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->work[0]; /* work vectors */ 152 G = snes->work[1]; 153 W = snes->work[2]; 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 Y <- X - lambda*Y 219 and evaluate G = function(Y) (depends on the line search). 220 */ 221 ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr); 222 gnorm = fnorm; 223 ierr = SNESLineSearchApply(linesearch, X, F, &fnorm, Y);CHKERRQ(ierr); 224 ierr = SNESLineSearchGetSuccess(linesearch, &lssucceed);CHKERRQ(ierr); 225 ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);CHKERRQ(ierr); 226 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); 227 if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break; 228 ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr); 229 if (domainerror) { 230 snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN; 231 PetscFunctionReturn(0); 232 } 233 if (!lssucceed) { 234 if (++snes->numFailures >= snes->maxFailures) { 235 PetscBool ismin; 236 snes->reason = SNES_DIVERGED_LINE_SEARCH; 237 ierr = SNESLSCheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr); 238 if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN; 239 break; 240 } 241 } 242 /* Monitor convergence */ 243 ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); 244 snes->iter = i+1; 245 snes->norm = fnorm; 246 ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); 247 SNESLogConvHistory(snes,snes->norm,lits); 248 ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr); 249 /* Test for convergence, xnorm = || X || */ 250 if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); } 251 ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); 252 if (snes->reason) break; 253 } 254 if (i == maxits) { 255 ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr); 256 if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT; 257 } 258 PetscFunctionReturn(0); 259 } 260 /* -------------------------------------------------------------------------- */ 261 /* 262 SNESSetUp_LS - Sets up the internal data structures for the later use 263 of the SNESLS nonlinear solver. 264 265 Input Parameter: 266 . snes - the SNES context 267 . x - the solution vector 268 269 Application Interface Routine: SNESSetUp() 270 271 Notes: 272 For basic use of the SNES solvers, the user need not explicitly call 273 SNESSetUp(), since these actions will automatically occur during 274 the call to SNESSolve(). 275 */ 276 #undef __FUNCT__ 277 #define __FUNCT__ "SNESSetUp_LS" 278 PetscErrorCode SNESSetUp_LS(SNES snes) 279 { 280 PetscErrorCode ierr; 281 282 PetscFunctionBegin; 283 ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr); 284 ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr); 285 286 PetscFunctionReturn(0); 287 } 288 /* -------------------------------------------------------------------------- */ 289 290 #undef __FUNCT__ 291 #define __FUNCT__ "SNESReset_LS" 292 PetscErrorCode SNESReset_LS(SNES snes) 293 { 294 PetscFunctionBegin; 295 PetscFunctionReturn(0); 296 } 297 298 /* 299 SNESDestroy_LS - Destroys the private SNES_LS context that was created 300 with SNESCreate_LS(). 301 302 Input Parameter: 303 . snes - the SNES context 304 305 Application Interface Routine: SNESDestroy() 306 */ 307 #undef __FUNCT__ 308 #define __FUNCT__ "SNESDestroy_LS" 309 PetscErrorCode SNESDestroy_LS(SNES snes) 310 { 311 PetscErrorCode ierr; 312 313 PetscFunctionBegin; 314 ierr = SNESReset_LS(snes);CHKERRQ(ierr); 315 ierr = PetscFree(snes->data);CHKERRQ(ierr); 316 PetscFunctionReturn(0); 317 } 318 /* -------------------------------------------------------------------------- */ 319 320 /* 321 SNESView_LS - Prints info from the SNESLS data structure. 322 323 Input Parameters: 324 . SNES - the SNES context 325 . viewer - visualization context 326 327 Application Interface Routine: SNESView() 328 */ 329 #undef __FUNCT__ 330 #define __FUNCT__ "SNESView_LS" 331 static PetscErrorCode SNESView_LS(SNES snes,PetscViewer viewer) 332 { 333 PetscErrorCode ierr; 334 PetscBool iascii; 335 336 PetscFunctionBegin; 337 ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 338 if (iascii) { 339 } 340 PetscFunctionReturn(0); 341 } 342 343 /* -------------------------------------------------------------------------- */ 344 /* 345 SNESSetFromOptions_LS - Sets various parameters for the SNESLS method. 346 347 Input Parameter: 348 . snes - the SNES context 349 350 Application Interface Routine: SNESSetFromOptions() 351 */ 352 #undef __FUNCT__ 353 #define __FUNCT__ "SNESSetFromOptions_LS" 354 static PetscErrorCode SNESSetFromOptions_LS(SNES snes) 355 { 356 PetscErrorCode ierr; 357 SNESLineSearch linesearch; 358 359 PetscFunctionBegin; 360 ierr = PetscOptionsHead("SNESLS options");CHKERRQ(ierr); 361 ierr = PetscOptionsTail();CHKERRQ(ierr); 362 /* set the default line search type */ 363 if (!snes->linesearch) { 364 ierr = SNESGetSNESLineSearch(snes, &linesearch);CHKERRQ(ierr); 365 ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);CHKERRQ(ierr); 366 } 367 PetscFunctionReturn(0); 368 } 369 370 /* -------------------------------------------------------------------------- */ 371 /*MC 372 SNESLS - Newton based nonlinear solver that uses a line search 373 374 Options Database: 375 + -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search 376 . -snes_ls_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient 377 . -snes_ls_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) 378 . -snes_ls_minlambda <minlambda> - Sets the minimum lambda the line search will use minlambda / max_i ( y[i]/x[i] ) 379 . -snes_ls_monitor - print information about progress of line searches 380 - -snes_ls_damping - damping factor used if -snes_ls is basic or basicnonorms 381 382 383 Notes: This is the default nonlinear solver in SNES 384 385 Level: beginner 386 387 .seealso: SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(), 388 SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(), 389 SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams() 390 391 M*/ 392 EXTERN_C_BEGIN 393 #undef __FUNCT__ 394 #define __FUNCT__ "SNESCreate_LS" 395 PetscErrorCode SNESCreate_LS(SNES snes) 396 { 397 PetscErrorCode ierr; 398 SNES_LS *neP; 399 400 PetscFunctionBegin; 401 snes->ops->setup = SNESSetUp_LS; 402 snes->ops->solve = SNESSolve_LS; 403 snes->ops->destroy = SNESDestroy_LS; 404 snes->ops->setfromoptions = SNESSetFromOptions_LS; 405 snes->ops->view = SNESView_LS; 406 snes->ops->reset = SNESReset_LS; 407 408 snes->usesksp = PETSC_TRUE; 409 snes->usespc = PETSC_FALSE; 410 ierr = PetscNewLog(snes,SNES_LS,&neP);CHKERRQ(ierr); 411 snes->data = (void*)neP; 412 PetscFunctionReturn(0); 413 } 414 EXTERN_C_END 415