/*
  Defines projective product routines where A is a SeqAIJ matrix
          C = P^T * A * P
*/

#include <../src/mat/impls/aij/seq/aij.h>   /*I "petscmat.h" I*/
#include <../src/mat/utils/freespace.h>
#include <petscbt.h>
#include <petsctime.h>

#undef __FUNCT__
#define __FUNCT__ "MatPtAP_SeqAIJ_SeqAIJ"
PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  const char     *algTypes[2] = {"scalable","nonscalable"};
  PetscInt       alg=0; /* set default algorithm */

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX) {
    /* 
     Alg 'scalable' determines which implementations to be used:
       "nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
       "scalable":    do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P. 
     */
    ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
    ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,2,algTypes[0],&alg,NULL);CHKERRQ(ierr);
    ierr = PetscOptionsEnd();CHKERRQ(ierr);
    ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
    switch (alg) {
    case 1:
      ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);CHKERRQ(ierr);
      break;
    default:
      ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr);
      break;
    }
    ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
  }
  ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
  ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_SeqAIJ_PtAP"
PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
{
  PetscErrorCode ierr;
  Mat_SeqAIJ     *a    = (Mat_SeqAIJ*)A->data;
  Mat_PtAP       *ptap = a->ptap;

  PetscFunctionBegin;
  ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
  ierr = PetscFree(ptap->api);CHKERRQ(ierr);
  ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
  ierr = (ptap->destroy)(A);CHKERRQ(ierr);
  ierr = PetscFree(ptap);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy"
PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
{
  PetscErrorCode     ierr;
  PetscFreeSpaceList free_space=NULL,current_space=NULL;
  Mat_SeqAIJ         *a        = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
  PetscInt           *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
  PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
  PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
  PetscInt           i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
  MatScalar          *ca;
  PetscBT            lnkbt;
  PetscReal          afill;

  PetscFunctionBegin;
  /* Get ij structure of P^T */
  ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
  ptJ  = ptj;

  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr  = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr);
  ci[0] = 0;

  ierr         = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr);
  ptasparserow = ptadenserow  + an;

  /* create and initialize a linked list */
  nlnk = pn+1;
  ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);

  /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
  ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+pi[pm])),&free_space);CHKERRQ(ierr);
  current_space = free_space;

  /* Determine symbolic info for each row of C: */
  for (i=0; i<pn; i++) {
    ptnzi  = pti[i+1] - pti[i];
    ptanzi = 0;
    /* Determine symbolic row of PtA: */
    for (j=0; j<ptnzi; j++) {
      arow = *ptJ++;
      anzj = ai[arow+1] - ai[arow];
      ajj  = aj + ai[arow];
      for (k=0; k<anzj; k++) {
        if (!ptadenserow[ajj[k]]) {
          ptadenserow[ajj[k]]    = -1;
          ptasparserow[ptanzi++] = ajj[k];
        }
      }
    }
    /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
    ptaj = ptasparserow;
    cnzi = 0;
    for (j=0; j<ptanzi; j++) {
      prow = *ptaj++;
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      /* add non-zero cols of P into the sorted linked list lnk */
      ierr  = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
      cnzi += nlnk;
    }

    /* If free space is not available, make more free space */
    /* Double the amount of total space in the list */
    if (current_space->local_remaining<cnzi) {
      ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
      nspacedouble++;
    }

    /* Copy data into free space, and zero out denserows */
    ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);

    current_space->array           += cnzi;
    current_space->local_used      += cnzi;
    current_space->local_remaining -= cnzi;

    for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;

    /* Aside: Perhaps we should save the pta info for the numerical factorization. */
    /*        For now, we will recompute what is needed. */
    ci[i+1] = ci[i] + cnzi;
  }
  /* nnz is now stored in ci[ptm], column indices are in the list of free space */
  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr);
  ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree(ptadenserow);CHKERRQ(ierr);
  ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);

  ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr);
  ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* Since these are PETSc arrays, change flags to free them as necessary. */
  c          = (Mat_SeqAIJ*)((*C)->data);
  c->free_a  = PETSC_TRUE;
  c->free_ij = PETSC_TRUE;
  c->nonew   = 0;
  (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;

  /* set MatInfo */
  afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
  if (afill < 1.0) afill = 1.0;
  c->maxnz                     = ci[pn];
  c->nz                        = ci[pn];
  (*C)->info.mallocs           = nspacedouble;
  (*C)->info.fill_ratio_given  = fill;
  (*C)->info.fill_ratio_needed = afill;

  /* Clean up. */
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
  if (ci[pn] != 0) {
    ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
    ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
  } else {
    ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy"
PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
{
  PetscErrorCode ierr;
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
  Mat_SeqAIJ     *p = (Mat_SeqAIJ*) P->data;
  Mat_SeqAIJ     *c = (Mat_SeqAIJ*) C->data;
  PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
  PetscInt       *ci=c->i,*cj=c->j,*cjj;
  PetscInt       am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
  PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
  MatScalar      *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;

  PetscFunctionBegin;
  /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
  ierr = PetscMalloc3(cn,&apa,cn,&apjdense,c->rmax,&apj);CHKERRQ(ierr);
  ierr = PetscMemzero(apa,cn*sizeof(MatScalar));CHKERRQ(ierr);
  ierr = PetscMemzero(apjdense,cn*sizeof(PetscInt));CHKERRQ(ierr);

  /* Clear old values in C */
  ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);

  for (i=0; i<am; i++) {
    /* Form sparse row of A*P */
    anzi  = ai[i+1] - ai[i];
    apnzj = 0;
    for (j=0; j<anzi; j++) {
      prow = *aj++;
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      paj  = pa + pi[prow];
      for (k=0; k<pnzj; k++) {
        if (!apjdense[pjj[k]]) {
          apjdense[pjj[k]] = -1;
          apj[apnzj++]     = pjj[k];
        }
        apa[pjj[k]] += (*aa)*paj[k];
      }
      ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr);
      aa++;
    }

    /* Sort the j index array for quick sparse axpy. */
    /* Note: a array does not need sorting as it is in dense storage locations. */
    ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr);

    /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    pnzi = pi[i+1] - pi[i];
    for (j=0; j<pnzi; j++) {
      nextap = 0;
      crow   = *pJ++;
      cjj    = cj + ci[crow];
      caj    = ca + ci[crow];
      /* Perform sparse axpy operation.  Note cjj includes apj. */
      for (k=0; nextap<apnzj; k++) {
#if defined(PETSC_USE_DEBUG)
        if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
#endif
        if (cjj[k]==apj[nextap]) {
          caj[k] += (*pA)*apa[apj[nextap++]];
        }
      }
      ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr);
      pA++;
    }

    /* Zero the current row info for A*P */
    for (j=0; j<apnzj; j++) {
      apa[apj[j]]      = 0.;
      apjdense[apj[j]] = 0;
    }
  }

  /* Assemble the final matrix and clean up */
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = PetscFree3(apa,apjdense,apj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy"
PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  Mat_SeqAIJ     *ap,*c;
  PetscInt       *api,*apj,*ci,pn=P->cmap->N;
  MatScalar      *ca;
  Mat_PtAP       *ptap;
  Mat            Pt,AP;

  PetscFunctionBegin;
  /* Get symbolic Pt = P^T */
  ierr = MatTransposeSymbolic_SeqAIJ(P,&Pt);CHKERRQ(ierr);

  /* Get symbolic AP = A*P */
  ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);CHKERRQ(ierr);

  ap          = (Mat_SeqAIJ*)AP->data;
  api         = ap->i;
  apj         = ap->j;
  ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */

  /* Get C = Pt*AP */
  ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);CHKERRQ(ierr);

  c         = (Mat_SeqAIJ*)(*C)->data;
  ci        = c->i;
  ierr      = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr);
  c->a      = ca;
  c->free_a = PETSC_TRUE;

  /* Create a supporting struct for reuse by MatPtAPNumeric() */
  ierr = PetscNew(&ptap);CHKERRQ(ierr);

  c->ptap            = ptap;
  ptap->destroy      = (*C)->ops->destroy;
  (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP;

  /* Allocate temporary array for storage of one row of A*P */
  ierr = PetscCalloc1(pn+1,&ptap->apa);CHKERRQ(ierr);

  (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;

  ptap->api = api;
  ptap->apj = apj;

  /* Clean up. */
  ierr = MatDestroy(&Pt);CHKERRQ(ierr);
  ierr = MatDestroy(&AP);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
  ierr = PetscInfo1((*C),"given fill %g\n",(double)fill);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

/* #define PROFILE_MatPtAPNumeric */
#undef __FUNCT__
#define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ"
PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
{
  PetscErrorCode    ierr;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*) A->data;
  Mat_SeqAIJ        *p = (Mat_SeqAIJ*) P->data;
  Mat_SeqAIJ        *c = (Mat_SeqAIJ*) C->data;
  const PetscInt    *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j;
  const PetscScalar *aa=a->a,*pa=p->a,*pval;
  const PetscInt    *apj,*pcol,*cjj;
  const PetscInt    am=A->rmap->N,cm=C->rmap->N;
  PetscInt          i,j,k,anz,apnz,pnz,prow,crow,cnz;
  PetscScalar       *apa,*ca=c->a,*caj,pvalj;
  Mat_PtAP          *ptap = c->ptap;
#if defined(PROFILE_MatPtAPNumeric)
  PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0;
  PetscInt       flops0=0,flops1=0;
#endif

  PetscFunctionBegin;
  /* Get temporary array for storage of one row of A*P */
  apa = ptap->apa;

  /* Clear old values in C */
  ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);

  for (i=0; i<am; i++) {
    /* Form sparse row of AP[i,:] = A[i,:]*P */
#if defined(PROFILE_MatPtAPNumeric)
    ierr = PetscTime(&t0);CHKERRQ(ierr);
#endif
    anz  = ai[i+1] - ai[i];
    apnz = 0;
    for (j=0; j<anz; j++) {
      prow = aj[j];
      pnz  = pi[prow+1] - pi[prow];
      pcol = pj + pi[prow];
      pval = pa + pi[prow];
      for (k=0; k<pnz; k++) {
        apa[pcol[k]] += aa[j]*pval[k];
      }
      ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
#if defined(PROFILE_MatPtAPNumeric)
      flops0 += 2.0*pnz;
#endif
    }
    aj += anz; aa += anz;
#if defined(PROFILE_MatPtAPNumeric)
    ierr = PetscTime(&tf);CHKERRQ(ierr);

    time_Cseq0 += tf - t0;
#endif

    /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */
#if defined(PROFILE_MatPtAPNumeric)
    ierr = PetscTime(&t0);CHKERRQ(ierr);
#endif
    apj  = ptap->apj + ptap->api[i];
    apnz = ptap->api[i+1] - ptap->api[i];
    pnz  = pi[i+1] - pi[i];
    pcol = pj + pi[i];
    pval = pa + pi[i];

    /* Perform dense axpy */
    for (j=0; j<pnz; j++) {
      crow  = pcol[j];
      cjj   = cj + ci[crow];
      caj   = ca + ci[crow];
      pvalj = pval[j];
      cnz   = ci[crow+1] - ci[crow];
      for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]];
      ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
#if defined(PROFILE_MatPtAPNumeric)
      flops1 += 2.0*cnz;
#endif
    }
#if defined(PROFILE_MatPtAPNumeric)
    ierr        = PetscTime(&tf);CHKERRQ(ierr);
    time_Cseq1 += tf - t0;
#endif

    /* Zero the current row info for A*P */
    for (j=0; j<apnz; j++) apa[apj[j]] = 0.0;
  }

  /* Assemble the final matrix and clean up */
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
#if defined(PROFILE_MatPtAPNumeric)
  printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1);
#endif
  PetscFunctionReturn(0);
}