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 /*T 27 Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares 28 Routines: TaoCreate(); 29 Routines: TaoSetType(); 30 Routines: TaoSetSeparableObjectiveRoutine(); 31 Routines: TaoSetJacobianRoutine(); 32 Routines: TaoSetInitialVector(); 33 Routines: TaoSetFromOptions(); 34 Routines: TaoSetConvergenceHistory(); TaoGetConvergenceHistory(); 35 Routines: TaoSolve(); 36 Routines: TaoView(); TaoDestroy(); 37 Processors: 1 38 T*/ 39 40 #define NOBSERVATIONS 214 41 #define NPARAMETERS 3 42 43 /* User-defined application context */ 44 typedef struct { 45 /* Working space */ 46 PetscReal t[NOBSERVATIONS]; /* array of independent variables of observation */ 47 PetscReal y[NOBSERVATIONS]; /* array of dependent variables */ 48 PetscReal j[NOBSERVATIONS][NPARAMETERS]; /* dense jacobian matrix array*/ 49 PetscInt idm[NOBSERVATIONS]; /* Matrix indices for jacobian */ 50 PetscInt idn[NPARAMETERS]; 51 } AppCtx; 52 53 /* User provided Routines */ 54 PetscErrorCode InitializeData(AppCtx *user); 55 PetscErrorCode FormStartingPoint(Vec); 56 PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *); 57 PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *); 58 59 /*--------------------------------------------------------------------*/ 60 int main(int argc,char **argv) 61 { 62 PetscErrorCode ierr; /* used to check for functions returning nonzeros */ 63 Vec x, f; /* solution, function */ 64 Mat J; /* Jacobian matrix */ 65 Tao tao; /* Tao solver context */ 66 PetscInt i; /* iteration information */ 67 PetscReal hist[100],resid[100]; 68 PetscInt lits[100]; 69 AppCtx user; /* user-defined work context */ 70 71 ierr = PetscInitialize(&argc,&argv,(char *)0,help);if (ierr) return ierr; 72 /* Allocate vectors */ 73 ierr = VecCreateSeq(MPI_COMM_SELF,NPARAMETERS,&x);CHKERRQ(ierr); 74 ierr = VecCreateSeq(MPI_COMM_SELF,NOBSERVATIONS,&f);CHKERRQ(ierr); 75 76 /* Create the Jacobian matrix. */ 77 ierr = MatCreateSeqDense(MPI_COMM_SELF,NOBSERVATIONS,NPARAMETERS,NULL,&J);CHKERRQ(ierr); 78 79 for (i=0;i<NOBSERVATIONS;i++) user.idm[i] = i; 80 81 for (i=0;i<NPARAMETERS;i++) user.idn[i] = i; 82 83 /* Create TAO solver and set desired solution method */ 84 ierr = TaoCreate(PETSC_COMM_SELF,&tao);CHKERRQ(ierr); 85 ierr = TaoSetType(tao,TAOPOUNDERS);CHKERRQ(ierr); 86 87 /* Set the function and Jacobian routines. */ 88 ierr = InitializeData(&user);CHKERRQ(ierr); 89 ierr = FormStartingPoint(x);CHKERRQ(ierr); 90 ierr = TaoSetInitialVector(tao,x);CHKERRQ(ierr); 91 ierr = TaoSetResidualRoutine(tao,f,EvaluateFunction,(void*)&user);CHKERRQ(ierr); 92 ierr = TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void*)&user);CHKERRQ(ierr); 93 94 /* Check for any TAO command line arguments */ 95 ierr = TaoSetFromOptions(tao);CHKERRQ(ierr); 96 97 ierr = TaoSetConvergenceHistory(tao,hist,resid,0,lits,100,PETSC_TRUE);CHKERRQ(ierr); 98 /* Perform the Solve */ 99 ierr = TaoSolve(tao);CHKERRQ(ierr); 100 101 /* View the vector; then destroy it. */ 102 ierr = VecView(x,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 103 104 /* Free TAO data structures */ 105 ierr = TaoDestroy(&tao);CHKERRQ(ierr); 106 107 /* Free PETSc data structures */ 108 ierr = VecDestroy(&x);CHKERRQ(ierr); 109 ierr = VecDestroy(&f);CHKERRQ(ierr); 110 ierr = MatDestroy(&J);CHKERRQ(ierr); 111 112 ierr = PetscFinalize(); 113 return ierr; 114 } 115 116 /*--------------------------------------------------------------------*/ 117 PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr) 118 { 119 AppCtx *user = (AppCtx *)ptr; 120 PetscInt i; 121 const PetscReal *x; 122 PetscReal *y=user->y,*f,*t=user->t; 123 PetscErrorCode ierr; 124 125 PetscFunctionBegin; 126 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); 127 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 128 129 for (i=0;i<NOBSERVATIONS;i++) { 130 f[i] = y[i] - PetscExpScalar(-x[0]*t[i])/(x[1] + x[2]*t[i]); 131 } 132 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr); 133 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 134 PetscLogFlops(6*NOBSERVATIONS); 135 PetscFunctionReturn(0); 136 } 137 138 /*------------------------------------------------------------*/ 139 /* J[i][j] = df[i]/dt[j] */ 140 PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr) 141 { 142 AppCtx *user = (AppCtx *)ptr; 143 PetscInt i; 144 const PetscReal *x; 145 PetscReal *t=user->t; 146 PetscReal base; 147 PetscErrorCode ierr; 148 149 PetscFunctionBegin; 150 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); 151 for (i=0;i<NOBSERVATIONS;i++) { 152 base = PetscExpScalar(-x[0]*t[i])/(x[1] + x[2]*t[i]); 153 154 user->j[i][0] = t[i]*base; 155 user->j[i][1] = base/(x[1] + x[2]*t[i]); 156 user->j[i][2] = base*t[i]/(x[1] + x[2]*t[i]); 157 } 158 159 /* Assemble the matrix */ 160 ierr = MatSetValues(J,NOBSERVATIONS,user->idm, NPARAMETERS, user->idn,(PetscReal *)user->j,INSERT_VALUES);CHKERRQ(ierr); 161 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 162 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 163 164 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr); 165 PetscLogFlops(NOBSERVATIONS * 13); 166 PetscFunctionReturn(0); 167 } 168 169 /* ------------------------------------------------------------ */ 170 PetscErrorCode FormStartingPoint(Vec X) 171 { 172 PetscReal *x; 173 PetscErrorCode ierr; 174 175 PetscFunctionBegin; 176 ierr = VecGetArray(X,&x);CHKERRQ(ierr); 177 x[0] = 0.15; 178 x[1] = 0.008; 179 x[2] = 0.010; 180 ierr = VecRestoreArray(X,&x);CHKERRQ(ierr); 181 PetscFunctionReturn(0); 182 } 183 184 /* ---------------------------------------------------------------------- */ 185 PetscErrorCode InitializeData(AppCtx *user) 186 { 187 PetscReal *t=user->t,*y=user->y; 188 PetscInt i=0; 189 190 PetscFunctionBegin; 191 y[i] = 92.9000; t[i++] = 0.5000; 192 y[i] = 78.7000; t[i++] = 0.6250; 193 y[i] = 64.2000; t[i++] = 0.7500; 194 y[i] = 64.9000; t[i++] = 0.8750; 195 y[i] = 57.1000; t[i++] = 1.0000; 196 y[i] = 43.3000; t[i++] = 1.2500; 197 y[i] = 31.1000; t[i++] = 1.7500; 198 y[i] = 23.6000; t[i++] = 2.2500; 199 y[i] = 31.0500; t[i++] = 1.7500; 200 y[i] = 23.7750; t[i++] = 2.2500; 201 y[i] = 17.7375; t[i++] = 2.7500; 202 y[i] = 13.8000; t[i++] = 3.2500; 203 y[i] = 11.5875; t[i++] = 3.7500; 204 y[i] = 9.4125; t[i++] = 4.2500; 205 y[i] = 7.7250; t[i++] = 4.7500; 206 y[i] = 7.3500; t[i++] = 5.2500; 207 y[i] = 8.0250; t[i++] = 5.7500; 208 y[i] = 90.6000; t[i++] = 0.5000; 209 y[i] = 76.9000; t[i++] = 0.6250; 210 y[i] = 71.6000; t[i++] = 0.7500; 211 y[i] = 63.6000; t[i++] = 0.8750; 212 y[i] = 54.0000; t[i++] = 1.0000; 213 y[i] = 39.2000; t[i++] = 1.2500; 214 y[i] = 29.3000; t[i++] = 1.7500; 215 y[i] = 21.4000; t[i++] = 2.2500; 216 y[i] = 29.1750; t[i++] = 1.7500; 217 y[i] = 22.1250; t[i++] = 2.2500; 218 y[i] = 17.5125; t[i++] = 2.7500; 219 y[i] = 14.2500; t[i++] = 3.2500; 220 y[i] = 9.4500; t[i++] = 3.7500; 221 y[i] = 9.1500; t[i++] = 4.2500; 222 y[i] = 7.9125; t[i++] = 4.7500; 223 y[i] = 8.4750; t[i++] = 5.2500; 224 y[i] = 6.1125; t[i++] = 5.7500; 225 y[i] = 80.0000; t[i++] = 0.5000; 226 y[i] = 79.0000; t[i++] = 0.6250; 227 y[i] = 63.8000; t[i++] = 0.7500; 228 y[i] = 57.2000; t[i++] = 0.8750; 229 y[i] = 53.2000; t[i++] = 1.0000; 230 y[i] = 42.5000; t[i++] = 1.2500; 231 y[i] = 26.8000; t[i++] = 1.7500; 232 y[i] = 20.4000; t[i++] = 2.2500; 233 y[i] = 26.8500; t[i++] = 1.7500; 234 y[i] = 21.0000; t[i++] = 2.2500; 235 y[i] = 16.4625; t[i++] = 2.7500; 236 y[i] = 12.5250; t[i++] = 3.2500; 237 y[i] = 10.5375; t[i++] = 3.7500; 238 y[i] = 8.5875; t[i++] = 4.2500; 239 y[i] = 7.1250; t[i++] = 4.7500; 240 y[i] = 6.1125; t[i++] = 5.2500; 241 y[i] = 5.9625; t[i++] = 5.7500; 242 y[i] = 74.1000; t[i++] = 0.5000; 243 y[i] = 67.3000; t[i++] = 0.6250; 244 y[i] = 60.8000; t[i++] = 0.7500; 245 y[i] = 55.5000; t[i++] = 0.8750; 246 y[i] = 50.3000; t[i++] = 1.0000; 247 y[i] = 41.0000; t[i++] = 1.2500; 248 y[i] = 29.4000; t[i++] = 1.7500; 249 y[i] = 20.4000; t[i++] = 2.2500; 250 y[i] = 29.3625; t[i++] = 1.7500; 251 y[i] = 21.1500; t[i++] = 2.2500; 252 y[i] = 16.7625; t[i++] = 2.7500; 253 y[i] = 13.2000; t[i++] = 3.2500; 254 y[i] = 10.8750; t[i++] = 3.7500; 255 y[i] = 8.1750; t[i++] = 4.2500; 256 y[i] = 7.3500; t[i++] = 4.7500; 257 y[i] = 5.9625; t[i++] = 5.2500; 258 y[i] = 5.6250; t[i++] = 5.7500; 259 y[i] = 81.5000; t[i++] = .5000; 260 y[i] = 62.4000; t[i++] = .7500; 261 y[i] = 32.5000; t[i++] = 1.5000; 262 y[i] = 12.4100; t[i++] = 3.0000; 263 y[i] = 13.1200; t[i++] = 3.0000; 264 y[i] = 15.5600; t[i++] = 3.0000; 265 y[i] = 5.6300; t[i++] = 6.0000; 266 y[i] = 78.0000; t[i++] = .5000; 267 y[i] = 59.9000; t[i++] = .7500; 268 y[i] = 33.2000; t[i++] = 1.5000; 269 y[i] = 13.8400; t[i++] = 3.0000; 270 y[i] = 12.7500; t[i++] = 3.0000; 271 y[i] = 14.6200; t[i++] = 3.0000; 272 y[i] = 3.9400; t[i++] = 6.0000; 273 y[i] = 76.8000; t[i++] = .5000; 274 y[i] = 61.0000; t[i++] = .7500; 275 y[i] = 32.9000; t[i++] = 1.5000; 276 y[i] = 13.8700; t[i++] = 3.0000; 277 y[i] = 11.8100; t[i++] = 3.0000; 278 y[i] = 13.3100; t[i++] = 3.0000; 279 y[i] = 5.4400; t[i++] = 6.0000; 280 y[i] = 78.0000; t[i++] = .5000; 281 y[i] = 63.5000; t[i++] = .7500; 282 y[i] = 33.8000; t[i++] = 1.5000; 283 y[i] = 12.5600; t[i++] = 3.0000; 284 y[i] = 5.6300; t[i++] = 6.0000; 285 y[i] = 12.7500; t[i++] = 3.0000; 286 y[i] = 13.1200; t[i++] = 3.0000; 287 y[i] = 5.4400; t[i++] = 6.0000; 288 y[i] = 76.8000; t[i++] = .5000; 289 y[i] = 60.0000; t[i++] = .7500; 290 y[i] = 47.8000; t[i++] = 1.0000; 291 y[i] = 32.0000; t[i++] = 1.5000; 292 y[i] = 22.2000; t[i++] = 2.0000; 293 y[i] = 22.5700; t[i++] = 2.0000; 294 y[i] = 18.8200; t[i++] = 2.5000; 295 y[i] = 13.9500; t[i++] = 3.0000; 296 y[i] = 11.2500; t[i++] = 4.0000; 297 y[i] = 9.0000; t[i++] = 5.0000; 298 y[i] = 6.6700; t[i++] = 6.0000; 299 y[i] = 75.8000; t[i++] = .5000; 300 y[i] = 62.0000; t[i++] = .7500; 301 y[i] = 48.8000; t[i++] = 1.0000; 302 y[i] = 35.2000; t[i++] = 1.5000; 303 y[i] = 20.0000; t[i++] = 2.0000; 304 y[i] = 20.3200; t[i++] = 2.0000; 305 y[i] = 19.3100; t[i++] = 2.5000; 306 y[i] = 12.7500; t[i++] = 3.0000; 307 y[i] = 10.4200; t[i++] = 4.0000; 308 y[i] = 7.3100; t[i++] = 5.0000; 309 y[i] = 7.4200; t[i++] = 6.0000; 310 y[i] = 70.5000; t[i++] = .5000; 311 y[i] = 59.5000; t[i++] = .7500; 312 y[i] = 48.5000; t[i++] = 1.0000; 313 y[i] = 35.8000; t[i++] = 1.5000; 314 y[i] = 21.0000; t[i++] = 2.0000; 315 y[i] = 21.6700; t[i++] = 2.0000; 316 y[i] = 21.0000; t[i++] = 2.5000; 317 y[i] = 15.6400; t[i++] = 3.0000; 318 y[i] = 8.1700; t[i++] = 4.0000; 319 y[i] = 8.5500; t[i++] = 5.0000; 320 y[i] = 10.1200; t[i++] = 6.0000; 321 y[i] = 78.0000; t[i++] = .5000; 322 y[i] = 66.0000; t[i++] = .6250; 323 y[i] = 62.0000; t[i++] = .7500; 324 y[i] = 58.0000; t[i++] = .8750; 325 y[i] = 47.7000; t[i++] = 1.0000; 326 y[i] = 37.8000; t[i++] = 1.2500; 327 y[i] = 20.2000; t[i++] = 2.2500; 328 y[i] = 21.0700; t[i++] = 2.2500; 329 y[i] = 13.8700; t[i++] = 2.7500; 330 y[i] = 9.6700; t[i++] = 3.2500; 331 y[i] = 7.7600; t[i++] = 3.7500; 332 y[i] = 5.4400; t[i++] = 4.2500; 333 y[i] = 4.8700; t[i++] = 4.7500; 334 y[i] = 4.0100; t[i++] = 5.2500; 335 y[i] = 3.7500; t[i++] = 5.7500; 336 y[i] = 24.1900; t[i++] = 3.0000; 337 y[i] = 25.7600; t[i++] = 3.0000; 338 y[i] = 18.0700; t[i++] = 3.0000; 339 y[i] = 11.8100; t[i++] = 3.0000; 340 y[i] = 12.0700; t[i++] = 3.0000; 341 y[i] = 16.1200; t[i++] = 3.0000; 342 y[i] = 70.8000; t[i++] = .5000; 343 y[i] = 54.7000; t[i++] = .7500; 344 y[i] = 48.0000; t[i++] = 1.0000; 345 y[i] = 39.8000; t[i++] = 1.5000; 346 y[i] = 29.8000; t[i++] = 2.0000; 347 y[i] = 23.7000; t[i++] = 2.5000; 348 y[i] = 29.6200; t[i++] = 2.0000; 349 y[i] = 23.8100; t[i++] = 2.5000; 350 y[i] = 17.7000; t[i++] = 3.0000; 351 y[i] = 11.5500; t[i++] = 4.0000; 352 y[i] = 12.0700; t[i++] = 5.0000; 353 y[i] = 8.7400; t[i++] = 6.0000; 354 y[i] = 80.7000; t[i++] = .5000; 355 y[i] = 61.3000; t[i++] = .7500; 356 y[i] = 47.5000; t[i++] = 1.0000; 357 y[i] = 29.0000; t[i++] = 1.5000; 358 y[i] = 24.0000; t[i++] = 2.0000; 359 y[i] = 17.7000; t[i++] = 2.5000; 360 y[i] = 24.5600; t[i++] = 2.0000; 361 y[i] = 18.6700; t[i++] = 2.5000; 362 y[i] = 16.2400; t[i++] = 3.0000; 363 y[i] = 8.7400; t[i++] = 4.0000; 364 y[i] = 7.8700; t[i++] = 5.0000; 365 y[i] = 8.5100; t[i++] = 6.0000; 366 y[i] = 66.7000; t[i++] = .5000; 367 y[i] = 59.2000; t[i++] = .7500; 368 y[i] = 40.8000; t[i++] = 1.0000; 369 y[i] = 30.7000; t[i++] = 1.5000; 370 y[i] = 25.7000; t[i++] = 2.0000; 371 y[i] = 16.3000; t[i++] = 2.5000; 372 y[i] = 25.9900; t[i++] = 2.0000; 373 y[i] = 16.9500; t[i++] = 2.5000; 374 y[i] = 13.3500; t[i++] = 3.0000; 375 y[i] = 8.6200; t[i++] = 4.0000; 376 y[i] = 7.2000; t[i++] = 5.0000; 377 y[i] = 6.6400; t[i++] = 6.0000; 378 y[i] = 13.6900; t[i++] = 3.0000; 379 y[i] = 81.0000; t[i++] = .5000; 380 y[i] = 64.5000; t[i++] = .7500; 381 y[i] = 35.5000; t[i++] = 1.5000; 382 y[i] = 13.3100; t[i++] = 3.0000; 383 y[i] = 4.8700; t[i++] = 6.0000; 384 y[i] = 12.9400; t[i++] = 3.0000; 385 y[i] = 5.0600; t[i++] = 6.0000; 386 y[i] = 15.1900; t[i++] = 3.0000; 387 y[i] = 14.6200; t[i++] = 3.0000; 388 y[i] = 15.6400; t[i++] = 3.0000; 389 y[i] = 25.5000; t[i++] = 1.7500; 390 y[i] = 25.9500; t[i++] = 1.7500; 391 y[i] = 81.7000; t[i++] = .5000; 392 y[i] = 61.6000; t[i++] = .7500; 393 y[i] = 29.8000; t[i++] = 1.7500; 394 y[i] = 29.8100; t[i++] = 1.7500; 395 y[i] = 17.1700; t[i++] = 2.7500; 396 y[i] = 10.3900; t[i++] = 3.7500; 397 y[i] = 28.4000; t[i++] = 1.7500; 398 y[i] = 28.6900; t[i++] = 1.7500; 399 y[i] = 81.3000; t[i++] = .5000; 400 y[i] = 60.9000; t[i++] = .7500; 401 y[i] = 16.6500; t[i++] = 2.7500; 402 y[i] = 10.0500; t[i++] = 3.7500; 403 y[i] = 28.9000; t[i++] = 1.7500; 404 y[i] = 28.9500; t[i++] = 1.7500; 405 PetscFunctionReturn(0); 406 } 407 408 /*TEST 409 410 build: 411 requires: !complex !single 412 413 test: 414 args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5 415 416 test: 417 suffix: 2 418 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-5 419 420 test: 421 suffix: 3 422 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-5 423 424 test: 425 suffix: 4 426 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 427 428 TEST*/ 429