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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    *      http://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.apache.commons.math4.legacy.ode.nonstiff;
19  
20  import java.io.IOException;
21  import java.io.ObjectInput;
22  import java.io.ObjectOutput;
23  
24  import org.apache.commons.math4.legacy.exception.MaxCountExceededException;
25  import org.apache.commons.math4.legacy.ode.AbstractIntegrator;
26  import org.apache.commons.math4.legacy.ode.EquationsMapper;
27  import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator;
28  
29  /**
30   * This class represents an interpolator over the last step during an
31   * ODE integration for the 8(5,3) Dormand-Prince integrator.
32   *
33   * @see DormandPrince853Integrator
34   *
35   * @since 1.2
36   */
37  
38  class DormandPrince853StepInterpolator
39    extends RungeKuttaStepInterpolator {
40  
41      /** Serializable version identifier. */
42      private static final long serialVersionUID = 20111120L;
43  
44      /** Propagation weights, element 1. */
45      private static final double B_01 =         104257.0 / 1920240.0;
46  
47      // elements 2 to 5 are zero, so they are neither stored nor used
48  
49      /** Propagation weights, element 6. */
50      private static final double B_06 =        3399327.0 / 763840.0;
51  
52      /** Propagation weights, element 7. */
53      private static final double B_07 =       66578432.0 / 35198415.0;
54  
55      /** Propagation weights, element 8. */
56      private static final double B_08 =    -1674902723.0 / 288716400.0;
57  
58      /** Propagation weights, element 9. */
59      private static final double B_09 = 54980371265625.0 / 176692375811392.0;
60  
61      /** Propagation weights, element 10. */
62      private static final double B_10 =        -734375.0 / 4826304.0;
63  
64      /** Propagation weights, element 11. */
65      private static final double B_11 =      171414593.0 / 851261400.0;
66  
67      /** Propagation weights, element 12. */
68      private static final double B_12 =         137909.0 / 3084480.0;
69  
70      /** Time step for stage 14 (interpolation only). */
71      private static final double C14    = 1.0 / 10.0;
72  
73      /** Internal weights for stage 14, element 1. */
74      private static final double K14_01 =       13481885573.0 / 240030000000.0      - B_01;
75  
76      // elements 2 to 5 are zero, so they are neither stored nor used
77  
78      /** Internal weights for stage 14, element 6. */
79      private static final double K14_06 =                 0.0                       - B_06;
80  
81      /** Internal weights for stage 14, element 7. */
82      private static final double K14_07 =      139418837528.0 / 549975234375.0      - B_07;
83  
84      /** Internal weights for stage 14, element 8. */
85      private static final double K14_08 =   -11108320068443.0 / 45111937500000.0    - B_08;
86  
87      /** Internal weights for stage 14, element 9. */
88      private static final double K14_09 = -1769651421925959.0 / 14249385146080000.0 - B_09;
89  
90      /** Internal weights for stage 14, element 10. */
91      private static final double K14_10 =          57799439.0 / 377055000.0         - B_10;
92  
93      /** Internal weights for stage 14, element 11. */
94      private static final double K14_11 =      793322643029.0 / 96734250000000.0    - B_11;
95  
96      /** Internal weights for stage 14, element 12. */
97      private static final double K14_12 =        1458939311.0 / 192780000000.0      - B_12;
98  
99      /** Internal weights for stage 14, element 13. */
100     private static final double K14_13 =             -4149.0 / 500000.0;
101 
102     /** Time step for stage 15 (interpolation only). */
103     private static final double C15    = 1.0 / 5.0;
104 
105 
106     /** Internal weights for stage 15, element 1. */
107     private static final double K15_01 =     1595561272731.0 / 50120273500000.0    - B_01;
108 
109     // elements 2 to 5 are zero, so they are neither stored nor used
110 
111     /** Internal weights for stage 15, element 6. */
112     private static final double K15_06 =      975183916491.0 / 34457688031250.0    - B_06;
113 
114     /** Internal weights for stage 15, element 7. */
115     private static final double K15_07 =    38492013932672.0 / 718912673015625.0   - B_07;
116 
117     /** Internal weights for stage 15, element 8. */
118     private static final double K15_08 = -1114881286517557.0 / 20298710767500000.0 - B_08;
119 
120     /** Internal weights for stage 15, element 9. */
121     private static final double K15_09 =                 0.0                       - B_09;
122 
123     /** Internal weights for stage 15, element 10. */
124     private static final double K15_10 =                 0.0                       - B_10;
125 
126     /** Internal weights for stage 15, element 11. */
127     private static final double K15_11 =    -2538710946863.0 / 23431227861250000.0 - B_11;
128 
129     /** Internal weights for stage 15, element 12. */
130     private static final double K15_12 =        8824659001.0 / 23066716781250.0    - B_12;
131 
132     /** Internal weights for stage 15, element 13. */
133     private static final double K15_13 =      -11518334563.0 / 33831184612500.0;
134 
135     /** Internal weights for stage 15, element 14. */
136     private static final double K15_14 =        1912306948.0 / 13532473845.0;
137 
138     /** Time step for stage 16 (interpolation only). */
139     private static final double C16    = 7.0 / 9.0;
140 
141 
142     /** Internal weights for stage 16, element 1. */
143     private static final double K16_01 =      -13613986967.0 / 31741908048.0       - B_01;
144 
145     // elements 2 to 5 are zero, so they are neither stored nor used
146 
147     /** Internal weights for stage 16, element 6. */
148     private static final double K16_06 =       -4755612631.0 / 1012344804.0        - B_06;
149 
150     /** Internal weights for stage 16, element 7. */
151     private static final double K16_07 =    42939257944576.0 / 5588559685701.0     - B_07;
152 
153     /** Internal weights for stage 16, element 8. */
154     private static final double K16_08 =    77881972900277.0 / 19140370552944.0    - B_08;
155 
156     /** Internal weights for stage 16, element 9. */
157     private static final double K16_09 =    22719829234375.0 / 63689648654052.0    - B_09;
158 
159     /** Internal weights for stage 16, element 10. */
160     private static final double K16_10 =                 0.0                       - B_10;
161 
162     /** Internal weights for stage 16, element 11. */
163     private static final double K16_11 =                 0.0                       - B_11;
164 
165     /** Internal weights for stage 16, element 12. */
166     private static final double K16_12 =                 0.0                       - B_12;
167 
168     /** Internal weights for stage 16, element 13. */
169     private static final double K16_13 =       -1199007803.0 / 857031517296.0;
170 
171     /** Internal weights for stage 16, element 14. */
172     private static final double K16_14 =      157882067000.0 / 53564469831.0;
173 
174     /** Internal weights for stage 16, element 15. */
175     private static final double K16_15 =     -290468882375.0 / 31741908048.0;
176 
177     /** Interpolation weights.
178      * (beware that only the non-null values are in the table)
179      */
180     private static final double[][] D = {
181 
182       {        -17751989329.0 / 2106076560.0,               4272954039.0 / 7539864640.0,
183               -118476319744.0 / 38604839385.0,            755123450731.0 / 316657731600.0,
184         3692384461234828125.0 / 1744130441634250432.0,     -4612609375.0 / 5293382976.0,
185               2091772278379.0 / 933644586600.0,             2136624137.0 / 3382989120.0,
186                     -126493.0 / 1421424.0,                    98350000.0 / 5419179.0,
187                   -18878125.0 / 2053168.0,                 -1944542619.0 / 438351368.0},
188 
189       {         32941697297.0 / 3159114840.0,             456696183123.0 / 1884966160.0,
190              19132610714624.0 / 115814518155.0,       -177904688592943.0 / 474986597400.0,
191        -4821139941836765625.0 / 218016305204281304.0,      30702015625.0 / 3970037232.0,
192             -85916079474274.0 / 2800933759800.0,           -5919468007.0 / 634310460.0,
193                     2479159.0 / 157936.0,                    -18750000.0 / 602131.0,
194                   -19203125.0 / 2053168.0,                 15700361463.0 / 438351368.0},
195 
196       {         12627015655.0 / 631822968.0,              -72955222965.0 / 188496616.0,
197             -13145744952320.0 / 69488710893.0,          30084216194513.0 / 56998391688.0,
198         -296858761006640625.0 / 25648977082856624.0,         569140625.0 / 82709109.0,
199                -18684190637.0 / 18672891732.0,                69644045.0 / 89549712.0,
200                   -11847025.0 / 4264272.0,                  -978650000.0 / 16257537.0,
201                   519371875.0 / 6159504.0,                  5256837225.0 / 438351368.0},
202 
203       {          -450944925.0 / 17550638.0,               -14532122925.0 / 94248308.0,
204               -595876966400.0 / 2573655959.0,             188748653015.0 / 527762886.0,
205         2545485458115234375.0 / 27252038150535163.0,       -1376953125.0 / 36759604.0,
206                 53995596795.0 / 518691437.0,                 210311225.0 / 7047894.0,
207                    -1718875.0 / 39484.0,                      58000000.0 / 602131.0,
208                    -1546875.0 / 39484.0,                   -1262172375.0 / 8429834.0}
209     };
210 
211     /** Last evaluations. */
212     private double[][] yDotKLast;
213 
214     /** Vectors for interpolation. */
215     private double[][] v;
216 
217     /** Initialization indicator for the interpolation vectors. */
218     private boolean vectorsInitialized;
219 
220   /** Simple constructor.
221    * This constructor builds an instance that is not usable yet, the
222    * {@link #reinitialize} method should be called before using the
223    * instance in order to initialize the internal arrays. This
224    * constructor is used only in order to delay the initialization in
225    * some cases. The {@link EmbeddedRungeKuttaIntegrator} uses the
226    * prototyping design pattern to create the step interpolators by
227    * cloning an uninitialized model and latter initializing the copy.
228    */
229   // CHECKSTYLE: stop RedundantModifier
230   // the public modifier here is needed for serialization
231   public DormandPrince853StepInterpolator() {
232     super();
233     yDotKLast = null;
234     v         = null;
235     vectorsInitialized = false;
236   }
237   // CHECKSTYLE: resume RedundantModifier
238 
239   /** Copy constructor.
240    * @param interpolator interpolator to copy from. The copy is a deep
241    * copy: its arrays are separated from the original arrays of the
242    * instance
243    */
244   DormandPrince853StepInterpolator(final DormandPrince853StepInterpolator interpolator) {
245 
246     super(interpolator);
247 
248     if (interpolator.currentState == null) {
249 
250       yDotKLast = null;
251       v         = null;
252       vectorsInitialized = false;
253     } else {
254 
255       final int dimension = interpolator.currentState.length;
256 
257       yDotKLast    = new double[3][];
258       for (int k = 0; k < yDotKLast.length; ++k) {
259         yDotKLast[k] = new double[dimension];
260         System.arraycopy(interpolator.yDotKLast[k], 0, yDotKLast[k], 0,
261                          dimension);
262       }
263 
264       v = new double[7][];
265       for (int k = 0; k < v.length; ++k) {
266         v[k] = new double[dimension];
267         System.arraycopy(interpolator.v[k], 0, v[k], 0, dimension);
268       }
269 
270       vectorsInitialized = interpolator.vectorsInitialized;
271     }
272   }
273 
274   /** {@inheritDoc} */
275   @Override
276   protected StepInterpolator doCopy() {
277     return new DormandPrince853StepInterpolator(this);
278   }
279 
280   /** {@inheritDoc} */
281   @Override
282   public void reinitialize(final AbstractIntegrator integrator,
283                            final double[] y, final double[][] yDotK, final boolean forward,
284                            final EquationsMapper primaryMapper,
285                            final EquationsMapper[] secondaryMappers) {
286 
287     super.reinitialize(integrator, y, yDotK, forward, primaryMapper, secondaryMappers);
288 
289     final int dimension = currentState.length;
290 
291     yDotKLast = new double[3][];
292     for (int k = 0; k < yDotKLast.length; ++k) {
293       yDotKLast[k] = new double[dimension];
294     }
295 
296     v = new double[7][];
297     for (int k = 0; k < v.length; ++k) {
298       v[k]  = new double[dimension];
299     }
300 
301     vectorsInitialized = false;
302   }
303 
304   /** {@inheritDoc} */
305   @Override
306   public void storeTime(final double t) {
307     super.storeTime(t);
308     vectorsInitialized = false;
309   }
310 
311   /** {@inheritDoc} */
312   @Override
313   protected void computeInterpolatedStateAndDerivatives(final double theta,
314                                           final double oneMinusThetaH)
315       throws MaxCountExceededException {
316 
317     if (! vectorsInitialized) {
318 
319       if (v == null) {
320         v = new double[7][];
321         for (int k = 0; k < 7; ++k) {
322           v[k] = new double[interpolatedState.length];
323         }
324       }
325 
326       // perform the last evaluations if they have not been done yet
327       finalizeStep();
328 
329       // compute the interpolation vectors for this time step
330       for (int i = 0; i < interpolatedState.length; ++i) {
331           final double yDot1  = yDotK[0][i];
332           final double yDot6  = yDotK[5][i];
333           final double yDot7  = yDotK[6][i];
334           final double yDot8  = yDotK[7][i];
335           final double yDot9  = yDotK[8][i];
336           final double yDot10 = yDotK[9][i];
337           final double yDot11 = yDotK[10][i];
338           final double yDot12 = yDotK[11][i];
339           final double yDot13 = yDotK[12][i];
340           final double yDot14 = yDotKLast[0][i];
341           final double yDot15 = yDotKLast[1][i];
342           final double yDot16 = yDotKLast[2][i];
343           v[0][i] = B_01 * yDot1  + B_06 * yDot6 + B_07 * yDot7 +
344                     B_08 * yDot8  + B_09 * yDot9 + B_10 * yDot10 +
345                     B_11 * yDot11 + B_12 * yDot12;
346           v[1][i] = yDot1 - v[0][i];
347           v[2][i] = v[0][i] - v[1][i] - yDotK[12][i];
348           for (int k = 0; k < D.length; ++k) {
349               v[k+3][i] = D[k][0] * yDot1  + D[k][1]  * yDot6  + D[k][2]  * yDot7  +
350                           D[k][3] * yDot8  + D[k][4]  * yDot9  + D[k][5]  * yDot10 +
351                           D[k][6] * yDot11 + D[k][7]  * yDot12 + D[k][8]  * yDot13 +
352                           D[k][9] * yDot14 + D[k][10] * yDot15 + D[k][11] * yDot16;
353           }
354       }
355 
356       vectorsInitialized = true;
357     }
358 
359     final double eta      = 1 - theta;
360     final double twoTheta = 2 * theta;
361     final double theta2   = theta * theta;
362     final double dot1 = 1 - twoTheta;
363     final double dot2 = theta * (2 - 3 * theta);
364     final double dot3 = twoTheta * (1 + theta * (twoTheta -3));
365     final double dot4 = theta2 * (3 + theta * (5 * theta - 8));
366     final double dot5 = theta2 * (3 + theta * (-12 + theta * (15 - 6 * theta)));
367     final double dot6 = theta2 * theta * (4 + theta * (-15 + theta * (18 - 7 * theta)));
368 
369     if (previousState != null && theta <= 0.5) {
370         for (int i = 0; i < interpolatedState.length; ++i) {
371             interpolatedState[i] = previousState[i] +
372                     theta * h * (v[0][i] +
373                             eta * (v[1][i] +
374                                     theta * (v[2][i] +
375                                             eta * (v[3][i] +
376                                                     theta * (v[4][i] +
377                                                             eta * (v[5][i] +
378                                                                     theta * (v[6][i])))))));
379             interpolatedDerivatives[i] =  v[0][i] + dot1 * v[1][i] + dot2 * v[2][i] +
380                     dot3 * v[3][i] + dot4 * v[4][i] +
381                     dot5 * v[5][i] + dot6 * v[6][i];
382         }
383     } else {
384         for (int i = 0; i < interpolatedState.length; ++i) {
385             interpolatedState[i] = currentState[i] -
386                     oneMinusThetaH * (v[0][i] -
387                             theta * (v[1][i] +
388                                     theta * (v[2][i] +
389                                             eta * (v[3][i] +
390                                                     theta * (v[4][i] +
391                                                             eta * (v[5][i] +
392                                                                     theta * (v[6][i])))))));
393             interpolatedDerivatives[i] =  v[0][i] + dot1 * v[1][i] + dot2 * v[2][i] +
394                     dot3 * v[3][i] + dot4 * v[4][i] +
395                     dot5 * v[5][i] + dot6 * v[6][i];
396         }
397     }
398   }
399 
400   /** {@inheritDoc} */
401   @Override
402   protected void doFinalize() throws MaxCountExceededException {
403 
404       if (currentState == null) {
405           // we are finalizing an uninitialized instance
406           return;
407       }
408 
409       double s;
410       final double[] yTmp = new double[currentState.length];
411       final double pT = getGlobalPreviousTime();
412 
413       // k14
414       for (int j = 0; j < currentState.length; ++j) {
415           s = K14_01 * yDotK[0][j]  + K14_06 * yDotK[5][j]  + K14_07 * yDotK[6][j] +
416                   K14_08 * yDotK[7][j]  + K14_09 * yDotK[8][j]  + K14_10 * yDotK[9][j] +
417                   K14_11 * yDotK[10][j] + K14_12 * yDotK[11][j] + K14_13 * yDotK[12][j];
418           yTmp[j] = currentState[j] + h * s;
419       }
420       integrator.computeDerivatives(pT + C14 * h, yTmp, yDotKLast[0]);
421 
422       // k15
423       for (int j = 0; j < currentState.length; ++j) {
424           s = K15_01 * yDotK[0][j]  + K15_06 * yDotK[5][j]  + K15_07 * yDotK[6][j] +
425                   K15_08 * yDotK[7][j]  + K15_09 * yDotK[8][j]  + K15_10 * yDotK[9][j] +
426                   K15_11 * yDotK[10][j] + K15_12 * yDotK[11][j] + K15_13 * yDotK[12][j] +
427                   K15_14 * yDotKLast[0][j];
428           yTmp[j] = currentState[j] + h * s;
429       }
430       integrator.computeDerivatives(pT + C15 * h, yTmp, yDotKLast[1]);
431 
432       // k16
433       for (int j = 0; j < currentState.length; ++j) {
434           s = K16_01 * yDotK[0][j]  + K16_06 * yDotK[5][j]  + K16_07 * yDotK[6][j] +
435                   K16_08 * yDotK[7][j]  + K16_09 * yDotK[8][j]  + K16_10 * yDotK[9][j] +
436                   K16_11 * yDotK[10][j] + K16_12 * yDotK[11][j] + K16_13 * yDotK[12][j] +
437                   K16_14 * yDotKLast[0][j] +  K16_15 * yDotKLast[1][j];
438           yTmp[j] = currentState[j] + h * s;
439       }
440       integrator.computeDerivatives(pT + C16 * h, yTmp, yDotKLast[2]);
441   }
442 
443   /** {@inheritDoc} */
444   @Override
445   public void writeExternal(final ObjectOutput out)
446     throws IOException {
447 
448     try {
449         // save the local attributes
450         finalizeStep();
451     } catch (MaxCountExceededException mcee) {
452         final IOException ioe = new IOException(mcee.getLocalizedMessage());
453         ioe.initCause(mcee);
454         throw ioe;
455     }
456 
457     final int dimension = (currentState == null) ? -1 : currentState.length;
458     out.writeInt(dimension);
459     for (int i = 0; i < dimension; ++i) {
460       out.writeDouble(yDotKLast[0][i]);
461       out.writeDouble(yDotKLast[1][i]);
462       out.writeDouble(yDotKLast[2][i]);
463     }
464 
465     // save the state of the base class
466     super.writeExternal(out);
467   }
468 
469   /** {@inheritDoc} */
470   @Override
471   public void readExternal(final ObjectInput in)
472     throws IOException, ClassNotFoundException {
473 
474     // read the local attributes
475     yDotKLast = new double[3][];
476     final int dimension = in.readInt();
477     yDotKLast[0] = (dimension < 0) ? null : new double[dimension];
478     yDotKLast[1] = (dimension < 0) ? null : new double[dimension];
479     yDotKLast[2] = (dimension < 0) ? null : new double[dimension];
480 
481     for (int i = 0; i < dimension; ++i) {
482       yDotKLast[0][i] = in.readDouble();
483       yDotKLast[1][i] = in.readDouble();
484       yDotKLast[2][i] = in.readDouble();
485     }
486 
487     // read the base state
488     super.readExternal(in);
489   }
490 }