Date: 2015-10-02T22:23:40+00:00

Actual source code: snesmfj2.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/snesimpl.h>   /*I  "petscsnes.h"   I*/
      3: /* matimpl.h is needed only for logging of matrix operation */
      4: #include <petsc/private/matimpl.h>

      6: extern PetscErrorCode SNESDiffParameterCreate_More(SNES,Vec,void**);
      7: extern PetscErrorCode SNESDiffParameterCompute_More(SNES,void*,Vec,Vec,PetscReal*,PetscReal*);
      8: extern PetscErrorCode SNESDiffParameterDestroy_More(void*);

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

     28: PetscErrorCode SNESMatrixFreeDestroy2_Private(Mat mat)
     29: {
     31:   MFCtx_Private  *ctx;

     34:   MatShellGetContext(mat,(void**)&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: }

     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: }

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

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

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

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

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

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

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

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

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

    127:         ctx->compute_err_iter = iter;
    128:         ctx->need_err         = PETSC_FALSE;
    129:       }

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

    139:       /* Safeguard for step sizes too small */
    140:       if (sum == 0.0) {
    141:         dot  = 1.0;
    142:         norm = 1.0;
    143:       } else if (PetscAbsScalar(dot) < umin*sum && PetscRealPart(dot) >= 0.0) dot = umin*sum;
    144:       else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin*sum) dot = -umin*sum;
    145:       h = PetscRealPart(ctx->error_rel*dot/(norm*norm));
    146:     }
    147:   } else h = ctx->h;

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

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

    159:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
    160:   return(0);
    161: }

    165: /*@C
    166:    SNESMatrixFreeCreate2 - Creates a matrix-free matrix
    167:    context for use with a SNES solver.  This matrix can be used as
    168:    the Jacobian argument for the routine SNESSetJacobian().

    170:    Input Parameters:
    171: .  snes - the SNES context
    172: .  x - vector where SNES solution is to be stored.

    174:    Output Parameter:
    175: .  J - the matrix-free matrix

    177:    Level: advanced

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

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

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

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

    202:    Options Database Keys:
    203: $  -snes_mf_err <error_rel>
    204: $  -snes_mf_unim <umin>
    205: $  -snes_mf_compute_err
    206: $  -snes_mf_freq_err <freq>
    207: $  -snes_mf_jorge

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

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

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

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

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

    275:   PetscLogObjectParent((PetscObject)*J,(PetscObject)mfctx->w);
    276:   PetscLogObjectParent((PetscObject)snes,(PetscObject)*J);
    277:   return(0);
    278: }

    282: /*@C
    283:    SNESDefaultMatrixFreeSetParameters2 - Sets the parameters for the approximation of
    284:    matrix-vector products using finite differences.

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

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

    290: $        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
    291: $          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
    292: $

    294:    Input Parameters:
    295: +  mat - the matrix
    296: .  error_rel - relative error (should be set to the square root of
    297:      the relative error in the function evaluations)
    298: .  umin - minimum allowable u-value
    299: -  h - differencing parameter

    301:    Level: advanced

    303:    Notes:
    304:    If the user sets the parameter h directly, then this value will be used
    305:    instead of the default computation indicated above.

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

    309: .seealso: MatCreateSNESMF()
    310: @*/
    311: PetscErrorCode  SNESDefaultMatrixFreeSetParameters2(Mat mat,PetscReal error,PetscReal umin,PetscReal h)
    312: {
    313:   MFCtx_Private  *ctx;

    317:   MatShellGetContext(mat,(void**)&ctx);
    318:   if (ctx) {
    319:     if (error != PETSC_DEFAULT) ctx->error_rel = error;
    320:     if (umin  != PETSC_DEFAULT) ctx->umin = umin;
    321:     if (h     != PETSC_DEFAULT) {
    322:       ctx->h      = h;
    323:       ctx->need_h = PETSC_FALSE;
    324:     }
    325:   }
    326:   return(0);
    327: }

    329: PetscErrorCode  SNESUnSetMatrixFreeParameter(SNES snes)
    330: {
    331:   MFCtx_Private  *ctx;
    333:   Mat            mat;

    336:   SNESGetJacobian(snes,&mat,NULL,NULL,NULL);
    337:   MatShellGetContext(mat,(void**)&ctx);
    338:   if (ctx) ctx->need_h = PETSC_TRUE;
    339:   return(0);
    340: }