Actual source code: snesmfj2.c


  2: #include <petsc/private/snesimpl.h>
  3: /* matimpl.h is needed only for logging of matrix operation */
  4: #include <petsc/private/matimpl.h>

  6: PETSC_INTERN PetscErrorCode SNESUnSetMatrixFreeParameter(SNES);
  7: PETSC_INTERN PetscErrorCode SNESDefaultMatrixFreeCreate2(SNES,Vec,Mat*);
  8: PETSC_INTERN PetscErrorCode SNESDefaultMatrixFreeSetParameters2(Mat,PetscReal,PetscReal,PetscReal);

 10: PETSC_INTERN PetscErrorCode SNESDiffParameterCreate_More(SNES,Vec,void**);
 11: PETSC_INTERN PetscErrorCode SNESDiffParameterCompute_More(SNES,void*,Vec,Vec,PetscReal*,PetscReal*);
 12: PETSC_INTERN PetscErrorCode SNESDiffParameterDestroy_More(void*);

 14: typedef struct {  /* default context for matrix-free SNES */
 15:   SNES         snes;             /* SNES context */
 16:   Vec          w;                /* work vector */
 17:   MatNullSpace sp;               /* null space context */
 18:   PetscReal    error_rel;        /* square root of relative error in computing function */
 19:   PetscReal    umin;             /* minimum allowable u'a value relative to |u|_1 */
 20:   PetscBool    jorge;            /* flag indicating use of Jorge's method for determining the differencing parameter */
 21:   PetscReal    h;                /* differencing parameter */
 22:   PetscBool    need_h;           /* flag indicating whether we must compute h */
 23:   PetscBool    need_err;         /* flag indicating whether we must currently compute error_rel */
 24:   PetscBool    compute_err;      /* flag indicating whether we must ever compute error_rel */
 25:   PetscInt     compute_err_iter; /* last iter where we've computer error_rel */
 26:   PetscInt     compute_err_freq; /* frequency of computing error_rel */
 27:   void         *data;            /* implementation-specific data */
 28: } MFCtx_Private;

 30: PetscErrorCode SNESMatrixFreeDestroy2_Private(Mat mat)
 31: {
 32:   MFCtx_Private  *ctx;

 34:   MatShellGetContext(mat,&ctx);
 35:   VecDestroy(&ctx->w);
 36:   MatNullSpaceDestroy(&ctx->sp);
 37:   if (ctx->jorge || ctx->compute_err) SNESDiffParameterDestroy_More(ctx->data);
 38:   PetscFree(ctx);
 39:   return 0;
 40: }

 42: /*
 43:    SNESMatrixFreeView2_Private - Views matrix-free parameters.
 44:  */
 45: PetscErrorCode SNESMatrixFreeView2_Private(Mat J,PetscViewer viewer)
 46: {
 47:   MFCtx_Private  *ctx;
 48:   PetscBool      iascii;

 50:   MatShellGetContext(J,&ctx);
 51:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
 52:   if (iascii) {
 53:     PetscViewerASCIIPrintf(viewer,"  SNES matrix-free approximation:\n");
 54:     if (ctx->jorge) {
 55:       PetscViewerASCIIPrintf(viewer,"    using Jorge's method of determining differencing parameter\n");
 56:     }
 57:     PetscViewerASCIIPrintf(viewer,"    err=%g (relative error in function evaluation)\n",(double)ctx->error_rel);
 58:     PetscViewerASCIIPrintf(viewer,"    umin=%g (minimum iterate parameter)\n",(double)ctx->umin);
 59:     if (ctx->compute_err) {
 60:       PetscViewerASCIIPrintf(viewer,"    freq_err=%D (frequency for computing err)\n",ctx->compute_err_freq);
 61:     }
 62:   }
 63:   return 0;
 64: }

 66: /*
 67:   SNESMatrixFreeMult2_Private - Default matrix-free form for Jacobian-vector
 68:   product, y = F'(u)*a:
 69:         y = (F(u + ha) - F(u)) /h,
 70:   where F = nonlinear function, as set by SNESSetFunction()
 71:         u = current iterate
 72:         h = difference interval
 73: */
 74: PetscErrorCode SNESMatrixFreeMult2_Private(Mat mat,Vec a,Vec y)
 75: {
 76:   MFCtx_Private  *ctx;
 77:   SNES           snes;
 78:   PetscReal      h,norm,sum,umin,noise;
 79:   PetscScalar    hs,dot;
 80:   Vec            w,U,F;
 81:   MPI_Comm       comm;
 82:   PetscInt       iter;
 83:   PetscErrorCode (*eval_fct)(SNES,Vec,Vec);

 85:   /* We log matrix-free matrix-vector products separately, so that we can
 86:      separate the performance monitoring from the cases that use conventional
 87:      storage.  We may eventually modify event logging to associate events
 88:      with particular objects, hence alleviating the more general problem. */
 89:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

 91:   PetscObjectGetComm((PetscObject)mat,&comm);
 92:   MatShellGetContext(mat,&ctx);
 93:   snes = ctx->snes;
 94:   w    = ctx->w;
 95:   umin = ctx->umin;

 97:   SNESGetSolution(snes,&U);
 98:   eval_fct = SNESComputeFunction;
 99:   SNESGetFunction(snes,&F,NULL,NULL);

101:   /* Determine a "good" step size, h */
102:   if (ctx->need_h) {

104:     /* Use Jorge's method to compute h */
105:     if (ctx->jorge) {
106:       SNESDiffParameterCompute_More(snes,ctx->data,U,a,&noise,&h);

108:       /* Use the Brown/Saad method to compute h */
109:     } else {
110:       /* Compute error if desired */
111:       SNESGetIterationNumber(snes,&iter);
112:       if ((ctx->need_err) || ((ctx->compute_err_freq) && (ctx->compute_err_iter != iter) && (!((iter-1)%ctx->compute_err_freq)))) {
113:         /* Use Jorge's method to compute noise */
114:         SNESDiffParameterCompute_More(snes,ctx->data,U,a,&noise,&h);

116:         ctx->error_rel = PetscSqrtReal(noise);

118:         PetscInfo(snes,"Using Jorge's noise: noise=%g, sqrt(noise)=%g, h_more=%g\n",(double)noise,(double)ctx->error_rel,(double)h);

120:         ctx->compute_err_iter = iter;
121:         ctx->need_err         = PETSC_FALSE;
122:       }

124:       VecDotBegin(U,a,&dot);
125:       VecNormBegin(a,NORM_1,&sum);
126:       VecNormBegin(a,NORM_2,&norm);
127:       VecDotEnd(U,a,&dot);
128:       VecNormEnd(a,NORM_1,&sum);
129:       VecNormEnd(a,NORM_2,&norm);

131:       /* Safeguard for step sizes too small */
132:       if (sum == 0.0) {
133:         dot  = 1.0;
134:         norm = 1.0;
135:       } else if (PetscAbsScalar(dot) < umin*sum && PetscRealPart(dot) >= 0.0) dot = umin*sum;
136:       else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin*sum) dot = -umin*sum;
137:       h = PetscRealPart(ctx->error_rel*dot/(norm*norm));
138:     }
139:   } else h = ctx->h;

141:   if (!ctx->jorge || !ctx->need_h) PetscInfo(snes,"h = %g\n",(double)h);

143:   /* Evaluate function at F(u + ha) */
144:   hs   = h;
145:   VecWAXPY(w,hs,a,U);
146:   eval_fct(snes,w,y);
147:   VecAXPY(y,-1.0,F);
148:   VecScale(y,1.0/hs);
149:   if (mat->nullsp) MatNullSpaceRemove(mat->nullsp,y);

151:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
152:   return 0;
153: }

155: /*@C
156:    SNESMatrixFreeCreate2 - Creates a matrix-free matrix
157:    context for use with a SNES solver.  This matrix can be used as
158:    the Jacobian argument for the routine SNESSetJacobian().

160:    Input Parameters:
161: +  snes - the SNES context
162: -  x - vector where SNES solution is to be stored.

164:    Output Parameter:
165: .  J - the matrix-free matrix

167:    Level: advanced

169:    Notes:
170:    The matrix-free matrix context merely contains the function pointers
171:    and work space for performing finite difference approximations of
172:    Jacobian-vector products, J(u)*a, via

174: $       J(u)*a = [J(u+h*a) - J(u)]/h,
175: $   where by default
176: $        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
177: $          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
178: $   where
179: $        error_rel = square root of relative error in
180: $                    function evaluation
181: $        umin = minimum iterate parameter
182: $   Alternatively, the differencing parameter, h, can be set using
183: $   Jorge's nifty new strategy if one specifies the option
184: $          -snes_mf_jorge

186:    The user can set these parameters via MatMFFDSetFunctionError().
187:    See Users-Manual: ch_snes for details

189:    The user should call MatDestroy() when finished with the matrix-free
190:    matrix context.

192:    Options Database Keys:
193: $  -snes_mf_err <error_rel>
194: $  -snes_mf_unim <umin>
195: $  -snes_mf_compute_err
196: $  -snes_mf_freq_err <freq>
197: $  -snes_mf_jorge

199: .seealso: MatDestroy(), MatMFFDSetFunctionError()
200: @*/
201: PetscErrorCode  SNESDefaultMatrixFreeCreate2(SNES snes,Vec x,Mat *J)
202: {
203:   MPI_Comm       comm;
204:   MFCtx_Private  *mfctx;
205:   PetscInt       n,nloc;
206:   PetscBool      flg;
207:   char           p[64];

209:   PetscNewLog(snes,&mfctx);
210:   mfctx->sp               = NULL;
211:   mfctx->snes             = snes;
212:   mfctx->error_rel        = PETSC_SQRT_MACHINE_EPSILON;
213:   mfctx->umin             = 1.e-6;
214:   mfctx->h                = 0.0;
215:   mfctx->need_h           = PETSC_TRUE;
216:   mfctx->need_err         = PETSC_FALSE;
217:   mfctx->compute_err      = PETSC_FALSE;
218:   mfctx->compute_err_freq = 0;
219:   mfctx->compute_err_iter = -1;
220:   mfctx->compute_err      = PETSC_FALSE;
221:   mfctx->jorge            = PETSC_FALSE;

223:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_err",&mfctx->error_rel,NULL);
224:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_umin",&mfctx->umin,NULL);
225:   PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_jorge",&mfctx->jorge,NULL);
226:   PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_compute_err",&mfctx->compute_err,NULL);
227:   PetscOptionsGetInt(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_freq_err",&mfctx->compute_err_freq,&flg);
228:   if (flg) {
229:     if (mfctx->compute_err_freq < 0) mfctx->compute_err_freq = 0;
230:     mfctx->compute_err = PETSC_TRUE;
231:   }
232:   if (mfctx->compute_err) mfctx->need_err = PETSC_TRUE;
233:   if (mfctx->jorge || mfctx->compute_err) {
234:     SNESDiffParameterCreate_More(snes,x,&mfctx->data);
235:   } else mfctx->data = NULL;

237:   PetscOptionsHasHelp(((PetscObject)snes)->options,&flg);
238:   PetscStrncpy(p,"-",sizeof(p));
239:   if (((PetscObject)snes)->prefix) PetscStrlcat(p,((PetscObject)snes)->prefix,sizeof(p));
240:   if (flg) {
241:     PetscPrintf(PetscObjectComm((PetscObject)snes)," Matrix-free Options (via SNES):\n");
242:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_err <err>: set sqrt of relative error in function (default %g)\n",p,(double)mfctx->error_rel);
243:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_umin <umin>: see users manual (default %g)\n",p,(double)mfctx->umin);
244:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_jorge: use Jorge More's method\n",p);
245:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_compute_err: compute sqrt or relative error in function\n",p);
246:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_freq_err <freq>: frequency to recompute this (default only once)\n",p);
247:     PetscPrintf(PetscObjectComm((PetscObject)snes),"   %ssnes_mf_noise_file <file>: set file for printing noise info\n",p);
248:   }
249:   VecDuplicate(x,&mfctx->w);
250:   PetscObjectGetComm((PetscObject)x,&comm);
251:   VecGetSize(x,&n);
252:   VecGetLocalSize(x,&nloc);
253:   MatCreate(comm,J);
254:   MatSetSizes(*J,nloc,n,n,n);
255:   MatSetType(*J,MATSHELL);
256:   MatShellSetContext(*J,mfctx);
257:   MatShellSetOperation(*J,MATOP_MULT,(void (*)(void))SNESMatrixFreeMult2_Private);
258:   MatShellSetOperation(*J,MATOP_DESTROY,(void (*)(void))SNESMatrixFreeDestroy2_Private);
259:   MatShellSetOperation(*J,MATOP_VIEW,(void (*)(void))SNESMatrixFreeView2_Private);
260:   MatSetUp(*J);

262:   PetscLogObjectParent((PetscObject)*J,(PetscObject)mfctx->w);
263:   PetscLogObjectParent((PetscObject)snes,(PetscObject)*J);
264:   return 0;
265: }

267: /*@C
268:    SNESDefaultMatrixFreeSetParameters2 - Sets the parameters for the approximation of
269:    matrix-vector products using finite differences.

271: $       J(u)*a = [J(u+h*a) - J(u)]/h where

273:    either the user sets h directly here, or this parameter is computed via

275: $        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
276: $          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
277: $

279:    Input Parameters:
280: +  mat - the matrix
281: .  error_rel - relative error (should be set to the square root of
282:      the relative error in the function evaluations)
283: .  umin - minimum allowable u-value
284: -  h - differencing parameter

286:    Level: advanced

288:    Notes:
289:    If the user sets the parameter h directly, then this value will be used
290:    instead of the default computation indicated above.

292: .seealso: MatCreateSNESMF()
293: @*/
294: PetscErrorCode  SNESDefaultMatrixFreeSetParameters2(Mat mat,PetscReal error,PetscReal umin,PetscReal h)
295: {
296:   MFCtx_Private  *ctx;

298:   MatShellGetContext(mat,&ctx);
299:   if (ctx) {
300:     if (error != PETSC_DEFAULT) ctx->error_rel = error;
301:     if (umin  != PETSC_DEFAULT) ctx->umin = umin;
302:     if (h     != PETSC_DEFAULT) {
303:       ctx->h      = h;
304:       ctx->need_h = PETSC_FALSE;
305:     }
306:   }
307:   return 0;
308: }

310: PetscErrorCode  SNESUnSetMatrixFreeParameter(SNES snes)
311: {
312:   MFCtx_Private  *ctx;
313:   Mat            mat;

315:   SNESGetJacobian(snes,&mat,NULL,NULL,NULL);
316:   MatShellGetContext(mat,&ctx);
317:   if (ctx) ctx->need_h = PETSC_TRUE;
318:   return 0;
319: }