1 /* 2 Include "petsctao.h" so that we can use TAO solvers. Note that this 3 file automatically includes libraries such as: 4 petsc.h - base PETSc routines petscvec.h - vectors 5 petscsys.h - system routines petscmat.h - matrices 6 petscis.h - index sets petscksp.h - Krylov subspace methods 7 petscviewer.h - viewers petscpc.h - preconditioners 8 9 */ 10 11 #include <petsctao.h> 12 13 /* 14 Description: These data are the result of a NIST study involving 15 ultrasonic calibration. The response variable is 16 ultrasonic response, and the predictor variable is 17 metal distance. 18 19 Reference: Chwirut, D., NIST (197?). 20 Ultrasonic Reference Block Study. 21 */ 22 23 static char help[] = "Finds the nonlinear least-squares solution to the model \n\ 24 y = exp[-b1*x]/(b2+b3*x) + e \n"; 25 26 #define NOBSERVATIONS 214 27 #define NPARAMETERS 3 28 29 /* User-defined application context */ 30 typedef struct { 31 /* Working space */ 32 PetscReal t[NOBSERVATIONS]; /* array of independent variables of observation */ 33 PetscReal y[NOBSERVATIONS]; /* array of dependent variables */ 34 PetscReal j[NOBSERVATIONS][NPARAMETERS]; /* dense jacobian matrix array*/ 35 PetscInt idm[NOBSERVATIONS]; /* Matrix indices for jacobian */ 36 PetscInt idn[NPARAMETERS]; 37 } AppCtx; 38 39 /* User provided Routines */ 40 PetscErrorCode InitializeData(AppCtx *user); 41 PetscErrorCode FormStartingPoint(Vec); 42 PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *); 43 PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *); 44 45 /*--------------------------------------------------------------------*/ 46 int main(int argc, char **argv) 47 { 48 Vec x, f; /* solution, function */ 49 Mat J; /* Jacobian matrix */ 50 Tao tao; /* Tao solver context */ 51 PetscInt i; /* iteration information */ 52 PetscReal hist[100], resid[100]; 53 PetscInt lits[100]; 54 AppCtx user; /* user-defined work context */ 55 56 PetscFunctionBeginUser; 57 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 58 /* Allocate vectors */ 59 PetscCall(VecCreateSeq(MPI_COMM_SELF, NPARAMETERS, &x)); 60 PetscCall(VecCreateSeq(MPI_COMM_SELF, NOBSERVATIONS, &f)); 61 62 /* Create the Jacobian matrix. */ 63 PetscCall(MatCreateSeqDense(MPI_COMM_SELF, NOBSERVATIONS, NPARAMETERS, NULL, &J)); 64 65 for (i = 0; i < NOBSERVATIONS; i++) user.idm[i] = i; 66 67 for (i = 0; i < NPARAMETERS; i++) user.idn[i] = i; 68 69 /* Create TAO solver and set desired solution method */ 70 PetscCall(TaoCreate(PETSC_COMM_SELF, &tao)); 71 PetscCall(TaoSetType(tao, TAOPOUNDERS)); 72 73 /* Set the function and Jacobian routines. */ 74 PetscCall(InitializeData(&user)); 75 PetscCall(FormStartingPoint(x)); 76 PetscCall(TaoSetSolution(tao, x)); 77 PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user)); 78 PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user)); 79 80 /* Check for any TAO command line arguments */ 81 PetscCall(TaoSetFromOptions(tao)); 82 83 PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE)); 84 /* Perform the Solve */ 85 PetscCall(TaoSolve(tao)); 86 87 /* View the vector; then destroy it. */ 88 PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF)); 89 90 /* Free TAO data structures */ 91 PetscCall(TaoDestroy(&tao)); 92 93 /* Free PETSc data structures */ 94 PetscCall(VecDestroy(&x)); 95 PetscCall(VecDestroy(&f)); 96 PetscCall(MatDestroy(&J)); 97 98 PetscCall(PetscFinalize()); 99 return 0; 100 } 101 102 /*--------------------------------------------------------------------*/ 103 PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr) 104 { 105 AppCtx *user = (AppCtx *)ptr; 106 PetscInt i; 107 const PetscReal *x; 108 PetscReal *y = user->y, *f, *t = user->t; 109 110 PetscFunctionBegin; 111 PetscCall(VecGetArrayRead(X, &x)); 112 PetscCall(VecGetArray(F, &f)); 113 114 for (i = 0; i < NOBSERVATIONS; i++) f[i] = y[i] - PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]); 115 PetscCall(VecRestoreArrayRead(X, &x)); 116 PetscCall(VecRestoreArray(F, &f)); 117 PetscCall(PetscLogFlops(6 * NOBSERVATIONS)); 118 PetscFunctionReturn(PETSC_SUCCESS); 119 } 120 121 /*------------------------------------------------------------*/ 122 /* J[i][j] = df[i]/dt[j] */ 123 PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr) 124 { 125 AppCtx *user = (AppCtx *)ptr; 126 PetscInt i; 127 const PetscReal *x; 128 PetscReal *t = user->t; 129 PetscReal base; 130 131 PetscFunctionBegin; 132 PetscCall(VecGetArrayRead(X, &x)); 133 for (i = 0; i < NOBSERVATIONS; i++) { 134 base = PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]); 135 136 user->j[i][0] = t[i] * base; 137 user->j[i][1] = base / (x[1] + x[2] * t[i]); 138 user->j[i][2] = base * t[i] / (x[1] + x[2] * t[i]); 139 } 140 141 /* Assemble the matrix */ 142 PetscCall(MatSetValues(J, NOBSERVATIONS, user->idm, NPARAMETERS, user->idn, (PetscReal *)user->j, INSERT_VALUES)); 143 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 144 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 145 146 PetscCall(VecRestoreArrayRead(X, &x)); 147 PetscCall(PetscLogFlops(NOBSERVATIONS * 13)); 148 PetscFunctionReturn(PETSC_SUCCESS); 149 } 150 151 /* ------------------------------------------------------------ */ 152 PetscErrorCode FormStartingPoint(Vec X) 153 { 154 PetscReal *x; 155 156 PetscFunctionBegin; 157 PetscCall(VecGetArray(X, &x)); 158 x[0] = 0.15; 159 x[1] = 0.008; 160 x[2] = 0.010; 161 PetscCall(VecRestoreArray(X, &x)); 162 PetscFunctionReturn(PETSC_SUCCESS); 163 } 164 165 /* ---------------------------------------------------------------------- */ 166 PetscErrorCode InitializeData(AppCtx *user) 167 { 168 PetscReal *t = user->t, *y = user->y; 169 PetscInt i = 0; 170 171 PetscFunctionBegin; 172 y[i] = 92.9000; 173 t[i++] = 0.5000; 174 y[i] = 78.7000; 175 t[i++] = 0.6250; 176 y[i] = 64.2000; 177 t[i++] = 0.7500; 178 y[i] = 64.9000; 179 t[i++] = 0.8750; 180 y[i] = 57.1000; 181 t[i++] = 1.0000; 182 y[i] = 43.3000; 183 t[i++] = 1.2500; 184 y[i] = 31.1000; 185 t[i++] = 1.7500; 186 y[i] = 23.6000; 187 t[i++] = 2.2500; 188 y[i] = 31.0500; 189 t[i++] = 1.7500; 190 y[i] = 23.7750; 191 t[i++] = 2.2500; 192 y[i] = 17.7375; 193 t[i++] = 2.7500; 194 y[i] = 13.8000; 195 t[i++] = 3.2500; 196 y[i] = 11.5875; 197 t[i++] = 3.7500; 198 y[i] = 9.4125; 199 t[i++] = 4.2500; 200 y[i] = 7.7250; 201 t[i++] = 4.7500; 202 y[i] = 7.3500; 203 t[i++] = 5.2500; 204 y[i] = 8.0250; 205 t[i++] = 5.7500; 206 y[i] = 90.6000; 207 t[i++] = 0.5000; 208 y[i] = 76.9000; 209 t[i++] = 0.6250; 210 y[i] = 71.6000; 211 t[i++] = 0.7500; 212 y[i] = 63.6000; 213 t[i++] = 0.8750; 214 y[i] = 54.0000; 215 t[i++] = 1.0000; 216 y[i] = 39.2000; 217 t[i++] = 1.2500; 218 y[i] = 29.3000; 219 t[i++] = 1.7500; 220 y[i] = 21.4000; 221 t[i++] = 2.2500; 222 y[i] = 29.1750; 223 t[i++] = 1.7500; 224 y[i] = 22.1250; 225 t[i++] = 2.2500; 226 y[i] = 17.5125; 227 t[i++] = 2.7500; 228 y[i] = 14.2500; 229 t[i++] = 3.2500; 230 y[i] = 9.4500; 231 t[i++] = 3.7500; 232 y[i] = 9.1500; 233 t[i++] = 4.2500; 234 y[i] = 7.9125; 235 t[i++] = 4.7500; 236 y[i] = 8.4750; 237 t[i++] = 5.2500; 238 y[i] = 6.1125; 239 t[i++] = 5.7500; 240 y[i] = 80.0000; 241 t[i++] = 0.5000; 242 y[i] = 79.0000; 243 t[i++] = 0.6250; 244 y[i] = 63.8000; 245 t[i++] = 0.7500; 246 y[i] = 57.2000; 247 t[i++] = 0.8750; 248 y[i] = 53.2000; 249 t[i++] = 1.0000; 250 y[i] = 42.5000; 251 t[i++] = 1.2500; 252 y[i] = 26.8000; 253 t[i++] = 1.7500; 254 y[i] = 20.4000; 255 t[i++] = 2.2500; 256 y[i] = 26.8500; 257 t[i++] = 1.7500; 258 y[i] = 21.0000; 259 t[i++] = 2.2500; 260 y[i] = 16.4625; 261 t[i++] = 2.7500; 262 y[i] = 12.5250; 263 t[i++] = 3.2500; 264 y[i] = 10.5375; 265 t[i++] = 3.7500; 266 y[i] = 8.5875; 267 t[i++] = 4.2500; 268 y[i] = 7.1250; 269 t[i++] = 4.7500; 270 y[i] = 6.1125; 271 t[i++] = 5.2500; 272 y[i] = 5.9625; 273 t[i++] = 5.7500; 274 y[i] = 74.1000; 275 t[i++] = 0.5000; 276 y[i] = 67.3000; 277 t[i++] = 0.6250; 278 y[i] = 60.8000; 279 t[i++] = 0.7500; 280 y[i] = 55.5000; 281 t[i++] = 0.8750; 282 y[i] = 50.3000; 283 t[i++] = 1.0000; 284 y[i] = 41.0000; 285 t[i++] = 1.2500; 286 y[i] = 29.4000; 287 t[i++] = 1.7500; 288 y[i] = 20.4000; 289 t[i++] = 2.2500; 290 y[i] = 29.3625; 291 t[i++] = 1.7500; 292 y[i] = 21.1500; 293 t[i++] = 2.2500; 294 y[i] = 16.7625; 295 t[i++] = 2.7500; 296 y[i] = 13.2000; 297 t[i++] = 3.2500; 298 y[i] = 10.8750; 299 t[i++] = 3.7500; 300 y[i] = 8.1750; 301 t[i++] = 4.2500; 302 y[i] = 7.3500; 303 t[i++] = 4.7500; 304 y[i] = 5.9625; 305 t[i++] = 5.2500; 306 y[i] = 5.6250; 307 t[i++] = 5.7500; 308 y[i] = 81.5000; 309 t[i++] = .5000; 310 y[i] = 62.4000; 311 t[i++] = .7500; 312 y[i] = 32.5000; 313 t[i++] = 1.5000; 314 y[i] = 12.4100; 315 t[i++] = 3.0000; 316 y[i] = 13.1200; 317 t[i++] = 3.0000; 318 y[i] = 15.5600; 319 t[i++] = 3.0000; 320 y[i] = 5.6300; 321 t[i++] = 6.0000; 322 y[i] = 78.0000; 323 t[i++] = .5000; 324 y[i] = 59.9000; 325 t[i++] = .7500; 326 y[i] = 33.2000; 327 t[i++] = 1.5000; 328 y[i] = 13.8400; 329 t[i++] = 3.0000; 330 y[i] = 12.7500; 331 t[i++] = 3.0000; 332 y[i] = 14.6200; 333 t[i++] = 3.0000; 334 y[i] = 3.9400; 335 t[i++] = 6.0000; 336 y[i] = 76.8000; 337 t[i++] = .5000; 338 y[i] = 61.0000; 339 t[i++] = .7500; 340 y[i] = 32.9000; 341 t[i++] = 1.5000; 342 y[i] = 13.8700; 343 t[i++] = 3.0000; 344 y[i] = 11.8100; 345 t[i++] = 3.0000; 346 y[i] = 13.3100; 347 t[i++] = 3.0000; 348 y[i] = 5.4400; 349 t[i++] = 6.0000; 350 y[i] = 78.0000; 351 t[i++] = .5000; 352 y[i] = 63.5000; 353 t[i++] = .7500; 354 y[i] = 33.8000; 355 t[i++] = 1.5000; 356 y[i] = 12.5600; 357 t[i++] = 3.0000; 358 y[i] = 5.6300; 359 t[i++] = 6.0000; 360 y[i] = 12.7500; 361 t[i++] = 3.0000; 362 y[i] = 13.1200; 363 t[i++] = 3.0000; 364 y[i] = 5.4400; 365 t[i++] = 6.0000; 366 y[i] = 76.8000; 367 t[i++] = .5000; 368 y[i] = 60.0000; 369 t[i++] = .7500; 370 y[i] = 47.8000; 371 t[i++] = 1.0000; 372 y[i] = 32.0000; 373 t[i++] = 1.5000; 374 y[i] = 22.2000; 375 t[i++] = 2.0000; 376 y[i] = 22.5700; 377 t[i++] = 2.0000; 378 y[i] = 18.8200; 379 t[i++] = 2.5000; 380 y[i] = 13.9500; 381 t[i++] = 3.0000; 382 y[i] = 11.2500; 383 t[i++] = 4.0000; 384 y[i] = 9.0000; 385 t[i++] = 5.0000; 386 y[i] = 6.6700; 387 t[i++] = 6.0000; 388 y[i] = 75.8000; 389 t[i++] = .5000; 390 y[i] = 62.0000; 391 t[i++] = .7500; 392 y[i] = 48.8000; 393 t[i++] = 1.0000; 394 y[i] = 35.2000; 395 t[i++] = 1.5000; 396 y[i] = 20.0000; 397 t[i++] = 2.0000; 398 y[i] = 20.3200; 399 t[i++] = 2.0000; 400 y[i] = 19.3100; 401 t[i++] = 2.5000; 402 y[i] = 12.7500; 403 t[i++] = 3.0000; 404 y[i] = 10.4200; 405 t[i++] = 4.0000; 406 y[i] = 7.3100; 407 t[i++] = 5.0000; 408 y[i] = 7.4200; 409 t[i++] = 6.0000; 410 y[i] = 70.5000; 411 t[i++] = .5000; 412 y[i] = 59.5000; 413 t[i++] = .7500; 414 y[i] = 48.5000; 415 t[i++] = 1.0000; 416 y[i] = 35.8000; 417 t[i++] = 1.5000; 418 y[i] = 21.0000; 419 t[i++] = 2.0000; 420 y[i] = 21.6700; 421 t[i++] = 2.0000; 422 y[i] = 21.0000; 423 t[i++] = 2.5000; 424 y[i] = 15.6400; 425 t[i++] = 3.0000; 426 y[i] = 8.1700; 427 t[i++] = 4.0000; 428 y[i] = 8.5500; 429 t[i++] = 5.0000; 430 y[i] = 10.1200; 431 t[i++] = 6.0000; 432 y[i] = 78.0000; 433 t[i++] = .5000; 434 y[i] = 66.0000; 435 t[i++] = .6250; 436 y[i] = 62.0000; 437 t[i++] = .7500; 438 y[i] = 58.0000; 439 t[i++] = .8750; 440 y[i] = 47.7000; 441 t[i++] = 1.0000; 442 y[i] = 37.8000; 443 t[i++] = 1.2500; 444 y[i] = 20.2000; 445 t[i++] = 2.2500; 446 y[i] = 21.0700; 447 t[i++] = 2.2500; 448 y[i] = 13.8700; 449 t[i++] = 2.7500; 450 y[i] = 9.6700; 451 t[i++] = 3.2500; 452 y[i] = 7.7600; 453 t[i++] = 3.7500; 454 y[i] = 5.4400; 455 t[i++] = 4.2500; 456 y[i] = 4.8700; 457 t[i++] = 4.7500; 458 y[i] = 4.0100; 459 t[i++] = 5.2500; 460 y[i] = 3.7500; 461 t[i++] = 5.7500; 462 y[i] = 24.1900; 463 t[i++] = 3.0000; 464 y[i] = 25.7600; 465 t[i++] = 3.0000; 466 y[i] = 18.0700; 467 t[i++] = 3.0000; 468 y[i] = 11.8100; 469 t[i++] = 3.0000; 470 y[i] = 12.0700; 471 t[i++] = 3.0000; 472 y[i] = 16.1200; 473 t[i++] = 3.0000; 474 y[i] = 70.8000; 475 t[i++] = .5000; 476 y[i] = 54.7000; 477 t[i++] = .7500; 478 y[i] = 48.0000; 479 t[i++] = 1.0000; 480 y[i] = 39.8000; 481 t[i++] = 1.5000; 482 y[i] = 29.8000; 483 t[i++] = 2.0000; 484 y[i] = 23.7000; 485 t[i++] = 2.5000; 486 y[i] = 29.6200; 487 t[i++] = 2.0000; 488 y[i] = 23.8100; 489 t[i++] = 2.5000; 490 y[i] = 17.7000; 491 t[i++] = 3.0000; 492 y[i] = 11.5500; 493 t[i++] = 4.0000; 494 y[i] = 12.0700; 495 t[i++] = 5.0000; 496 y[i] = 8.7400; 497 t[i++] = 6.0000; 498 y[i] = 80.7000; 499 t[i++] = .5000; 500 y[i] = 61.3000; 501 t[i++] = .7500; 502 y[i] = 47.5000; 503 t[i++] = 1.0000; 504 y[i] = 29.0000; 505 t[i++] = 1.5000; 506 y[i] = 24.0000; 507 t[i++] = 2.0000; 508 y[i] = 17.7000; 509 t[i++] = 2.5000; 510 y[i] = 24.5600; 511 t[i++] = 2.0000; 512 y[i] = 18.6700; 513 t[i++] = 2.5000; 514 y[i] = 16.2400; 515 t[i++] = 3.0000; 516 y[i] = 8.7400; 517 t[i++] = 4.0000; 518 y[i] = 7.8700; 519 t[i++] = 5.0000; 520 y[i] = 8.5100; 521 t[i++] = 6.0000; 522 y[i] = 66.7000; 523 t[i++] = .5000; 524 y[i] = 59.2000; 525 t[i++] = .7500; 526 y[i] = 40.8000; 527 t[i++] = 1.0000; 528 y[i] = 30.7000; 529 t[i++] = 1.5000; 530 y[i] = 25.7000; 531 t[i++] = 2.0000; 532 y[i] = 16.3000; 533 t[i++] = 2.5000; 534 y[i] = 25.9900; 535 t[i++] = 2.0000; 536 y[i] = 16.9500; 537 t[i++] = 2.5000; 538 y[i] = 13.3500; 539 t[i++] = 3.0000; 540 y[i] = 8.6200; 541 t[i++] = 4.0000; 542 y[i] = 7.2000; 543 t[i++] = 5.0000; 544 y[i] = 6.6400; 545 t[i++] = 6.0000; 546 y[i] = 13.6900; 547 t[i++] = 3.0000; 548 y[i] = 81.0000; 549 t[i++] = .5000; 550 y[i] = 64.5000; 551 t[i++] = .7500; 552 y[i] = 35.5000; 553 t[i++] = 1.5000; 554 y[i] = 13.3100; 555 t[i++] = 3.0000; 556 y[i] = 4.8700; 557 t[i++] = 6.0000; 558 y[i] = 12.9400; 559 t[i++] = 3.0000; 560 y[i] = 5.0600; 561 t[i++] = 6.0000; 562 y[i] = 15.1900; 563 t[i++] = 3.0000; 564 y[i] = 14.6200; 565 t[i++] = 3.0000; 566 y[i] = 15.6400; 567 t[i++] = 3.0000; 568 y[i] = 25.5000; 569 t[i++] = 1.7500; 570 y[i] = 25.9500; 571 t[i++] = 1.7500; 572 y[i] = 81.7000; 573 t[i++] = .5000; 574 y[i] = 61.6000; 575 t[i++] = .7500; 576 y[i] = 29.8000; 577 t[i++] = 1.7500; 578 y[i] = 29.8100; 579 t[i++] = 1.7500; 580 y[i] = 17.1700; 581 t[i++] = 2.7500; 582 y[i] = 10.3900; 583 t[i++] = 3.7500; 584 y[i] = 28.4000; 585 t[i++] = 1.7500; 586 y[i] = 28.6900; 587 t[i++] = 1.7500; 588 y[i] = 81.3000; 589 t[i++] = .5000; 590 y[i] = 60.9000; 591 t[i++] = .7500; 592 y[i] = 16.6500; 593 t[i++] = 2.7500; 594 y[i] = 10.0500; 595 t[i++] = 3.7500; 596 y[i] = 28.9000; 597 t[i++] = 1.7500; 598 y[i] = 28.9500; 599 t[i++] = 1.7500; 600 PetscFunctionReturn(PETSC_SUCCESS); 601 } 602 603 /*TEST 604 605 build: 606 requires: !complex !single 607 608 test: 609 args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5 610 611 test: 612 suffix: 2 613 args: -tao_monitor_short -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-4 -tao_gatol 1.e-5 614 615 test: 616 suffix: 3 617 args: -tao_monitor_short -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-4 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-5 618 619 test: 620 suffix: 4 621 args: -tao_monitor_short -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_type bnls 622 623 TEST*/ 624