#include <petsc/private/petscfeimpl.h> /*I "petscfe.h" I*/
#include <petsc/private/dtimpl.h>      /*I "petscdt.h" I*/
#include <petscblaslapack.h>
#include <petscdmplextransform.h>

static PetscErrorCode PetscFEDestroy_Composite(PetscFE fem)
{
  PetscFE_Composite *cmp = (PetscFE_Composite *)fem->data;

  PetscFunctionBegin;
  PetscCall(PetscFree(cmp->embedding));
  PetscCall(PetscFree(cmp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscFESetUp_Composite(PetscFE fem)
{
  PetscFE_Composite *cmp = (PetscFE_Composite *)fem->data;
  DM                 K;
  DMPolytopeType     ct;
  DMPlexTransform    tr;
  PetscReal         *subpoint;
  PetscBLASInt      *pivots;
  PetscBLASInt       n, info;
  PetscScalar       *work, *invVscalar;
  PetscInt           dim, pdim, spdim, j, s;
  PetscSection       section;

  PetscFunctionBegin;
  /* Get affine mapping from reference cell to each subcell */
  PetscCall(PetscDualSpaceGetDM(fem->dualSpace, &K));
  PetscCall(DMGetDimension(K, &dim));
  PetscCall(DMPlexGetCellType(K, 0, &ct));
  PetscCall(DMPlexTransformCreate(PETSC_COMM_SELF, &tr));
  PetscCall(DMPlexTransformSetType(tr, DMPLEXREFINEREGULAR));
  PetscCall(DMPlexRefineRegularGetAffineTransforms(tr, ct, &cmp->numSubelements, &cmp->v0, &cmp->jac, &cmp->invjac));
  PetscCall(DMPlexTransformDestroy(&tr));
  /* Determine dof embedding into subelements */
  PetscCall(PetscDualSpaceGetDimension(fem->dualSpace, &pdim));
  PetscCall(PetscSpaceGetDimension(fem->basisSpace, &spdim));
  PetscCall(PetscMalloc1(cmp->numSubelements * spdim, &cmp->embedding));
  PetscCall(DMGetWorkArray(K, dim, MPIU_REAL, &subpoint));
  PetscCall(PetscDualSpaceGetSection(fem->dualSpace, &section));
  for (s = 0; s < cmp->numSubelements; ++s) {
    PetscInt  sd = 0;
    PetscInt  closureSize;
    PetscInt *closure = NULL;

    PetscCall(DMPlexGetTransitiveClosure(K, s, PETSC_TRUE, &closureSize, &closure));
    for (j = 0; j < closureSize; j++) {
      PetscInt point = closure[2 * j];
      PetscInt dof, off, k;

      PetscCall(PetscSectionGetDof(section, point, &dof));
      PetscCall(PetscSectionGetOffset(section, point, &off));
      for (k = 0; k < dof; k++) cmp->embedding[s * spdim + sd++] = off + k;
    }
    PetscCall(DMPlexRestoreTransitiveClosure(K, s, PETSC_TRUE, &closureSize, &closure));
    PetscCheck(sd == spdim, PetscObjectComm((PetscObject)fem), PETSC_ERR_PLIB, "Subelement %" PetscInt_FMT " has %" PetscInt_FMT " dual basis vectors != %" PetscInt_FMT, s, sd, spdim);
  }
  PetscCall(DMRestoreWorkArray(K, dim, MPIU_REAL, &subpoint));
  /* Construct the change of basis from prime basis to nodal basis for each subelement */
  PetscCall(PetscMalloc1(cmp->numSubelements * spdim * spdim, &fem->invV));
  PetscCall(PetscMalloc2(spdim, &pivots, spdim, &work));
#if defined(PETSC_USE_COMPLEX)
  PetscCall(PetscMalloc1(cmp->numSubelements * spdim * spdim, &invVscalar));
#else
  invVscalar = fem->invV;
#endif
  for (s = 0; s < cmp->numSubelements; ++s) {
    for (j = 0; j < spdim; ++j) {
      PetscReal       *Bf;
      PetscQuadrature  f;
      const PetscReal *points, *weights;
      PetscInt         Nc, Nq, q, k;

      PetscCall(PetscDualSpaceGetFunctional(fem->dualSpace, cmp->embedding[s * spdim + j], &f));
      PetscCall(PetscQuadratureGetData(f, NULL, &Nc, &Nq, &points, &weights));
      PetscCall(PetscMalloc1(f->numPoints * spdim * Nc, &Bf));
      PetscCall(PetscSpaceEvaluate(fem->basisSpace, Nq, points, Bf, NULL, NULL));
      for (k = 0; k < spdim; ++k) {
        /* n_j \cdot \phi_k */
        invVscalar[(s * spdim + j) * spdim + k] = 0.0;
        for (q = 0; q < Nq; ++q) invVscalar[(s * spdim + j) * spdim + k] += Bf[q * spdim + k] * weights[q];
      }
      PetscCall(PetscFree(Bf));
    }
    PetscCall(PetscBLASIntCast(spdim, &n));
    PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&n, &n, &invVscalar[s * spdim * spdim], &n, pivots, &info));
    PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&n, &invVscalar[s * spdim * spdim], &n, pivots, work, &n, &info));
  }
#if defined(PETSC_USE_COMPLEX)
  for (s = 0; s < cmp->numSubelements * spdim * spdim; s++) fem->invV[s] = PetscRealPart(invVscalar[s]);
  PetscCall(PetscFree(invVscalar));
#endif
  PetscCall(PetscFree2(pivots, work));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscFECreateTabulation_Composite(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
{
  PetscFE_Composite *cmp = (PetscFE_Composite *)fem->data;
  DM                 dm;
  DMPolytopeType     ct;
  PetscInt           pdim;  /* Dimension of FE space P */
  PetscInt           spdim; /* Dimension of subelement FE space P */
  PetscInt           dim;   /* Spatial dimension */
  PetscInt           comp;  /* Field components */
  PetscInt          *subpoints;
  PetscReal         *B    = K >= 0 ? T->T[0] : NULL;
  PetscReal         *D    = K >= 1 ? T->T[1] : NULL;
  PetscReal         *H    = K >= 2 ? T->T[2] : NULL;
  PetscReal         *tmpB = NULL, *tmpD = NULL, *tmpH = NULL, *subpoint;
  PetscInt           p, s, d, e, j, k;

  PetscFunctionBegin;
  PetscCall(PetscDualSpaceGetDM(fem->dualSpace, &dm));
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMPlexGetCellType(dm, 0, &ct));
  PetscCall(PetscSpaceGetDimension(fem->basisSpace, &spdim));
  PetscCall(PetscDualSpaceGetDimension(fem->dualSpace, &pdim));
  PetscCall(PetscFEGetNumComponents(fem, &comp));
  /* Divide points into subelements */
  PetscCall(DMGetWorkArray(dm, npoints, MPIU_INT, &subpoints));
  PetscCall(DMGetWorkArray(dm, dim, MPIU_REAL, &subpoint));
  for (p = 0; p < npoints; ++p) {
    for (s = 0; s < cmp->numSubelements; ++s) {
      PetscBool inside;

      /* Apply transform, and check that point is inside cell */
      for (d = 0; d < dim; ++d) {
        subpoint[d] = -1.0;
        for (e = 0; e < dim; ++e) subpoint[d] += cmp->invjac[(s * dim + d) * dim + e] * (points[p * dim + e] - cmp->v0[s * dim + e]);
      }
      PetscCall(DMPolytopeInCellTest(ct, subpoint, &inside));
      if (inside) {
        subpoints[p] = s;
        break;
      }
    }
    PetscCheck(s < cmp->numSubelements, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %" PetscInt_FMT " was not found in any subelement", p);
  }
  PetscCall(DMRestoreWorkArray(dm, dim, MPIU_REAL, &subpoint));
  /* Evaluate the prime basis functions at all points */
  if (K >= 0) PetscCall(DMGetWorkArray(dm, npoints * spdim, MPIU_REAL, &tmpB));
  if (K >= 1) PetscCall(DMGetWorkArray(dm, npoints * spdim * dim, MPIU_REAL, &tmpD));
  if (K >= 2) PetscCall(DMGetWorkArray(dm, npoints * spdim * dim * dim, MPIU_REAL, &tmpH));
  PetscCall(PetscSpaceEvaluate(fem->basisSpace, npoints, points, tmpB, tmpD, tmpH));
  /* Translate to the nodal basis */
  if (K >= 0) PetscCall(PetscArrayzero(B, npoints * pdim * comp));
  if (K >= 1) PetscCall(PetscArrayzero(D, npoints * pdim * comp * dim));
  if (K >= 2) PetscCall(PetscArrayzero(H, npoints * pdim * comp * dim * dim));
  for (p = 0; p < npoints; ++p) {
    const PetscInt s = subpoints[p];

    if (B) {
      /* Multiply by V^{-1} (spdim x spdim) */
      for (j = 0; j < spdim; ++j) {
        const PetscInt i = (p * pdim + cmp->embedding[s * spdim + j]) * comp;

        B[i] = 0.0;
        for (k = 0; k < spdim; ++k) B[i] += fem->invV[(s * spdim + k) * spdim + j] * tmpB[p * spdim + k];
      }
    }
    if (D) {
      /* Multiply by V^{-1} (spdim x spdim) */
      for (j = 0; j < spdim; ++j) {
        for (d = 0; d < dim; ++d) {
          const PetscInt i = ((p * pdim + cmp->embedding[s * spdim + j]) * comp + 0) * dim + d;

          D[i] = 0.0;
          for (k = 0; k < spdim; ++k) D[i] += fem->invV[(s * spdim + k) * spdim + j] * tmpD[(p * spdim + k) * dim + d];
        }
      }
    }
    if (H) {
      /* Multiply by V^{-1} (pdim x pdim) */
      for (j = 0; j < spdim; ++j) {
        for (d = 0; d < dim * dim; ++d) {
          const PetscInt i = ((p * pdim + cmp->embedding[s * spdim + j]) * comp + 0) * dim * dim + d;

          H[i] = 0.0;
          for (k = 0; k < spdim; ++k) H[i] += fem->invV[(s * spdim + k) * spdim + j] * tmpH[(p * spdim + k) * dim * dim + d];
        }
      }
    }
  }
  PetscCall(DMRestoreWorkArray(dm, npoints, MPIU_INT, &subpoints));
  if (K >= 0) PetscCall(DMRestoreWorkArray(dm, npoints * spdim, MPIU_REAL, &tmpB));
  if (K >= 1) PetscCall(DMRestoreWorkArray(dm, npoints * spdim * dim, MPIU_REAL, &tmpD));
  if (K >= 2) PetscCall(DMRestoreWorkArray(dm, npoints * spdim * dim * dim, MPIU_REAL, &tmpH));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscFEInitialize_Composite(PetscFE fem)
{
  PetscFunctionBegin;
  fem->ops->setfromoptions          = NULL;
  fem->ops->setup                   = PetscFESetUp_Composite;
  fem->ops->view                    = NULL;
  fem->ops->destroy                 = PetscFEDestroy_Composite;
  fem->ops->getdimension            = PetscFEGetDimension_Basic;
  fem->ops->createtabulation        = PetscFECreateTabulation_Composite;
  fem->ops->integrateresidual       = PetscFEIntegrateResidual_Basic;
  fem->ops->integratebdresidual     = PetscFEIntegrateBdResidual_Basic;
  fem->ops->integratejacobianaction = NULL /* PetscFEIntegrateJacobianAction_Basic */;
  fem->ops->integratejacobian       = PetscFEIntegrateJacobian_Basic;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  PETSCFECOMPOSITE = "composite" - A `PetscFEType` that represents a composite element

  Level: intermediate

.seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
M*/
PETSC_EXTERN PetscErrorCode PetscFECreate_Composite(PetscFE fem)
{
  PetscFE_Composite *cmp;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(fem, PETSCFE_CLASSID, 1);
  PetscCall(PetscNew(&cmp));
  fem->data = cmp;

  cmp->numSubelements = -1;
  cmp->v0             = NULL;
  cmp->jac            = NULL;

  PetscCall(PetscFEInitialize_Composite(fem));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscFECompositeGetMapping - Returns the mappings from the reference element to each subelement

  Not Collective

  Input Parameter:
. fem - The `PetscFE` object

  Output Parameters:
+ numSubelements - The number of sub elements
. v0             - The affine transformation for each element, an array of length $dim * Nc$. Pass `NULL` to ignore.
. jac            - The Jacobian for each element, an array of length $dim^2 * Nc$. Pass `NULL` to ignore.
- invjac         - The inverse of the Jacobian, an array of length $dim^2 * Nc$. Pass `NULL` to ignore.

  Level: intermediate

  Note:
  Do not free the output arrays.

.seealso: `PetscFE`, `PetscFECreate()`
@*/
PetscErrorCode PetscFECompositeGetMapping(PetscFE fem, PetscInt *numSubelements, const PetscReal *v0[], const PetscReal *jac[], const PetscReal *invjac[])
{
  PetscFE_Composite *cmp = (PetscFE_Composite *)fem->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(fem, PETSCFE_CLASSID, 1);
  if (numSubelements) {
    PetscAssertPointer(numSubelements, 2);
    *numSubelements = cmp->numSubelements;
  }
  if (v0) {
    PetscAssertPointer(v0, 3);
    *v0 = cmp->v0;
  }
  if (jac) {
    PetscAssertPointer(jac, 4);
    *jac = cmp->jac;
  }
  if (invjac) {
    PetscAssertPointer(invjac, 5);
    *invjac = cmp->invjac;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
