1 2 #include <../src/snes/impls/ls/lsimpl.h> 3 4 /* 5 Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function, 6 || F(u) ||_2 but not a zero, F(u) = 0. In the case when one cannot compute J^T F we use the fact that 7 0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More 8 for this trick. One assumes that the probability that W is in the null space of J is very, very small. 9 */ 10 #undef __FUNCT__ 11 #define __FUNCT__ "SNESNEWTONLSCheckLocalMin_Private" 12 PetscErrorCode SNESNEWTONLSCheckLocalMin_Private(SNES snes,Mat A,Vec F,Vec W,PetscReal fnorm,PetscBool *ismin) 13 { 14 PetscReal a1; 15 PetscErrorCode ierr; 16 PetscBool hastranspose; 17 18 PetscFunctionBegin; 19 *ismin = PETSC_FALSE; 20 ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr); 21 if (hastranspose) { 22 /* Compute || J^T F|| */ 23 ierr = MatMultTranspose(A,F,W);CHKERRQ(ierr); 24 ierr = VecNorm(W,NORM_2,&a1);CHKERRQ(ierr); 25 ierr = PetscInfo1(snes,"|| J^T F|| %14.12e near zero implies found a local minimum\n",(double)(a1/fnorm));CHKERRQ(ierr); 26 if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE; 27 } else { 28 Vec work; 29 PetscScalar result; 30 PetscReal wnorm; 31 32 ierr = VecSetRandom(W,NULL);CHKERRQ(ierr); 33 ierr = VecNorm(W,NORM_2,&wnorm);CHKERRQ(ierr); 34 ierr = VecDuplicate(W,&work);CHKERRQ(ierr); 35 ierr = MatMult(A,W,work);CHKERRQ(ierr); 36 ierr = VecDot(F,work,&result);CHKERRQ(ierr); 37 ierr = VecDestroy(&work);CHKERRQ(ierr); 38 a1 = PetscAbsScalar(result)/(fnorm*wnorm); 39 ierr = PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %14.12e near zero implies found a local minimum\n",(double)a1);CHKERRQ(ierr); 40 if (a1 < 1.e-4) *ismin = PETSC_TRUE; 41 } 42 PetscFunctionReturn(0); 43 } 44 45 /* 46 Checks if J^T(F - J*X) = 0 47 */ 48 #undef __FUNCT__ 49 #define __FUNCT__ "SNESNEWTONLSCheckResidual_Private" 50 PetscErrorCode SNESNEWTONLSCheckResidual_Private(SNES snes,Mat A,Vec F,Vec X,Vec W1,Vec W2) 51 { 52 PetscReal a1,a2; 53 PetscErrorCode ierr; 54 PetscBool hastranspose; 55 56 PetscFunctionBegin; 57 ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr); 58 if (hastranspose) { 59 ierr = MatMult(A,X,W1);CHKERRQ(ierr); 60 ierr = VecAXPY(W1,-1.0,F);CHKERRQ(ierr); 61 62 /* Compute || J^T W|| */ 63 ierr = MatMultTranspose(A,W1,W2);CHKERRQ(ierr); 64 ierr = VecNorm(W1,NORM_2,&a1);CHKERRQ(ierr); 65 ierr = VecNorm(W2,NORM_2,&a2);CHKERRQ(ierr); 66 if (a1 != 0.0) { 67 ierr = PetscInfo1(snes,"||J^T(F-Ax)||/||F-AX|| %14.12e near zero implies inconsistent rhs\n",(double)(a2/a1));CHKERRQ(ierr); 68 } 69 } 70 PetscFunctionReturn(0); 71 } 72 73 /* -------------------------------------------------------------------- 74 75 This file implements a truncated Newton method with a line search, 76 for solving a system of nonlinear equations, using the KSP, Vec, 77 and Mat interfaces for linear solvers, vectors, and matrices, 78 respectively. 79 80 The following basic routines are required for each nonlinear solver: 81 SNESCreate_XXX() - Creates a nonlinear solver context 82 SNESSetFromOptions_XXX() - Sets runtime options 83 SNESSolve_XXX() - Solves the nonlinear system 84 SNESDestroy_XXX() - Destroys the nonlinear solver context 85 The suffix "_XXX" denotes a particular implementation, in this case 86 we use _NEWTONLS (e.g., SNESCreate_NEWTONLS, SNESSolve_NEWTONLS) for solving 87 systems of nonlinear equations with a line search (LS) method. 88 These routines are actually called via the common user interface 89 routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and 90 SNESDestroy(), so the application code interface remains identical 91 for all nonlinear solvers. 92 93 Another key routine is: 94 SNESSetUp_XXX() - Prepares for the use of a nonlinear solver 95 by setting data structures and options. The interface routine SNESSetUp() 96 is not usually called directly by the user, but instead is called by 97 SNESSolve() if necessary. 98 99 Additional basic routines are: 100 SNESView_XXX() - Prints details of runtime options that 101 have actually been used. 102 These are called by application codes via the interface routines 103 SNESView(). 104 105 The various types of solvers (preconditioners, Krylov subspace methods, 106 nonlinear solvers, timesteppers) are all organized similarly, so the 107 above description applies to these categories also. 108 109 -------------------------------------------------------------------- */ 110 /* 111 SNESSolve_NEWTONLS - Solves a nonlinear system with a truncated Newton 112 method with a line search. 113 114 Input Parameters: 115 . snes - the SNES context 116 117 Output Parameter: 118 . outits - number of iterations until termination 119 120 Application Interface Routine: SNESSolve() 121 122 Notes: 123 This implements essentially a truncated Newton method with a 124 line search. By default a cubic backtracking line search 125 is employed, as described in the text "Numerical Methods for 126 Unconstrained Optimization and Nonlinear Equations" by Dennis 127 and Schnabel. 128 */ 129 #undef __FUNCT__ 130 #define __FUNCT__ "SNESSolve_NEWTONLS" 131 PetscErrorCode SNESSolve_NEWTONLS(SNES snes) 132 { 133 PetscErrorCode ierr; 134 PetscInt maxits,i,lits; 135 PetscBool lssucceed; 136 MatStructure flg = DIFFERENT_NONZERO_PATTERN; 137 PetscReal fnorm,gnorm,xnorm,ynorm; 138 Vec Y,X,F,G,W; 139 KSPConvergedReason kspreason; 140 PetscBool domainerror; 141 SNESLineSearch linesearch; 142 SNESConvergedReason reason; 143 144 PetscFunctionBegin; 145 snes->numFailures = 0; 146 snes->numLinearSolveFailures = 0; 147 snes->reason = SNES_CONVERGED_ITERATING; 148 149 maxits = snes->max_its; /* maximum number of iterations */ 150 X = snes->vec_sol; /* solution vector */ 151 F = snes->vec_func; /* residual vector */ 152 Y = snes->vec_sol_update; /* newton step */ 153 G = snes->work[0]; 154 W = snes->work[1]; 155 156 ierr = PetscObjectAMSTakeAccess((PetscObject)snes);CHKERRQ(ierr); 157 snes->iter = 0; 158 snes->norm = 0.0; 159 ierr = PetscObjectAMSGrantAccess((PetscObject)snes);CHKERRQ(ierr); 160 ierr = SNESGetLineSearch(snes, &linesearch);CHKERRQ(ierr); 161 162 /* compute the preconditioned function first in the case of left preconditioning with preconditioned function */ 163 if (snes->pc && snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_PRECONDITIONED) { 164 ierr = SNESApplyPC(snes,X,PETSC_NULL,PETSC_NULL,F);CHKERRQ(ierr); 165 ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr); 166 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 167 snes->reason = SNES_DIVERGED_INNER; 168 PetscFunctionReturn(0); 169 } 170 171 ierr = VecNormBegin(F,NORM_2,&fnorm);CHKERRQ(ierr); 172 ierr = VecNormEnd(F,NORM_2,&fnorm);CHKERRQ(ierr); 173 } else { 174 if (!snes->vec_func_init_set) { 175 ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr); 176 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 177 if (domainerror) { 178 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 179 PetscFunctionReturn(0); 180 } 181 } else snes->vec_func_init_set = PETSC_FALSE; 182 183 if (!snes->norm_init_set) { 184 ierr = VecNormBegin(F,NORM_2,&fnorm);CHKERRQ(ierr); /* fnorm <- ||F|| */ 185 ierr = VecNormEnd(F,NORM_2,&fnorm);CHKERRQ(ierr); 186 if (PetscIsInfOrNanReal(fnorm)) { 187 snes->reason = SNES_DIVERGED_FNORM_NAN; 188 PetscFunctionReturn(0); 189 } 190 } else { 191 fnorm = snes->norm_init; 192 snes->norm_init_set = PETSC_FALSE; 193 } 194 } 195 196 ierr = PetscObjectAMSTakeAccess((PetscObject)snes);CHKERRQ(ierr); 197 snes->norm = fnorm; 198 ierr = PetscObjectAMSGrantAccess((PetscObject)snes);CHKERRQ(ierr); 199 ierr = SNESLogConvergenceHistory(snes,fnorm,0);CHKERRQ(ierr); 200 ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr); 201 202 /* test convergence */ 203 ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 204 if (snes->reason) PetscFunctionReturn(0); 205 206 for (i=0; i<maxits; i++) { 207 208 /* Call general purpose update function */ 209 if (snes->ops->update) { 210 ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr); 211 } 212 213 /* apply the nonlinear preconditioner */ 214 if (snes->pc) { 215 if (snes->pcside == PC_RIGHT) { 216 ierr = SNESSetInitialFunction(snes->pc, F);CHKERRQ(ierr); 217 ierr = SNESSetInitialFunctionNorm(snes->pc, fnorm);CHKERRQ(ierr); 218 ierr = PetscLogEventBegin(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);CHKERRQ(ierr); 219 ierr = SNESSolve(snes->pc, snes->vec_rhs, X);CHKERRQ(ierr); 220 ierr = PetscLogEventEnd(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);CHKERRQ(ierr); 221 ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr); 222 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 223 snes->reason = SNES_DIVERGED_INNER; 224 PetscFunctionReturn(0); 225 } 226 ierr = SNESGetPCFunction(snes,F,&fnorm);CHKERRQ(ierr); 227 } else if (snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_UNPRECONDITIONED) { 228 ierr = SNESApplyPC(snes,X,F,&fnorm,F);CHKERRQ(ierr); 229 ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr); 230 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 231 snes->reason = SNES_DIVERGED_INNER; 232 PetscFunctionReturn(0); 233 } 234 } 235 } 236 237 /* Solve J Y = F, where J is Jacobian matrix */ 238 ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr); 239 ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr); 240 ierr = KSPSolve(snes->ksp,F,Y);CHKERRQ(ierr); 241 ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr); 242 if (kspreason < 0) { 243 if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) { 244 ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr); 245 snes->reason = SNES_DIVERGED_LINEAR_SOLVE; 246 break; 247 } 248 } 249 ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr); 250 snes->linear_its += lits; 251 ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr); 252 253 if (PetscLogPrintInfo) { 254 ierr = SNESNEWTONLSCheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr); 255 } 256 257 /* Compute a (scaled) negative update in the line search routine: 258 X <- X - lambda*Y 259 and evaluate F = function(X) (depends on the line search). 260 */ 261 gnorm = fnorm; 262 ierr = SNESLineSearchApply(linesearch, X, F, &fnorm, Y);CHKERRQ(ierr); 263 ierr = SNESLineSearchGetSuccess(linesearch, &lssucceed);CHKERRQ(ierr); 264 ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);CHKERRQ(ierr); 265 ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)gnorm,(double)fnorm,(double)ynorm,(int)lssucceed);CHKERRQ(ierr); 266 if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break; 267 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 268 if (domainerror) { 269 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 270 PetscFunctionReturn(0); 271 } 272 if (!lssucceed) { 273 if (snes->stol*xnorm > ynorm) { 274 snes->reason = SNES_CONVERGED_SNORM_RELATIVE; 275 PetscFunctionReturn(0); 276 } 277 if (++snes->numFailures >= snes->maxFailures) { 278 PetscBool ismin; 279 snes->reason = SNES_DIVERGED_LINE_SEARCH; 280 ierr = SNESNEWTONLSCheckLocalMin_Private(snes,snes->jacobian,F,W,fnorm,&ismin);CHKERRQ(ierr); 281 if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN; 282 break; 283 } 284 } 285 /* Monitor convergence */ 286 ierr = PetscObjectAMSTakeAccess((PetscObject)snes);CHKERRQ(ierr); 287 snes->iter = i+1; 288 snes->norm = fnorm; 289 ierr = PetscObjectAMSGrantAccess((PetscObject)snes);CHKERRQ(ierr); 290 ierr = SNESLogConvergenceHistory(snes,snes->norm,lits);CHKERRQ(ierr); 291 ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr); 292 /* Test for convergence */ 293 ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 294 if (snes->reason) break; 295 } 296 if (i == maxits) { 297 ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr); 298 if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT; 299 } 300 PetscFunctionReturn(0); 301 } 302 /* -------------------------------------------------------------------------- */ 303 /* 304 SNESSetUp_NEWTONLS - Sets up the internal data structures for the later use 305 of the SNESNEWTONLS nonlinear solver. 306 307 Input Parameter: 308 . snes - the SNES context 309 . x - the solution vector 310 311 Application Interface Routine: SNESSetUp() 312 313 Notes: 314 For basic use of the SNES solvers, the user need not explicitly call 315 SNESSetUp(), since these actions will automatically occur during 316 the call to SNESSolve(). 317 */ 318 #undef __FUNCT__ 319 #define __FUNCT__ "SNESSetUp_NEWTONLS" 320 PetscErrorCode SNESSetUp_NEWTONLS(SNES snes) 321 { 322 PetscErrorCode ierr; 323 324 PetscFunctionBegin; 325 ierr = SNESSetWorkVecs(snes,2);CHKERRQ(ierr); 326 ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr); 327 if (snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_PRECONDITIONED; 328 PetscFunctionReturn(0); 329 } 330 /* -------------------------------------------------------------------------- */ 331 332 #undef __FUNCT__ 333 #define __FUNCT__ "SNESReset_NEWTONLS" 334 PetscErrorCode SNESReset_NEWTONLS(SNES snes) 335 { 336 PetscFunctionBegin; 337 PetscFunctionReturn(0); 338 } 339 340 /* 341 SNESDestroy_NEWTONLS - Destroys the private SNES_NEWTONLS context that was created 342 with SNESCreate_NEWTONLS(). 343 344 Input Parameter: 345 . snes - the SNES context 346 347 Application Interface Routine: SNESDestroy() 348 */ 349 #undef __FUNCT__ 350 #define __FUNCT__ "SNESDestroy_NEWTONLS" 351 PetscErrorCode SNESDestroy_NEWTONLS(SNES snes) 352 { 353 PetscErrorCode ierr; 354 355 PetscFunctionBegin; 356 ierr = SNESReset_NEWTONLS(snes);CHKERRQ(ierr); 357 ierr = PetscFree(snes->data);CHKERRQ(ierr); 358 PetscFunctionReturn(0); 359 } 360 /* -------------------------------------------------------------------------- */ 361 362 /* 363 SNESView_NEWTONLS - Prints info from the SNESNEWTONLS data structure. 364 365 Input Parameters: 366 . SNES - the SNES context 367 . viewer - visualization context 368 369 Application Interface Routine: SNESView() 370 */ 371 #undef __FUNCT__ 372 #define __FUNCT__ "SNESView_NEWTONLS" 373 static PetscErrorCode SNESView_NEWTONLS(SNES snes,PetscViewer viewer) 374 { 375 PetscErrorCode ierr; 376 PetscBool iascii; 377 378 PetscFunctionBegin; 379 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 380 if (iascii) { 381 } 382 PetscFunctionReturn(0); 383 } 384 385 /* -------------------------------------------------------------------------- */ 386 /* 387 SNESSetFromOptions_NEWTONLS - Sets various parameters for the SNESNEWTONLS method. 388 389 Input Parameter: 390 . snes - the SNES context 391 392 Application Interface Routine: SNESSetFromOptions() 393 */ 394 #undef __FUNCT__ 395 #define __FUNCT__ "SNESSetFromOptions_NEWTONLS" 396 static PetscErrorCode SNESSetFromOptions_NEWTONLS(SNES snes) 397 { 398 PetscErrorCode ierr; 399 SNESLineSearch linesearch; 400 401 PetscFunctionBegin; 402 ierr = PetscOptionsHead("SNESNEWTONLS options");CHKERRQ(ierr); 403 ierr = PetscOptionsTail();CHKERRQ(ierr); 404 /* set the default line search type */ 405 if (!snes->linesearch) { 406 ierr = SNESGetLineSearch(snes, &linesearch);CHKERRQ(ierr); 407 ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);CHKERRQ(ierr); 408 } 409 PetscFunctionReturn(0); 410 } 411 412 /* -------------------------------------------------------------------------- */ 413 /*MC 414 SNESNEWTONLS - Newton based nonlinear solver that uses a line search 415 416 Options Database: 417 + -snes_linesearch_type <bt> - bt,basic. Select line search type 418 . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt 419 . -snes_linesearch_norms <true> - Turns on/off computation of the norms for basic linesearch 420 . -snes_linesearch_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient 421 . -snes_linesearch_maxstep <maxstep> - Sets the maximum stepsize the line search will use (if the 2-norm(y) > maxstep then scale y to be y = (maxstep/2-norm(y)) *y) 422 . -snes_linesearch_minlambda <minlambda> - Sets the minimum lambda the line search will tolerate 423 . -snes_linesearch_monitor - print information about progress of line searches 424 - -snes_linesearch_damping - damping factor used for basic line search 425 426 Notes: This is the default nonlinear solver in SNES 427 428 Level: beginner 429 430 .seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONTR, SNESQN, SNESLineSearchSetType(), SNESLineSearchSetOrder() 431 SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck() SNESLineSearchSetComputeNorms() 432 433 M*/ 434 #undef __FUNCT__ 435 #define __FUNCT__ "SNESCreate_NEWTONLS" 436 PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONLS(SNES snes) 437 { 438 PetscErrorCode ierr; 439 SNES_NEWTONLS *neP; 440 441 PetscFunctionBegin; 442 snes->ops->setup = SNESSetUp_NEWTONLS; 443 snes->ops->solve = SNESSolve_NEWTONLS; 444 snes->ops->destroy = SNESDestroy_NEWTONLS; 445 snes->ops->setfromoptions = SNESSetFromOptions_NEWTONLS; 446 snes->ops->view = SNESView_NEWTONLS; 447 snes->ops->reset = SNESReset_NEWTONLS; 448 449 snes->pcside = PC_RIGHT; 450 snes->usesksp = PETSC_TRUE; 451 snes->usespc = PETSC_TRUE; 452 ierr = PetscNewLog(snes,SNES_NEWTONLS,&neP);CHKERRQ(ierr); 453 snes->data = (void*)neP; 454 PetscFunctionReturn(0); 455 } 456