#include <../src/tao/bound/impls/tron/tron.h>
#include <../src/tao/matrix/submatfree.h>

/* TRON Routines */
static PetscErrorCode TronGradientProjections(Tao, TAO_TRON *);
/*------------------------------------------------------------*/
static PetscErrorCode TaoDestroy_TRON(Tao tao)
{
  TAO_TRON *tron = (TAO_TRON *)tao->data;

  PetscFunctionBegin;
  PetscCall(VecDestroy(&tron->X_New));
  PetscCall(VecDestroy(&tron->G_New));
  PetscCall(VecDestroy(&tron->Work));
  PetscCall(VecDestroy(&tron->DXFree));
  PetscCall(VecDestroy(&tron->R));
  PetscCall(VecDestroy(&tron->diag));
  PetscCall(VecScatterDestroy(&tron->scatter));
  PetscCall(ISDestroy(&tron->Free_Local));
  PetscCall(MatDestroy(&tron->H_sub));
  PetscCall(MatDestroy(&tron->Hpre_sub));
  PetscCall(KSPDestroy(&tao->ksp));
  PetscCall(PetscFree(tao->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/
static PetscErrorCode TaoSetFromOptions_TRON(Tao tao, PetscOptionItems *PetscOptionsObject)
{
  TAO_TRON *tron = (TAO_TRON *)tao->data;
  PetscBool flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "Newton Trust Region Method for bound constrained optimization");
  PetscCall(PetscOptionsInt("-tao_tron_maxgpits", "maximum number of gradient projections per TRON iterate", "TaoSetMaxGPIts", tron->maxgpits, &tron->maxgpits, &flg));
  PetscOptionsHeadEnd();
  PetscCall(KSPSetFromOptions(tao->ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/
static PetscErrorCode TaoView_TRON(Tao tao, PetscViewer viewer)
{
  TAO_TRON *tron = (TAO_TRON *)tao->data;
  PetscBool isascii;

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

/* ---------------------------------------------------------- */
static PetscErrorCode TaoSetup_TRON(Tao tao)
{
  TAO_TRON *tron = (TAO_TRON *)tao->data;

  PetscFunctionBegin;
  /* Allocate some arrays */
  PetscCall(VecDuplicate(tao->solution, &tron->diag));
  PetscCall(VecDuplicate(tao->solution, &tron->X_New));
  PetscCall(VecDuplicate(tao->solution, &tron->G_New));
  PetscCall(VecDuplicate(tao->solution, &tron->Work));
  PetscCall(VecDuplicate(tao->solution, &tao->gradient));
  PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSolve_TRON(Tao tao)
{
  TAO_TRON                    *tron = (TAO_TRON *)tao->data;
  PetscInt                     its;
  TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
  PetscReal                    prered, actred, delta, f, f_new, rhok, gdx, xdiff, stepsize;

  PetscFunctionBegin;
  tron->pgstepsize = 1.0;
  tao->trust       = tao->trust0;
  /*   Project the current point onto the feasible set */
  PetscCall(TaoComputeVariableBounds(tao));
  PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));

  /* Project the initial point onto the feasible region */
  PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));

  /* Compute the objective function and gradient */
  PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &tron->f, tao->gradient));
  PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
  PetscCheck(!PetscIsInfOrNanReal(tron->f) && !PetscIsInfOrNanReal(tron->gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");

  /* Project the gradient and calculate the norm */
  PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
  PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

  /* Initialize trust region radius */
  tao->trust = tao->trust0;
  if (tao->trust <= 0) tao->trust = PetscMax(tron->gnorm * tron->gnorm, 1.0);

  /* Initialize step sizes for the line searches */
  tron->pgstepsize = 1.0;
  tron->stepsize   = tao->trust;

  tao->reason = TAO_CONTINUE_ITERATING;
  PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
  PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, tron->stepsize));
  PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
  while (tao->reason == TAO_CONTINUE_ITERATING) {
    /* Call general purpose update function */
    if (tao->ops->update) {
      PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
      PetscCall(TaoComputeObjective(tao, tao->solution, &tron->f));
    }

    /* Perform projected gradient iterations */
    PetscCall(TronGradientProjections(tao, tron));

    PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
    PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

    tao->ksp_its      = 0;
    f                 = tron->f;
    delta             = tao->trust;
    tron->n_free_last = tron->n_free;
    PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));

    /* Generate index set (IS) of which bound constraints are active */
    PetscCall(ISDestroy(&tron->Free_Local));
    PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
    PetscCall(ISGetSize(tron->Free_Local, &tron->n_free));

    /* If no free variables */
    if (tron->n_free == 0) {
      PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
      PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
      PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta));
      PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
      if (!tao->reason) tao->reason = TAO_CONVERGED_STEPTOL;
      break;
    }
    /* use free_local to mask/submat gradient, hessian, stepdirection */
    PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->R));
    PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->DXFree));
    PetscCall(VecSet(tron->DXFree, 0.0));
    PetscCall(VecScale(tron->R, -1.0));
    PetscCall(TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub));
    if (tao->hessian == tao->hessian_pre) {
      PetscCall(MatDestroy(&tron->Hpre_sub));
      PetscCall(PetscObjectReference((PetscObject)tron->H_sub));
      tron->Hpre_sub = tron->H_sub;
    } else {
      PetscCall(TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type, &tron->Hpre_sub));
    }
    PetscCall(KSPReset(tao->ksp));
    PetscCall(KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub));
    while (1) {
      /* Approximately solve the reduced linear system */
      PetscCall(KSPCGSetRadius(tao->ksp, delta));

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

      /* Add dxfree matrix to compute step direction vector */
      PetscCall(VecISAXPY(tao->stepdirection, tron->Free_Local, 1.0, tron->DXFree));

      PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
      PetscCall(VecCopy(tao->solution, tron->X_New));
      PetscCall(VecCopy(tao->gradient, tron->G_New));

      stepsize = 1.0;
      f_new    = f;

      PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0));
      PetscCall(TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection, &stepsize, &ls_reason));
      PetscCall(TaoAddLineSearchCounts(tao));

      PetscCall(MatMult(tao->hessian, tao->stepdirection, tron->Work));
      PetscCall(VecAYPX(tron->Work, 0.5, tao->gradient));
      PetscCall(VecDot(tao->stepdirection, tron->Work, &prered));
      actred = f_new - f;
      if ((PetscAbsScalar(actred) <= 1e-6) && (PetscAbsScalar(prered) <= 1e-6)) {
        rhok = 1.0;
      } else if (actred < 0) {
        rhok = PetscAbs(-actred / prered);
      } else {
        rhok = 0.0;
      }

      /* Compare actual improvement to the quadratic model */
      if (rhok > tron->eta1) { /* Accept the point */
        /* d = x_new - x */
        PetscCall(VecCopy(tron->X_New, tao->stepdirection));
        PetscCall(VecAXPY(tao->stepdirection, -1.0, tao->solution));

        PetscCall(VecNorm(tao->stepdirection, NORM_2, &xdiff));
        xdiff *= stepsize;

        /* Adjust trust region size */
        if (rhok < tron->eta2) {
          delta = PetscMin(xdiff, delta) * tron->sigma1;
        } else if (rhok > tron->eta4) {
          delta = PetscMin(xdiff, delta) * tron->sigma3;
        } else if (rhok > tron->eta3) {
          delta = PetscMin(xdiff, delta) * tron->sigma2;
        }
        PetscCall(VecBoundGradientProjection(tron->G_New, tron->X_New, tao->XL, tao->XU, tao->gradient));
        PetscCall(ISDestroy(&tron->Free_Local));
        PetscCall(VecWhichInactive(tao->XL, tron->X_New, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
        f = f_new;
        PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
        PetscCall(VecCopy(tron->X_New, tao->solution));
        PetscCall(VecCopy(tron->G_New, tao->gradient));
        break;
      } else if (delta <= 1e-30) {
        break;
      } else {
        delta /= 4.0;
      }
    } /* end linear solve loop */

    tron->f      = f;
    tron->actred = actred;
    tao->trust   = delta;
    tao->niter++;
    PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
    PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, stepsize));
    PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
  } /* END MAIN LOOP  */
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TronGradientProjections(Tao tao, TAO_TRON *tron)
{
  PetscInt                     i;
  TaoLineSearchConvergedReason ls_reason;
  PetscReal                    actred = -1.0, actred_max = 0.0;
  PetscReal                    f_new;
  /*
     The gradient and function value passed into and out of this
     routine should be current and correct.

     The free, active, and binding variables should be already identified
  */

  PetscFunctionBegin;
  for (i = 0; i < tron->maxgpits; ++i) {
    if (-actred <= (tron->pg_ftol) * actred_max) break;

    ++tron->gp_iterates;
    ++tron->total_gp_its;
    f_new = tron->f;

    PetscCall(VecCopy(tao->gradient, tao->stepdirection));
    PetscCall(VecScale(tao->stepdirection, -1.0));
    PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, tron->pgstepsize));
    PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &tron->pgstepsize, &ls_reason));
    PetscCall(TaoAddLineSearchCounts(tao));

    PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
    PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

    /* Update the iterate */
    actred     = f_new - tron->f;
    actred_max = PetscMax(actred_max, -(f_new - tron->f));
    tron->f    = f_new;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU)
{
  TAO_TRON *tron = (TAO_TRON *)tao->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(tao, TAO_CLASSID, 1);
  PetscValidHeaderSpecific(DXL, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(DXU, VEC_CLASSID, 3);
  PetscCheck(tron->Work && tao->gradient, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Dual variables don't exist yet or no longer exist.");

  PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tron->Work));
  PetscCall(VecCopy(tron->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, tron->Work));
  PetscCall(VecSet(tron->Work, 0.0));
  PetscCall(VecPointwiseMin(DXU, tron->Work, DXU));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/
/*MC
  TAOTRON - The TRON algorithm is an active-set Newton trust region method
  for bound-constrained minimization.

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

  Level: beginner
M*/
PETSC_EXTERN PetscErrorCode TaoCreate_TRON(Tao tao)
{
  TAO_TRON   *tron;
  const char *morethuente_type = TAOLINESEARCHMT;

  PetscFunctionBegin;
  tao->ops->setup          = TaoSetup_TRON;
  tao->ops->solve          = TaoSolve_TRON;
  tao->ops->view           = TaoView_TRON;
  tao->ops->setfromoptions = TaoSetFromOptions_TRON;
  tao->ops->destroy        = TaoDestroy_TRON;
  tao->ops->computedual    = TaoComputeDual_TRON;

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

  /* Override default settings (unless already changed) */
  PetscCall(TaoParametersInitialize(tao));
  PetscObjectParameterSetDefault(tao, max_it, 50);
  PetscObjectParameterSetDefault(tao, trust0, 1.0);
  PetscObjectParameterSetDefault(tao, steptol, 0.0);

  /* Initialize pointers and variables */
  tron->n        = 0;
  tron->maxgpits = 3;
  tron->pg_ftol  = 0.001;

  tron->eta1 = 1.0e-4;
  tron->eta2 = 0.25;
  tron->eta3 = 0.50;
  tron->eta4 = 0.90;

  tron->sigma1 = 0.5;
  tron->sigma2 = 2.0;
  tron->sigma3 = 4.0;

  tron->gp_iterates  = 0; /* Cumulative number */
  tron->total_gp_its = 0;
  tron->n_free       = 0;

  tron->DXFree     = NULL;
  tron->R          = NULL;
  tron->X_New      = NULL;
  tron->G_New      = NULL;
  tron->Work       = NULL;
  tron->Free_Local = NULL;
  tron->H_sub      = NULL;
  tron->Hpre_sub   = NULL;
  tao->subset_type = TAO_SUBSET_SUBVEC;

  PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
  PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type));
  PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
  PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));

  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, KSPSTCG));
  PetscFunctionReturn(PETSC_SUCCESS);
}
