interface/noise/snesmfj2.c

#include <petsc/private/snesimpl.h> /*I  "petscsnes.h"   I*/
/* matimpl.h is needed only for logging of matrix operation */
#include <petsc/private/matimpl.h>

PETSC_INTERN PetscErrorCode SNESUnSetMatrixFreeParameter(SNES);

PETSC_INTERN PetscErrorCode SNESDiffParameterCreate_More(SNES, Vec, void **);
PETSC_INTERN PetscErrorCode SNESDiffParameterCompute_More(SNES, void *, Vec, Vec, PetscReal *, PetscReal *);
PETSC_INTERN PetscErrorCode SNESDiffParameterDestroy_More(void *);

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

static PetscErrorCode SNESMatrixFreeDestroy2_Private(Mat mat)
{
  MFCtx_Private *ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(mat, &ctx));
  PetscCall(VecDestroy(&ctx->w));
  PetscCall(MatNullSpaceDestroy(&ctx->sp));
  if (ctx->jorge || ctx->compute_err) PetscCall(SNESDiffParameterDestroy_More(ctx->data));
  PetscCall(PetscFree(ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   SNESMatrixFreeView2_Private - Views matrix-free parameters.
 */
static PetscErrorCode SNESMatrixFreeView2_Private(Mat J, PetscViewer viewer)
{
  MFCtx_Private *ctx;
  PetscBool      iascii;

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

/*
  SNESMatrixFreeMult2_Private - Default matrix-free form for Jacobian-vector
  product, y = F'(u)*a:
        y = (F(u + ha) - F(u)) /h,
  where F = nonlinear function, as set by SNESSetFunction()
        u = current iterate
        h = difference interval
*/
static PetscErrorCode SNESMatrixFreeMult2_Private(Mat mat, Vec a, Vec y)
{
  MFCtx_Private *ctx;
  SNES           snes;
  PetscReal      h, norm, sum, umin, noise;
  PetscScalar    hs, dot;
  Vec            w, U, F;
  MPI_Comm       comm;
  PetscInt       iter;
  PetscErrorCode (*eval_fct)(SNES, Vec, Vec);

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

  PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
  PetscCall(MatShellGetContext(mat, &ctx));
  snes = ctx->snes;
  w    = ctx->w;
  umin = ctx->umin;

  PetscCall(SNESGetSolution(snes, &U));
  eval_fct = SNESComputeFunction;
  PetscCall(SNESGetFunction(snes, &F, NULL, NULL));

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

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

        ctx->error_rel = PetscSqrtReal(noise);

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

        ctx->compute_err_iter = iter;
        ctx->need_err         = PETSC_FALSE;
      }

      PetscCall(VecDotBegin(U, a, &dot));
      PetscCall(VecNormBegin(a, NORM_1, &sum));
      PetscCall(VecNormBegin(a, NORM_2, &norm));
      PetscCall(VecDotEnd(U, a, &dot));
      PetscCall(VecNormEnd(a, NORM_1, &sum));
      PetscCall(VecNormEnd(a, NORM_2, &norm));

      /* Safeguard for step sizes too small */
      if (sum == 0.0) {
        dot  = 1.0;
        norm = 1.0;
      } else if (PetscAbsScalar(dot) < umin * sum && PetscRealPart(dot) >= 0.0) dot = umin * sum;
      else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin * sum) dot = -umin * sum;
      h = PetscRealPart(ctx->error_rel * dot / (norm * norm));
    }
  } else h = ctx->h;

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

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

  PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatCreateSNESMFMore - Creates a matrix-free matrix
  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
  the Jacobian argument for the routine `SNESSetJacobian()`.

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

  Output Parameter:
. J - the matrix-free matrix

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

  Level: advanced

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

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

.vb
       J(u)*a = [J(u+h*a) - J(u)]/h,
   where by default
        h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
          = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
   where
        error_rel = square root of relative error in function evaluation
        umin = minimum iterate parameter
   Alternatively, the differencing parameter, h, can be set using
   Jorge's nifty new strategy if one specifies the option
          -snes_mf_jorge
.ve

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

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

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

  PetscFunctionBegin;
  PetscCall(PetscNew(&mfctx));
  mfctx->sp               = NULL;
  mfctx->snes             = snes;
  mfctx->error_rel        = PETSC_SQRT_MACHINE_EPSILON;
  mfctx->umin             = 1.e-6;
  mfctx->h                = 0.0;
  mfctx->need_h           = PETSC_TRUE;
  mfctx->need_err         = PETSC_FALSE;
  mfctx->compute_err      = PETSC_FALSE;
  mfctx->compute_err_freq = 0;
  mfctx->compute_err_iter = -1;
  mfctx->compute_err      = PETSC_FALSE;
  mfctx->jorge            = PETSC_FALSE;

  PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_err", &mfctx->error_rel, NULL));
  PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_umin", &mfctx->umin, NULL));
  PetscCall(PetscOptionsGetBool(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_jorge", &mfctx->jorge, NULL));
  PetscCall(PetscOptionsGetBool(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_compute_err", &mfctx->compute_err, NULL));
  PetscCall(PetscOptionsGetInt(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_freq_err", &mfctx->compute_err_freq, &flg));
  if (flg) {
    if (mfctx->compute_err_freq < 0) mfctx->compute_err_freq = 0;
    mfctx->compute_err = PETSC_TRUE;
  }
  if (mfctx->compute_err) mfctx->need_err = PETSC_TRUE;
  if (mfctx->jorge || mfctx->compute_err) {
    PetscCall(SNESDiffParameterCreate_More(snes, x, &mfctx->data));
  } else mfctx->data = NULL;

  PetscCall(PetscOptionsHasHelp(((PetscObject)snes)->options, &flg));
  PetscCall(PetscStrncpy(p, "-", sizeof(p)));
  if (((PetscObject)snes)->prefix) PetscCall(PetscStrlcat(p, ((PetscObject)snes)->prefix, sizeof(p)));
  if (flg) {
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " Matrix-free Options (via SNES):\n"));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_err <err>: set sqrt of relative error in function (default %g)\n", p, (double)mfctx->error_rel));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_umin <umin>: see users manual (default %g)\n", p, (double)mfctx->umin));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_jorge: use Jorge More's method\n", p));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_compute_err: compute sqrt or relative error in function\n", p));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_freq_err <freq>: frequency to recompute this (default only once)\n", p));
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), "   %ssnes_mf_noise_file <file>: set file for printing noise info\n", p));
  }
  PetscCall(VecDuplicate(x, &mfctx->w));
  PetscCall(PetscObjectGetComm((PetscObject)x, &comm));
  PetscCall(VecGetSize(x, &n));
  PetscCall(VecGetLocalSize(x, &nloc));
  PetscCall(MatCreate(comm, J));
  PetscCall(MatSetSizes(*J, nloc, n, n, n));
  PetscCall(MatSetType(*J, MATSHELL));
  PetscCall(MatShellSetContext(*J, mfctx));
  PetscCall(MatShellSetOperation(*J, MATOP_MULT, (void (*)(void))SNESMatrixFreeMult2_Private));
  PetscCall(MatShellSetOperation(*J, MATOP_DESTROY, (void (*)(void))SNESMatrixFreeDestroy2_Private));
  PetscCall(MatShellSetOperation(*J, MATOP_VIEW, (void (*)(void))SNESMatrixFreeView2_Private));
  PetscCall(MatSetUp(*J));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

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

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

  Level: advanced

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

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

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(mat, &ctx));
  if (ctx) {
    if (error != (PetscReal)PETSC_DEFAULT) ctx->error_rel = error;
    if (umin != (PetscReal)PETSC_DEFAULT) ctx->umin = umin;
    if (h != (PetscReal)PETSC_DEFAULT) {
      ctx->h      = h;
      ctx->need_h = PETSC_FALSE;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode SNESUnSetMatrixFreeParameter(SNES snes)
{
  MFCtx_Private *ctx;
  Mat            mat;

  PetscFunctionBegin;
  PetscCall(SNESGetJacobian(snes, &mat, NULL, NULL, NULL));
  PetscCall(MatShellGetContext(mat, &ctx));
  if (ctx) ctx->need_h = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}