#include <petscksp.h>
#include <../src/tao/quadratic/impls/gpcg/gpcg.h> /*I "gpcg.h" I*/

static PetscErrorCode GPCGGradProjections(Tao tao);
static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch, Vec, PetscReal *, Vec, void *);

static PetscErrorCode TaoDestroy_GPCG(Tao tao)
{
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

  /* Free allocated memory in GPCG structure */
  PetscFunctionBegin;
  PetscCall(VecDestroy(&gpcg->B));
  PetscCall(VecDestroy(&gpcg->Work));
  PetscCall(VecDestroy(&gpcg->X_New));
  PetscCall(VecDestroy(&gpcg->G_New));
  PetscCall(VecDestroy(&gpcg->DXFree));
  PetscCall(VecDestroy(&gpcg->R));
  PetscCall(VecDestroy(&gpcg->PG));
  PetscCall(MatDestroy(&gpcg->Hsub));
  PetscCall(MatDestroy(&gpcg->Hsub_pre));
  PetscCall(ISDestroy(&gpcg->Free_Local));
  PetscCall(KSPDestroy(&tao->ksp));
  PetscCall(PetscFree(tao->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetFromOptions_GPCG(Tao tao, PetscOptionItems PetscOptionsObject)
{
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
  PetscBool flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "Gradient Projection, Conjugate Gradient method for bound constrained optimization");
  PetscCall(PetscOptionsInt("-tao_gpcg_maxpgits", "maximum number of gradient projections per GPCG iterate", NULL, gpcg->maxgpits, &gpcg->maxgpits, &flg));
  PetscOptionsHeadEnd();
  PetscCall(KSPSetFromOptions(tao->ksp));
  PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoView_GPCG(Tao tao, PetscViewer viewer)
{
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
  PetscBool isascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  if (isascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "Total PG its: %" PetscInt_FMT ",", gpcg->total_gp_its));
    PetscCall(PetscViewerASCIIPrintf(viewer, "PG tolerance: %g \n", (double)gpcg->pg_ftol));
  }
  PetscCall(TaoLineSearchView(tao->linesearch, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* GPCGObjectiveAndGradient()
   Compute f=0.5 * x'Hx + b'x + c
           g=Hx + b
*/
static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *tptr)
{
  Tao       tao  = (Tao)tptr;
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
  PetscReal f1, f2;

  PetscFunctionBegin;
  PetscCall(MatMult(tao->hessian, X, G));
  PetscCall(VecDot(G, X, &f1));
  PetscCall(VecDot(gpcg->B, X, &f2));
  PetscCall(VecAXPY(G, 1.0, gpcg->B));
  *f = f1 / 2.0 + f2 + gpcg->c;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetup_GPCG(Tao tao)
{
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

  PetscFunctionBegin;
  /* Allocate some arrays */
  if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
  if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));

  PetscCall(VecDuplicate(tao->solution, &gpcg->B));
  PetscCall(VecDuplicate(tao->solution, &gpcg->Work));
  PetscCall(VecDuplicate(tao->solution, &gpcg->X_New));
  PetscCall(VecDuplicate(tao->solution, &gpcg->G_New));
  PetscCall(VecDuplicate(tao->solution, &gpcg->DXFree));
  PetscCall(VecDuplicate(tao->solution, &gpcg->R));
  PetscCall(VecDuplicate(tao->solution, &gpcg->PG));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSolve_GPCG(Tao tao)
{
  TAO_GPCG                    *gpcg = (TAO_GPCG *)tao->data;
  PetscInt                     its;
  PetscReal                    actred, f, f_new, gnorm, gdx, stepsize, xtb;
  PetscReal                    xtHx;
  TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

  PetscFunctionBegin;
  PetscCall(TaoComputeVariableBounds(tao));
  PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));
  PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));

  /* Using f = .5*x'Hx + x'b + c and g=Hx + b,  compute b,c */
  PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
  PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient));
  PetscCall(VecCopy(tao->gradient, gpcg->B));
  PetscCall(MatMult(tao->hessian, tao->solution, gpcg->Work));
  PetscCall(VecDot(gpcg->Work, tao->solution, &xtHx));
  PetscCall(VecAXPY(gpcg->B, -1.0, gpcg->Work));
  PetscCall(VecDot(gpcg->B, tao->solution, &xtb));
  gpcg->c = f - xtHx / 2.0 - xtb;
  PetscCall(ISDestroy(&gpcg->Free_Local));
  PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local));

  /* Project the gradient and calculate the norm */
  PetscCall(VecCopy(tao->gradient, gpcg->G_New));
  PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG));
  PetscCall(VecNorm(gpcg->PG, NORM_2, &gpcg->gnorm));
  tao->step = 1.0;
  gpcg->f   = f;

  /* Check Stopping Condition      */
  tao->reason = TAO_CONTINUE_ITERATING;
  PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its));
  PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step));
  PetscUseTypeMethod(tao, convergencetest, tao->cnvP);

  while (tao->reason == TAO_CONTINUE_ITERATING) {
    /* Call general purpose update function */
    PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
    tao->ksp_its = 0;

    PetscCall(GPCGGradProjections(tao));
    PetscCall(ISGetSize(gpcg->Free_Local, &gpcg->n_free));

    f     = gpcg->f;
    gnorm = gpcg->gnorm;

    PetscCall(KSPReset(tao->ksp));

    if (gpcg->n_free > 0) {
      /* Create a reduced linear system */
      PetscCall(VecDestroy(&gpcg->R));
      PetscCall(VecDestroy(&gpcg->DXFree));
      PetscCall(TaoVecGetSubVec(tao->gradient, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R));
      PetscCall(VecScale(gpcg->R, -1.0));
      PetscCall(TaoVecGetSubVec(tao->stepdirection, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->DXFree));
      PetscCall(VecSet(gpcg->DXFree, 0.0));

      PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub));

      if (tao->hessian_pre == tao->hessian) {
        PetscCall(MatDestroy(&gpcg->Hsub_pre));
        PetscCall(PetscObjectReference((PetscObject)gpcg->Hsub));
        gpcg->Hsub_pre = gpcg->Hsub;
      } else {
        PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre));
      }

      PetscCall(KSPReset(tao->ksp));
      PetscCall(KSPSetOperators(tao->ksp, gpcg->Hsub, gpcg->Hsub_pre));

      PetscCall(KSPSolve(tao->ksp, gpcg->R, gpcg->DXFree));
      PetscCall(KSPGetIterationNumber(tao->ksp, &its));
      tao->ksp_its += its;
      tao->ksp_tot_its += its;
      PetscCall(VecSet(tao->stepdirection, 0.0));
      PetscCall(VecISAXPY(tao->stepdirection, gpcg->Free_Local, 1.0, gpcg->DXFree));

      PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
      PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0));
      f_new = f;
      PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &stepsize, &ls_status));

      actred = f_new - f;

      /* Evaluate the function and gradient at the new point */
      PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG));
      PetscCall(VecNorm(gpcg->PG, NORM_2, &gnorm));
      f = f_new;
      PetscCall(ISDestroy(&gpcg->Free_Local));
      PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local));
    } else {
      actred     = 0;
      gpcg->step = 1.0;
      /* if there were no free variables, no cg method */
    }

    tao->niter++;
    gpcg->f      = f;
    gpcg->gnorm  = gnorm;
    gpcg->actred = actred;
    PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its));
    PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step));
    PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    if (tao->reason != TAO_CONTINUE_ITERATING) break;
  } /* END MAIN LOOP  */
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GPCGGradProjections(Tao tao)
{
  TAO_GPCG                    *gpcg = (TAO_GPCG *)tao->data;
  PetscInt                     i;
  PetscReal                    actred = -1.0, actred_max = 0.0, gAg, gtg = gpcg->gnorm, alpha;
  PetscReal                    f_new, gdx, stepsize;
  Vec                          DX = tao->stepdirection, XL = tao->XL, XU = tao->XU, Work = gpcg->Work;
  Vec                          X = tao->solution, G = tao->gradient;
  TaoLineSearchConvergedReason lsflag = TAOLINESEARCH_CONTINUE_ITERATING;

  /*
     The free, active, and binding variables should be already identified
  */
  PetscFunctionBegin;
  for (i = 0; i < gpcg->maxgpits; i++) {
    if (-actred <= (gpcg->pg_ftol) * actred_max) break;
    PetscCall(VecBoundGradientProjection(G, X, XL, XU, DX));
    PetscCall(VecScale(DX, -1.0));
    PetscCall(VecDot(DX, G, &gdx));

    PetscCall(MatMult(tao->hessian, DX, Work));
    PetscCall(VecDot(DX, Work, &gAg));

    gpcg->gp_iterates++;
    gpcg->total_gp_its++;

    gtg = -gdx;
    if (PetscAbsReal(gAg) == 0.0) {
      alpha = 1.0;
    } else {
      alpha = PetscAbsReal(gtg / gAg);
    }
    PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, alpha));
    f_new = gpcg->f;
    PetscCall(TaoLineSearchApply(tao->linesearch, X, &f_new, G, DX, &stepsize, &lsflag));

    /* Update the iterate */
    actred     = f_new - gpcg->f;
    actred_max = PetscMax(actred_max, -(f_new - gpcg->f));
    gpcg->f    = f_new;
    PetscCall(ISDestroy(&gpcg->Free_Local));
    PetscCall(VecWhichInactive(XL, X, tao->gradient, XU, PETSC_TRUE, &gpcg->Free_Local));
  }

  gpcg->gnorm = gtg;
  PetscFunctionReturn(PETSC_SUCCESS);
} /* End gradient projections */

static PetscErrorCode TaoComputeDual_GPCG(Tao tao, Vec DXL, Vec DXU)
{
  TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

  PetscFunctionBegin;
  PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->Work));
  PetscCall(VecCopy(gpcg->Work, DXL));
  PetscCall(VecAXPY(DXL, -1.0, tao->gradient));
  PetscCall(VecSet(DXU, 0.0));
  PetscCall(VecPointwiseMax(DXL, DXL, DXU));

  PetscCall(VecCopy(tao->gradient, DXU));
  PetscCall(VecAXPY(DXU, -1.0, gpcg->Work));
  PetscCall(VecSet(gpcg->Work, 0.0));
  PetscCall(VecPointwiseMin(DXU, gpcg->Work, DXU));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  TAOGPCG - gradient projected conjugate gradient algorithm is an active-set
            conjugate-gradient based method for bound-constrained minimization

  Options Database Keys:
+ -tao_gpcg_maxpgits - maximum number of gradient projections for GPCG iterate
- -tao_subset_type   - "subvec","mask","matrix-free", strategies for handling active-sets

  Level: beginner

.seealso: `Tao`, `TaoType`, `TAOTRON`, `TAOBQPIP`, `TAOLINESEARCHGPCG`
M*/
PETSC_EXTERN PetscErrorCode TaoCreate_GPCG(Tao tao)
{
  TAO_GPCG *gpcg;

  PetscFunctionBegin;
  tao->ops->setup            = TaoSetup_GPCG;
  tao->ops->solve            = TaoSolve_GPCG;
  tao->ops->view             = TaoView_GPCG;
  tao->ops->setfromoptions   = TaoSetFromOptions_GPCG;
  tao->ops->destroy          = TaoDestroy_GPCG;
  tao->ops->computedual      = TaoComputeDual_GPCG;
  tao->uses_gradient         = PETSC_TRUE;
  tao->uses_hessian_matrices = PETSC_TRUE;

  PetscCall(PetscNew(&gpcg));
  tao->data = (void *)gpcg;

  /* Override default settings (unless already changed) */
  PetscCall(TaoParametersInitialize(tao));
  PetscObjectParameterSetDefault(tao, max_it, 500);
  PetscObjectParameterSetDefault(tao, max_funcs, 100000);
  PetscObjectParameterSetDefault(tao, gatol, PetscDefined(USE_REAL_SINGLE) ? 1e-6 : 1e-12);
  PetscObjectParameterSetDefault(tao, grtol, PetscDefined(USE_REAL_SINGLE) ? 1e-6 : 1e-12);

  /* Initialize pointers and variables */
  gpcg->n        = 0;
  gpcg->maxgpits = 8;
  gpcg->pg_ftol  = 0.1;

  gpcg->gp_iterates  = 0; /* Cumulative number */
  gpcg->total_gp_its = 0;

  /* Initialize pointers and variables */
  gpcg->n_bind      = 0;
  gpcg->n_free      = 0;
  gpcg->n_upper     = 0;
  gpcg->n_lower     = 0;
  gpcg->subset_type = TAO_SUBSET_MASK;
  gpcg->Hsub        = NULL;
  gpcg->Hsub_pre    = NULL;

  PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
  PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
  PetscCall(KSPSetType(tao->ksp, KSPNASH));

  PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
  PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG));
  PetscCall(TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao));
  PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));
  PetscFunctionReturn(PETSC_SUCCESS);
}
