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.math.ode.nonstiff; 19 20 import java.io.IOException; 21 import java.io.ObjectInput; 22 import java.io.ObjectOutput; 23 24 import org.apache.commons.math.ode.AbstractIntegrator; 25 import org.apache.commons.math.ode.DerivativeException; 26 import org.apache.commons.math.ode.sampling.StepInterpolator; 27 28 /** 29 * This class represents an interpolator over the last step during an 30 * ODE integration for the 8(5,3) Dormand-Prince integrator. 31 * 32 * @see DormandPrince853Integrator 33 * 34 * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 fvr. 2011) $ 35 * @since 1.2 36 */ 37 38 class DormandPrince853StepInterpolator 39 extends RungeKuttaStepInterpolator { 40 41 /** Serializable version identifier */ 42 private static final long serialVersionUID = 7152276390558450974L; 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 }; 211 212 /** Last evaluations. */ 213 private double[][] yDotKLast; 214 215 /** Vectors for interpolation. */ 216 private double[][] v; 217 218 /** Initialization indicator for the interpolation vectors. */ 219 private boolean vectorsInitialized; 220 221 /** Simple constructor. 222 * This constructor builds an instance that is not usable yet, the 223 * {@link #reinitialize} method should be called before using the 224 * instance in order to initialize the internal arrays. This 225 * constructor is used only in order to delay the initialization in 226 * some cases. The {@link EmbeddedRungeKuttaIntegrator} uses the 227 * prototyping design pattern to create the step interpolators by 228 * cloning an uninitialized model and latter initializing the copy. 229 */ 230 public DormandPrince853StepInterpolator() { 231 super(); 232 yDotKLast = null; 233 v = null; 234 vectorsInitialized = false; 235 } 236 237 /** Copy constructor. 238 * @param interpolator interpolator to copy from. The copy is a deep 239 * copy: its arrays are separated from the original arrays of the 240 * instance 241 */ 242 public DormandPrince853StepInterpolator(final DormandPrince853StepInterpolator interpolator) { 243 244 super(interpolator); 245 246 if (interpolator.currentState == null) { 247 248 yDotKLast = null; 249 v = null; 250 vectorsInitialized = false; 251 252 } else { 253 254 final int dimension = interpolator.currentState.length; 255 256 yDotKLast = new double[3][]; 257 for (int k = 0; k < yDotKLast.length; ++k) { 258 yDotKLast[k] = new double[dimension]; 259 System.arraycopy(interpolator.yDotKLast[k], 0, yDotKLast[k], 0, 260 dimension); 261 } 262 263 v = new double[7][]; 264 for (int k = 0; k < v.length; ++k) { 265 v[k] = new double[dimension]; 266 System.arraycopy(interpolator.v[k], 0, v[k], 0, dimension); 267 } 268 269 vectorsInitialized = interpolator.vectorsInitialized; 270 271 } 272 273 } 274 275 /** {@inheritDoc} */ 276 @Override 277 protected StepInterpolator doCopy() { 278 return new DormandPrince853StepInterpolator(this); 279 } 280 281 /** {@inheritDoc} */ 282 @Override 283 public void reinitialize(final AbstractIntegrator integrator, 284 final double[] y, final double[][] yDotK, final boolean forward) { 285 286 super.reinitialize(integrator, y, yDotK, forward); 287 288 final int dimension = currentState.length; 289 290 yDotKLast = new double[3][]; 291 for (int k = 0; k < yDotKLast.length; ++k) { 292 yDotKLast[k] = new double[dimension]; 293 } 294 295 v = new double[7][]; 296 for (int k = 0; k < v.length; ++k) { 297 v[k] = new double[dimension]; 298 } 299 300 vectorsInitialized = false; 301 302 } 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 DerivativeException { 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 } 359 360 final double eta = 1 - theta; 361 final double twoTheta = 2 * theta; 362 final double theta2 = theta * theta; 363 final double dot1 = 1 - twoTheta; 364 final double dot2 = theta * (2 - 3 * theta); 365 final double dot3 = twoTheta * (1 + theta * (twoTheta -3)); 366 final double dot4 = theta2 * (3 + theta * (5 * theta - 8)); 367 final double dot5 = theta2 * (3 + theta * (-12 + theta * (15 - 6 * theta))); 368 final double dot6 = theta2 * theta * (4 + theta * (-15 + theta * (18 - 7 * theta))); 369 370 for (int i = 0; i < interpolatedState.length; ++i) { 371 interpolatedState[i] = currentState[i] - 372 oneMinusThetaH * (v[0][i] - 373 theta * (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 } 383 384 } 385 386 /** {@inheritDoc} */ 387 @Override 388 protected void doFinalize() 389 throws DerivativeException { 390 391 if (currentState == null) { 392 // we are finalizing an uninitialized instance 393 return; 394 } 395 396 double s; 397 final double[] yTmp = new double[currentState.length]; 398 final double pT = getGlobalPreviousTime(); 399 400 // k14 401 for (int j = 0; j < currentState.length; ++j) { 402 s = K14_01 * yDotK[0][j] + K14_06 * yDotK[5][j] + K14_07 * yDotK[6][j] + 403 K14_08 * yDotK[7][j] + K14_09 * yDotK[8][j] + K14_10 * yDotK[9][j] + 404 K14_11 * yDotK[10][j] + K14_12 * yDotK[11][j] + K14_13 * yDotK[12][j]; 405 yTmp[j] = currentState[j] + h * s; 406 } 407 integrator.computeDerivatives(pT + C14 * h, yTmp, yDotKLast[0]); 408 409 // k15 410 for (int j = 0; j < currentState.length; ++j) { 411 s = K15_01 * yDotK[0][j] + K15_06 * yDotK[5][j] + K15_07 * yDotK[6][j] + 412 K15_08 * yDotK[7][j] + K15_09 * yDotK[8][j] + K15_10 * yDotK[9][j] + 413 K15_11 * yDotK[10][j] + K15_12 * yDotK[11][j] + K15_13 * yDotK[12][j] + 414 K15_14 * yDotKLast[0][j]; 415 yTmp[j] = currentState[j] + h * s; 416 } 417 integrator.computeDerivatives(pT + C15 * h, yTmp, yDotKLast[1]); 418 419 // k16 420 for (int j = 0; j < currentState.length; ++j) { 421 s = K16_01 * yDotK[0][j] + K16_06 * yDotK[5][j] + K16_07 * yDotK[6][j] + 422 K16_08 * yDotK[7][j] + K16_09 * yDotK[8][j] + K16_10 * yDotK[9][j] + 423 K16_11 * yDotK[10][j] + K16_12 * yDotK[11][j] + K16_13 * yDotK[12][j] + 424 K16_14 * yDotKLast[0][j] + K16_15 * yDotKLast[1][j]; 425 yTmp[j] = currentState[j] + h * s; 426 } 427 integrator.computeDerivatives(pT + C16 * h, yTmp, yDotKLast[2]); 428 429 } 430 431 /** {@inheritDoc} */ 432 @Override 433 public void writeExternal(final ObjectOutput out) 434 throws IOException { 435 436 try { 437 // save the local attributes 438 finalizeStep(); 439 } catch (DerivativeException e) { 440 IOException ioe = new IOException(e.getLocalizedMessage()); 441 ioe.initCause(e); 442 throw ioe; 443 } 444 final int dimension = (currentState == null) ? -1 : currentState.length; 445 out.writeInt(dimension); 446 for (int i = 0; i < dimension; ++i) { 447 out.writeDouble(yDotKLast[0][i]); 448 out.writeDouble(yDotKLast[1][i]); 449 out.writeDouble(yDotKLast[2][i]); 450 } 451 452 // save the state of the base class 453 super.writeExternal(out); 454 455 } 456 457 /** {@inheritDoc} */ 458 @Override 459 public void readExternal(final ObjectInput in) 460 throws IOException { 461 462 // read the local attributes 463 yDotKLast = new double[3][]; 464 final int dimension = in.readInt(); 465 yDotKLast[0] = (dimension < 0) ? null : new double[dimension]; 466 yDotKLast[1] = (dimension < 0) ? null : new double[dimension]; 467 yDotKLast[2] = (dimension < 0) ? null : new double[dimension]; 468 469 for (int i = 0; i < dimension; ++i) { 470 yDotKLast[0][i] = in.readDouble(); 471 yDotKLast[1][i] = in.readDouble(); 472 yDotKLast[2][i] = in.readDouble(); 473 } 474 475 // read the base state 476 super.readExternal(in); 477 478 } 479 480 } 481
