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__ "SNESLSCheckLocalMin_Private" 12 PetscErrorCode SNESLSCheckLocalMin_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,PETSC_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__ "SNESLSCheckResidual_Private" 50 PetscErrorCode SNESLSCheckResidual_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 _LS (e.g., SNESCreate_LS, SNESSolve_LS) 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_LS - 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_LS" 131 PetscErrorCode SNESSolve_LS(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; 142 143 PetscFunctionBegin; 144 snes->numFailures = 0; 145 snes->numLinearSolveFailures = 0; 146 snes->reason = SNES_CONVERGED_ITERATING; 147 148 maxits = snes->max_its; /* maximum number of iterations */ 149 X = snes->vec_sol; /* solution vector */ 150 F = snes->vec_func; /* residual vector */ 151 Y = snes->vec_sol_update; /* newton step */ 152 G = snes->work[0]; 153 W = snes->work[1]; 154 155 ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); 156 snes->iter = 0; 157 snes->norm = 0.0; 158 ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); 159 ierr = SNESGetSNESLineSearch(snes, &linesearch);CHKERRQ(ierr); 160 if (!snes->vec_func_init_set) { 161 ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr); 162 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 163 if (domainerror) { 164 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 165 PetscFunctionReturn(0); 166 } 167 } else { 168 snes->vec_func_init_set = PETSC_FALSE; 169 } 170 if (!snes->norm_init_set) { 171 ierr = VecNormBegin(F,NORM_2,&fnorm);CHKERRQ(ierr); /* fnorm <- ||F|| */ 172 ierr = VecNormEnd(F,NORM_2,&fnorm);CHKERRQ(ierr); 173 if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number"); 174 } else { 175 fnorm = snes->norm_init; 176 snes->norm_init_set = PETSC_FALSE; 177 } 178 ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); 179 snes->norm = fnorm; 180 ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); 181 SNESLogConvHistory(snes,fnorm,0); 182 ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr); 183 184 /* set parameter for default relative tolerance convergence test */ 185 snes->ttol = fnorm*snes->rtol; 186 /* test convergence */ 187 ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 188 if (snes->reason) PetscFunctionReturn(0); 189 190 for (i=0; i<maxits; i++) { 191 192 /* Call general purpose update function */ 193 if (snes->ops->update) { 194 ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr); 195 } 196 197 /* Solve J Y = F, where J is Jacobian matrix */ 198 ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr); 199 ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr); 200 ierr = SNES_KSPSolve(snes,snes->ksp,F,Y);CHKERRQ(ierr); 201 ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr); 202 if (kspreason < 0) { 203 if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) { 204 ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr); 205 snes->reason = SNES_DIVERGED_LINEAR_SOLVE; 206 break; 207 } 208 } 209 ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr); 210 snes->linear_its += lits; 211 ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr); 212 213 if (PetscLogPrintInfo){ 214 ierr = SNESLSCheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr); 215 } 216 217 /* Compute a (scaled) negative update in the line search routine: 218 X <- X - lambda*Y 219 and evaluate F = function(X) (depends on the line search). 220 */ 221 gnorm = fnorm; 222 ierr = SNESLineSearchApply(linesearch, X, F, &fnorm, Y);CHKERRQ(ierr); 223 ierr = SNESLineSearchGetSuccess(linesearch, &lssucceed);CHKERRQ(ierr); 224 ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);CHKERRQ(ierr); 225 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); 226 if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break; 227 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 228 if (domainerror) { 229 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 230 PetscFunctionReturn(0); 231 } 232 if (!lssucceed) { 233 if (++snes->numFailures >= snes->maxFailures) { 234 PetscBool ismin; 235 snes->reason = SNES_DIVERGED_LINE_SEARCH; 236 ierr = SNESLSCheckLocalMin_Private(snes,snes->jacobian,F,X,fnorm,&ismin);CHKERRQ(ierr); 237 if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN; 238 break; 239 } 240 } 241 /* Monitor convergence */ 242 ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); 243 snes->iter = i+1; 244 snes->norm = fnorm; 245 ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); 246 SNESLogConvHistory(snes,snes->norm,lits); 247 ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr); 248 /* Test for convergence, xnorm = || X || */ 249 if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); } 250 ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 251 if (snes->reason) break; 252 } 253 if (i == maxits) { 254 ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr); 255 if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT; 256 } 257 PetscFunctionReturn(0); 258 } 259 /* -------------------------------------------------------------------------- */ 260 /* 261 SNESSetUp_LS - Sets up the internal data structures for the later use 262 of the SNESLS nonlinear solver. 263 264 Input Parameter: 265 . snes - the SNES context 266 . x - the solution vector 267 268 Application Interface Routine: SNESSetUp() 269 270 Notes: 271 For basic use of the SNES solvers, the user need not explicitly call 272 SNESSetUp(), since these actions will automatically occur during 273 the call to SNESSolve(). 274 */ 275 #undef __FUNCT__ 276 #define __FUNCT__ "SNESSetUp_LS" 277 PetscErrorCode SNESSetUp_LS(SNES snes) 278 { 279 PetscErrorCode ierr; 280 281 PetscFunctionBegin; 282 ierr = SNESDefaultGetWork(snes,2);CHKERRQ(ierr); 283 ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr); 284 285 PetscFunctionReturn(0); 286 } 287 /* -------------------------------------------------------------------------- */ 288 289 #undef __FUNCT__ 290 #define __FUNCT__ "SNESReset_LS" 291 PetscErrorCode SNESReset_LS(SNES snes) 292 { 293 PetscFunctionBegin; 294 PetscFunctionReturn(0); 295 } 296 297 /* 298 SNESDestroy_LS - Destroys the private SNES_LS context that was created 299 with SNESCreate_LS(). 300 301 Input Parameter: 302 . snes - the SNES context 303 304 Application Interface Routine: SNESDestroy() 305 */ 306 #undef __FUNCT__ 307 #define __FUNCT__ "SNESDestroy_LS" 308 PetscErrorCode SNESDestroy_LS(SNES snes) 309 { 310 PetscErrorCode ierr; 311 312 PetscFunctionBegin; 313 ierr = SNESReset_LS(snes);CHKERRQ(ierr); 314 ierr = PetscFree(snes->data);CHKERRQ(ierr); 315 PetscFunctionReturn(0); 316 } 317 /* -------------------------------------------------------------------------- */ 318 319 /* 320 SNESView_LS - Prints info from the SNESLS data structure. 321 322 Input Parameters: 323 . SNES - the SNES context 324 . viewer - visualization context 325 326 Application Interface Routine: SNESView() 327 */ 328 #undef __FUNCT__ 329 #define __FUNCT__ "SNESView_LS" 330 static PetscErrorCode SNESView_LS(SNES snes,PetscViewer viewer) 331 { 332 PetscErrorCode ierr; 333 PetscBool iascii; 334 335 PetscFunctionBegin; 336 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 337 if (iascii) { 338 } 339 PetscFunctionReturn(0); 340 } 341 342 /* -------------------------------------------------------------------------- */ 343 /* 344 SNESSetFromOptions_LS - Sets various parameters for the SNESLS method. 345 346 Input Parameter: 347 . snes - the SNES context 348 349 Application Interface Routine: SNESSetFromOptions() 350 */ 351 #undef __FUNCT__ 352 #define __FUNCT__ "SNESSetFromOptions_LS" 353 static PetscErrorCode SNESSetFromOptions_LS(SNES snes) 354 { 355 PetscErrorCode ierr; 356 SNESLineSearch linesearch; 357 358 PetscFunctionBegin; 359 ierr = PetscOptionsHead("SNESLS options");CHKERRQ(ierr); 360 ierr = PetscOptionsTail();CHKERRQ(ierr); 361 /* set the default line search type */ 362 if (!snes->linesearch) { 363 ierr = SNESGetSNESLineSearch(snes, &linesearch);CHKERRQ(ierr); 364 ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);CHKERRQ(ierr); 365 } 366 PetscFunctionReturn(0); 367 } 368 369 /* -------------------------------------------------------------------------- */ 370 /*MC 371 SNESLS - Newton based nonlinear solver that uses a line search 372 373 Options Database: 374 + -snes_linesearch_type <bt> - bt,basic. Select line search type 375 . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt 376 . -snes_linesearch_norms <true> - Turns on/off computation of the norms for basic linesearch 377 . -snes_linesearch_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient 378 . -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) 379 . -snes_linesearch_minlambda <minlambda> - Sets the minimum lambda the line search will tolerate 380 . -snes_linesearch_monitor - print information about progress of line searches 381 - -snes_linesearch_damping - damping factor used for basic line search 382 383 Notes: This is the default nonlinear solver in SNES 384 385 Level: beginner 386 387 .seealso: SNESCreate(), SNES, SNESSetType(), SNESTR, SNESQN, SNESLineSearchSetType(), SNESLineSearchSetOrder() 388 SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck() SNESLineSearchSetComputeNorms() 389 390 M*/ 391 EXTERN_C_BEGIN 392 #undef __FUNCT__ 393 #define __FUNCT__ "SNESCreate_LS" 394 PetscErrorCode SNESCreate_LS(SNES snes) 395 { 396 PetscErrorCode ierr; 397 SNES_LS *neP; 398 399 PetscFunctionBegin; 400 snes->ops->setup = SNESSetUp_LS; 401 snes->ops->solve = SNESSolve_LS; 402 snes->ops->destroy = SNESDestroy_LS; 403 snes->ops->setfromoptions = SNESSetFromOptions_LS; 404 snes->ops->view = SNESView_LS; 405 snes->ops->reset = SNESReset_LS; 406 407 snes->usesksp = PETSC_TRUE; 408 snes->usespc = PETSC_FALSE; 409 ierr = PetscNewLog(snes,SNES_LS,&neP);CHKERRQ(ierr); 410 snes->data = (void*)neP; 411 PetscFunctionReturn(0); 412 } 413 EXTERN_C_END 414