tMed = 0.5 * (sMed.getPreviousTime() + sMed.getCurrentTime());
290    
291            if ((FastMath.abs(tMed - tMin) < 1e-6) || (FastMath.abs(tMax - tMed) < 1e-6)) {
292              // too close to the bounds, we estimate using a simple dichotomy
293              index = iMed;
294            } else {
295              // estimate the index using a reverse quadratic polynom
296              // (reverse means we have i = P(t), thus allowing to simply
297              // compute index = P(time) rather than solving a quadratic equation)
298              final double d12 = tMax - tMed;
299              final double d23 = tMed - tMin;
300              final double d13 = tMax - tMin;
301              final double dt1 = time - tMax;
302              final double dt2 = time - tMed;
303              final double dt3 = time - tMin;
304              final double iLagrange = ((dt2 * dt3 * d23) * iMax -
305                                        (dt1 * dt3 * d13) * iMed +
306                                        (dt1 * dt2 * d12) * iMin) /
307                                       (d12 * d23 * d13);
308              index = (int) FastMath.rint(iLagrange);
309            }
310    
311            // force the next size reduction to be at least one tenth
312            final int low  = FastMath.max(iMin + 1, (9 * iMin + iMax) / 10);
313            final int high = FastMath.min(iMax - 1, (iMin + 9 * iMax) / 10);
314            if (index < low) {
315              index = low;
316            } else if (index > high) {
317              index = high;
318            }
319    
320          }
321    
322          // now the table slice is very small, we perform an iterative search
323          index = iMin;
324          while ((index <= iMax) && (locatePoint(time, steps.get(index)) > 0)) {
325            ++index;
326          }
327    
328          steps.get(index).setInterpolatedTime(time);
329    
330      }
331    
332      /**
333       * Get the state vector of the interpolated point.
334       * @return state vector at time {@link #getInterpolatedTime}
335       * @exception MaxCountExceededException if the number of functions evaluations is exceeded
336       */
337      public double[] getInterpolatedState() throws MaxCountExceededException {
338        return steps.get(index).getInterpolatedState();
339      }
340    
341      /** Compare a step interval and a double.
342       * @param time point to locate
343       * @param interval step interval
344       * @return -1 if the double is before the interval, 0 if it is in
345       * the interval, and +1 if it is after the interval, according to
346       * the interval direction
347       */
348      private int locatePoint(final double time, final StepInterpolator interval) {
349        if (forward) {
350          if (time < interval.getPreviousTime()) {
351            return -1;
352          } else if (time > interval.getCurrentTime()) {
353            return +1;
354          } else {
355            return 0;
356          }
357        }
358        if (time > interval.getPreviousTime()) {
359          return -1;
360        } else if (time < interval.getCurrentTime()) {
361          return +1;
362        } else {
363          return 0;
364        }
365      }
366    
367    }