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18 package org.apache.commons.math.ode;
19
20 import java.io.ObjectOutput;
21 import java.io.ObjectInput;
22 import java.io.IOException;
23
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32
33
34 class DormandPrince853StepInterpolator
35 extends RungeKuttaStepInterpolator {
36
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44
45
46 public DormandPrince853StepInterpolator() {
47 super();
48 yDotKLast = null;
49 v = null;
50 vectorsInitialized = false;
51 }
52
53
54
55
56
57
58 public DormandPrince853StepInterpolator(DormandPrince853StepInterpolator interpolator) {
59
60 super(interpolator);
61
62 if (interpolator.currentState == null) {
63
64 yDotKLast = null;
65 v = null;
66 vectorsInitialized = false;
67
68 } else {
69
70 int dimension = interpolator.currentState.length;
71
72 yDotKLast = new double[3][];
73 for (int k = 0; k < yDotKLast.length; ++k) {
74 yDotKLast[k] = new double[dimension];
75 System.arraycopy(interpolator.yDotKLast[k], 0, yDotKLast[k], 0,
76 dimension);
77 }
78
79 v = new double[7][];
80 for (int k = 0; k < v.length; ++k) {
81 v[k] = new double[dimension];
82 System.arraycopy(interpolator.v[k], 0, v[k], 0, dimension);
83 }
84
85 vectorsInitialized = interpolator.vectorsInitialized;
86
87 }
88
89 }
90
91
92
93
94 protected StepInterpolator doCopy() {
95 return new DormandPrince853StepInterpolator(this);
96 }
97
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119 public void reinitialize(FirstOrderDifferentialEquations equations,
120 double[] y, double[][] yDotK, boolean forward) {
121
122 super.reinitialize(equations, y, yDotK, forward);
123
124 int dimension = currentState.length;
125
126 yDotKLast = new double[3][];
127 for (int k = 0; k < yDotKLast.length; ++k) {
128 yDotKLast[k] = new double[dimension];
129 }
130
131 v = new double[7][];
132 for (int k = 0; k < v.length; ++k) {
133 v[k] = new double[dimension];
134 }
135
136 vectorsInitialized = false;
137
138 }
139
140
141
142
143 public void storeTime(double t) {
144 super.storeTime(t);
145 vectorsInitialized = false;
146 }
147
148
149
150
151
152
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155
156
157
158 protected void computeInterpolatedState(double theta,
159 double oneMinusThetaH)
160 throws DerivativeException {
161
162 if (! vectorsInitialized) {
163
164 if (v == null) {
165 v = new double[7][];
166 for (int k = 0; k < 7; ++k) {
167 v[k] = new double[interpolatedState.length];
168 }
169 }
170
171
172 finalizeStep();
173
174
175 for (int i = 0; i < interpolatedState.length; ++i) {
176 v[0][i] = h * (b_01 * yDotK[0][i] + b_06 * yDotK[5][i] + b_07 * yDotK[6][i] +
177 b_08 * yDotK[7][i] + b_09 * yDotK[8][i] + b_10 * yDotK[9][i] +
178 b_11 * yDotK[10][i] + b_12 * yDotK[11][i]);
179 v[1][i] = h * yDotK[0][i] - v[0][i];
180 v[2][i] = v[0][i] - v[1][i] - h * yDotK[12][i];
181 for (int k = 0; k < d.length; ++k) {
182 v[k+3][i] = h * (d[k][0] * yDotK[0][i] + d[k][1] * yDotK[5][i] + d[k][2] * yDotK[6][i] +
183 d[k][3] * yDotK[7][i] + d[k][4] * yDotK[8][i] + d[k][5] * yDotK[9][i] +
184 d[k][6] * yDotK[10][i] + d[k][7] * yDotK[11][i] + d[k][8] * yDotK[12][i] +
185 d[k][9] * yDotKLast[0][i] +
186 d[k][10] * yDotKLast[1][i] +
187 d[k][11] * yDotKLast[2][i]);
188 }
189 }
190
191 vectorsInitialized = true;
192
193 }
194
195 double eta = oneMinusThetaH / h;
196
197 for (int i = 0; i < interpolatedState.length; ++i) {
198 interpolatedState[i] =
199 currentState[i] - eta * (v[0][i] - theta * (v[1][i] +
200 theta * (v[2][i] + eta * (v[3][i] + theta * (v[4][i] +
201 eta * (v[5][i] + theta * (v[6][i])))))));
202 }
203
204 }
205
206
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209
210
211
212 protected void doFinalize()
213 throws DerivativeException {
214
215 if (currentState == null) {
216
217 return;
218 }
219
220 double s;
221 double[] yTmp = new double[currentState.length];
222
223
224 for (int j = 0; j < currentState.length; ++j) {
225 s = k14_01 * yDotK[0][j] + k14_06 * yDotK[5][j] + k14_07 * yDotK[6][j] +
226 k14_08 * yDotK[7][j] + k14_09 * yDotK[8][j] + k14_10 * yDotK[9][j] +
227 k14_11 * yDotK[10][j] + k14_12 * yDotK[11][j] + k14_13 * yDotK[12][j];
228 yTmp[j] = currentState[j] + h * s;
229 }
230 equations.computeDerivatives(previousTime + c14 * h, yTmp, yDotKLast[0]);
231
232
233 for (int j = 0; j < currentState.length; ++j) {
234 s = k15_01 * yDotK[0][j] + k15_06 * yDotK[5][j] + k15_07 * yDotK[6][j] +
235 k15_08 * yDotK[7][j] + k15_09 * yDotK[8][j] + k15_10 * yDotK[9][j] +
236 k15_11 * yDotK[10][j] + k15_12 * yDotK[11][j] + k15_13 * yDotK[12][j] +
237 k15_14 * yDotKLast[0][j];
238 yTmp[j] = currentState[j] + h * s;
239 }
240 equations.computeDerivatives(previousTime + c15 * h, yTmp, yDotKLast[1]);
241
242
243 for (int j = 0; j < currentState.length; ++j) {
244 s = k16_01 * yDotK[0][j] + k16_06 * yDotK[5][j] + k16_07 * yDotK[6][j] +
245 k16_08 * yDotK[7][j] + k16_09 * yDotK[8][j] + k16_10 * yDotK[9][j] +
246 k16_11 * yDotK[10][j] + k16_12 * yDotK[11][j] + k16_13 * yDotK[12][j] +
247 k16_14 * yDotKLast[0][j] + k16_15 * yDotKLast[1][j];
248 yTmp[j] = currentState[j] + h * s;
249 }
250 equations.computeDerivatives(previousTime + c16 * h, yTmp, yDotKLast[2]);
251
252 }
253
254
255
256
257
258 public void writeExternal(ObjectOutput out)
259 throws IOException {
260
261 try {
262
263 finalizeStep();
264 } catch (DerivativeException e) {
265 throw new IOException(e.getMessage());
266 }
267 out.writeInt(currentState.length);
268 for (int i = 0; i < currentState.length; ++i) {
269 out.writeDouble(yDotKLast[0][i]);
270 out.writeDouble(yDotKLast[1][i]);
271 out.writeDouble(yDotKLast[2][i]);
272 }
273
274
275 super.writeExternal(out);
276
277 }
278
279
280
281
282
283 public void readExternal(ObjectInput in)
284 throws IOException {
285
286
287 yDotKLast = new double[3][];
288 int dimension = in.readInt();
289 yDotKLast[0] = new double[dimension];
290 yDotKLast[1] = new double[dimension];
291 yDotKLast[2] = new double[dimension];
292
293 for (int i = 0; i < dimension; ++i) {
294 yDotKLast[0][i] = in.readDouble();
295 yDotKLast[1][i] = in.readDouble();
296 yDotKLast[2][i] = in.readDouble();
297 }
298
299
300 super.readExternal(in);
301
302 }
303
304
305 private double[][] yDotKLast;
306
307
308 private double[][] v;
309
310
311 private boolean vectorsInitialized;
312
313
314 private static final double b_01 = 104257.0 / 1920240.0;
315
316
317
318
319 private static final double b_06 = 3399327.0 / 763840.0;
320
321
322 private static final double b_07 = 66578432.0 / 35198415.0;
323
324
325 private static final double b_08 = -1674902723.0 / 288716400.0;
326
327
328 private static final double b_09 = 54980371265625.0 / 176692375811392.0;
329
330
331 private static final double b_10 = -734375.0 / 4826304.0;
332
333
334 private static final double b_11 = 171414593.0 / 851261400.0;
335
336
337 private static final double b_12 = 137909.0 / 3084480.0;
338
339
340 private static final double c14 = 1.0 / 10.0;
341
342
343 private static final double k14_01 = 13481885573.0 / 240030000000.0 - b_01;
344
345
346
347
348 private static final double k14_06 = 0.0 - b_06;
349
350
351 private static final double k14_07 = 139418837528.0 / 549975234375.0 - b_07;
352
353
354 private static final double k14_08 = -11108320068443.0 / 45111937500000.0 - b_08;
355
356
357 private static final double k14_09 = -1769651421925959.0 / 14249385146080000.0 - b_09;
358
359
360 private static final double k14_10 = 57799439.0 / 377055000.0 - b_10;
361
362
363 private static final double k14_11 = 793322643029.0 / 96734250000000.0 - b_11;
364
365
366 private static final double k14_12 = 1458939311.0 / 192780000000.0 - b_12;
367
368
369 private static final double k14_13 = -4149.0 / 500000.0;
370
371
372 private static final double c15 = 1.0 / 5.0;
373
374
375
376 private static final double k15_01 = 1595561272731.0 / 50120273500000.0 - b_01;
377
378
379
380
381 private static final double k15_06 = 975183916491.0 / 34457688031250.0 - b_06;
382
383
384 private static final double k15_07 = 38492013932672.0 / 718912673015625.0 - b_07;
385
386
387 private static final double k15_08 = -1114881286517557.0 / 20298710767500000.0 - b_08;
388
389
390 private static final double k15_09 = 0.0 - b_09;
391
392
393 private static final double k15_10 = 0.0 - b_10;
394
395
396 private static final double k15_11 = -2538710946863.0 / 23431227861250000.0 - b_11;
397
398
399 private static final double k15_12 = 8824659001.0 / 23066716781250.0 - b_12;
400
401
402 private static final double k15_13 = -11518334563.0 / 33831184612500.0;
403
404
405 private static final double k15_14 = 1912306948.0 / 13532473845.0;
406
407
408 private static final double c16 = 7.0 / 9.0;
409
410
411
412 private static final double k16_01 = -13613986967.0 / 31741908048.0 - b_01;
413
414
415
416
417 private static final double k16_06 = -4755612631.0 / 1012344804.0 - b_06;
418
419
420 private static final double k16_07 = 42939257944576.0 / 5588559685701.0 - b_07;
421
422
423 private static final double k16_08 = 77881972900277.0 / 19140370552944.0 - b_08;
424
425
426 private static final double k16_09 = 22719829234375.0 / 63689648654052.0 - b_09;
427
428
429 private static final double k16_10 = 0.0 - b_10;
430
431
432 private static final double k16_11 = 0.0 - b_11;
433
434
435 private static final double k16_12 = 0.0 - b_12;
436
437
438 private static final double k16_13 = -1199007803.0 / 857031517296.0;
439
440
441 private static final double k16_14 = 157882067000.0 / 53564469831.0;
442
443
444 private static final double k16_15 = -290468882375.0 / 31741908048.0;
445
446
447
448
449 private static final double[][] d = {
450
451 { -17751989329.0 / 2106076560.0, 4272954039.0 / 7539864640.0,
452 -118476319744.0 / 38604839385.0, 755123450731.0 / 316657731600.0,
453 3692384461234828125.0 / 1744130441634250432.0, -4612609375.0 / 5293382976.0,
454 2091772278379.0 / 933644586600.0, 2136624137.0 / 3382989120.0,
455 -126493.0 / 1421424.0, 98350000.0 / 5419179.0,
456 -18878125.0 / 2053168.0, -1944542619.0 / 438351368.0},
457
458 { 32941697297.0 / 3159114840.0, 456696183123.0 / 1884966160.0,
459 19132610714624.0 / 115814518155.0, -177904688592943.0 / 474986597400.0,
460 -4821139941836765625.0 / 218016305204281304.0, 30702015625.0 / 3970037232.0,
461 -85916079474274.0 / 2800933759800.0, -5919468007.0 / 634310460.0,
462 2479159.0 / 157936.0, -18750000.0 / 602131.0,
463 -19203125.0 / 2053168.0, 15700361463.0 / 438351368.0},
464
465 { 12627015655.0 / 631822968.0, -72955222965.0 / 188496616.0,
466 -13145744952320.0 / 69488710893.0, 30084216194513.0 / 56998391688.0,
467 -296858761006640625.0 / 25648977082856624.0, 569140625.0 / 82709109.0,
468 -18684190637.0 / 18672891732.0, 69644045.0 / 89549712.0,
469 -11847025.0 / 4264272.0, -978650000.0 / 16257537.0,
470 519371875.0 / 6159504.0, 5256837225.0 / 438351368.0},
471
472 { -450944925.0 / 17550638.0, -14532122925.0 / 94248308.0,
473 -595876966400.0 / 2573655959.0, 188748653015.0 / 527762886.0,
474 2545485458115234375.0 / 27252038150535163.0, -1376953125.0 / 36759604.0,
475 53995596795.0 / 518691437.0, 210311225.0 / 7047894.0,
476 -1718875.0 / 39484.0, 58000000.0 / 602131.0,
477 -1546875.0 / 39484.0, -1262172375.0 / 8429834.0}
478
479 };
480
481
482 private static final long serialVersionUID = 7152276390558450974L;
483
484 }