#include <petsctaolinesearch.h>
#include <../src/tao/unconstrained/impls/owlqn/owlqn.h>

#define OWLQN_BFGS            0
#define OWLQN_SCALED_GRADIENT 1
#define OWLQN_GRADIENT        2

static PetscErrorCode ProjDirect_OWLQN(Vec d, Vec g)
{
  const PetscReal *gptr;
  PetscReal       *dptr;
  PetscInt         low, high, low1, high1, i;

  PetscFunctionBegin;
  PetscCall(VecGetOwnershipRange(d, &low, &high));
  PetscCall(VecGetOwnershipRange(g, &low1, &high1));

  PetscCall(VecGetArrayRead(g, &gptr));
  PetscCall(VecGetArray(d, &dptr));
  for (i = 0; i < high - low; i++) {
    if (dptr[i] * gptr[i] <= 0.0) dptr[i] = 0.0;
  }
  PetscCall(VecRestoreArray(d, &dptr));
  PetscCall(VecRestoreArrayRead(g, &gptr));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode ComputePseudoGrad_OWLQN(Vec x, Vec gv, PetscReal lambda)
{
  const PetscReal *xptr;
  PetscReal       *gptr;
  PetscInt         low, high, low1, high1, i;

  PetscFunctionBegin;
  PetscCall(VecGetOwnershipRange(x, &low, &high));
  PetscCall(VecGetOwnershipRange(gv, &low1, &high1));

  PetscCall(VecGetArrayRead(x, &xptr));
  PetscCall(VecGetArray(gv, &gptr));
  for (i = 0; i < high - low; i++) {
    if (xptr[i] < 0.0) gptr[i] = gptr[i] - lambda;
    else if (xptr[i] > 0.0) gptr[i] = gptr[i] + lambda;
    else if (gptr[i] + lambda < 0.0) gptr[i] = gptr[i] + lambda;
    else if (gptr[i] - lambda > 0.0) gptr[i] = gptr[i] - lambda;
    else gptr[i] = 0.0;
  }
  PetscCall(VecRestoreArray(gv, &gptr));
  PetscCall(VecRestoreArrayRead(x, &xptr));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSolve_OWLQN(Tao tao)
{
  TAO_OWLQN                   *lmP = (TAO_OWLQN *)tao->data;
  PetscReal                    f, fold, gdx, gnorm;
  PetscReal                    step = 1.0;
  PetscReal                    delta;
  PetscInt                     stepType;
  TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

  PetscFunctionBegin;
  if (tao->XL || tao->XU || tao->ops->computebounds) PetscCall(PetscInfo(tao, "WARNING: Variable bounds have been set but will be ignored by owlqn algorithm\n"));

  /* Check convergence criteria */
  PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient));
  PetscCall(VecCopy(tao->gradient, lmP->GV));
  PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));
  PetscCall(VecNorm(lmP->GV, NORM_2, &gnorm));
  PetscCheck(!PetscIsInfOrNanReal(f) && !PetscIsInfOrNanReal(gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");

  tao->reason = TAO_CONTINUE_ITERATING;
  PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
  PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step));
  PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
  if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

  /* Set initial scaling for the function */
  delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
  PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));

  /* Set counter for gradient/reset steps */
  lmP->bfgs  = 0;
  lmP->sgrad = 0;
  lmP->grad  = 0;

  /* Have not converged; continue with Newton method */
  while (tao->reason == TAO_CONTINUE_ITERATING) {
    /* Call general purpose update function */
    PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);

    /* Compute direction */
    PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
    PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

    PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

    ++lmP->bfgs;

    /* Check for success (descent direction) */
    PetscCall(VecDot(lmP->D, lmP->GV, &gdx));
    if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
      /* Step is not descent or direction produced not a number
         We can assert bfgsUpdates > 1 in this case because
         the first solve produces the scaled gradient direction,
         which is guaranteed to be descent

         Use steepest descent direction (scaled) */
      ++lmP->grad;

      delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
      PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));
      PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
      PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
      PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

      PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

      lmP->bfgs = 1;
      ++lmP->sgrad;
      stepType = OWLQN_SCALED_GRADIENT;
    } else {
      if (1 == lmP->bfgs) {
        /* The first BFGS direction is always the scaled gradient */
        ++lmP->sgrad;
        stepType = OWLQN_SCALED_GRADIENT;
      } else {
        ++lmP->bfgs;
        stepType = OWLQN_BFGS;
      }
    }

    PetscCall(VecScale(lmP->D, -1.0));

    /* Perform the linesearch */
    fold = f;
    PetscCall(VecCopy(tao->solution, lmP->Xold));
    PetscCall(VecCopy(tao->gradient, lmP->Gold));

    PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status));
    PetscCall(TaoAddLineSearchCounts(tao));

    while (((int)ls_status < 0) && (stepType != OWLQN_GRADIENT)) {
      /* Reset factors and use scaled gradient step */
      f = fold;
      PetscCall(VecCopy(lmP->Xold, tao->solution));
      PetscCall(VecCopy(lmP->Gold, tao->gradient));
      PetscCall(VecCopy(tao->gradient, lmP->GV));

      PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));

      switch (stepType) {
      case OWLQN_BFGS:
        /* Failed to obtain acceptable iterate with BFGS step
           Attempt to use the scaled gradient direction */

        delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
        PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));
        PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
        PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
        PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

        PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

        lmP->bfgs = 1;
        ++lmP->sgrad;
        stepType = OWLQN_SCALED_GRADIENT;
        break;

      case OWLQN_SCALED_GRADIENT:
        /* The scaled gradient step did not produce a new iterate;
           attempt to use the gradient direction.
           Need to make sure we are not using a different diagonal scaling */
        PetscCall(MatLMVMSetJ0Scale(lmP->M, 1.0));
        PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
        PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
        PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

        PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

        lmP->bfgs = 1;
        ++lmP->grad;
        stepType = OWLQN_GRADIENT;
        break;
      }
      PetscCall(VecScale(lmP->D, -1.0));

      /* Perform the linesearch */
      PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status));
      PetscCall(TaoAddLineSearchCounts(tao));
    }

    if ((int)ls_status < 0) {
      /* Failed to find an improving point*/
      f = fold;
      PetscCall(VecCopy(lmP->Xold, tao->solution));
      PetscCall(VecCopy(lmP->Gold, tao->gradient));
      PetscCall(VecCopy(tao->gradient, lmP->GV));
      step = 0.0;
    } else {
      /* a little hack here, because that gv is used to store g */
      PetscCall(VecCopy(lmP->GV, tao->gradient));
    }

    PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));

    /* Check for termination */

    PetscCall(VecNorm(lmP->GV, NORM_2, &gnorm));

    ++tao->niter;
    PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
    PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step));
    PetscUseTypeMethod(tao, convergencetest, tao->cnvP);

    if ((int)ls_status < 0) break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetUp_OWLQN(Tao tao)
{
  TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;
  PetscInt   n, N;

  PetscFunctionBegin;
  /* Existence of tao->solution checked in TaoSetUp() */
  if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
  if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
  if (!lmP->D) PetscCall(VecDuplicate(tao->solution, &lmP->D));
  if (!lmP->GV) PetscCall(VecDuplicate(tao->solution, &lmP->GV));
  if (!lmP->Xold) PetscCall(VecDuplicate(tao->solution, &lmP->Xold));
  if (!lmP->Gold) PetscCall(VecDuplicate(tao->solution, &lmP->Gold));

  /* Create matrix for the limited memory approximation */
  PetscCall(VecGetLocalSize(tao->solution, &n));
  PetscCall(VecGetSize(tao->solution, &N));
  PetscCall(MatCreateLMVMBFGS(((PetscObject)tao)->comm, n, N, &lmP->M));
  PetscCall(MatLMVMAllocate(lmP->M, tao->solution, tao->gradient));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoDestroy_OWLQN(Tao tao)
{
  TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;

  PetscFunctionBegin;
  if (tao->setupcalled) {
    PetscCall(VecDestroy(&lmP->Xold));
    PetscCall(VecDestroy(&lmP->Gold));
    PetscCall(VecDestroy(&lmP->D));
    PetscCall(MatDestroy(&lmP->M));
    PetscCall(VecDestroy(&lmP->GV));
  }
  PetscCall(PetscFree(tao->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetFromOptions_OWLQN(Tao tao, PetscOptionItems PetscOptionsObject)
{
  TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "Orthant-Wise Limited-memory method for Quasi-Newton unconstrained optimization");
  PetscCall(PetscOptionsReal("-tao_owlqn_lambda", "regulariser weight", "", 100, &lmP->lambda, NULL));
  PetscOptionsHeadEnd();
  PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoView_OWLQN(Tao tao, PetscViewer viewer)
{
  TAO_OWLQN *lm = (TAO_OWLQN *)tao->data;
  PetscBool  isascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  if (isascii) {
    PetscCall(PetscViewerASCIIPushTab(viewer));
    PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", lm->bfgs));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", lm->sgrad));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", lm->grad));
    PetscCall(PetscViewerASCIIPopTab(viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  TAOOWLQN - orthant-wise limited memory quasi-Newton algorithm

. - tao_owlqn_lambda - regulariser weight

  Level: beginner

.seealso: `Tao`, `TaoType`, `TaoCreate()`
M*/

PETSC_EXTERN PetscErrorCode TaoCreate_OWLQN(Tao tao)
{
  TAO_OWLQN  *lmP;
  const char *owarmijo_type = TAOLINESEARCHOWARMIJO;

  PetscFunctionBegin;
  tao->ops->setup          = TaoSetUp_OWLQN;
  tao->ops->solve          = TaoSolve_OWLQN;
  tao->ops->view           = TaoView_OWLQN;
  tao->ops->setfromoptions = TaoSetFromOptions_OWLQN;
  tao->ops->destroy        = TaoDestroy_OWLQN;
  tao->uses_gradient       = PETSC_TRUE;

  PetscCall(PetscNew(&lmP));
  lmP->D      = NULL;
  lmP->M      = NULL;
  lmP->GV     = NULL;
  lmP->Xold   = NULL;
  lmP->Gold   = NULL;
  lmP->lambda = 1.0;

  tao->data = (void *)lmP;
  /* Override default settings (unless already changed) */
  PetscCall(TaoParametersInitialize(tao));
  PetscObjectParameterSetDefault(tao, max_it, 2000);
  PetscObjectParameterSetDefault(tao, max_funcs, 4000);

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