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 = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr); 157 snes->iter = 0; 158 snes->norm = 0.0; 159 ierr = PetscObjectSAWsGrantAccess((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 } 183 184 ierr = VecNorm(F,NORM_2,&fnorm);CHKERRQ(ierr); /* fnorm <- ||F|| */ 185 if (PetscIsInfOrNanReal(fnorm)) { 186 snes->reason = SNES_DIVERGED_FNORM_NAN; 187 PetscFunctionReturn(0); 188 } 189 190 ierr = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr); 191 snes->norm = fnorm; 192 ierr = PetscObjectSAWsGrantAccess((PetscObject)snes);CHKERRQ(ierr); 193 ierr = SNESLogConvergenceHistory(snes,fnorm,0);CHKERRQ(ierr); 194 ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr); 195 196 /* test convergence */ 197 ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 198 if (snes->reason) PetscFunctionReturn(0); 199 200 for (i=0; i<maxits; i++) { 201 202 /* Call general purpose update function */ 203 if (snes->ops->update) { 204 ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr); 205 } 206 207 /* apply the nonlinear preconditioner */ 208 if (snes->pc) { 209 if (snes->pcside == PC_RIGHT) { 210 ierr = SNESSetInitialFunction(snes->pc, F);CHKERRQ(ierr); 211 ierr = PetscLogEventBegin(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);CHKERRQ(ierr); 212 ierr = SNESSolve(snes->pc, snes->vec_rhs, X);CHKERRQ(ierr); 213 ierr = PetscLogEventEnd(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);CHKERRQ(ierr); 214 ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr); 215 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 216 snes->reason = SNES_DIVERGED_INNER; 217 PetscFunctionReturn(0); 218 } 219 ierr = SNESGetPCFunction(snes,F,&fnorm);CHKERRQ(ierr); 220 } else if (snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_UNPRECONDITIONED) { 221 ierr = SNESApplyPC(snes,X,F,&fnorm,F);CHKERRQ(ierr); 222 ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr); 223 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 224 snes->reason = SNES_DIVERGED_INNER; 225 PetscFunctionReturn(0); 226 } 227 } 228 } 229 230 /* Solve J Y = F, where J is Jacobian matrix */ 231 ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr); 232 ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr); 233 ierr = KSPSolve(snes->ksp,F,Y);CHKERRQ(ierr); 234 ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr); 235 if (kspreason < 0) { 236 if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) { 237 ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr); 238 snes->reason = SNES_DIVERGED_LINEAR_SOLVE; 239 break; 240 } 241 } 242 ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr); 243 snes->linear_its += lits; 244 ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr); 245 246 if (PetscLogPrintInfo) { 247 ierr = SNESNEWTONLSCheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr); 248 } 249 250 /* Compute a (scaled) negative update in the line search routine: 251 X <- X - lambda*Y 252 and evaluate F = function(X) (depends on the line search). 253 */ 254 gnorm = fnorm; 255 ierr = SNESLineSearchApply(linesearch, X, F, &fnorm, Y);CHKERRQ(ierr); 256 ierr = SNESLineSearchGetSuccess(linesearch, &lssucceed);CHKERRQ(ierr); 257 ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);CHKERRQ(ierr); 258 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); 259 if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break; 260 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 261 if (domainerror) { 262 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 263 PetscFunctionReturn(0); 264 } 265 if (!lssucceed) { 266 if (snes->stol*xnorm > ynorm) { 267 snes->reason = SNES_CONVERGED_SNORM_RELATIVE; 268 PetscFunctionReturn(0); 269 } 270 if (++snes->numFailures >= snes->maxFailures) { 271 PetscBool ismin; 272 snes->reason = SNES_DIVERGED_LINE_SEARCH; 273 ierr = SNESNEWTONLSCheckLocalMin_Private(snes,snes->jacobian,F,W,fnorm,&ismin);CHKERRQ(ierr); 274 if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN; 275 break; 276 } 277 } 278 /* Monitor convergence */ 279 ierr = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr); 280 snes->iter = i+1; 281 snes->norm = fnorm; 282 ierr = PetscObjectSAWsGrantAccess((PetscObject)snes);CHKERRQ(ierr); 283 ierr = SNESLogConvergenceHistory(snes,snes->norm,lits);CHKERRQ(ierr); 284 ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr); 285 /* Test for convergence */ 286 ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 287 if (snes->reason) break; 288 } 289 if (i == maxits) { 290 ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr); 291 if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT; 292 } 293 PetscFunctionReturn(0); 294 } 295 /* -------------------------------------------------------------------------- */ 296 /* 297 SNESSetUp_NEWTONLS - Sets up the internal data structures for the later use 298 of the SNESNEWTONLS nonlinear solver. 299 300 Input Parameter: 301 . snes - the SNES context 302 . x - the solution vector 303 304 Application Interface Routine: SNESSetUp() 305 306 Notes: 307 For basic use of the SNES solvers, the user need not explicitly call 308 SNESSetUp(), since these actions will automatically occur during 309 the call to SNESSolve(). 310 */ 311 #undef __FUNCT__ 312 #define __FUNCT__ "SNESSetUp_NEWTONLS" 313 PetscErrorCode SNESSetUp_NEWTONLS(SNES snes) 314 { 315 PetscErrorCode ierr; 316 317 PetscFunctionBegin; 318 ierr = SNESSetWorkVecs(snes,2);CHKERRQ(ierr); 319 ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr); 320 if (snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_PRECONDITIONED; 321 PetscFunctionReturn(0); 322 } 323 /* -------------------------------------------------------------------------- */ 324 325 #undef __FUNCT__ 326 #define __FUNCT__ "SNESReset_NEWTONLS" 327 PetscErrorCode SNESReset_NEWTONLS(SNES snes) 328 { 329 PetscFunctionBegin; 330 PetscFunctionReturn(0); 331 } 332 333 /* 334 SNESDestroy_NEWTONLS - Destroys the private SNES_NEWTONLS context that was created 335 with SNESCreate_NEWTONLS(). 336 337 Input Parameter: 338 . snes - the SNES context 339 340 Application Interface Routine: SNESDestroy() 341 */ 342 #undef __FUNCT__ 343 #define __FUNCT__ "SNESDestroy_NEWTONLS" 344 PetscErrorCode SNESDestroy_NEWTONLS(SNES snes) 345 { 346 PetscErrorCode ierr; 347 348 PetscFunctionBegin; 349 ierr = SNESReset_NEWTONLS(snes);CHKERRQ(ierr); 350 ierr = PetscFree(snes->data);CHKERRQ(ierr); 351 PetscFunctionReturn(0); 352 } 353 /* -------------------------------------------------------------------------- */ 354 355 /* 356 SNESView_NEWTONLS - Prints info from the SNESNEWTONLS data structure. 357 358 Input Parameters: 359 . SNES - the SNES context 360 . viewer - visualization context 361 362 Application Interface Routine: SNESView() 363 */ 364 #undef __FUNCT__ 365 #define __FUNCT__ "SNESView_NEWTONLS" 366 static PetscErrorCode SNESView_NEWTONLS(SNES snes,PetscViewer viewer) 367 { 368 PetscErrorCode ierr; 369 PetscBool iascii; 370 371 PetscFunctionBegin; 372 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 373 if (iascii) { 374 } 375 PetscFunctionReturn(0); 376 } 377 378 /* -------------------------------------------------------------------------- */ 379 /* 380 SNESSetFromOptions_NEWTONLS - Sets various parameters for the SNESNEWTONLS method. 381 382 Input Parameter: 383 . snes - the SNES context 384 385 Application Interface Routine: SNESSetFromOptions() 386 */ 387 #undef __FUNCT__ 388 #define __FUNCT__ "SNESSetFromOptions_NEWTONLS" 389 static PetscErrorCode SNESSetFromOptions_NEWTONLS(SNES snes) 390 { 391 PetscErrorCode ierr; 392 SNESLineSearch linesearch; 393 394 PetscFunctionBegin; 395 ierr = PetscOptionsHead("SNESNEWTONLS options");CHKERRQ(ierr); 396 ierr = PetscOptionsTail();CHKERRQ(ierr); 397 /* set the default line search type */ 398 if (!snes->linesearch) { 399 ierr = SNESGetLineSearch(snes, &linesearch);CHKERRQ(ierr); 400 ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);CHKERRQ(ierr); 401 } 402 PetscFunctionReturn(0); 403 } 404 405 /* -------------------------------------------------------------------------- */ 406 /*MC 407 SNESNEWTONLS - Newton based nonlinear solver that uses a line search 408 409 Options Database: 410 + -snes_linesearch_type <bt> - bt,basic. Select line search type 411 . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt 412 . -snes_linesearch_norms <true> - Turns on/off computation of the norms for basic linesearch 413 . -snes_linesearch_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient 414 . -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) 415 . -snes_linesearch_minlambda <minlambda> - Sets the minimum lambda the line search will tolerate 416 . -snes_linesearch_monitor - print information about progress of line searches 417 - -snes_linesearch_damping - damping factor used for basic line search 418 419 Notes: This is the default nonlinear solver in SNES 420 421 Level: beginner 422 423 .seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONTR, SNESQN, SNESLineSearchSetType(), SNESLineSearchSetOrder() 424 SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck() SNESLineSearchSetComputeNorms() 425 426 M*/ 427 #undef __FUNCT__ 428 #define __FUNCT__ "SNESCreate_NEWTONLS" 429 PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONLS(SNES snes) 430 { 431 PetscErrorCode ierr; 432 SNES_NEWTONLS *neP; 433 434 PetscFunctionBegin; 435 snes->ops->setup = SNESSetUp_NEWTONLS; 436 snes->ops->solve = SNESSolve_NEWTONLS; 437 snes->ops->destroy = SNESDestroy_NEWTONLS; 438 snes->ops->setfromoptions = SNESSetFromOptions_NEWTONLS; 439 snes->ops->view = SNESView_NEWTONLS; 440 snes->ops->reset = SNESReset_NEWTONLS; 441 442 snes->pcside = PC_RIGHT; 443 snes->usesksp = PETSC_TRUE; 444 snes->usespc = PETSC_TRUE; 445 ierr = PetscNewLog(snes,SNES_NEWTONLS,&neP);CHKERRQ(ierr); 446 snes->data = (void*)neP; 447 PetscFunctionReturn(0); 448 } 449