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: {
 33:   MFCtx_Private  *ctx;

 36:   MatShellGetContext(mat,&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,&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,&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);

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

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

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

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

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

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

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

172:    Level: advanced

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

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

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

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

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

204: .seealso: MatDestroy(), MatMFFDSetFunctionError()
205: @*/
206: PetscErrorCode  SNESDefaultMatrixFreeCreate2(SNES snes,Vec x,Mat *J)
207: {
208:   MPI_Comm       comm;
209:   MFCtx_Private  *mfctx;
211:   PetscInt       n,nloc;
212:   PetscBool      flg;
213:   char           p[64];

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

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

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

269:   PetscLogObjectParent((PetscObject)*J,(PetscObject)mfctx->w);
270:   PetscLogObjectParent((PetscObject)snes,(PetscObject)*J);
271:   return(0);
272: }

274: /*@C
275:    SNESDefaultMatrixFreeSetParameters2 - Sets the parameters for the approximation of
276:    matrix-vector products using finite differences.

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

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

282: $        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
283: $          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
284: $

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

293:    Level: advanced

295:    Notes:
296:    If the user sets the parameter h directly, then this value will be used
297:    instead of the default computation indicated above.

299: .seealso: MatCreateSNESMF()
300: @*/
301: PetscErrorCode  SNESDefaultMatrixFreeSetParameters2(Mat mat,PetscReal error,PetscReal umin,PetscReal h)
302: {
303:   MFCtx_Private  *ctx;

307:   MatShellGetContext(mat,&ctx);
308:   if (ctx) {
309:     if (error != PETSC_DEFAULT) ctx->error_rel = error;
310:     if (umin  != PETSC_DEFAULT) ctx->umin = umin;
311:     if (h     != PETSC_DEFAULT) {
312:       ctx->h      = h;
313:       ctx->need_h = PETSC_FALSE;
314:     }
315:   }
316:   return(0);
317: }

319: PetscErrorCode  SNESUnSetMatrixFreeParameter(SNES snes)
320: {
321:   MFCtx_Private  *ctx;
323:   Mat            mat;

326:   SNESGetJacobian(snes,&mat,NULL,NULL,NULL);
327:   MatShellGetContext(mat,&ctx);
328:   if (ctx) ctx->need_h = PETSC_TRUE;
329:   return(0);
330: }