/*
    Routines used for the orthogonalization of the Hessenberg matrix.

    Note that for the complex numbers version, the VecDot() and
    VecMDot() arguments within the code MUST remain in the order
    given for correct computation of inner products.
*/
#include <../src/ksp/ksp/impls/gmres/gmresimpl.h>

/*@C
  KSPGMRESClassicalGramSchmidtOrthogonalization -  This is the basic orthogonalization routine
  using classical Gram-Schmidt with possible iterative refinement to improve the stability

  Collective

  Input Parameters:
+ ksp - `KSP` object, must be associated with `KSPGMRES`, `KSPFGMRES`, or `KSPLGMRES` Krylov method
- it  - one less than the current GMRES restart iteration, i.e. the size of the Krylov space

  Options Database Keys:
+ -ksp_gmres_classicalgramschmidt                                             - Activates `KSPGMRESClassicalGramSchmidtOrthogonalization()`
- -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is
                                   used to increase the stability of the classical Gram-Schmidt  orthogonalization.

  Level: intermediate

  Note:
  Use `KSPGMRESSetCGSRefinementType()` to determine if iterative refinement is to be used.
  This is much faster than `KSPGMRESModifiedGramSchmidtOrthogonalization()` but has the small possibility of stability issues
  that can usually be handled by using a a single step of iterative refinement with `KSPGMRESSetCGSRefinementType()`

.seealso: [](ch_ksp), `KSPGMRESCGSRefinementType`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetCGSRefinementType()`,
           `KSPGMRESGetCGSRefinementType()`, `KSPGMRESGetOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`
@*/
PetscErrorCode KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp, PetscInt it)
{
  KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);
  PetscInt     j;
  PetscScalar *hh, *hes, *lhh;
  PetscReal    hnrm, wnrm;
  PetscBool    refine = (PetscBool)(gmres->cgstype == KSP_GMRES_CGS_REFINE_ALWAYS);

  PetscFunctionBegin;
  PetscCall(PetscLogEventBegin(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
  if (!gmres->orthogwork) PetscCall(PetscMalloc1(gmres->max_k + 2, &gmres->orthogwork));
  lhh = gmres->orthogwork;

  /* update Hessenberg matrix and do unmodified Gram-Schmidt */
  hh  = HH(0, it);
  hes = HES(0, it);

  /* Clear hh and hes since we will accumulate values into them */
  for (j = 0; j <= it; j++) {
    hh[j]  = 0.0;
    hes[j] = 0.0;
  }

  /*
     This is really a matrix-vector product, with the matrix stored
     as pointer to rows
  */
  PetscCall(VecMDot(VEC_VV(it + 1), it + 1, &(VEC_VV(0)), lhh)); /* <v,vnew> */
  for (j = 0; j <= it; j++) {
    KSPCheckDot(ksp, lhh[j]);
    if (ksp->reason) goto done;
    lhh[j] = -lhh[j];
  }

  /*
         This is really a matrix-vector product:
         [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
  */
  PetscCall(VecMAXPY(VEC_VV(it + 1), it + 1, lhh, &VEC_VV(0)));
  /* note lhh[j] is -<v,vnew> , hence the subtraction */
  for (j = 0; j <= it; j++) {
    hh[j] -= lhh[j];  /* hh += <v,vnew> */
    hes[j] -= lhh[j]; /* hes += <v,vnew> */
  }

  /*
     the second step classical Gram-Schmidt is only necessary
     when a simple test criteria is not passed
  */
  if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
    hnrm = 0.0;
    for (j = 0; j <= it; j++) hnrm += PetscRealPart(lhh[j] * PetscConj(lhh[j]));

    hnrm = PetscSqrtReal(hnrm);
    PetscCall(VecNorm(VEC_VV(it + 1), NORM_2, &wnrm));
    KSPCheckNorm(ksp, wnrm);
    if (ksp->reason) goto done;
    if (wnrm < hnrm) {
      refine = PETSC_TRUE;
      PetscCall(PetscInfo(ksp, "Performing iterative refinement wnorm %g hnorm %g\n", (double)wnrm, (double)hnrm));
    }
  }

  if (refine) {
    PetscCall(VecMDot(VEC_VV(it + 1), it + 1, &(VEC_VV(0)), lhh)); /* <v,vnew> */
    for (j = 0; j <= it; j++) {
      KSPCheckDot(ksp, lhh[j]);
      if (ksp->reason) goto done;
      lhh[j] = -lhh[j];
    }
    PetscCall(VecMAXPY(VEC_VV(it + 1), it + 1, lhh, &VEC_VV(0)));
    /* note lhh[j] is -<v,vnew> , hence the subtraction */
    for (j = 0; j <= it; j++) {
      hh[j] -= lhh[j];  /* hh += <v,vnew> */
      hes[j] -= lhh[j]; /* hes += <v,vnew> */
    }
  }
done:
  PetscCall(PetscLogEventEnd(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}
