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

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

#undef __FUNCT__
#define __FUNCT__ "ProjDirect_OWLQN"
static PetscErrorCode ProjDirect_OWLQN(Vec d, Vec g)
{
  PetscErrorCode  ierr;
  const PetscReal *gptr;
  PetscReal       *dptr;
  PetscInt        low,high,low1,high1,i;

  PetscFunctionBegin;
  ierr=VecGetOwnershipRange(d,&low,&high);CHKERRQ(ierr);
  ierr=VecGetOwnershipRange(g,&low1,&high1);CHKERRQ(ierr);

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

#undef __FUNCT__
#define __FUNCT__ "ComputePseudoGrad_OWLQN"
static PetscErrorCode ComputePseudoGrad_OWLQN(Vec x, Vec gv, PetscReal lambda)
{
  PetscErrorCode  ierr;
  const PetscReal *xptr;
  PetscReal       *gptr;
  PetscInt        low,high,low1,high1,i;

  PetscFunctionBegin;
  ierr=VecGetOwnershipRange(x,&low,&high);CHKERRQ(ierr);
  ierr=VecGetOwnershipRange(gv,&low1,&high1);CHKERRQ(ierr);

  ierr = VecGetArrayRead(x,&xptr);CHKERRQ(ierr);
  ierr = VecGetArray(gv,&gptr);CHKERRQ(ierr);
  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;
  }
  ierr = VecRestoreArray(gv,&gptr);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(x,&xptr);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TaoSolve_OWLQN"
static PetscErrorCode TaoSolve_OWLQN(Tao tao)
{
  TAO_OWLQN                    *lmP = (TAO_OWLQN *)tao->data;
  PetscReal                    f, fold, gdx, gnorm;
  PetscReal                    step = 1.0;
  PetscReal                    delta;
  PetscErrorCode               ierr;
  PetscInt                     stepType;
  PetscInt                     iter = 0;
  TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
  TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

  PetscFunctionBegin;
  if (tao->XL || tao->XU || tao->ops->computebounds) {
    ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by owlqn algorithm\n");CHKERRQ(ierr);
  }

  /* Check convergence criteria */
  ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr);

  ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr);

  ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);

  ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr);

  if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");

  ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
  if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Set initial scaling for the function */
  if (f != 0.0) {
    delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
  } else {
    delta = 2.0 / (gnorm*gnorm);
  }
  ierr = MatLMVMSetDelta(lmP->M,delta);CHKERRQ(ierr);

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

  /* Have not converged; continue with Newton method */
  while (reason == TAO_CONTINUE_ITERATING) {
    /* Compute direction */
    ierr = MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);CHKERRQ(ierr);
    ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);

    ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);

    ++lmP->bfgs;

    /* Check for success (descent direction) */
    ierr = VecDot(lmP->D, lmP->GV , &gdx);CHKERRQ(ierr);
    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;

      if (f != 0.0) {
        delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
      } else {
        delta = 2.0 / (gnorm*gnorm);
      }
      ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr);
      ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
      ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
      ierr = MatLMVMSolve(lmP->M,lmP->GV, lmP->D);CHKERRQ(ierr);

      ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);

      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;
      }
    }

    ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr);

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

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

    while (((int)ls_status < 0) && (stepType != OWLQN_GRADIENT)) {

      /* Reset factors and use scaled gradient step */
      f = fold;
      ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr);
      ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr);
      ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr);

      ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);

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

        if (f != 0.0) {
          delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
        } else {
          delta = 2.0 / (gnorm*gnorm);
        }
        ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr);
        ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
        ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
        ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);

        ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);

        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 */
        ierr = MatLMVMSetDelta(lmP->M, 1.0);CHKERRQ(ierr);
        ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
        ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
        ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);

        ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);

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


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

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

    ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);

    /* Check for termination */

    ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr);

    iter++;
    ierr = TaoMonitor(tao,iter,f,gnorm,0.0,step,&reason);CHKERRQ(ierr);

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

#undef __FUNCT__
#define __FUNCT__ "TaoSetUp_OWLQN"
static PetscErrorCode TaoSetUp_OWLQN(Tao tao)
{
  TAO_OWLQN      *lmP = (TAO_OWLQN *)tao->data;
  PetscInt       n,N;
  PetscErrorCode ierr;

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

  /* Create matrix for the limited memory approximation */
  ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
  ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
  ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&lmP->M);CHKERRQ(ierr);
  ierr = MatLMVMAllocateVectors(lmP->M,tao->solution);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ---------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "TaoDestroy_OWLQN"
static PetscErrorCode TaoDestroy_OWLQN(Tao tao)
{
  TAO_OWLQN      *lmP = (TAO_OWLQN *)tao->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (tao->setupcalled) {
    ierr = VecDestroy(&lmP->Xold);CHKERRQ(ierr);
    ierr = VecDestroy(&lmP->Gold);CHKERRQ(ierr);
    ierr = VecDestroy(&lmP->D);CHKERRQ(ierr);
    ierr = MatDestroy(&lmP->M);CHKERRQ(ierr);
    ierr = VecDestroy(&lmP->GV);CHKERRQ(ierr);
  }
  ierr = PetscFree(tao->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "TaoSetFromOptions_OWLQN"
static PetscErrorCode TaoSetFromOptions_OWLQN(PetscOptions *PetscOptionsObject,Tao tao)
{
  TAO_OWLQN      *lmP = (TAO_OWLQN *)tao->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"Orthant-Wise Limited-memory method for Quasi-Newton unconstrained optimization");CHKERRQ(ierr);
  ierr = PetscOptionsReal("-tao_owlqn_lambda", "regulariser weight","", 100,&lmP->lambda,NULL); CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "TaoView_OWLQN"
static PetscErrorCode TaoView_OWLQN(Tao tao, PetscViewer viewer)
{
  TAO_OWLQN      *lm = (TAO_OWLQN *)tao->data;
  PetscBool      isascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
  if (isascii) {
    ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", lm->bfgs);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", lm->sgrad);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", lm->grad);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

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

. - tao_owlqn_lambda - regulariser weight

  Level: beginner
M*/


#undef __FUNCT__
#define __FUNCT__ "TaoCreate_OWLQN"
PETSC_EXTERN PetscErrorCode TaoCreate_OWLQN(Tao tao)
{
  TAO_OWLQN      *lmP;
  const char     *owarmijo_type = TAOLINESEARCHOWARMIJO;
  PetscErrorCode ierr;

  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;

  ierr = PetscNewLog(tao,&lmP);CHKERRQ(ierr);
  lmP->D = 0;
  lmP->M = 0;
  lmP->GV = 0;
  lmP->Xold = 0;
  lmP->Gold = 0;
  lmP->lambda = 1.0;

  tao->data = (void*)lmP;
  /* Override default settings (unless already changed) */
  if (!tao->max_it_changed) tao->max_it = 2000;
  if (!tao->max_funcs_changed) tao->max_funcs = 4000;
  if (!tao->fatol_changed) tao->fatol = 1.0e-4;
  if (!tao->frtol_changed) tao->frtol = 1.0e-4;

  ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr);
  ierr = TaoLineSearchSetType(tao->linesearch,owarmijo_type);CHKERRQ(ierr);
  ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr);
  ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}