/*
    This file implements the FCG (Flexible Conjugate Gradient) method
*/

#include <../src/ksp/ksp/impls/fcg/fcgimpl.h> /*I  "petscksp.h"  I*/
extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP, PetscReal *, PetscReal *);
extern PetscErrorCode KSPComputeEigenvalues_CG(KSP, PetscInt, PetscReal *, PetscReal *, PetscInt *);

#define KSPFCG_DEFAULT_MMAX       30 /* maximum number of search directions to keep */
#define KSPFCG_DEFAULT_NPREALLOC  10 /* number of search directions to preallocate */
#define KSPFCG_DEFAULT_VECB       5  /* number of search directions to allocate each time new direction vectors are needed */
#define KSPFCG_DEFAULT_TRUNCSTRAT KSP_FCD_TRUNC_TYPE_NOTAY

static PetscErrorCode KSPAllocateVectors_FCG(KSP ksp, PetscInt nvecsneeded, PetscInt chunksize)
{
  PetscInt i;
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;
  PetscInt nnewvecs, nvecsprev;

  PetscFunctionBegin;
  /* Allocate enough new vectors to add chunksize new vectors, reach nvecsneedtotal, or to reach mmax+1, whichever is smallest */
  if (fcg->nvecs < PetscMin(fcg->mmax + 1, nvecsneeded)) {
    nvecsprev = fcg->nvecs;
    nnewvecs  = PetscMin(PetscMax(nvecsneeded - fcg->nvecs, chunksize), fcg->mmax + 1 - fcg->nvecs);
    PetscCall(KSPCreateVecs(ksp, nnewvecs, &fcg->pCvecs[fcg->nchunks], 0, NULL));
    PetscCall(KSPCreateVecs(ksp, nnewvecs, &fcg->pPvecs[fcg->nchunks], 0, NULL));
    fcg->nvecs += nnewvecs;
    for (i = 0; i < nnewvecs; ++i) {
      fcg->Cvecs[nvecsprev + i] = fcg->pCvecs[fcg->nchunks][i];
      fcg->Pvecs[nvecsprev + i] = fcg->pPvecs[fcg->nchunks][i];
    }
    fcg->chunksizes[fcg->nchunks] = nnewvecs;
    ++fcg->nchunks;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPSetUp_FCG(KSP ksp)
{
  KSP_FCG       *fcg      = (KSP_FCG *)ksp->data;
  PetscInt       maxit    = ksp->max_it;
  const PetscInt nworkstd = 2;

  PetscFunctionBegin;

  /* Allocate "standard" work vectors (not including the basis and transformed basis vectors) */
  PetscCall(KSPSetWorkVecs(ksp, nworkstd));

  /* Allocated space for pointers to additional work vectors
   note that mmax is the number of previous directions, so we add 1 for the current direction,
   and an extra 1 for the prealloc (which might be empty) */
  PetscCall(PetscMalloc5(fcg->mmax + 1, &fcg->Pvecs, fcg->mmax + 1, &fcg->Cvecs, fcg->mmax + 1, &fcg->pPvecs, fcg->mmax + 1, &fcg->pCvecs, fcg->mmax + 2, &fcg->chunksizes));

  /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
  if (fcg->nprealloc > fcg->mmax + 1) PetscCall(PetscInfo(NULL, "Requested nprealloc=%" PetscInt_FMT " is greater than m_max+1=%" PetscInt_FMT ". Resetting nprealloc = m_max+1.\n", fcg->nprealloc, fcg->mmax + 1));

  /* Preallocate additional work vectors */
  PetscCall(KSPAllocateVectors_FCG(ksp, fcg->nprealloc, fcg->nprealloc));
  /*
  If user requested computations of eigenvalues then allocate work
  work space needed
  */
  if (ksp->calc_sings) {
    /* get space to store tridiagonal matrix for Lanczos */
    PetscCall(PetscMalloc4(maxit, &fcg->e, maxit, &fcg->d, maxit, &fcg->ee, maxit, &fcg->dd));

    ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
    ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPSolve_FCG(KSP ksp)
{
  PetscInt    i, k, idx, mi;
  KSP_FCG    *fcg   = (KSP_FCG *)ksp->data;
  PetscScalar alpha = 0.0, beta = 0.0, dpi, s;
  PetscReal   dp = 0.0;
  Vec         B, R, Z, X, Pcurr, Ccurr;
  Mat         Amat, Pmat;
  PetscInt    eigs          = ksp->calc_sings; /* Variables for eigen estimation - START*/
  PetscInt    stored_max_it = ksp->max_it;
  PetscScalar alphaold = 0, betaold = 1.0, *e = NULL, *d = NULL; /* Variables for eigen estimation  - FINISH */

  PetscFunctionBegin;

#define VecXDot(x, y, a)     (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x, y, a) : VecTDot(x, y, a))
#define VecXMDot(a, b, c, d) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecMDot(a, b, c, d) : VecMTDot(a, b, c, d))

  X = ksp->vec_sol;
  B = ksp->vec_rhs;
  R = ksp->work[0];
  Z = ksp->work[1];

  PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
  if (eigs) {
    e    = fcg->e;
    d    = fcg->d;
    e[0] = 0.0;
  }
  /* Compute initial residual needed for convergence check*/
  ksp->its = 0;
  if (!ksp->guess_zero) {
    PetscCall(KSP_MatMult(ksp, Amat, X, R));
    PetscCall(VecAYPX(R, -1.0, B)); /*   r <- b - Ax     */
  } else {
    PetscCall(VecCopy(B, R)); /*   r <- b (x is 0) */
  }
  switch (ksp->normtype) {
  case KSP_NORM_PRECONDITIONED:
    PetscCall(KSP_PCApply(ksp, R, Z));  /*   z <- Br         */
    PetscCall(VecNorm(Z, NORM_2, &dp)); /*   dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e)     */
    KSPCheckNorm(ksp, dp);
    break;
  case KSP_NORM_UNPRECONDITIONED:
    PetscCall(VecNorm(R, NORM_2, &dp)); /*   dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)     */
    KSPCheckNorm(ksp, dp);
    break;
  case KSP_NORM_NATURAL:
    PetscCall(KSP_PCApply(ksp, R, Z)); /*   z <- Br         */
    PetscCall(VecXDot(R, Z, &s));
    KSPCheckDot(ksp, s);
    dp = PetscSqrtReal(PetscAbsScalar(s)); /*   dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)  */
    break;
  case KSP_NORM_NONE:
    dp = 0.0;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
  }

  /* Initial Convergence Check */
  PetscCall(KSPLogResidualHistory(ksp, dp));
  PetscCall(KSPMonitor(ksp, 0, dp));
  ksp->rnorm = dp;
  if (ksp->normtype == KSP_NORM_NONE) {
    PetscCall(KSPConvergedSkip(ksp, 0, dp, &ksp->reason, ksp->cnvP));
  } else {
    PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
  }
  if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

  /* Apply PC if not already done for convergence check */
  if (ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE) { PetscCall(KSP_PCApply(ksp, R, Z)); /*   z <- Br         */ }

  i = 0;
  do {
    ksp->its = i + 1;

    /*  If needbe, allocate a new chunk of vectors in P and C */
    PetscCall(KSPAllocateVectors_FCG(ksp, i + 1, fcg->vecb));

    /* Note that we wrap around and start clobbering old vectors */
    idx   = i % (fcg->mmax + 1);
    Pcurr = fcg->Pvecs[idx];
    Ccurr = fcg->Cvecs[idx];

    /* number of old directions to orthogonalize against */
    switch (fcg->truncstrat) {
    case KSP_FCD_TRUNC_TYPE_STANDARD:
      mi = fcg->mmax;
      break;
    case KSP_FCD_TRUNC_TYPE_NOTAY:
      mi = ((i - 1) % fcg->mmax) + 1;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unrecognized Truncation Strategy");
    }

    /* Compute a new column of P (Currently does not support modified G-S or iterative refinement)*/
    PetscCall(VecCopy(Z, Pcurr));

    {
      PetscInt l, ndots;

      l     = PetscMax(0, i - mi);
      ndots = i - l;
      if (ndots) {
        PetscInt     j;
        Vec         *Pold, *Cold;
        PetscScalar *dots;

        PetscCall(PetscMalloc3(ndots, &dots, ndots, &Cold, ndots, &Pold));
        for (k = l, j = 0; j < ndots; ++k, ++j) {
          idx     = k % (fcg->mmax + 1);
          Cold[j] = fcg->Cvecs[idx];
          Pold[j] = fcg->Pvecs[idx];
        }
        PetscCall(VecXMDot(Z, ndots, Cold, dots));
        for (k = 0; k < ndots; ++k) dots[k] = -dots[k];
        PetscCall(VecMAXPY(Pcurr, ndots, dots, Pold));
        PetscCall(PetscFree3(dots, Cold, Pold));
      }
    }

    /* Update X and R */
    betaold = beta;
    PetscCall(VecXDot(Pcurr, R, &beta)); /*  beta <- pi'*r       */
    KSPCheckDot(ksp, beta);
    PetscCall(KSP_MatMult(ksp, Amat, Pcurr, Ccurr)); /*  w <- A*pi (stored in ci)   */
    PetscCall(VecXDot(Pcurr, Ccurr, &dpi));          /*  dpi <- pi'*w        */
    alphaold = alpha;
    alpha    = beta / dpi;                /*  alpha <- beta/dpi    */
    PetscCall(VecAXPY(X, alpha, Pcurr));  /*  x <- x + alpha * pi  */
    PetscCall(VecAXPY(R, -alpha, Ccurr)); /*  r <- r - alpha * wi  */

    /* Compute norm for convergence check */
    switch (ksp->normtype) {
    case KSP_NORM_PRECONDITIONED:
      PetscCall(KSP_PCApply(ksp, R, Z));  /*   z <- Br             */
      PetscCall(VecNorm(Z, NORM_2, &dp)); /*   dp <- sqrt(z'*z) = sqrt(e'*A'*B'*B*A*e)  */
      KSPCheckNorm(ksp, dp);
      break;
    case KSP_NORM_UNPRECONDITIONED:
      PetscCall(VecNorm(R, NORM_2, &dp)); /*   dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)   */
      KSPCheckNorm(ksp, dp);
      break;
    case KSP_NORM_NATURAL:
      PetscCall(KSP_PCApply(ksp, R, Z)); /*   z <- Br             */
      PetscCall(VecXDot(R, Z, &s));
      KSPCheckDot(ksp, s);
      dp = PetscSqrtReal(PetscAbsScalar(s)); /*   dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)  */
      break;
    case KSP_NORM_NONE:
      dp = 0.0;
      break;
    default:
      SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
    }

    if (eigs) {
      if (i > 0) {
        PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
        e[i] = PetscSqrtReal(PetscAbsScalar(beta / betaold)) / alphaold;
        d[i] = PetscSqrtReal(PetscAbsScalar(beta / betaold)) * e[i] + 1.0 / alpha;
      } else {
        d[i] = PetscSqrtReal(PetscAbsScalar(beta)) * e[i] + 1.0 / alpha;
      }
    }

    /* Check for convergence */
    ksp->rnorm = dp;
    PetscCall(KSPLogResidualHistory(ksp, dp));
    PetscCall(KSPMonitor(ksp, i + 1, dp));
    PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
    if (ksp->reason) break;

    /* Apply PC if not already done for convergence check */
    if (ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE) { PetscCall(KSP_PCApply(ksp, R, Z)); /*   z <- Br         */ }

    /* Compute current C (which is W/dpi) */
    PetscCall(VecScale(Ccurr, 1.0 / dpi)); /*   w <- ci/dpi   */
    ++i;
  } while (i < ksp->max_it);
  if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPDestroy_FCG(KSP ksp)
{
  PetscInt i;
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;

  /* Destroy "standard" work vecs */
  PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));

  /* Destroy P and C vectors and the arrays that manage pointers to them */
  if (fcg->nvecs) {
    for (i = 0; i < fcg->nchunks; ++i) {
      PetscCall(VecDestroyVecs(fcg->chunksizes[i], &fcg->pPvecs[i]));
      PetscCall(VecDestroyVecs(fcg->chunksizes[i], &fcg->pCvecs[i]));
    }
  }
  PetscCall(PetscFree5(fcg->Pvecs, fcg->Cvecs, fcg->pPvecs, fcg->pCvecs, fcg->chunksizes));
  /* free space used for singular value calculations */
  if (ksp->calc_sings) PetscCall(PetscFree4(fcg->e, fcg->d, fcg->ee, fcg->dd));
  PetscCall(KSPDestroyDefault(ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPView_FCG(KSP ksp, PetscViewer viewer)
{
  KSP_FCG    *fcg = (KSP_FCG *)ksp->data;
  PetscBool   iascii, isstring;
  const char *truncstr;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));

  if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD) truncstr = "Using standard truncation strategy";
  else if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY) truncstr = "Using Notay's truncation strategy";
  else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Undefined FCG truncation strategy");

  if (iascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "  m_max=%" PetscInt_FMT "\n", fcg->mmax));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  preallocated %" PetscInt_FMT " directions\n", PetscMin(fcg->nprealloc, fcg->mmax + 1)));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", truncstr));
  } else if (isstring) {
    PetscCall(PetscViewerStringSPrintf(viewer, "m_max %" PetscInt_FMT " nprealloc %" PetscInt_FMT " %s", fcg->mmax, fcg->nprealloc, truncstr));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGSetMmax - set the maximum number of previous directions `KSPFCG` will store for orthogonalization

  Logically Collective

  Input Parameters:
+ ksp  - the Krylov space context
- mmax - the maximum number of previous directions to orthogonalize against

  Options Database Key:
. -ksp_fcg_mmax <N> - maximum number of search directions

  Level: intermediate

  Note:
  `mmax` + 1 directions are stored (`mmax` previous ones along with a current one)
  and whether all are used in each iteration also depends on the truncation strategy, see `KSPFCGSetTruncationType()`

.seealso: [](ch_ksp), `KSPFCG`, `KSPFCGGetTruncationType()`, `KSPFCGGetNprealloc()`, `KSPFCGetMmax()`
@*/
PetscErrorCode KSPFCGSetMmax(KSP ksp, PetscInt mmax)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  PetscValidLogicalCollectiveInt(ksp, mmax, 2);
  fcg->mmax = mmax;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGGetMmax - get the maximum number of previous directions `KSPFCG` will store

  Not Collective

  Input Parameter:
. ksp - the Krylov space context

  Output Parameter:
. mmax - the maximum number of previous directions allowed for orthogonalization

  Level: intermediate

  Note:
  `KSPFCG` stores `mmax`+1 directions at most (`mmax` previous ones, and one current one)

.seealso: [](ch_ksp), `KSPFCG`, `KSPFCGGetTruncationType()`, `KSPFCGGetNprealloc()`, `KSPFCGSetMmax()`
@*/
PetscErrorCode KSPFCGGetMmax(KSP ksp, PetscInt *mmax)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  *mmax = fcg->mmax;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGSetNprealloc - set the number of directions to preallocate with `KSPFCG`

  Logically Collective

  Input Parameters:
+ ksp       - the Krylov space context
- nprealloc - the number of vectors to preallocate

  Options Database Key:
. -ksp_fcg_nprealloc <N> - number of directions to preallocate

  Level: advanced

.seealso: [](ch_ksp), `KSPFCG`, `KSPFCGGetTruncationType()`, `KSPFCGGetNprealloc()`, `KSPFCGSetMmax()`, `KSPFCGGetMmax()`
@*/
PetscErrorCode KSPFCGSetNprealloc(KSP ksp, PetscInt nprealloc)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  PetscValidLogicalCollectiveInt(ksp, nprealloc, 2);
  PetscCheck(nprealloc <= fcg->mmax + 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot preallocate more than m_max+1 vectors");
  fcg->nprealloc = nprealloc;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGGetNprealloc - get the number of directions preallocate by `KSPFCG`

  Not Collective

  Input Parameter:
. ksp - the Krylov space context

  Output Parameter:
. nprealloc - the number of directions preallocated

  Level: advanced

.seealso: [](ch_ksp), `KSPFCG`, `KSPFCGGetTruncationType()`, `KSPFCGSetNprealloc()`, `KSPFCGSetMmax()`, `KSPFCGGetMmax()`
@*/
PetscErrorCode KSPFCGGetNprealloc(KSP ksp, PetscInt *nprealloc)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  *nprealloc = fcg->nprealloc;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGSetTruncationType - specify how many of its stored previous directions `KSPFCG` uses during orthoganalization

  Logically Collective

  Input Parameters:
+ ksp        - the Krylov space context
- truncstrat - the choice of strategy
.vb
  KSP_FCD_TRUNC_TYPE_STANDARD uses all (up to mmax) stored directions
  KSP_FCD_TRUNC_TYPE_NOTAY uses the last max(1,mod(i,mmax)) stored directions at iteration i=0,1,..
.ve

  Options Database Key:
. -ksp_fcg_truncation_type <standard, notay> - specify how many of its stored previous directions `KSPFCG` uses during orthoganalization

  Level: intermediate

.seealso: [](ch_ksp), `KSPFCDTruncationType`, `KSPFCGGetTruncationType()`, `KSPFCGSetNprealloc()`, `KSPFCGSetMmax()`, `KSPFCGGetMmax()`,
          `KSP_FCD_TRUNC_TYPE_STANDARD`, `KSP_FCD_TRUNC_TYPE_NOTAY`
@*/
PetscErrorCode KSPFCGSetTruncationType(KSP ksp, KSPFCDTruncationType truncstrat)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  PetscValidLogicalCollectiveEnum(ksp, truncstrat, 2);
  fcg->truncstrat = truncstrat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPFCGGetTruncationType - get the truncation strategy employed by `KSPFCG`

  Not Collective

  Input Parameter:
. ksp - the Krylov space context

  Output Parameter:
. truncstrat - the strategy type

  Level: intermediate

.seealso: [](ch_ksp), `KSPFCG`, `KSPFCGSetTruncationType()`, `KSPFCDTruncationType`, `KSP_FCD_TRUNC_TYPE_STANDARD`, `KSP_FCD_TRUNC_TYPE_NOTAY`
@*/
PetscErrorCode KSPFCGGetTruncationType(KSP ksp, KSPFCDTruncationType *truncstrat)
{
  KSP_FCG *fcg = (KSP_FCG *)ksp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 1);
  *truncstrat = fcg->truncstrat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPSetFromOptions_FCG(KSP ksp, PetscOptionItems *PetscOptionsObject)
{
  KSP_FCG  *fcg = (KSP_FCG *)ksp->data;
  PetscInt  mmax, nprealloc;
  PetscBool flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "KSP FCG Options");
  PetscCall(PetscOptionsInt("-ksp_fcg_mmax", "Maximum number of search directions to store", "KSPFCGSetMmax", fcg->mmax, &mmax, &flg));
  if (flg) PetscCall(KSPFCGSetMmax(ksp, mmax));
  PetscCall(PetscOptionsInt("-ksp_fcg_nprealloc", "Number of directions to preallocate", "KSPFCGSetNprealloc", fcg->nprealloc, &nprealloc, &flg));
  if (flg) PetscCall(KSPFCGSetNprealloc(ksp, nprealloc));
  PetscCall(PetscOptionsEnum("-ksp_fcg_truncation_type", "Truncation approach for directions", "KSPFCGSetTruncationType", KSPFCDTruncationTypes, (PetscEnum)fcg->truncstrat, (PetscEnum *)&fcg->truncstrat, NULL));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  KSPFCG - Implements the Flexible Conjugate Gradient method (FCG) {cite}`flexiblecg`, {cite}`generalizedcg`.
  Unlike most `KSP` methods this allows the preconditioner to be nonlinear. [](sec_flexibleksp)

  Options Database Keys:
+   -ksp_fcg_mmax <N>  - maximum number of search directions
.   -ksp_fcg_nprealloc <N> - number of directions to preallocate
-   -ksp_fcg_truncation_type <standard,notay> - truncation approach for directions

  Level: beginner

  Notes:
  Compare to `KSPFCG`

  Supports left preconditioning only.

  Contributed by:
  Patrick Sanan

.seealso: [](ch_ksp), [](sec_flexibleksp), `KSPGCR`, `KSPFGMRES`, `KSPCG`, `KSPFCGSetMmax()`, `KSPFCGGetMmax()`, `KSPFCGSetNprealloc()`, `KSPFCGGetNprealloc()`, `KSPFCGSetTruncationType()`, `KSPFCGGetTruncationType()`,
           `KSPFCGGetTruncationType`
M*/
PETSC_EXTERN PetscErrorCode KSPCreate_FCG(KSP ksp)
{
  KSP_FCG *fcg;

  PetscFunctionBegin;
  PetscCall(PetscNew(&fcg));
#if !defined(PETSC_USE_COMPLEX)
  fcg->type = KSP_CG_SYMMETRIC;
#else
  fcg->type = KSP_CG_HERMITIAN;
#endif
  fcg->mmax       = KSPFCG_DEFAULT_MMAX;
  fcg->nprealloc  = KSPFCG_DEFAULT_NPREALLOC;
  fcg->nvecs      = 0;
  fcg->vecb       = KSPFCG_DEFAULT_VECB;
  fcg->nchunks    = 0;
  fcg->truncstrat = KSPFCG_DEFAULT_TRUNCSTRAT;

  ksp->data = (void *)fcg;

  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 2));
  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 1));
  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 1));
  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

  ksp->ops->setup          = KSPSetUp_FCG;
  ksp->ops->solve          = KSPSolve_FCG;
  ksp->ops->destroy        = KSPDestroy_FCG;
  ksp->ops->view           = KSPView_FCG;
  ksp->ops->setfromoptions = KSPSetFromOptions_FCG;
  ksp->ops->buildsolution  = KSPBuildSolutionDefault;
  ksp->ops->buildresidual  = KSPBuildResidualDefault;
  PetscFunctionReturn(PETSC_SUCCESS);
}
