Actual source code: snesmfj2.c

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

      5: PETSC_INTERN PetscErrorCode SNESUnSetMatrixFreeParameter(SNES);

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

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

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

     31:   PetscFunctionBegin;
     32:   PetscCall(MatShellGetContext(mat, &ctx));
     33:   PetscCall(VecDestroy(&ctx->w));
     34:   PetscCall(MatNullSpaceDestroy(&ctx->sp));
     35:   if (ctx->jorge || ctx->compute_err) PetscCall(SNESDiffParameterDestroy_More(ctx->data));
     36:   PetscCall(PetscFree(ctx));
     37:   PetscFunctionReturn(PETSC_SUCCESS);
     38: }

     40: /*
     41:    SNESMatrixFreeView2_Private - Views matrix-free parameters.
     42:  */
     43: static PetscErrorCode SNESMatrixFreeView2_Private(Mat J, PetscViewer viewer)
     44: {
     45:   MFCtx_Private *ctx;
     46:   PetscBool      isascii;

     48:   PetscFunctionBegin;
     49:   PetscCall(MatShellGetContext(J, &ctx));
     50:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
     51:   if (isascii) {
     52:     PetscCall(PetscViewerASCIIPrintf(viewer, "  SNES matrix-free approximation:\n"));
     53:     if (ctx->jorge) PetscCall(PetscViewerASCIIPrintf(viewer, "    using Jorge's method of determining differencing parameter\n"));
     54:     PetscCall(PetscViewerASCIIPrintf(viewer, "    err=%g (relative error in function evaluation)\n", (double)ctx->error_rel));
     55:     PetscCall(PetscViewerASCIIPrintf(viewer, "    umin=%g (minimum iterate parameter)\n", (double)ctx->umin));
     56:     if (ctx->compute_err) PetscCall(PetscViewerASCIIPrintf(viewer, "    freq_err=%" PetscInt_FMT " (frequency for computing err)\n", ctx->compute_err_freq));
     57:   }
     58:   PetscFunctionReturn(PETSC_SUCCESS);
     59: }

     61: /*
     62:   SNESMatrixFreeMult2_Private - Default matrix-free form for Jacobian-vector
     63:   product, y = F'(u)*a:
     64:         y = (F(u + ha) - F(u)) /h,
     65:   where F = nonlinear function, as set by SNESSetFunction()
     66:         u = current iterate
     67:         h = difference interval
     68: */
     69: static PetscErrorCode SNESMatrixFreeMult2_Private(Mat mat, Vec a, Vec y)
     70: {
     71:   MFCtx_Private *ctx;
     72:   SNES           snes;
     73:   PetscReal      h, norm, sum, umin, noise;
     74:   PetscScalar    hs, dot;
     75:   Vec            w, U, F;
     76:   MPI_Comm       comm;
     77:   PetscInt       iter;
     78:   PetscErrorCode (*eval_fct)(SNES, Vec, Vec);

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

     87:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
     88:   PetscCall(MatShellGetContext(mat, &ctx));
     89:   snes = ctx->snes;
     90:   w    = ctx->w;
     91:   umin = ctx->umin;

     93:   PetscCall(SNESGetSolution(snes, &U));
     94:   eval_fct = SNESComputeFunction;
     95:   PetscCall(SNESGetFunction(snes, &F, NULL, NULL));

     97:   /* Determine a "good" step size, h */
     98:   if (ctx->need_h) {
     99:     /* Use Jorge's method to compute h */
    100:     if (ctx->jorge) {
    101:       PetscCall(SNESDiffParameterCompute_More(snes, ctx->data, U, a, &noise, &h));

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

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

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

    115:         ctx->compute_err_iter = iter;
    116:         ctx->need_err         = PETSC_FALSE;
    117:       }

    119:       PetscCall(VecDotBegin(U, a, &dot));
    120:       PetscCall(VecNormBegin(a, NORM_1, &sum));
    121:       PetscCall(VecNormBegin(a, NORM_2, &norm));
    122:       PetscCall(VecDotEnd(U, a, &dot));
    123:       PetscCall(VecNormEnd(a, NORM_1, &sum));
    124:       PetscCall(VecNormEnd(a, NORM_2, &norm));

    126:       /* Safeguard for step sizes too small */
    127:       if (sum == 0.0) {
    128:         dot  = 1.0;
    129:         norm = 1.0;
    130:       } else if (PetscAbsScalar(dot) < umin * sum && PetscRealPart(dot) >= 0.0) dot = umin * sum;
    131:       else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin * sum) dot = -umin * sum;
    132:       h = PetscRealPart(ctx->error_rel * dot / (norm * norm));
    133:     }
    134:   } else h = ctx->h;

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

    138:   /* Evaluate function at F(u + ha) */
    139:   hs = h;
    140:   PetscCall(VecWAXPY(w, hs, a, U));
    141:   PetscCall(eval_fct(snes, w, y));
    142:   PetscCall(VecAXPY(y, -1.0, F));
    143:   PetscCall(VecScale(y, 1.0 / hs));
    144:   if (mat->nullsp) PetscCall(MatNullSpaceRemove(mat->nullsp, y));

    146:   PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
    147:   PetscFunctionReturn(PETSC_SUCCESS);
    148: }

    150: /*@
    151:   MatCreateSNESMFMore - Creates a matrix-free matrix
    152:   context for use with a `SNES` solver that uses the More method to compute an optimal h based on the noise of the function.  This matrix can be used as
    153:   the Jacobian argument for the routine `SNESSetJacobian()`.

    155:   Input Parameters:
    156: + snes - the `SNES` context
    157: - x    - vector where `SNES` solution is to be stored.

    159:   Output Parameter:
    160: . J - the matrix-free matrix

    162:   Options Database Keys:
    163: + -snes_mf_err <error_rel> - see `MatCreateSNESMF()`
    164: . -snes_mf_umin <umin>     - see `MatCreateSNESMF()`
    165: . -snes_mf_compute_err     - compute the square root or relative error in function
    166: . -snes_mf_freq_err <freq> - set the frequency to recompute the parameters
    167: - -snes_mf_jorge           - use the method of Jorge More

    169:   Level: advanced

    171:   Notes:
    172:   This is an experimental approach, use `MatCreateSNESMF()`.

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

    178: .vb
    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 function evaluation
    185:         umin = minimum iterate parameter
    186:    Alternatively, the differencing parameter, h, can be set using
    187:    Jorge's nifty new strategy if one specifies the option
    188:           -snes_mf_jorge
    189: .ve

    191:   The user can set these parameters via `MatMFFDSetFunctionError()`.

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

    196: .seealso: [](ch_snes), `SNESCreateMF()`, `MatCreateMFFD()`, `MatDestroy()`, `MatMFFDSetFunctionError()`
    197: @*/
    198: PetscErrorCode MatCreateSNESMFMore(SNES snes, Vec x, Mat *J)
    199: {
    200:   MPI_Comm       comm;
    201:   MFCtx_Private *mfctx;
    202:   PetscInt       n, nloc;
    203:   PetscBool      flg;
    204:   char           p[64];

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

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

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

    261: /*@
    262:   MatSNESMFMoreSetParameters - Sets the parameters for the approximation of
    263:   matrix-vector products using finite differences, see  `MatCreateSNESMFMore()`

    265:   Input Parameters:
    266: + mat   - the matrix
    267: . error - relative error (should be set to the square root of the relative error in the function evaluations)
    268: . umin  - minimum allowable u-value
    269: - h     - differencing parameter

    271:   Options Database Keys:
    272: + -snes_mf_err <error_rel> - see `MatCreateSNESMF()`
    273: . -snes_mf_umin <umin>     - see `MatCreateSNESMF()`
    274: . -snes_mf_compute_err     - compute the square root or relative error in function
    275: . -snes_mf_freq_err <freq> - set the frequency to recompute the parameters
    276: - -snes_mf_jorge           - use the method of Jorge More

    278:   Level: advanced

    280:   Note:
    281:   If the user sets the parameter `h` directly, then this value will be used
    282:   instead of the default computation as discussed in `MatCreateSNESMFMore()`

    284: .seealso: [](ch_snes), `SNES`, `MatCreateSNESMF()`, `MatCreateSNESMFMore()`
    285: @*/
    286: PetscErrorCode MatSNESMFMoreSetParameters(Mat mat, PetscReal error, PetscReal umin, PetscReal h)
    287: {
    288:   MFCtx_Private *ctx;

    290:   PetscFunctionBegin;
    291:   PetscCall(MatShellGetContext(mat, &ctx));
    292:   if (ctx) {
    293:     if (error != (PetscReal)PETSC_DEFAULT) ctx->error_rel = error;
    294:     if (umin != (PetscReal)PETSC_DEFAULT) ctx->umin = umin;
    295:     if (h != (PetscReal)PETSC_DEFAULT) {
    296:       ctx->h      = h;
    297:       ctx->need_h = PETSC_FALSE;
    298:     }
    299:   }
    300:   PetscFunctionReturn(PETSC_SUCCESS);
    301: }

    303: PetscErrorCode SNESUnSetMatrixFreeParameter(SNES snes)
    304: {
    305:   MFCtx_Private *ctx;
    306:   Mat            mat;

    308:   PetscFunctionBegin;
    309:   PetscCall(SNESGetJacobian(snes, &mat, NULL, NULL, NULL));
    310:   PetscCall(MatShellGetContext(mat, &ctx));
    311:   if (ctx) ctx->need_h = PETSC_TRUE;
    312:   PetscFunctionReturn(PETSC_SUCCESS);
    313: }