#include <petsctao.h> /*I "petsctao.h" I*/
#include <petsc/private/vecimpl.h>
#include <petsc/private/taoimpl.h>
#include <../src/tao/matrix/submatfree.h>

/*@C
  TaoVecGetSubVec - Gets a subvector using the `IS`

  Input Parameters:
+ vfull        - the full matrix
. is           - the index set for the subvector
. reduced_type - the method `Tao` is using for subsetting
- maskvalue    - the value to set the unused vector elements to (for `TAO_SUBSET_MASK` or `TAO_SUBSET_MATRIXFREE`)

  Output Parameter:
. vreduced - the subvector

  Level: developer

  Notes:
  `maskvalue` should usually be `0.0`, unless a pointwise divide will be used.

.seealso: `TaoMatGetSubMat()`, `TaoSubsetType`
@*/
PetscErrorCode TaoVecGetSubVec(Vec vfull, IS is, TaoSubsetType reduced_type, PetscReal maskvalue, Vec *vreduced)
{
  PetscInt        nfull, nreduced, nreduced_local, rlow, rhigh, flow, fhigh;
  PetscInt        i, nlocal;
  PetscReal      *fv, *rv;
  const PetscInt *s;
  IS              ident;
  VecType         vtype;
  VecScatter      scatter;
  MPI_Comm        comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(vfull, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(is, IS_CLASSID, 2);

  PetscCall(VecGetSize(vfull, &nfull));
  PetscCall(ISGetSize(is, &nreduced));

  if (nreduced == nfull) {
    PetscCall(VecDestroy(vreduced));
    PetscCall(VecDuplicate(vfull, vreduced));
    PetscCall(VecCopy(vfull, *vreduced));
  } else {
    switch (reduced_type) {
    case TAO_SUBSET_SUBVEC:
      PetscCall(VecGetType(vfull, &vtype));
      PetscCall(VecGetOwnershipRange(vfull, &flow, &fhigh));
      PetscCall(ISGetLocalSize(is, &nreduced_local));
      PetscCall(PetscObjectGetComm((PetscObject)vfull, &comm));
      if (*vreduced) PetscCall(VecDestroy(vreduced));
      PetscCall(VecCreate(comm, vreduced));
      PetscCall(VecSetType(*vreduced, vtype));

      PetscCall(VecSetSizes(*vreduced, nreduced_local, nreduced));
      PetscCall(VecGetOwnershipRange(*vreduced, &rlow, &rhigh));
      PetscCall(ISCreateStride(comm, nreduced_local, rlow, 1, &ident));
      PetscCall(VecScatterCreate(vfull, is, *vreduced, ident, &scatter));
      PetscCall(VecScatterBegin(scatter, vfull, *vreduced, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(scatter, vfull, *vreduced, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterDestroy(&scatter));
      PetscCall(ISDestroy(&ident));
      break;

    case TAO_SUBSET_MASK:
    case TAO_SUBSET_MATRIXFREE:
      /* vr[i] = vf[i]   if i in is
       vr[i] = 0       otherwise */
      if (!*vreduced) PetscCall(VecDuplicate(vfull, vreduced));

      PetscCall(VecSet(*vreduced, maskvalue));
      PetscCall(ISGetLocalSize(is, &nlocal));
      PetscCall(VecGetOwnershipRange(vfull, &flow, &fhigh));
      PetscCall(VecGetArray(vfull, &fv));
      PetscCall(VecGetArray(*vreduced, &rv));
      PetscCall(ISGetIndices(is, &s));
      PetscCheck(nlocal <= (fhigh - flow), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "IS local size %" PetscInt_FMT " > Vec local size %" PetscInt_FMT, nlocal, fhigh - flow);
      for (i = 0; i < nlocal; ++i) rv[s[i] - flow] = fv[s[i] - flow];
      PetscCall(ISRestoreIndices(is, &s));
      PetscCall(VecRestoreArray(vfull, &fv));
      PetscCall(VecRestoreArray(*vreduced, &rv));
      break;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  TaoMatGetSubMat - Gets a submatrix using the `IS`

  Input Parameters:
+ M           - the full matrix (`n x n`)
. is          - the index set for the submatrix (both row and column index sets need to be the same)
. v1          - work vector of dimension n, needed for `TAO_SUBSET_MASK` option
- subset_type - the method `Tao` is using for subsetting

  Output Parameter:
. Msub - the submatrix

  Level: developer

.seealso: `TaoVecGetSubVec()`, `TaoSubsetType`
@*/
PetscErrorCode TaoMatGetSubMat(Mat M, IS is, Vec v1, TaoSubsetType subset_type, Mat *Msub)
{
  IS        iscomp;
  PetscBool flg = PETSC_TRUE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(M, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(is, IS_CLASSID, 2);
  PetscCall(MatDestroy(Msub));
  switch (subset_type) {
  case TAO_SUBSET_SUBVEC:
    PetscCall(MatCreateSubMatrix(M, is, is, MAT_INITIAL_MATRIX, Msub));
    break;

  case TAO_SUBSET_MASK:
    /* Get Reduced Hessian
     Msub[i,j] = M[i,j] if i,j in Free_Local or i==j
     Msub[i,j] = 0      if i!=j and i or j not in Free_Local
     */
    PetscObjectOptionsBegin((PetscObject)M);
    PetscCall(PetscOptionsBool("-overwrite_hessian", "modify the existing hessian matrix when computing submatrices", "TaoSubsetType", flg, &flg, NULL));
    PetscOptionsEnd();
    if (flg) {
      PetscCall(MatDuplicate(M, MAT_COPY_VALUES, Msub));
    } else {
      /* Act on hessian directly (default) */
      PetscCall(PetscObjectReference((PetscObject)M));
      *Msub = M;
    }
    /* Save the diagonal to temporary vector */
    PetscCall(MatGetDiagonal(*Msub, v1));

    /* Zero out rows and columns */
    PetscCall(ISComplementVec(is, v1, &iscomp));

    /* Use v1 instead of 0 here because of PETSc bug */
    PetscCall(MatZeroRowsColumnsIS(*Msub, iscomp, 1.0, v1, v1));

    PetscCall(ISDestroy(&iscomp));
    break;
  case TAO_SUBSET_MATRIXFREE:
    PetscCall(ISComplementVec(is, v1, &iscomp));
    PetscCall(MatCreateSubMatrixFree(M, iscomp, iscomp, Msub));
    PetscCall(ISDestroy(&iscomp));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  TaoEstimateActiveBounds - Generates index sets for variables at the lower and upper
  bounds, as well as fixed variables where lower and upper bounds equal each other.

  Input Parameters:
+ X       - solution vector
. XL      - lower bound vector
. XU      - upper bound vector
. G       - unprojected gradient
. S       - step direction with which the active bounds will be estimated
. W       - work vector of type and size of `X`
- steplen - the step length at which the active bounds will be estimated (needs to be conservative)

  Output Parameters:
+ bound_tol    - tolerance for the bound estimation
. active_lower - index set for active variables at the lower bound
. active_upper - index set for active variables at the upper bound
. active_fixed - index set for fixed variables
. active       - index set for all active variables
- inactive     - complementary index set for inactive variables

  Level: developer

  Notes:
  This estimation is based on Bertsekas' method, with a built in diagonal scaling value of `1.0e-3`.

.seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundSolution()`
@*/
PetscErrorCode TaoEstimateActiveBounds(Vec X, Vec XL, Vec XU, Vec G, Vec S, Vec W, PetscReal steplen, PetscReal *bound_tol, IS *active_lower, IS *active_upper, IS *active_fixed, IS *active, IS *inactive)
{
  PetscReal          wnorm;
  PetscReal          zero = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0 / 3.0);
  PetscInt           i, n_isl = 0, n_isu = 0, n_isf = 0, n_isa = 0, n_isi = 0;
  PetscInt           N_isl, N_isu, N_isf, N_isa, N_isi;
  PetscInt           n, low, high, nDiff;
  PetscInt          *isl = NULL, *isu = NULL, *isf = NULL, *isa = NULL, *isi = NULL;
  const PetscScalar *xl, *xu, *x, *g;
  MPI_Comm           comm = PetscObjectComm((PetscObject)X);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(X, VEC_CLASSID, 1);
  if (XL) PetscValidHeaderSpecific(XL, VEC_CLASSID, 2);
  if (XU) PetscValidHeaderSpecific(XU, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(G, VEC_CLASSID, 4);
  PetscValidHeaderSpecific(S, VEC_CLASSID, 5);
  PetscValidHeaderSpecific(W, VEC_CLASSID, 6);

  if (XL) PetscCheckSameType(X, 1, XL, 2);
  if (XU) PetscCheckSameType(X, 1, XU, 3);
  PetscCheckSameType(X, 1, G, 4);
  PetscCheckSameType(X, 1, S, 5);
  PetscCheckSameType(X, 1, W, 6);
  if (XL) PetscCheckSameComm(X, 1, XL, 2);
  if (XU) PetscCheckSameComm(X, 1, XU, 3);
  PetscCheckSameComm(X, 1, G, 4);
  PetscCheckSameComm(X, 1, S, 5);
  PetscCheckSameComm(X, 1, W, 6);
  if (XL) VecCheckSameSize(X, 1, XL, 2);
  if (XU) VecCheckSameSize(X, 1, XU, 3);
  VecCheckSameSize(X, 1, G, 4);
  VecCheckSameSize(X, 1, S, 5);
  VecCheckSameSize(X, 1, W, 6);

  /* Update the tolerance for bound detection (this is based on Bertsekas' method) */
  PetscCall(VecCopy(X, W));
  PetscCall(VecAXPBY(W, steplen, 1.0, S));
  PetscCall(TaoBoundSolution(W, XL, XU, 0.0, &nDiff, W));
  PetscCall(VecAXPBY(W, 1.0, -1.0, X));
  PetscCall(VecNorm(W, NORM_2, &wnorm));
  *bound_tol = PetscMin(*bound_tol, wnorm);

  /* Clear all index sets */
  PetscCall(ISDestroy(active_lower));
  PetscCall(ISDestroy(active_upper));
  PetscCall(ISDestroy(active_fixed));
  PetscCall(ISDestroy(active));
  PetscCall(ISDestroy(inactive));

  PetscCall(VecGetOwnershipRange(X, &low, &high));
  PetscCall(VecGetLocalSize(X, &n));
  if (!XL && !XU) {
    PetscCall(ISCreateStride(comm, n, low, 1, inactive));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (n > 0) {
    PetscCall(VecGetArrayRead(X, &x));
    PetscCall(VecGetArrayRead(XL, &xl));
    PetscCall(VecGetArrayRead(XU, &xu));
    PetscCall(VecGetArrayRead(G, &g));

    /* Loop over variables and categorize the indexes */
    PetscCall(PetscMalloc1(n, &isl));
    PetscCall(PetscMalloc1(n, &isu));
    PetscCall(PetscMalloc1(n, &isf));
    PetscCall(PetscMalloc1(n, &isa));
    PetscCall(PetscMalloc1(n, &isi));
    for (i = 0; i < n; ++i) {
      if (xl[i] == xu[i]) {
        /* Fixed variables */
        isf[n_isf] = low + i;
        ++n_isf;
        isa[n_isa] = low + i;
        ++n_isa;
      } else if (xl[i] > PETSC_NINFINITY && x[i] <= xl[i] + *bound_tol && g[i] > zero) {
        /* Lower bounded variables */
        isl[n_isl] = low + i;
        ++n_isl;
        isa[n_isa] = low + i;
        ++n_isa;
      } else if (xu[i] < PETSC_INFINITY && x[i] >= xu[i] - *bound_tol && g[i] < zero) {
        /* Upper bounded variables */
        isu[n_isu] = low + i;
        ++n_isu;
        isa[n_isa] = low + i;
        ++n_isa;
      } else {
        /* Inactive variables */
        isi[n_isi] = low + i;
        ++n_isi;
      }
    }

    PetscCall(VecRestoreArrayRead(X, &x));
    PetscCall(VecRestoreArrayRead(XL, &xl));
    PetscCall(VecRestoreArrayRead(XU, &xu));
    PetscCall(VecRestoreArrayRead(G, &g));
  }

  /* Collect global sizes */
  PetscCall(MPIU_Allreduce(&n_isl, &N_isl, 1, MPIU_INT, MPI_SUM, comm));
  PetscCall(MPIU_Allreduce(&n_isu, &N_isu, 1, MPIU_INT, MPI_SUM, comm));
  PetscCall(MPIU_Allreduce(&n_isf, &N_isf, 1, MPIU_INT, MPI_SUM, comm));
  PetscCall(MPIU_Allreduce(&n_isa, &N_isa, 1, MPIU_INT, MPI_SUM, comm));
  PetscCall(MPIU_Allreduce(&n_isi, &N_isi, 1, MPIU_INT, MPI_SUM, comm));

  /* Create index set for lower bounded variables */
  if (N_isl > 0) {
    PetscCall(ISCreateGeneral(comm, n_isl, isl, PETSC_OWN_POINTER, active_lower));
  } else {
    PetscCall(PetscFree(isl));
  }
  /* Create index set for upper bounded variables */
  if (N_isu > 0) {
    PetscCall(ISCreateGeneral(comm, n_isu, isu, PETSC_OWN_POINTER, active_upper));
  } else {
    PetscCall(PetscFree(isu));
  }
  /* Create index set for fixed variables */
  if (N_isf > 0) {
    PetscCall(ISCreateGeneral(comm, n_isf, isf, PETSC_OWN_POINTER, active_fixed));
  } else {
    PetscCall(PetscFree(isf));
  }
  /* Create index set for all actively bounded variables */
  if (N_isa > 0) {
    PetscCall(ISCreateGeneral(comm, n_isa, isa, PETSC_OWN_POINTER, active));
  } else {
    PetscCall(PetscFree(isa));
  }
  /* Create index set for all inactive variables */
  if (N_isi > 0) {
    PetscCall(ISCreateGeneral(comm, n_isi, isi, PETSC_OWN_POINTER, inactive));
  } else {
    PetscCall(PetscFree(isi));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  TaoBoundStep - Ensures the correct zero or adjusted step direction values for active
  variables.

  Input Parameters:
+ X            - solution vector
. XL           - lower bound vector
. XU           - upper bound vector
. active_lower - index set for lower bounded active variables
. active_upper - index set for lower bounded active variables
. active_fixed - index set for fixed active variables
- scale        - amplification factor for the step that needs to be taken on actively bounded variables

  Output Parameter:
. S - step direction to be modified

  Level: developer

.seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundSolution()`
@*/
PetscErrorCode TaoBoundStep(Vec X, Vec XL, Vec XU, IS active_lower, IS active_upper, IS active_fixed, PetscReal scale, Vec S)
{
  Vec step_lower, step_upper, step_fixed;
  Vec x_lower, x_upper;
  Vec bound_lower, bound_upper;

  PetscFunctionBegin;
  /* Adjust step for variables at the estimated lower bound */
  if (active_lower) {
    PetscCall(VecGetSubVector(S, active_lower, &step_lower));
    PetscCall(VecGetSubVector(X, active_lower, &x_lower));
    PetscCall(VecGetSubVector(XL, active_lower, &bound_lower));
    PetscCall(VecCopy(bound_lower, step_lower));
    PetscCall(VecAXPY(step_lower, -1.0, x_lower));
    PetscCall(VecScale(step_lower, scale));
    PetscCall(VecRestoreSubVector(S, active_lower, &step_lower));
    PetscCall(VecRestoreSubVector(X, active_lower, &x_lower));
    PetscCall(VecRestoreSubVector(XL, active_lower, &bound_lower));
  }

  /* Adjust step for the variables at the estimated upper bound */
  if (active_upper) {
    PetscCall(VecGetSubVector(S, active_upper, &step_upper));
    PetscCall(VecGetSubVector(X, active_upper, &x_upper));
    PetscCall(VecGetSubVector(XU, active_upper, &bound_upper));
    PetscCall(VecCopy(bound_upper, step_upper));
    PetscCall(VecAXPY(step_upper, -1.0, x_upper));
    PetscCall(VecScale(step_upper, scale));
    PetscCall(VecRestoreSubVector(S, active_upper, &step_upper));
    PetscCall(VecRestoreSubVector(X, active_upper, &x_upper));
    PetscCall(VecRestoreSubVector(XU, active_upper, &bound_upper));
  }

  /* Zero out step for fixed variables */
  if (active_fixed) {
    PetscCall(VecGetSubVector(S, active_fixed, &step_fixed));
    PetscCall(VecSet(step_fixed, 0.0));
    PetscCall(VecRestoreSubVector(S, active_fixed, &step_fixed));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  TaoBoundSolution - Ensures that the solution vector is snapped into the bounds within a given tolerance.

  Collective

  Input Parameters:
+ X         - solution vector
. XL        - lower bound vector
. XU        - upper bound vector
- bound_tol - absolute tolerance in enforcing the bound

  Output Parameters:
+ nDiff - total number of vector entries that have been bounded
- Xout  - modified solution vector satisfying bounds to `bound_tol`

  Level: developer

.seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundStep()`
@*/
PetscErrorCode TaoBoundSolution(Vec X, Vec XL, Vec XU, PetscReal bound_tol, PetscInt *nDiff, Vec Xout)
{
  PetscInt           i, n, low, high, nDiff_loc = 0;
  PetscScalar       *xout;
  const PetscScalar *x, *xl, *xu;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(X, VEC_CLASSID, 1);
  if (XL) PetscValidHeaderSpecific(XL, VEC_CLASSID, 2);
  if (XU) PetscValidHeaderSpecific(XU, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(Xout, VEC_CLASSID, 6);
  if (!XL && !XU) {
    PetscCall(VecCopy(X, Xout));
    *nDiff = 0.0;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCheckSameType(X, 1, XL, 2);
  PetscCheckSameType(X, 1, XU, 3);
  PetscCheckSameType(X, 1, Xout, 6);
  PetscCheckSameComm(X, 1, XL, 2);
  PetscCheckSameComm(X, 1, XU, 3);
  PetscCheckSameComm(X, 1, Xout, 6);
  VecCheckSameSize(X, 1, XL, 2);
  VecCheckSameSize(X, 1, XU, 3);
  VecCheckSameSize(X, 1, Xout, 4);

  PetscCall(VecGetOwnershipRange(X, &low, &high));
  PetscCall(VecGetLocalSize(X, &n));
  if (n > 0) {
    PetscCall(VecGetArrayRead(X, &x));
    PetscCall(VecGetArrayRead(XL, &xl));
    PetscCall(VecGetArrayRead(XU, &xu));
    PetscCall(VecGetArray(Xout, &xout));

    for (i = 0; i < n; ++i) {
      if (xl[i] > PETSC_NINFINITY && x[i] <= xl[i] + bound_tol) {
        xout[i] = xl[i];
        ++nDiff_loc;
      } else if (xu[i] < PETSC_INFINITY && x[i] >= xu[i] - bound_tol) {
        xout[i] = xu[i];
        ++nDiff_loc;
      }
    }

    PetscCall(VecRestoreArrayRead(X, &x));
    PetscCall(VecRestoreArrayRead(XL, &xl));
    PetscCall(VecRestoreArrayRead(XU, &xu));
    PetscCall(VecRestoreArray(Xout, &xout));
  }
  PetscCall(MPIU_Allreduce(&nDiff_loc, nDiff, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)X)));
  PetscFunctionReturn(PETSC_SUCCESS);
}
