xref: /petsc/src/snes/impls/ngmres/anderson.c (revision 4dfa11a44d5adf2389f1d3acbc8f3c1116dc6c3a)

#include <../src/snes/impls/ngmres/snesngmres.h> /*I "petscsnes.h" I*/

static PetscErrorCode SNESSetFromOptions_Anderson(SNES snes, PetscOptionItems *PetscOptionsObject) {
  SNES_NGMRES *ngmres  = (SNES_NGMRES *)snes->data;
  PetscBool    monitor = PETSC_FALSE;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "SNES NGMRES options");
  PetscCall(PetscOptionsInt("-snes_anderson_m", "Number of directions", "SNES", ngmres->msize, &ngmres->msize, NULL));
  PetscCall(PetscOptionsReal("-snes_anderson_beta", "Mixing parameter", "SNES", ngmres->andersonBeta, &ngmres->andersonBeta, NULL));
  PetscCall(PetscOptionsInt("-snes_anderson_restart", "Iterations before forced restart", "SNES", ngmres->restart_periodic, &ngmres->restart_periodic, NULL));
  PetscCall(PetscOptionsInt("-snes_anderson_restart_it", "Tolerance iterations before restart", "SNES", ngmres->restart_it, &ngmres->restart_it, NULL));
  PetscCall(PetscOptionsEnum("-snes_anderson_restart_type", "Restart type", "SNESNGMRESSetRestartType", SNESNGMRESRestartTypes, (PetscEnum)ngmres->restart_type, (PetscEnum *)&ngmres->restart_type, NULL));
  PetscCall(PetscOptionsBool("-snes_anderson_monitor", "Monitor steps of Anderson Mixing", "SNES", ngmres->monitor ? PETSC_TRUE : PETSC_FALSE, &monitor, NULL));
  if (monitor) ngmres->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(0);
}

static PetscErrorCode SNESSolve_Anderson(SNES snes) {
  SNES_NGMRES *ngmres = (SNES_NGMRES *)snes->data;
  /* present solution, residual, and preconditioned residual */
  Vec          X, F, B, D;
  /* candidate linear combination answers */
  Vec          XA, FA, XM, FM;

  /* coefficients and RHS to the minimization problem */
  PetscReal           fnorm, fMnorm, fAnorm;
  PetscReal           xnorm, ynorm;
  PetscReal           dnorm, dminnorm = 0.0, fminnorm;
  PetscInt            restart_count = 0;
  PetscInt            k, k_restart, l, ivec;
  PetscBool           selectRestart;
  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));
  /* variable initialization */
  snes->reason = SNES_CONVERGED_ITERATING;
  X            = snes->vec_sol;
  F            = snes->vec_func;
  B            = snes->vec_rhs;
  XA           = snes->vec_sol_update;
  FA           = snes->work[0];
  D            = snes->work[1];

  /* work for the line search */
  XM = snes->work[3];
  FM = snes->work[4];

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

  /* initialization */

  /* r = F(x) */

  if (snes->npc && snes->npcside == PC_LEFT) {
    PetscCall(SNESApplyNPC(snes, X, NULL, F));
    PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
      snes->reason = SNES_DIVERGED_INNER;
      PetscFunctionReturn(0);
    }
    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;

    PetscCall(VecNorm(F, NORM_2, &fnorm));
    SNESCheckFunctionNorm(snes, fnorm);
  }
  fminnorm = fnorm;

  PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
  snes->norm = fnorm;
  PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
  PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));
  PetscCall(SNESMonitor(snes, 0, fnorm));
  PetscUseTypeMethod(snes, converged, 0, 0.0, 0.0, fnorm, &snes->reason, snes->cnvP);
  if (snes->reason) PetscFunctionReturn(0);

  k_restart = 0;
  l         = 0;
  ivec      = 0;
  for (k = 1; k < snes->max_its + 1; k++) {
    /* select which vector of the stored subspace will be updated */
    if (snes->npc && snes->npcside == PC_RIGHT) {
      PetscCall(VecCopy(X, XM));
      PetscCall(SNESSetInitialFunction(snes->npc, F));

      PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, XM, B, 0));
      PetscCall(SNESSolve(snes->npc, B, XM));
      PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, XM, B, 0));

      PetscCall(SNESGetConvergedReason(snes->npc, &reason));
      if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
        snes->reason = SNES_DIVERGED_INNER;
        PetscFunctionReturn(0);
      }
      PetscCall(SNESGetNPCFunction(snes, FM, &fMnorm));
      if (ngmres->andersonBeta != 1.0) PetscCall(VecAXPBY(XM, (1.0 - ngmres->andersonBeta), ngmres->andersonBeta, X));
    } else {
      PetscCall(VecCopy(F, FM));
      PetscCall(VecCopy(X, XM));
      PetscCall(VecAXPY(XM, -ngmres->andersonBeta, FM));
      fMnorm = fnorm;
    }

    PetscCall(SNESNGMRESFormCombinedSolution_Private(snes, ivec, l, XM, FM, fMnorm, X, XA, FA));
    ivec = k_restart % ngmres->msize;
    if (ngmres->restart_type == SNES_NGMRES_RESTART_DIFFERENCE) {
      PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, &dnorm, &dminnorm, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm));
      PetscCall(SNESNGMRESSelectRestart_Private(snes, l, fMnorm, fnorm, dnorm, fminnorm, dminnorm, &selectRestart));
      /* if the restart conditions persist for more than restart_it iterations, restart. */
      if (selectRestart) restart_count++;
      else restart_count = 0;
    } else if (ngmres->restart_type == SNES_NGMRES_RESTART_PERIODIC) {
      PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, NULL, NULL, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm));
      if (k_restart > ngmres->restart_periodic) {
        if (ngmres->monitor) PetscCall(PetscViewerASCIIPrintf(ngmres->monitor, "periodic restart after %" PetscInt_FMT " iterations\n", k_restart));
        restart_count = ngmres->restart_it;
      }
    } else {
      PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, NULL, NULL, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm));
    }
    /* restart after restart conditions have persisted for a fixed number of iterations */
    if (restart_count >= ngmres->restart_it) {
      if (ngmres->monitor) PetscCall(PetscViewerASCIIPrintf(ngmres->monitor, "Restarted at iteration %" PetscInt_FMT "\n", k_restart));
      restart_count = 0;
      k_restart     = 0;
      l             = 0;
      ivec          = 0;
    } else {
      if (l < ngmres->msize) l++;
      k_restart++;
      PetscCall(SNESNGMRESUpdateSubspace_Private(snes, ivec, l, FM, fnorm, XM));
    }

    fnorm = fAnorm;
    if (fminnorm > fnorm) fminnorm = fnorm;

    PetscCall(VecCopy(XA, X));
    PetscCall(VecCopy(FA, F));

    PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
    snes->iter  = k;
    snes->norm  = fnorm;
    snes->xnorm = xnorm;
    snes->ynorm = ynorm;
    PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
    PetscCall(SNESLogConvergenceHistory(snes, snes->norm, snes->iter));
    PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
    PetscUseTypeMethod(snes, converged, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP);
    if (snes->reason) PetscFunctionReturn(0);
  }
  snes->reason = SNES_DIVERGED_MAX_IT;
  PetscFunctionReturn(0);
}

/*MC
  SNESANDERSON - Anderson Mixing nonlinear solver

   Level: beginner

   Options Database Keys:
+  -snes_anderson_m                - Number of stored previous solutions and residuals
.  -snes_anderson_beta             - Anderson mixing parameter
.  -snes_anderson_restart_type     - Type of restart (see SNESNGMRES)
.  -snes_anderson_restart_it       - Number of iterations of restart conditions before restart
.  -snes_anderson_restart          - Number of iterations before periodic restart
-  -snes_anderson_monitor          - Prints relevant information about the ngmres iteration

   Notes:
   The Anderson Mixing method combines m previous solutions into a minimum-residual solution by solving a small linearized
   optimization problem at each iteration.

   Very similar to the `SNESNGMRES` algorithm.

   References:
+  * -  D. G. Anderson. Iterative procedures for nonlinear integral equations.
    J. Assoc. Comput. Mach., 12, 1965."
-  * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
   SIAM Review, 57(4), 2015

.seealso: `SNESNGMRES`, `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESType`
M*/

PETSC_EXTERN PetscErrorCode SNESCreate_Anderson(SNES snes) {
  SNES_NGMRES   *ngmres;
  SNESLineSearch linesearch;

  PetscFunctionBegin;
  snes->ops->destroy        = SNESDestroy_NGMRES;
  snes->ops->setup          = SNESSetUp_NGMRES;
  snes->ops->setfromoptions = SNESSetFromOptions_Anderson;
  snes->ops->view           = SNESView_NGMRES;
  snes->ops->solve          = SNESSolve_Anderson;
  snes->ops->reset          = SNESReset_NGMRES;

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

  snes->alwayscomputesfinalresidual = PETSC_TRUE;

  PetscCall(PetscNew(&ngmres));
  snes->data    = (void *)ngmres;
  ngmres->msize = 30;

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

  PetscCall(SNESGetLineSearch(snes, &linesearch));
  if (!((PetscObject)linesearch)->type_name) PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHBASIC));

  ngmres->additive_linesearch = NULL;
  ngmres->approxfunc          = PETSC_FALSE;
  ngmres->restart_type        = SNES_NGMRES_RESTART_NONE;
  ngmres->restart_it          = 2;
  ngmres->restart_periodic    = 30;
  ngmres->gammaA              = 2.0;
  ngmres->gammaC              = 2.0;
  ngmres->deltaB              = 0.9;
  ngmres->epsilonB            = 0.1;

  ngmres->andersonBeta = 1.0;
  PetscFunctionReturn(0);
}