impls/ncg/snesncg.c

#include <../src/snes/impls/ncg/snesncgimpl.h> /*I "petscsnes.h" I*/
const char *const SNESNCGTypes[] = {"FR", "PRP", "HS", "DY", "CD", "SNESNCGType", "SNES_NCG_", NULL};

static PetscErrorCode SNESReset_NCG(SNES snes)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESDestroy_NCG(SNES snes)
{
  PetscFunctionBegin;
  PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", NULL));
  PetscCall(PetscFree(snes->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESSetUp_NCG(SNES snes)
{
  PetscFunctionBegin;
  PetscCall(SNESSetWorkVecs(snes, 2));
  PetscCheck(snes->npcside != PC_RIGHT, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
  if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
{
  PetscScalar alpha, ptAp;
  Vec         X, Y, F, W;
  SNES        snes;
  PetscReal  *fnorm, *xnorm, *ynorm;

  PetscFunctionBegin;
  PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
  X     = linesearch->vec_sol;
  W     = linesearch->vec_sol_new;
  F     = linesearch->vec_func;
  Y     = linesearch->vec_update;
  fnorm = &linesearch->fnorm;
  xnorm = &linesearch->xnorm;
  ynorm = &linesearch->ynorm;

  if (!snes->jacobian) PetscCall(SNESSetUpMatrices(snes));

  /*
   The exact step size for unpreconditioned linear CG is just:
   alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
   */
  PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
  PetscCall(VecDot(F, F, &alpha));
  PetscCall(MatMult(snes->jacobian, Y, W));
  PetscCall(VecDot(Y, W, &ptAp));
  alpha = alpha / ptAp;
  PetscCall(VecAXPY(X, -alpha, Y));
  PetscCall(SNESComputeFunction(snes, X, F));

  PetscCall(VecNorm(F, NORM_2, fnorm));
  PetscCall(VecNorm(X, NORM_2, xnorm));
  PetscCall(VecNorm(Y, NORM_2, ynorm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   SNESLINESEARCHNCGLINEAR - Special line search only for the nonlinear CG solver `SNESNCG`

   This line search uses the length "as if" the problem is linear (that is what is computed by the linear CG method) using the Jacobian of the function.
   alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) where r (f) is the current residual (function value), p (y) is the current search direction.

   Notes:
   This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian

   This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone.

   Level: advanced

.seealso: `SNESLineSearchCreate()`, `SNESLineSearchSetType()`
M*/

PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
{
  PetscFunctionBegin;
  linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
  linesearch->ops->destroy        = NULL;
  linesearch->ops->setfromoptions = NULL;
  linesearch->ops->reset          = NULL;
  linesearch->ops->view           = NULL;
  linesearch->ops->setup          = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESSetFromOptions_NCG(SNES snes, PetscOptionItems *PetscOptionsObject)
{
  SNES_NCG      *ncg     = (SNES_NCG *)snes->data;
  PetscBool      debug   = PETSC_FALSE;
  SNESNCGType    ncgtype = ncg->type;
  SNESLineSearch linesearch;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "SNES NCG options");
  PetscCall(PetscOptionsBool("-snes_ncg_monitor", "Monitor the beta values used in the NCG iterations", "SNES", ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL));
  if (debug) ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
  PetscCall(PetscOptionsEnum("-snes_ncg_type", "NCG Beta type used", "SNESNCGSetType", SNESNCGTypes, (PetscEnum)ncg->type, (PetscEnum *)&ncgtype, NULL));
  PetscCall(SNESNCGSetType(snes, ncgtype));
  PetscOptionsHeadEnd();
  if (!snes->linesearch) {
    PetscCall(SNESGetLineSearch(snes, &linesearch));
    if (!((PetscObject)linesearch)->type_name) {
      if (!snes->npc) {
        PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHCP));
      } else {
        PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHL2));
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
{
  SNES_NCG *ncg = (SNES_NCG *)snes->data;
  PetscBool iascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, "  type: %s\n", SNESNCGTypes[ncg->type]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*

 Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.

 This routine is not currently used. I don't know what its intended purpose is.

 Note it has a hardwired differencing parameter of 1e-5

 */
PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar *ytJtf)
{
  PetscScalar ftf, ftg, fty, h;

  PetscFunctionBegin;
  PetscCall(VecDot(F, F, &ftf));
  PetscCall(VecDot(F, Y, &fty));
  h = 1e-5 * fty / fty;
  PetscCall(VecCopy(X, W));
  PetscCall(VecAXPY(W, -h, Y)); /* this is arbitrary */
  PetscCall(SNESComputeFunction(snes, W, G));
  PetscCall(VecDot(G, F, &ftg));
  *ytJtf = (ftg - ftf) / h;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
    SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`.

    Logically Collective

    Input Parameters:
+   snes - the iterative context
-   btype - update type

    Options Database Key:
.   -snes_ncg_type <prp,fr,hs,dy,cd> -strategy for selecting algorithm for computing beta

    Level: intermediate

    `SNESNCGType`s:
+   `SNES_NCG_FR` - Fletcher-Reeves update
.   `SNES_NCG_PRP` - Polak-Ribiere-Polyak update
.   `SNES_NCG_HS` - Hestenes-Steifel update
.   `SNES_NCG_DY` - Dai-Yuan update
-   `SNES_NCG_CD` - Conjugate Descent update

   Notes:
   `SNES_NCG_PRP` is the default, and the only one that tolerates generalized search directions.

   It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner,
   that is using -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()`?

   Developer Note:
   There should be a `SNESNCGSetType()`

.seealso: `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
@*/
PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
  PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
{
  SNES_NCG *ncg = (SNES_NCG *)snes->data;

  PetscFunctionBegin;
  ncg->type = btype;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

  Input Parameter:
. snes - the `SNES` context

  Output Parameter:
. outits - number of iterations until termination

  Application Interface Routine: SNESSolve()
*/
static PetscErrorCode SNESSolve_NCG(SNES snes)
{
  SNES_NCG            *ncg = (SNES_NCG *)snes->data;
  Vec                  X, dX, lX, F, dXold;
  PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
  PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
  PetscInt             maxits, i;
  SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
  SNESLineSearch       linesearch;
  SNESConvergedReason  reason;

  PetscFunctionBegin;
  PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

  PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite));
  snes->reason = SNES_CONVERGED_ITERATING;

  maxits = snes->max_its;        /* maximum number of iterations */
  X      = snes->vec_sol;        /* X^n */
  dXold  = snes->work[0];        /* The previous iterate of X */
  dX     = snes->work[1];        /* the preconditioned direction */
  lX     = snes->vec_sol_update; /* the conjugate direction */
  F      = snes->vec_func;       /* residual vector */

  PetscCall(SNESGetLineSearch(snes, &linesearch));

  PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
  snes->iter = 0;
  snes->norm = 0.;
  PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

  /* compute the initial function and preconditioned update dX */

  if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    PetscCall(SNESApplyNPC(snes, X, NULL, dX));
    PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
      snes->reason = SNES_DIVERGED_INNER;
      PetscFunctionReturn(PETSC_SUCCESS);
    }
    PetscCall(VecCopy(dX, F));
    PetscCall(VecNorm(F, NORM_2, &fnorm));
  } else {
    if (!snes->vec_func_init_set) {
      PetscCall(SNESComputeFunction(snes, X, F));
    } else snes->vec_func_init_set = PETSC_FALSE;

    /* convergence test */
    PetscCall(VecNorm(F, NORM_2, &fnorm));
    SNESCheckFunctionNorm(snes, fnorm);
    PetscCall(VecCopy(F, dX));
  }
  if (snes->npc) {
    if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
      PetscCall(SNESApplyNPC(snes, X, F, dX));
      PetscCall(SNESGetConvergedReason(snes->npc, &reason));
      if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
        snes->reason = SNES_DIVERGED_INNER;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
    }
  }
  PetscCall(VecCopy(dX, lX));
  PetscCall(VecDot(dX, dX, &dXdotdX));

  PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
  snes->norm = fnorm;
  PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
  PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

  /* test convergence */
  PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
  PetscCall(SNESMonitor(snes, 0, fnorm));
  if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

  /* Call general purpose update function */
  PetscTryTypeMethod(snes, update, snes->iter);

  /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */

  for (i = 1; i < maxits + 1; i++) {
    /* some update types require the old update direction or conjugate direction */
    if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
    PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
    PetscCall(SNESLineSearchGetReason(linesearch, &lsresult));
    PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
    if (lsresult) {
      if (++snes->numFailures >= snes->maxFailures) {
        snes->reason = SNES_DIVERGED_LINE_SEARCH;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
    }
    if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
      snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
      PetscFunctionReturn(PETSC_SUCCESS);
    }
    /* Monitor convergence */
    PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
    snes->iter  = i;
    snes->norm  = fnorm;
    snes->xnorm = xnorm;
    snes->ynorm = ynorm;
    PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
    PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));

    /* Test for convergence */
    PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
    PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
    if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

    /* Call general purpose update function */
    PetscTryTypeMethod(snes, update, snes->iter);
    if (snes->npc) {
      if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
        PetscCall(SNESApplyNPC(snes, X, NULL, dX));
        PetscCall(SNESGetConvergedReason(snes->npc, &reason));
        if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
          snes->reason = SNES_DIVERGED_INNER;
          PetscFunctionReturn(PETSC_SUCCESS);
        }
        PetscCall(VecCopy(dX, F));
      } else {
        PetscCall(SNESApplyNPC(snes, X, F, dX));
        PetscCall(SNESGetConvergedReason(snes->npc, &reason));
        if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
          snes->reason = SNES_DIVERGED_INNER;
          PetscFunctionReturn(PETSC_SUCCESS);
        }
      }
    } else {
      PetscCall(VecCopy(F, dX));
    }

    /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
    switch (ncg->type) {
    case SNES_NCG_FR: /* Fletcher-Reeves */
      dXolddotdXold = dXdotdX;
      PetscCall(VecDot(dX, dX, &dXdotdX));
      beta = PetscRealPart(dXdotdX / dXolddotdXold);
      break;
    case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
      dXolddotdXold = dXdotdX;
      PetscCall(VecDotBegin(dX, dX, &dXdotdXold));
      PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
      PetscCall(VecDotEnd(dX, dX, &dXdotdX));
      PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
      beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
      if (beta < 0.0) beta = 0.0; /* restart */
      break;
    case SNES_NCG_HS: /* Hestenes-Stiefel */
      PetscCall(VecDotBegin(dX, dX, &dXdotdX));
      PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
      PetscCall(VecDotBegin(lX, dX, &lXdotdX));
      PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
      PetscCall(VecDotEnd(dX, dX, &dXdotdX));
      PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
      PetscCall(VecDotEnd(lX, dX, &lXdotdX));
      PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
      beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
      break;
    case SNES_NCG_DY: /* Dai-Yuan */
      PetscCall(VecDotBegin(dX, dX, &dXdotdX));
      PetscCall(VecDotBegin(lX, dX, &lXdotdX));
      PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
      PetscCall(VecDotEnd(dX, dX, &dXdotdX));
      PetscCall(VecDotEnd(lX, dX, &lXdotdX));
      PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
      beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
      break;
    case SNES_NCG_CD: /* Conjugate Descent */
      PetscCall(VecDotBegin(dX, dX, &dXdotdX));
      PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
      PetscCall(VecDotEnd(dX, dX, &dXdotdX));
      PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
      beta = PetscRealPart(dXdotdX / lXdotdXold);
      break;
    }
    if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
    PetscCall(VecAYPX(lX, beta, dX));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems.

  Level: beginner

  Options Database Keys:
+   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
.   -snes_linesearch_type <cp,l2,basic> - Line search type.
-   -snes_ncg_monitor - Print the beta values used in the ncg iteration, .

   Notes:
   This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
   gradient method.  This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
   chooses the initial search direction as F(x) for the initial guess x.

   Only supports left non-linear preconditioning.

   Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()` then
   `SNESLINESEARCHL2` is used. Also supports the special purpose line search `SNESLINESEARCHNCGLINEAR`

   References:
.  * -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
   SIAM Review, 57(4), 2015

.seealso: `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
M*/
PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
{
  SNES_NCG *neP;

  PetscFunctionBegin;
  snes->ops->destroy        = SNESDestroy_NCG;
  snes->ops->setup          = SNESSetUp_NCG;
  snes->ops->setfromoptions = SNESSetFromOptions_NCG;
  snes->ops->view           = SNESView_NCG;
  snes->ops->solve          = SNESSolve_NCG;
  snes->ops->reset          = SNESReset_NCG;

  snes->usesksp = PETSC_FALSE;
  snes->usesnpc = PETSC_TRUE;
  snes->npcside = PC_LEFT;

  snes->alwayscomputesfinalresidual = PETSC_TRUE;

  if (!snes->tolerancesset) {
    snes->max_funcs = 30000;
    snes->max_its   = 10000;
    snes->stol      = 1e-20;
  }

  PetscCall(PetscNew(&neP));
  snes->data   = (void *)neP;
  neP->monitor = NULL;
  neP->type    = SNES_NCG_PRP;
  PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
  PetscFunctionReturn(PETSC_SUCCESS);
}