Actual source code: snesmfj2.c

petsc-3.11.3 2019-06-26
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  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: {
 33:   MFCtx_Private  *ctx;

 36:   MatShellGetContext(mat,(void**)&ctx);
 37:   VecDestroy(&ctx->w);
 38:   MatNullSpaceDestroy(&ctx->sp);
 39:   if (ctx->jorge || ctx->compute_err) {SNESDiffParameterDestroy_More(ctx->data);}
 40:   PetscFree(ctx);
 41:   return(0);
 42: }

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

 54:   MatShellGetContext(J,(void**)&ctx);
 55:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
 56:   if (iascii) {
 57:     PetscViewerASCIIPrintf(viewer,"  SNES matrix-free approximation:\n");
 58:     if (ctx->jorge) {
 59:       PetscViewerASCIIPrintf(viewer,"    using Jorge's method of determining differencing parameter\n");
 60:     }
 61:     PetscViewerASCIIPrintf(viewer,"    err=%g (relative error in function evaluation)\n",(double)ctx->error_rel);
 62:     PetscViewerASCIIPrintf(viewer,"    umin=%g (minimum iterate parameter)\n",(double)ctx->umin);
 63:     if (ctx->compute_err) {
 64:       PetscViewerASCIIPrintf(viewer,"    freq_err=%D (frequency for computing err)\n",ctx->compute_err_freq);
 65:     }
 66:   }
 67:   return(0);
 68: }

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

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

 96:   PetscObjectGetComm((PetscObject)mat,&comm);
 97:   MatShellGetContext(mat,(void**)&ctx);
 98:   snes = ctx->snes;
 99:   w    = ctx->w;
100:   umin = ctx->umin;

102:   SNESGetSolution(snes,&U);
103:   eval_fct = SNESComputeFunction;
104:   SNESGetFunction(snes,&F,NULL,NULL);

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

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

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

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

123:         PetscInfo3(snes,"Using Jorge's noise: noise=%g, sqrt(noise)=%g, h_more=%g\n",(double)noise,(double)ctx->error_rel,(double)h);

125:         ctx->compute_err_iter = iter;
126:         ctx->need_err         = PETSC_FALSE;
127:       }

129:       VecDotBegin(U,a,&dot);
130:       VecNormBegin(a,NORM_1,&sum);
131:       VecNormBegin(a,NORM_2,&norm);
132:       VecDotEnd(U,a,&dot);
133:       VecNormEnd(a,NORM_1,&sum);
134:       VecNormEnd(a,NORM_2,&norm);


137:       /* Safeguard for step sizes too small */
138:       if (sum == 0.0) {
139:         dot  = 1.0;
140:         norm = 1.0;
141:       } else if (PetscAbsScalar(dot) < umin*sum && PetscRealPart(dot) >= 0.0) dot = umin*sum;
142:       else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin*sum) dot = -umin*sum;
143:       h = PetscRealPart(ctx->error_rel*dot/(norm*norm));
144:     }
145:   } else h = ctx->h;

147:   if (!ctx->jorge || !ctx->need_h) {PetscInfo1(snes,"h = %g\n",(double)h);}

149:   /* Evaluate function at F(u + ha) */
150:   hs   = h;
151:   VecWAXPY(w,hs,a,U);
152:   eval_fct(snes,w,y);
153:   VecAXPY(y,-1.0,F);
154:   VecScale(y,1.0/hs);
155:   if (mat->nullsp) {MatNullSpaceRemove(mat->nullsp,y);}

157:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
158:   return(0);
159: }

161: /*@C
162:    SNESMatrixFreeCreate2 - Creates a matrix-free matrix
163:    context for use with a SNES solver.  This matrix can be used as
164:    the Jacobian argument for the routine SNESSetJacobian().

166:    Input Parameters:
167: .  snes - the SNES context
168: .  x - vector where SNES solution is to be stored.

170:    Output Parameter:
171: .  J - the matrix-free matrix

173:    Level: advanced

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

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

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

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

198:    Options Database Keys:
199: $  -snes_mf_err <error_rel>
200: $  -snes_mf_unim <umin>
201: $  -snes_mf_compute_err
202: $  -snes_mf_freq_err <freq>
203: $  -snes_mf_jorge

205: .keywords: SNES, default, matrix-free, create, matrix

207: .seealso: MatDestroy(), MatMFFDSetFunctionError()
208: @*/
209: PetscErrorCode  SNESDefaultMatrixFreeCreate2(SNES snes,Vec x,Mat *J)
210: {
211:   MPI_Comm       comm;
212:   MFCtx_Private  *mfctx;
214:   PetscInt       n,nloc;
215:   PetscBool      flg;
216:   char           p[64];

219:   PetscNewLog(snes,&mfctx);
220:   mfctx->sp               = 0;
221:   mfctx->snes             = snes;
222:   mfctx->error_rel        = PETSC_SQRT_MACHINE_EPSILON;
223:   mfctx->umin             = 1.e-6;
224:   mfctx->h                = 0.0;
225:   mfctx->need_h           = PETSC_TRUE;
226:   mfctx->need_err         = PETSC_FALSE;
227:   mfctx->compute_err      = PETSC_FALSE;
228:   mfctx->compute_err_freq = 0;
229:   mfctx->compute_err_iter = -1;
230:   mfctx->compute_err      = PETSC_FALSE;
231:   mfctx->jorge            = PETSC_FALSE;

233:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_err",&mfctx->error_rel,NULL);
234:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_umin",&mfctx->umin,NULL);
235:   PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_jorge",&mfctx->jorge,NULL);
236:   PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_compute_err",&mfctx->compute_err,NULL);
237:   PetscOptionsGetInt(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_freq_err",&mfctx->compute_err_freq,&flg);
238:   if (flg) {
239:     if (mfctx->compute_err_freq < 0) mfctx->compute_err_freq = 0;
240:     mfctx->compute_err = PETSC_TRUE;
241:   }
242:   if (mfctx->compute_err) mfctx->need_err = PETSC_TRUE;
243:   if (mfctx->jorge || mfctx->compute_err) {
244:     SNESDiffParameterCreate_More(snes,x,&mfctx->data);
245:   } else mfctx->data = 0;

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

272:   PetscLogObjectParent((PetscObject)*J,(PetscObject)mfctx->w);
273:   PetscLogObjectParent((PetscObject)snes,(PetscObject)*J);
274:   return(0);
275: }

277: /*@C
278:    SNESDefaultMatrixFreeSetParameters2 - Sets the parameters for the approximation of
279:    matrix-vector products using finite differences.

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

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

285: $        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
286: $          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
287: $

289:    Input Parameters:
290: +  mat - the matrix
291: .  error_rel - relative error (should be set to the square root of
292:      the relative error in the function evaluations)
293: .  umin - minimum allowable u-value
294: -  h - differencing parameter

296:    Level: advanced

298:    Notes:
299:    If the user sets the parameter h directly, then this value will be used
300:    instead of the default computation indicated above.

302: .keywords: SNES, matrix-free, parameters

304: .seealso: MatCreateSNESMF()
305: @*/
306: PetscErrorCode  SNESDefaultMatrixFreeSetParameters2(Mat mat,PetscReal error,PetscReal umin,PetscReal h)
307: {
308:   MFCtx_Private  *ctx;

312:   MatShellGetContext(mat,(void**)&ctx);
313:   if (ctx) {
314:     if (error != PETSC_DEFAULT) ctx->error_rel = error;
315:     if (umin  != PETSC_DEFAULT) ctx->umin = umin;
316:     if (h     != PETSC_DEFAULT) {
317:       ctx->h      = h;
318:       ctx->need_h = PETSC_FALSE;
319:     }
320:   }
321:   return(0);
322: }

324: PetscErrorCode  SNESUnSetMatrixFreeParameter(SNES snes)
325: {
326:   MFCtx_Private  *ctx;
328:   Mat            mat;

331:   SNESGetJacobian(snes,&mat,NULL,NULL,NULL);
332:   MatShellGetContext(mat,(void**)&ctx);
333:   if (ctx) ctx->need_h = PETSC_TRUE;
334:   return(0);
335: }