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++) { 115 f[i] = y[i] - PetscExpScalar(-x[0]*t[i])/(x[1] + x[2]*t[i]); 116 } 117 PetscCall(VecRestoreArrayRead(X,&x)); 118 PetscCall(VecRestoreArray(F,&f)); 119 PetscLogFlops(6*NOBSERVATIONS); 120 PetscFunctionReturn(0); 121 } 122 123 /*------------------------------------------------------------*/ 124 /* J[i][j] = df[i]/dt[j] */ 125 PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr) 126 { 127 AppCtx *user = (AppCtx *)ptr; 128 PetscInt i; 129 const PetscReal *x; 130 PetscReal *t=user->t; 131 PetscReal base; 132 133 PetscFunctionBegin; 134 PetscCall(VecGetArrayRead(X,&x)); 135 for (i=0;i<NOBSERVATIONS;i++) { 136 base = PetscExpScalar(-x[0]*t[i])/(x[1] + x[2]*t[i]); 137 138 user->j[i][0] = t[i]*base; 139 user->j[i][1] = base/(x[1] + x[2]*t[i]); 140 user->j[i][2] = base*t[i]/(x[1] + x[2]*t[i]); 141 } 142 143 /* Assemble the matrix */ 144 PetscCall(MatSetValues(J,NOBSERVATIONS,user->idm, NPARAMETERS, user->idn,(PetscReal *)user->j,INSERT_VALUES)); 145 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 146 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 147 148 PetscCall(VecRestoreArrayRead(X,&x)); 149 PetscLogFlops(NOBSERVATIONS * 13); 150 PetscFunctionReturn(0); 151 } 152 153 /* ------------------------------------------------------------ */ 154 PetscErrorCode FormStartingPoint(Vec X) 155 { 156 PetscReal *x; 157 158 PetscFunctionBegin; 159 PetscCall(VecGetArray(X,&x)); 160 x[0] = 0.15; 161 x[1] = 0.008; 162 x[2] = 0.010; 163 PetscCall(VecRestoreArray(X,&x)); 164 PetscFunctionReturn(0); 165 } 166 167 /* ---------------------------------------------------------------------- */ 168 PetscErrorCode InitializeData(AppCtx *user) 169 { 170 PetscReal *t=user->t,*y=user->y; 171 PetscInt i=0; 172 173 PetscFunctionBegin; 174 y[i] = 92.9000; t[i++] = 0.5000; 175 y[i] = 78.7000; t[i++] = 0.6250; 176 y[i] = 64.2000; t[i++] = 0.7500; 177 y[i] = 64.9000; t[i++] = 0.8750; 178 y[i] = 57.1000; t[i++] = 1.0000; 179 y[i] = 43.3000; t[i++] = 1.2500; 180 y[i] = 31.1000; t[i++] = 1.7500; 181 y[i] = 23.6000; t[i++] = 2.2500; 182 y[i] = 31.0500; t[i++] = 1.7500; 183 y[i] = 23.7750; t[i++] = 2.2500; 184 y[i] = 17.7375; t[i++] = 2.7500; 185 y[i] = 13.8000; t[i++] = 3.2500; 186 y[i] = 11.5875; t[i++] = 3.7500; 187 y[i] = 9.4125; t[i++] = 4.2500; 188 y[i] = 7.7250; t[i++] = 4.7500; 189 y[i] = 7.3500; t[i++] = 5.2500; 190 y[i] = 8.0250; t[i++] = 5.7500; 191 y[i] = 90.6000; t[i++] = 0.5000; 192 y[i] = 76.9000; t[i++] = 0.6250; 193 y[i] = 71.6000; t[i++] = 0.7500; 194 y[i] = 63.6000; t[i++] = 0.8750; 195 y[i] = 54.0000; t[i++] = 1.0000; 196 y[i] = 39.2000; t[i++] = 1.2500; 197 y[i] = 29.3000; t[i++] = 1.7500; 198 y[i] = 21.4000; t[i++] = 2.2500; 199 y[i] = 29.1750; t[i++] = 1.7500; 200 y[i] = 22.1250; t[i++] = 2.2500; 201 y[i] = 17.5125; t[i++] = 2.7500; 202 y[i] = 14.2500; t[i++] = 3.2500; 203 y[i] = 9.4500; t[i++] = 3.7500; 204 y[i] = 9.1500; t[i++] = 4.2500; 205 y[i] = 7.9125; t[i++] = 4.7500; 206 y[i] = 8.4750; t[i++] = 5.2500; 207 y[i] = 6.1125; t[i++] = 5.7500; 208 y[i] = 80.0000; t[i++] = 0.5000; 209 y[i] = 79.0000; t[i++] = 0.6250; 210 y[i] = 63.8000; t[i++] = 0.7500; 211 y[i] = 57.2000; t[i++] = 0.8750; 212 y[i] = 53.2000; t[i++] = 1.0000; 213 y[i] = 42.5000; t[i++] = 1.2500; 214 y[i] = 26.8000; t[i++] = 1.7500; 215 y[i] = 20.4000; t[i++] = 2.2500; 216 y[i] = 26.8500; t[i++] = 1.7500; 217 y[i] = 21.0000; t[i++] = 2.2500; 218 y[i] = 16.4625; t[i++] = 2.7500; 219 y[i] = 12.5250; t[i++] = 3.2500; 220 y[i] = 10.5375; t[i++] = 3.7500; 221 y[i] = 8.5875; t[i++] = 4.2500; 222 y[i] = 7.1250; t[i++] = 4.7500; 223 y[i] = 6.1125; t[i++] = 5.2500; 224 y[i] = 5.9625; t[i++] = 5.7500; 225 y[i] = 74.1000; t[i++] = 0.5000; 226 y[i] = 67.3000; t[i++] = 0.6250; 227 y[i] = 60.8000; t[i++] = 0.7500; 228 y[i] = 55.5000; t[i++] = 0.8750; 229 y[i] = 50.3000; t[i++] = 1.0000; 230 y[i] = 41.0000; t[i++] = 1.2500; 231 y[i] = 29.4000; t[i++] = 1.7500; 232 y[i] = 20.4000; t[i++] = 2.2500; 233 y[i] = 29.3625; t[i++] = 1.7500; 234 y[i] = 21.1500; t[i++] = 2.2500; 235 y[i] = 16.7625; t[i++] = 2.7500; 236 y[i] = 13.2000; t[i++] = 3.2500; 237 y[i] = 10.8750; t[i++] = 3.7500; 238 y[i] = 8.1750; t[i++] = 4.2500; 239 y[i] = 7.3500; t[i++] = 4.7500; 240 y[i] = 5.9625; t[i++] = 5.2500; 241 y[i] = 5.6250; t[i++] = 5.7500; 242 y[i] = 81.5000; t[i++] = .5000; 243 y[i] = 62.4000; t[i++] = .7500; 244 y[i] = 32.5000; t[i++] = 1.5000; 245 y[i] = 12.4100; t[i++] = 3.0000; 246 y[i] = 13.1200; t[i++] = 3.0000; 247 y[i] = 15.5600; t[i++] = 3.0000; 248 y[i] = 5.6300; t[i++] = 6.0000; 249 y[i] = 78.0000; t[i++] = .5000; 250 y[i] = 59.9000; t[i++] = .7500; 251 y[i] = 33.2000; t[i++] = 1.5000; 252 y[i] = 13.8400; t[i++] = 3.0000; 253 y[i] = 12.7500; t[i++] = 3.0000; 254 y[i] = 14.6200; t[i++] = 3.0000; 255 y[i] = 3.9400; t[i++] = 6.0000; 256 y[i] = 76.8000; t[i++] = .5000; 257 y[i] = 61.0000; t[i++] = .7500; 258 y[i] = 32.9000; t[i++] = 1.5000; 259 y[i] = 13.8700; t[i++] = 3.0000; 260 y[i] = 11.8100; t[i++] = 3.0000; 261 y[i] = 13.3100; t[i++] = 3.0000; 262 y[i] = 5.4400; t[i++] = 6.0000; 263 y[i] = 78.0000; t[i++] = .5000; 264 y[i] = 63.5000; t[i++] = .7500; 265 y[i] = 33.8000; t[i++] = 1.5000; 266 y[i] = 12.5600; t[i++] = 3.0000; 267 y[i] = 5.6300; t[i++] = 6.0000; 268 y[i] = 12.7500; t[i++] = 3.0000; 269 y[i] = 13.1200; t[i++] = 3.0000; 270 y[i] = 5.4400; t[i++] = 6.0000; 271 y[i] = 76.8000; t[i++] = .5000; 272 y[i] = 60.0000; t[i++] = .7500; 273 y[i] = 47.8000; t[i++] = 1.0000; 274 y[i] = 32.0000; t[i++] = 1.5000; 275 y[i] = 22.2000; t[i++] = 2.0000; 276 y[i] = 22.5700; t[i++] = 2.0000; 277 y[i] = 18.8200; t[i++] = 2.5000; 278 y[i] = 13.9500; t[i++] = 3.0000; 279 y[i] = 11.2500; t[i++] = 4.0000; 280 y[i] = 9.0000; t[i++] = 5.0000; 281 y[i] = 6.6700; t[i++] = 6.0000; 282 y[i] = 75.8000; t[i++] = .5000; 283 y[i] = 62.0000; t[i++] = .7500; 284 y[i] = 48.8000; t[i++] = 1.0000; 285 y[i] = 35.2000; t[i++] = 1.5000; 286 y[i] = 20.0000; t[i++] = 2.0000; 287 y[i] = 20.3200; t[i++] = 2.0000; 288 y[i] = 19.3100; t[i++] = 2.5000; 289 y[i] = 12.7500; t[i++] = 3.0000; 290 y[i] = 10.4200; t[i++] = 4.0000; 291 y[i] = 7.3100; t[i++] = 5.0000; 292 y[i] = 7.4200; t[i++] = 6.0000; 293 y[i] = 70.5000; t[i++] = .5000; 294 y[i] = 59.5000; t[i++] = .7500; 295 y[i] = 48.5000; t[i++] = 1.0000; 296 y[i] = 35.8000; t[i++] = 1.5000; 297 y[i] = 21.0000; t[i++] = 2.0000; 298 y[i] = 21.6700; t[i++] = 2.0000; 299 y[i] = 21.0000; t[i++] = 2.5000; 300 y[i] = 15.6400; t[i++] = 3.0000; 301 y[i] = 8.1700; t[i++] = 4.0000; 302 y[i] = 8.5500; t[i++] = 5.0000; 303 y[i] = 10.1200; t[i++] = 6.0000; 304 y[i] = 78.0000; t[i++] = .5000; 305 y[i] = 66.0000; t[i++] = .6250; 306 y[i] = 62.0000; t[i++] = .7500; 307 y[i] = 58.0000; t[i++] = .8750; 308 y[i] = 47.7000; t[i++] = 1.0000; 309 y[i] = 37.8000; t[i++] = 1.2500; 310 y[i] = 20.2000; t[i++] = 2.2500; 311 y[i] = 21.0700; t[i++] = 2.2500; 312 y[i] = 13.8700; t[i++] = 2.7500; 313 y[i] = 9.6700; t[i++] = 3.2500; 314 y[i] = 7.7600; t[i++] = 3.7500; 315 y[i] = 5.4400; t[i++] = 4.2500; 316 y[i] = 4.8700; t[i++] = 4.7500; 317 y[i] = 4.0100; t[i++] = 5.2500; 318 y[i] = 3.7500; t[i++] = 5.7500; 319 y[i] = 24.1900; t[i++] = 3.0000; 320 y[i] = 25.7600; t[i++] = 3.0000; 321 y[i] = 18.0700; t[i++] = 3.0000; 322 y[i] = 11.8100; t[i++] = 3.0000; 323 y[i] = 12.0700; t[i++] = 3.0000; 324 y[i] = 16.1200; t[i++] = 3.0000; 325 y[i] = 70.8000; t[i++] = .5000; 326 y[i] = 54.7000; t[i++] = .7500; 327 y[i] = 48.0000; t[i++] = 1.0000; 328 y[i] = 39.8000; t[i++] = 1.5000; 329 y[i] = 29.8000; t[i++] = 2.0000; 330 y[i] = 23.7000; t[i++] = 2.5000; 331 y[i] = 29.6200; t[i++] = 2.0000; 332 y[i] = 23.8100; t[i++] = 2.5000; 333 y[i] = 17.7000; t[i++] = 3.0000; 334 y[i] = 11.5500; t[i++] = 4.0000; 335 y[i] = 12.0700; t[i++] = 5.0000; 336 y[i] = 8.7400; t[i++] = 6.0000; 337 y[i] = 80.7000; t[i++] = .5000; 338 y[i] = 61.3000; t[i++] = .7500; 339 y[i] = 47.5000; t[i++] = 1.0000; 340 y[i] = 29.0000; t[i++] = 1.5000; 341 y[i] = 24.0000; t[i++] = 2.0000; 342 y[i] = 17.7000; t[i++] = 2.5000; 343 y[i] = 24.5600; t[i++] = 2.0000; 344 y[i] = 18.6700; t[i++] = 2.5000; 345 y[i] = 16.2400; t[i++] = 3.0000; 346 y[i] = 8.7400; t[i++] = 4.0000; 347 y[i] = 7.8700; t[i++] = 5.0000; 348 y[i] = 8.5100; t[i++] = 6.0000; 349 y[i] = 66.7000; t[i++] = .5000; 350 y[i] = 59.2000; t[i++] = .7500; 351 y[i] = 40.8000; t[i++] = 1.0000; 352 y[i] = 30.7000; t[i++] = 1.5000; 353 y[i] = 25.7000; t[i++] = 2.0000; 354 y[i] = 16.3000; t[i++] = 2.5000; 355 y[i] = 25.9900; t[i++] = 2.0000; 356 y[i] = 16.9500; t[i++] = 2.5000; 357 y[i] = 13.3500; t[i++] = 3.0000; 358 y[i] = 8.6200; t[i++] = 4.0000; 359 y[i] = 7.2000; t[i++] = 5.0000; 360 y[i] = 6.6400; t[i++] = 6.0000; 361 y[i] = 13.6900; t[i++] = 3.0000; 362 y[i] = 81.0000; t[i++] = .5000; 363 y[i] = 64.5000; t[i++] = .7500; 364 y[i] = 35.5000; t[i++] = 1.5000; 365 y[i] = 13.3100; t[i++] = 3.0000; 366 y[i] = 4.8700; t[i++] = 6.0000; 367 y[i] = 12.9400; t[i++] = 3.0000; 368 y[i] = 5.0600; t[i++] = 6.0000; 369 y[i] = 15.1900; t[i++] = 3.0000; 370 y[i] = 14.6200; t[i++] = 3.0000; 371 y[i] = 15.6400; t[i++] = 3.0000; 372 y[i] = 25.5000; t[i++] = 1.7500; 373 y[i] = 25.9500; t[i++] = 1.7500; 374 y[i] = 81.7000; t[i++] = .5000; 375 y[i] = 61.6000; t[i++] = .7500; 376 y[i] = 29.8000; t[i++] = 1.7500; 377 y[i] = 29.8100; t[i++] = 1.7500; 378 y[i] = 17.1700; t[i++] = 2.7500; 379 y[i] = 10.3900; t[i++] = 3.7500; 380 y[i] = 28.4000; t[i++] = 1.7500; 381 y[i] = 28.6900; t[i++] = 1.7500; 382 y[i] = 81.3000; t[i++] = .5000; 383 y[i] = 60.9000; t[i++] = .7500; 384 y[i] = 16.6500; t[i++] = 2.7500; 385 y[i] = 10.0500; t[i++] = 3.7500; 386 y[i] = 28.9000; t[i++] = 1.7500; 387 y[i] = 28.9500; t[i++] = 1.7500; 388 PetscFunctionReturn(0); 389 } 390 391 /*TEST 392 393 build: 394 requires: !complex !single 395 396 test: 397 args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5 398 399 test: 400 suffix: 2 401 args: -tao_smonitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-4 -tao_gatol 1.e-5 402 403 test: 404 suffix: 3 405 args: -tao_smonitor -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-5 406 407 test: 408 suffix: 4 409 args: -tao_smonitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_type bnls 410 411 TEST*/ 412