/*
   Implementation of BiCGstab(L) the paper by D.R. Fokkema,
   "Enhanced implementation of BiCGStab(L) for solving linear systems
   of equations". This uses tricky delayed updating ideas to prevent
   round-off buildup.
*/
#include <petsc/private/kspimpl.h> /*I   "petscksp.h" I*/
#include <../src/ksp/ksp/impls/bcgsl/bcgslimpl.h>
#include <petscblaslapack.h>

static PetscErrorCode KSPSolve_BCGSL(KSP ksp)
{
  KSP_BCGSL   *bcgsl = (KSP_BCGSL *)ksp->data;
  PetscScalar  alpha, beta, omega, sigma;
  PetscScalar  rho0, rho1;
  PetscReal    kappa0, kappaA, kappa1;
  PetscReal    ghat;
  PetscReal    zeta, zeta0, rnmax_computed, rnmax_true, nrm0;
  PetscBool    bUpdateX;
  PetscInt     maxit;
  PetscInt     h, i, j, k, vi, ell;
  PetscBLASInt ldMZ, bierr;
  PetscScalar  utb;
  PetscReal    max_s, pinv_tol;

  PetscFunctionBegin;
  /* set up temporary vectors */
  vi        = 0;
  ell       = bcgsl->ell;
  bcgsl->vB = ksp->work[vi];
  vi++;
  bcgsl->vRt = ksp->work[vi];
  vi++;
  bcgsl->vTm = ksp->work[vi];
  vi++;
  bcgsl->vvR = ksp->work + vi;
  vi += ell + 1;
  bcgsl->vvU = ksp->work + vi;
  vi += ell + 1;
  bcgsl->vXr = ksp->work[vi];
  vi++;
  PetscCall(PetscBLASIntCast(ell + 1, &ldMZ));

  /* Prime the iterative solver */
  PetscCall(KSPInitialResidual(ksp, VX, VTM, VB, VVR[0], ksp->vec_rhs));
  PetscCall(VecNorm(VVR[0], NORM_2, &zeta0));
  KSPCheckNorm(ksp, zeta0);
  rnmax_computed = zeta0;
  rnmax_true     = zeta0;

  PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
  ksp->its = 0;
  if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = zeta0;
  else ksp->rnorm = 0.0;
  PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
  PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
  PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
  PetscCall((*ksp->converged)(ksp, 0, ksp->rnorm, &ksp->reason, ksp->cnvP));
  if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(VecSet(VVU[0], 0.0));
  alpha = 0.;
  rho0 = omega = 1;

  if (bcgsl->delta > 0.0) {
    PetscCall(VecCopy(VX, VXR));
    PetscCall(VecSet(VX, 0.0));
    PetscCall(VecCopy(VVR[0], VB));
  } else {
    PetscCall(VecCopy(ksp->vec_rhs, VB));
  }

  /* Life goes on */
  PetscCall(VecCopy(VVR[0], VRT));
  zeta = zeta0;

  PetscCall(KSPGetTolerances(ksp, NULL, NULL, NULL, &maxit));

  for (k = 0; k < maxit; k += bcgsl->ell) {
    ksp->its = k;
    if (k > 0) {
      if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = zeta;
      else ksp->rnorm = 0.0;

      PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
      PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));

      PetscCall((*ksp->converged)(ksp, k, ksp->rnorm, &ksp->reason, ksp->cnvP));
      if (ksp->reason < 0) PetscFunctionReturn(PETSC_SUCCESS);
      if (ksp->reason) {
        if (bcgsl->delta > 0.0) PetscCall(VecAXPY(VX, 1.0, VXR));
        PetscFunctionReturn(PETSC_SUCCESS);
      }
    }

    /* BiCG part */
    rho0 = -omega * rho0;
    nrm0 = zeta;
    for (j = 0; j < bcgsl->ell; j++) {
      /* rho1 <- r_j' * r_tilde */
      PetscCall(VecDot(VVR[j], VRT, &rho1));
      KSPCheckDot(ksp, rho1);
      if (rho1 == 0.0) {
        ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
      beta = alpha * (rho1 / rho0);
      rho0 = rho1;
      for (i = 0; i <= j; i++) {
        /* u_i <- r_i - beta*u_i */
        PetscCall(VecAYPX(VVU[i], -beta, VVR[i]));
      }
      /* u_{j+1} <- inv(K)*A*u_j */
      PetscCall(KSP_PCApplyBAorAB(ksp, VVU[j], VVU[j + 1], VTM));

      PetscCall(VecDot(VVU[j + 1], VRT, &sigma));
      KSPCheckDot(ksp, sigma);
      if (sigma == 0.0) {
        ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
      alpha = rho1 / sigma;

      /* x <- x + alpha*u_0 */
      PetscCall(VecAXPY(VX, alpha, VVU[0]));

      for (i = 0; i <= j; i++) {
        /* r_i <- r_i - alpha*u_{i+1} */
        PetscCall(VecAXPY(VVR[i], -alpha, VVU[i + 1]));
      }

      /* r_{j+1} <- inv(K)*A*r_j */
      PetscCall(KSP_PCApplyBAorAB(ksp, VVR[j], VVR[j + 1], VTM));

      PetscCall(VecNorm(VVR[0], NORM_2, &nrm0));
      KSPCheckNorm(ksp, nrm0);
      if (bcgsl->delta > 0.0) {
        if (rnmax_computed < nrm0) rnmax_computed = nrm0;
        if (rnmax_true < nrm0) rnmax_true = nrm0;
      }

      /* NEW: check for early exit */
      PetscCall((*ksp->converged)(ksp, k + j, nrm0, &ksp->reason, ksp->cnvP));
      if (ksp->reason) {
        PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
        ksp->its   = k + j;
        ksp->rnorm = nrm0;

        PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
        if (ksp->reason < 0) PetscFunctionReturn(PETSC_SUCCESS);
      }
    }

    /* Polynomial part */
    for (i = 0; i <= bcgsl->ell; ++i) PetscCall(VecMDot(VVR[i], i + 1, VVR, &MZa[i * ldMZ]));
    /* Symmetrize MZa */
    for (i = 0; i <= bcgsl->ell; ++i) {
      for (j = i + 1; j <= bcgsl->ell; ++j) MZa[i * ldMZ + j] = MZa[j * ldMZ + i] = PetscConj(MZa[j * ldMZ + i]);
    }
    /* Copy MZa to MZb */
    PetscCall(PetscArraycpy(MZb, MZa, ldMZ * ldMZ));

    if (!bcgsl->bConvex || bcgsl->ell == 1) {
      PetscBLASInt ione = 1, bell;
      PetscCall(PetscBLASIntCast(bcgsl->ell, &bell));

      AY0c[0] = -1;
      if (bcgsl->pinv) {
#if defined(PETSC_USE_COMPLEX)
        PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "A", &bell, &bell, &MZa[1 + ldMZ], &ldMZ, bcgsl->s, bcgsl->u, &bell, bcgsl->v, &bell, bcgsl->work, &bcgsl->lwork, bcgsl->realwork, &bierr));
#else
        PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "A", &bell, &bell, &MZa[1 + ldMZ], &ldMZ, bcgsl->s, bcgsl->u, &bell, bcgsl->v, &bell, bcgsl->work, &bcgsl->lwork, &bierr));
#endif
        if (bierr != 0) {
          ksp->reason = KSP_DIVERGED_BREAKDOWN;
          PetscFunctionReturn(PETSC_SUCCESS);
        }
        /* Apply pseudo-inverse */
        max_s = bcgsl->s[0];
        for (i = 1; i < bell; i++) {
          if (bcgsl->s[i] > max_s) max_s = bcgsl->s[i];
        }
        /* tolerance is hardwired to bell*max(s)*PETSC_MACHINE_EPSILON */
        pinv_tol = bell * max_s * PETSC_MACHINE_EPSILON;
        PetscCall(PetscArrayzero(&AY0c[1], bell));
        for (i = 0; i < bell; i++) {
          if (bcgsl->s[i] >= pinv_tol) {
            utb = 0.;
            for (j = 0; j < bell; j++) utb += MZb[1 + j] * bcgsl->u[i * bell + j];

            for (j = 0; j < bell; j++) AY0c[1 + j] += utb / bcgsl->s[i] * bcgsl->v[j * bell + i];
          }
        }
      } else {
        PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("Lower", &bell, &MZa[1 + ldMZ], &ldMZ, &bierr));
        if (bierr != 0) {
          ksp->reason = KSP_DIVERGED_BREAKDOWN;
          PetscFunctionReturn(PETSC_SUCCESS);
        }
        PetscCall(PetscArraycpy(&AY0c[1], &MZb[1], bcgsl->ell));
        PetscCallBLAS("LAPACKpotrs", LAPACKpotrs_("Lower", &bell, &ione, &MZa[1 + ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
      }
    } else {
      PetscBLASInt ione = 1;
      PetscScalar  aone = 1.0, azero = 0.0;
      PetscBLASInt neqs;
      PetscCall(PetscBLASIntCast(bcgsl->ell - 1, &neqs));

      PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("Lower", &neqs, &MZa[1 + ldMZ], &ldMZ, &bierr));
      if (bierr != 0) {
        ksp->reason = KSP_DIVERGED_BREAKDOWN;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
      PetscCall(PetscArraycpy(&AY0c[1], &MZb[1], bcgsl->ell - 1));
      PetscCallBLAS("LAPACKpotrs", LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1 + ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
      AY0c[0]          = -1;
      AY0c[bcgsl->ell] = 0.;

      PetscCall(PetscArraycpy(&AYlc[1], &MZb[1 + ldMZ * (bcgsl->ell)], bcgsl->ell - 1));
      PetscCallBLAS("LAPACKpotrs", LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1 + ldMZ], &ldMZ, &AYlc[1], &ldMZ, &bierr));

      AYlc[0]          = 0.;
      AYlc[bcgsl->ell] = -1;

      PetscCallBLAS("BLASgemv", BLASgemv_("NoTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AY0c, &ione, &azero, AYtc, &ione));

      kappa0 = PetscRealPart(BLASdot_(&ldMZ, AY0c, &ione, AYtc, &ione));

      /* round-off can cause negative kappa's */
      if (kappa0 < 0) kappa0 = -kappa0;
      kappa0 = PetscSqrtReal(kappa0);

      kappaA = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));

      PetscCallBLAS("BLASgemv", BLASgemv_("noTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AYlc, &ione, &azero, AYtc, &ione));

      kappa1 = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));

      if (kappa1 < 0) kappa1 = -kappa1;
      kappa1 = PetscSqrtReal(kappa1);

      if (kappa0 != 0.0 && kappa1 != 0.0) {
        if (kappaA < 0.7 * kappa0 * kappa1) {
          ghat = (kappaA < 0.0) ? -0.7 * kappa0 / kappa1 : 0.7 * kappa0 / kappa1;
        } else {
          ghat = kappaA / (kappa1 * kappa1);
        }
        for (i = 0; i <= bcgsl->ell; i++) AY0c[i] = AY0c[i] - ghat * AYlc[i];
      }
    }

    omega = AY0c[bcgsl->ell];
    for (h = bcgsl->ell; h > 0 && omega == 0.0; h--) omega = AY0c[h];
    if (omega == 0.0) {
      ksp->reason = KSP_DIVERGED_BREAKDOWN;
      PetscFunctionReturn(PETSC_SUCCESS);
    }

    PetscCall(VecMAXPY(VX, bcgsl->ell, AY0c + 1, VVR));
    for (i = 1; i <= bcgsl->ell; i++) AY0c[i] *= -1.0;
    PetscCall(VecMAXPY(VVU[0], bcgsl->ell, AY0c + 1, VVU + 1));
    PetscCall(VecMAXPY(VVR[0], bcgsl->ell, AY0c + 1, VVR + 1));
    for (i = 1; i <= bcgsl->ell; i++) AY0c[i] *= -1.0;
    PetscCall(VecNorm(VVR[0], NORM_2, &zeta));
    KSPCheckNorm(ksp, zeta);

    /* Accurate Update */
    if (bcgsl->delta > 0.0) {
      if (rnmax_computed < zeta) rnmax_computed = zeta;
      if (rnmax_true < zeta) rnmax_true = zeta;

      bUpdateX = (PetscBool)(zeta < bcgsl->delta * zeta0 && zeta0 <= rnmax_computed);
      if ((zeta < bcgsl->delta * rnmax_true && zeta0 <= rnmax_true) || bUpdateX) {
        /* r0 <- b-inv(K)*A*X */
        PetscCall(KSP_PCApplyBAorAB(ksp, VX, VVR[0], VTM));
        PetscCall(VecAYPX(VVR[0], -1.0, VB));
        rnmax_true = zeta;

        if (bUpdateX) {
          PetscCall(VecAXPY(VXR, 1.0, VX));
          PetscCall(VecSet(VX, 0.0));
          PetscCall(VecCopy(VVR[0], VB));
          rnmax_computed = zeta;
        }
      }
    }
  }
  if (bcgsl->delta > 0.0) PetscCall(VecAXPY(VX, 1.0, VXR));

  ksp->its = k;
  if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = zeta;
  else ksp->rnorm = 0.0;
  PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
  PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
  PetscCall((*ksp->converged)(ksp, k, ksp->rnorm, &ksp->reason, ksp->cnvP));
  if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPBCGSLSetXRes - Sets the parameter governing when
  exact residuals will be used instead of computed residuals for `KSPCBGSL`.

  Logically Collective

  Input Parameters:
+ ksp   - iterative context of type `KSPBCGSL`
- delta - computed residuals are used alone when delta is not positive

  Options Database Key:
. -ksp_bcgsl_xres delta - Threshold used to decide when to refresh computed residuals

  Level: intermediate

.seealso: [](ch_ksp), `KSPBCGSLSetEll()`, `KSPBCGSLSetPol()`, `KSP`, `KSPCBGSL`, `KSPBCGSLSetUsePseudoinverse()`
@*/
PetscErrorCode KSPBCGSLSetXRes(KSP ksp, PetscReal delta)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveReal(ksp, delta, 2);
  if (ksp->setupstage) {
    if ((delta <= 0 && bcgsl->delta > 0) || (delta > 0 && bcgsl->delta <= 0)) {
      PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));
      PetscCall(PetscFree5(AY0c, AYlc, AYtc, MZa, MZb));
      PetscCall(PetscFree4(bcgsl->work, bcgsl->s, bcgsl->u, bcgsl->v));
      ksp->setupstage = KSP_SETUP_NEW;
    }
  }
  bcgsl->delta = delta;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPBCGSLSetUsePseudoinverse - Use pseudoinverse (via SVD) to solve polynomial part of the update in `KSPCBGSL` solver

  Logically Collective

  Input Parameters:
+ ksp      - iterative context of type `KSPCBGSL`
- use_pinv - set to `PETSC_TRUE` when using pseudoinverse

  Options Database Key:
. -ksp_bcgsl_pinv (true|false) - use pseudoinverse

  Level: intermediate

.seealso: [](ch_ksp), `KSPBCGSLSetEll()`, `KSP`, `KSPCBGSL`, `KSPBCGSLSetPol()`, `KSPBCGSLSetXRes()`
@*/
PetscErrorCode KSPBCGSLSetUsePseudoinverse(KSP ksp, PetscBool use_pinv)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;

  PetscFunctionBegin;
  bcgsl->pinv = use_pinv;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPBCGSLSetPol - Sets the type of polynomial part that will
  be used in the `KSPCBGSL` `KSPSolve()`

  Logically Collective

  Input Parameters:
+ ksp   - iterative context of type `KSPCBGSL`
- uMROR - set to `PETSC_TRUE` when the polynomial is a convex combination of an MR and an OR step.

  Options Database Keys:
+ -ksp_bcgsl_cxpoly - use enhanced polynomial
- -ksp_bcgsl_mrpoly - use standard polynomial

  Level: intermediate

.seealso: [](ch_ksp), `KSP`, `KSPBCGSL`, `KSPCreate()`, `KSPSetType()`, `KSPCBGSL`, `KSPBCGSLSetUsePseudoinverse()`, `KSPBCGSLSetEll()`, `KSPBCGSLSetXRes()`
@*/
PetscErrorCode KSPBCGSLSetPol(KSP ksp, PetscBool uMROR)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveBool(ksp, uMROR, 2);

  if (!ksp->setupstage) bcgsl->bConvex = uMROR;
  else if (bcgsl->bConvex != uMROR) {
    /* free the data structures,
       then create them again
     */
    PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));
    PetscCall(PetscFree5(AY0c, AYlc, AYtc, MZa, MZb));
    PetscCall(PetscFree4(bcgsl->work, bcgsl->s, bcgsl->u, bcgsl->v));

    bcgsl->bConvex  = uMROR;
    ksp->setupstage = KSP_SETUP_NEW;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  KSPBCGSLSetEll - Sets the number of search directions to use in the `KSPBCGSL` Krylov solver

  Logically Collective

  Input Parameters:
+ ksp - iterative context, `KSP`, of type `KSPBCGSL`
- ell - number of search directions to use

  Options Database Key:
. -ksp_bcgsl_ell ell - Number of Krylov search directions

  Level: intermediate

  Notes:
  For large `ell` it is common for the polynomial update problem to become singular (due to happy breakdown for smallish
  test problems, but also for larger problems). Consequently, by default, the system is solved by using the pseudoinverse, which
  allows the iteration to complete successfully. See `KSPBCGSLSetUsePseudoinverse()` to switch to a conventional solve.

.seealso: [](ch_ksp), `KSPBCGSLSetUsePseudoinverse()`, `KSP`, `KSPBCGSL`, `KSPBCGSLSetPol()`, `KSPBCGSLSetXRes()`
@*/
PetscErrorCode KSPBCGSLSetEll(KSP ksp, PetscInt ell)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;

  PetscFunctionBegin;
  PetscCheck(ell >= 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "KSPBCGSLSetEll: second argument must be positive");
  PetscValidLogicalCollectiveInt(ksp, ell, 2);

  if (!ksp->setupstage) bcgsl->ell = ell;
  else if (bcgsl->ell != ell) {
    /* free the data structures, then create them again */
    PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));
    PetscCall(PetscFree5(AY0c, AYlc, AYtc, MZa, MZb));
    PetscCall(PetscFree4(bcgsl->work, bcgsl->s, bcgsl->u, bcgsl->v));

    bcgsl->ell      = ell;
    ksp->setupstage = KSP_SETUP_NEW;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPView_BCGSL(KSP ksp, PetscViewer viewer)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;
  PetscBool  isascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));

  if (isascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Ell = %" PetscInt_FMT "\n", bcgsl->ell));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Delta = %g\n", (double)bcgsl->delta));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPSetFromOptions_BCGSL(KSP ksp, PetscOptionItems PetscOptionsObject)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;
  PetscInt   this_ell;
  PetscReal  delta;
  PetscBool  flga = PETSC_FALSE, flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "KSPBCGSL Options");

  /* Set number of search directions */
  PetscCall(PetscOptionsInt("-ksp_bcgsl_ell", "Number of Krylov search directions", "KSPBCGSLSetEll", bcgsl->ell, &this_ell, &flg));
  if (flg) PetscCall(KSPBCGSLSetEll(ksp, this_ell));

  /* Set polynomial type */
  PetscCall(PetscOptionsBool("-ksp_bcgsl_cxpoly", "Polynomial part of BiCGStabL is MinRes + OR", "KSPBCGSLSetPol", flga, &flga, NULL));
  if (flga) PetscCall(KSPBCGSLSetPol(ksp, PETSC_TRUE));
  else {
    flg = PETSC_FALSE;
    PetscCall(PetscOptionsBool("-ksp_bcgsl_mrpoly", "Polynomial part of BiCGStabL is MinRes", "KSPBCGSLSetPol", flg, &flg, NULL));
    PetscCall(KSPBCGSLSetPol(ksp, PETSC_FALSE));
  }

  /* Will computed residual be refreshed? */
  PetscCall(PetscOptionsReal("-ksp_bcgsl_xres", "Threshold used to decide when to refresh computed residuals", "KSPBCGSLSetXRes", bcgsl->delta, &delta, &flg));
  if (flg) PetscCall(KSPBCGSLSetXRes(ksp, delta));

  /* Use pseudoinverse? */
  flg = bcgsl->pinv;
  PetscCall(PetscOptionsBool("-ksp_bcgsl_pinv", "Polynomial correction via pseudoinverse", "KSPBCGSLSetUsePseudoinverse", flg, &flg, NULL));
  PetscCall(KSPBCGSLSetUsePseudoinverse(ksp, flg));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPSetUp_BCGSL(KSP ksp)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;
  PetscInt   ell = bcgsl->ell, ldMZ = ell + 1;

  PetscFunctionBegin;
  PetscCall(KSPSetWorkVecs(ksp, 6 + 2 * ell));
  PetscCall(PetscMalloc5(ldMZ, &AY0c, ldMZ, &AYlc, ldMZ, &AYtc, ldMZ * ldMZ, &MZa, ldMZ * ldMZ, &MZb));
  PetscCall(PetscBLASIntCast(5 * ell, &bcgsl->lwork));
  PetscCall(PetscMalloc5(bcgsl->lwork, &bcgsl->work, ell, &bcgsl->s, ell * ell, &bcgsl->u, ell * ell, &bcgsl->v, 5 * ell, &bcgsl->realwork));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPReset_BCGSL(KSP ksp)
{
  KSP_BCGSL *bcgsl = (KSP_BCGSL *)ksp->data;

  PetscFunctionBegin;
  PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));
  PetscCall(PetscFree5(AY0c, AYlc, AYtc, MZa, MZb));
  PetscCall(PetscFree5(bcgsl->work, bcgsl->s, bcgsl->u, bcgsl->v, bcgsl->realwork));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode KSPDestroy_BCGSL(KSP ksp)
{
  PetscFunctionBegin;
  PetscCall(KSPReset_BCGSL(ksp));
  PetscCall(KSPDestroyDefault(ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
    KSPBCGSL - Implements a slight variant of the Enhanced BiCGStab(L) algorithm in {cite}`fokkema1996enhanced`
               and {cite}`sleijpen1994bicgstab`, see also {cite}`sleijpen1995overview`. The variation
               concerns cases when either kappa0**2 or kappa1**2 is
               negative due to round-off. Kappa0 has also been pulled
               out of the denominator in the formula for ghat.

   Options Database Keys:
+  -ksp_bcgsl_ell ell             - Number of Krylov search directions to use, defaults to 2, cf. `KSPBCGSLSetEll()`
.  -ksp_bcgsl_cxpol (true|false)  - Use a convex function of the MinRes and OR polynomials after the BiCG step instead of default MinRes, cf. `KSPBCGSLSetPol()`
.  -ksp_bcgsl_mrpoly (true|false) - Use the default MinRes polynomial after the BiCG step, cf. `KSPBCGSLSetPol()`
.  -ksp_bcgsl_xres res            - Threshold used to decide when to refresh computed residuals, cf. `KSPBCGSLSetXRes()`
-  -ksp_bcgsl_pinv (true|false)   - (de)activate use of pseudoinverse, cf. `KSPBCGSLSetUsePseudoinverse()`

   Level: intermediate

   Note:
   The "sub-iterations" of this solver are not reported by `-ksp_monitor` or recorded in `KSPSetResidualHistory()` since the solution is not directly computed for
   these sub-iterations.

   Contributed by:
   Joel M. Malard, email jm.malard@pnl.gov

   Developer Notes:
   This has not been completely cleaned up into PETSc style.

   All the BLAS and LAPACK calls in the source should be removed and replaced with loops and the macros for block solvers converted from LINPACK.

.seealso: [](ch_ksp), `KSPFBCGS`, `KSPFBCGSR`, `KSPBCGS`, `KSPPIPEBCGS`, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPSetPCSide()`,
          `KSPBCGSLSetEll()`, `KSPBCGSLSetXRes()`, `KSPBCGSLSetUsePseudoinverse()`, `KSPBCGSLSetPol()`
M*/
PETSC_EXTERN PetscErrorCode KSPCreate_BCGSL(KSP ksp)
{
  KSP_BCGSL *bcgsl;

  PetscFunctionBegin;
  /* allocate BiCGStab(L) context */
  PetscCall(PetscNew(&bcgsl));
  ksp->data = (void *)bcgsl;

  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
  PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

  ksp->ops->setup          = KSPSetUp_BCGSL;
  ksp->ops->solve          = KSPSolve_BCGSL;
  ksp->ops->reset          = KSPReset_BCGSL;
  ksp->ops->destroy        = KSPDestroy_BCGSL;
  ksp->ops->buildsolution  = KSPBuildSolutionDefault;
  ksp->ops->buildresidual  = KSPBuildResidualDefault;
  ksp->ops->setfromoptions = KSPSetFromOptions_BCGSL;
  ksp->ops->view           = KSPView_BCGSL;

  /* Let the user redefine the number of directions vectors */
  bcgsl->ell = 2;

  /*Choose between a single MR step or an averaged MR/OR */
  bcgsl->bConvex = PETSC_FALSE;

  bcgsl->pinv = PETSC_TRUE; /* Use the reliable method by default */

  /* Set the threshold for when exact residuals will be used */
  bcgsl->delta = 0.0;
  PetscFunctionReturn(PETSC_SUCCESS);
}
