Actual source code: mffddef.c

      2: /*
      3:   Implements the DS PETSc approach for computing the h
      4:   parameter used with the finite difference based matrix-free
      5:   Jacobian-vector products.

      7:   To make your own: clone this file and modify for your needs.

      9:   Mandatory functions:
     10:   -------------------
     11:       MatMFFDCompute_  - for a given point and direction computes h

     13:       MatCreateMFFD _ - fills in the MatMFFD data structure
     14:                            for this particular implementation

     17:    Optional functions:
     18:    -------------------
     19:       MatMFFDView_ - prints information about the parameters being used.
     20:                        This is called when SNESView() or -snes_view is used.

     22:       MatMFFDSetFromOptions_ - checks the options database for options that
     23:                                apply to this method.

     25:       MatMFFDDestroy_ - frees any space allocated by the routines above

     27: */

     29: /*
     30:     This include file defines the data structure  MatMFFD that
     31:    includes information about the computation of h. It is shared by
     32:    all implementations that people provide
     33: */
     34: #include <petsc/private/matimpl.h>
     35: #include <../src/mat/impls/mffd/mffdimpl.h>

     37: /*
     38:       The  method has one parameter that is used to
     39:    "cutoff" very small values. This is stored in a data structure
     40:    that is only visible to this file. If your method has no parameters
     41:    it can omit this, if it has several simply reorganize the data structure.
     42:    The data structure is "hung-off" the MatMFFD data structure in
     43:    the void *hctx; field.
     44: */
     45: typedef struct {
     46:   PetscReal umin;          /* minimum allowable u'a value relative to |u|_1 */
     47: } MatMFFD_DS;

     49: /*
     50:    MatMFFDCompute_DS - Standard PETSc code for computing the
     51:    differencing parameter (h) for use with matrix-free finite differences.

     53:    Input Parameters:
     54: +  ctx - the matrix free context
     55: .  U - the location at which you want the Jacobian
     56: -  a - the direction you want the derivative

     59:    Output Parameter:
     60: .  h - the scale computed

     62: */
     63: static PetscErrorCode MatMFFDCompute_DS(MatMFFD ctx,Vec U,Vec a,PetscScalar *h,PetscBool  *zeroa)
     64: {
     65:   MatMFFD_DS     *hctx = (MatMFFD_DS*)ctx->hctx;
     66:   PetscReal      nrm,sum,umin = hctx->umin;
     67:   PetscScalar    dot;

     71:   if (!(ctx->count % ctx->recomputeperiod)) {
     72:     /*
     73:      This algorithm requires 2 norms and 1 inner product. Rather than
     74:      use directly the VecNorm() and VecDot() routines (and thus have
     75:      three separate collective operations, we use the VecxxxBegin/End() routines
     76:     */
     77:     VecDotBegin(U,a,&dot);
     78:     VecNormBegin(a,NORM_1,&sum);
     79:     VecNormBegin(a,NORM_2,&nrm);
     80:     VecDotEnd(U,a,&dot);
     81:     VecNormEnd(a,NORM_1,&sum);
     82:     VecNormEnd(a,NORM_2,&nrm);

     84:     if (nrm == 0.0) {
     85:       *zeroa = PETSC_TRUE;
     86:       return(0);
     87:     }
     88:     *zeroa = PETSC_FALSE;

     90:     /*
     91:       Safeguard for step sizes that are "too small"
     92:     */
     93:     if (PetscAbsScalar(dot) < umin*sum && PetscRealPart(dot) >= 0.0) dot = umin*sum;
     94:     else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin*sum) dot = -umin*sum;
     95:     *h = ctx->error_rel*dot/(nrm*nrm);
     96:     if (PetscIsInfOrNanScalar(*h)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Differencing parameter is not a number sum = %g dot = %g norm = %g",(double)sum,(double)PetscRealPart(dot),(double)nrm);
     97:   } else {
     98:     *h = ctx->currenth;
     99:   }
    100:   ctx->count++;
    101:   return(0);
    102: }

    104: /*
    105:    MatMFFDView_DS - Prints information about this particular
    106:    method for computing h. Note that this does not print the general
    107:    information about the matrix-free method, as such info is printed
    108:    by the calling routine.

    110:    Input Parameters:
    111: +  ctx - the matrix free context
    112: -  viewer - the PETSc viewer
    113: */
    114: static PetscErrorCode MatMFFDView_DS(MatMFFD ctx,PetscViewer viewer)
    115: {
    116:   MatMFFD_DS     *hctx = (MatMFFD_DS*)ctx->hctx;
    118:   PetscBool      iascii;

    121:   /*
    122:      Currently this only handles the ascii file viewers, others
    123:      could be added, but for this type of object other viewers
    124:      make less sense
    125:   */
    126:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    127:   if (iascii) {
    128:     PetscViewerASCIIPrintf(viewer,"    umin=%g (minimum iterate parameter)\n",(double)hctx->umin);
    129:   }
    130:   return(0);
    131: }

    133: /*
    134:    MatMFFDSetFromOptions_DS - Looks in the options database for
    135:    any options appropriate for this method.

    137:    Input Parameter:
    138: .  ctx - the matrix free context

    140: */
    141: static PetscErrorCode MatMFFDSetFromOptions_DS(PetscOptionItems *PetscOptionsObject,MatMFFD ctx)
    142: {
    144:   MatMFFD_DS     *hctx = (MatMFFD_DS*)ctx->hctx;

    147:   PetscOptionsHead(PetscOptionsObject,"Finite difference matrix free parameters");
    148:   PetscOptionsReal("-mat_mffd_umin","umin","MatMFFDDSSetUmin",hctx->umin,&hctx->umin,NULL);
    149:   PetscOptionsTail();
    150:   return(0);
    151: }

    153: /*
    154:    MatMFFDDestroy_DS - Frees the space allocated by
    155:    MatCreateMFFD_DS().

    157:    Input Parameter:
    158: .  ctx - the matrix free context

    160:    Notes:
    161:    Does not free the ctx, that is handled by the calling routine
    162: */
    163: static PetscErrorCode MatMFFDDestroy_DS(MatMFFD ctx)
    164: {

    168:   PetscFree(ctx->hctx);
    169:   return(0);
    170: }

    172: /*
    173:    The following two routines use the PetscObjectCompose() and PetscObjectQuery()
    174:    mechanism to allow the user to change the Umin parameter used in this method.
    175: */
    176: PetscErrorCode MatMFFDDSSetUmin_DS(Mat mat,PetscReal umin)
    177: {
    178:   MatMFFD        ctx=NULL;
    179:   MatMFFD_DS     *hctx;

    183:   MatShellGetContext(mat,&ctx);
    184:   if (!ctx) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MatMFFDDSSetUmin() attached to non-shell matrix");
    185:   hctx       = (MatMFFD_DS*)ctx->hctx;
    186:   hctx->umin = umin;
    187:   return(0);
    188: }

    190: /*@
    191:     MatMFFDDSSetUmin - Sets the "umin" parameter used by the
    192:     PETSc routine for computing the differencing parameter, h, which is used
    193:     for matrix-free Jacobian-vector products.

    195:    Input Parameters:
    196: +  A - the matrix created with MatCreateSNESMF()
    197: -  umin - the parameter

    199:    Level: advanced

    201:    Notes:
    202:    See the manual page for MatCreateSNESMF() for a complete description of the
    203:    algorithm used to compute h.

    205: .seealso: MatMFFDSetFunctionError(), MatCreateSNESMF()

    207: @*/
    208: PetscErrorCode  MatMFFDDSSetUmin(Mat A,PetscReal umin)
    209: {

    214:   PetscTryMethod(A,"MatMFFDDSSetUmin_C",(Mat,PetscReal),(A,umin));
    215:   return(0);
    216: }

    218: /*MC
    219:      MATMFFD_DS - the code for compute the "h" used in the finite difference
    220:             matrix-free matrix vector product.  This code
    221:         implements the strategy in Dennis and Schnabel, "Numerical Methods for Unconstrained
    222:         Optimization and Nonlinear Equations".

    224:    Options Database Keys:
    225: .  -mat_mffd_umin <umin> see MatMFFDDSSetUmin()

    227:    Level: intermediate

    229:    Notes:
    230:     Requires 2 norms and 1 inner product, but they are computed together
    231:        so only one parallel collective operation is needed. See MATMFFD_WP for a method
    232:        (with GMRES) that requires NO collective operations.

    234:    Formula used:
    235:      F'(u)*a = [F(u+h*a) - F(u)]/h where
    236:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
    237:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
    238:  where
    239:      error_rel = square root of relative error in function evaluation
    240:      umin = minimum iterate parameter

    242: .seealso: MATMFFD, MatCreateMFFD(), MatCreateSNESMF(), MATMFFD_WP, MatMFFDDSSetUmin()

    244: M*/
    245: PETSC_EXTERN PetscErrorCode MatCreateMFFD_DS(MatMFFD ctx)
    246: {
    247:   MatMFFD_DS     *hctx;

    251:   /* allocate my own private data structure */
    252:   PetscNewLog(ctx,&hctx);
    253:   ctx->hctx = (void*)hctx;
    254:   /* set a default for my parameter */
    255:   hctx->umin = 1.e-6;

    257:   /* set the functions I am providing */
    258:   ctx->ops->compute        = MatMFFDCompute_DS;
    259:   ctx->ops->destroy        = MatMFFDDestroy_DS;
    260:   ctx->ops->view           = MatMFFDView_DS;
    261:   ctx->ops->setfromoptions = MatMFFDSetFromOptions_DS;

    263:   PetscObjectComposeFunction((PetscObject)ctx->mat,"MatMFFDDSSetUmin_C",MatMFFDDSSetUmin_DS);
    264:   return(0);
    265: }