/*$Id: matmatmult.c,v 1.15 2001/09/07 20:04:44 buschelm Exp $*/
/*
  Defines matrix-matrix product routines for pairs of SeqAIJ matrices
          C = A * B
*/

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

static int logkey_matmatmult          = 0;
static int logkey_matmatmult_symbolic = 0;
static int logkey_matmatmult_numeric  = 0;

#undef __FUNCT__
#define __FUNCT__ "MatMatMult"
/*@
   MatMatMult - Performs Matrix-Matrix Multiplication C=A*B.

   Collective on Mat

   Input Parameters:
+  A - the left matrix
-  B - the right matrix

   Output Parameters:
.  C - the product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for pairs of SeqAIJ matrices.

   Level: intermediate

.seealso: MatMatMultSymbolic(),MatMatMultNumeric()
@*/
int MatMatMult(Mat A,Mat B, Mat *C) {
  /* Perhaps this "interface" routine should be moved into the interface directory.*/
  /* To facilitate implementations with varying types, QueryFunction is used.*/
  /* It is assumed that implementations will be composed as "MatMatMult_<type of A><type of B>". */
  int ierr;
  char funct[80];
  int (*mult)(Mat,Mat,Mat*);

  PetscFunctionBegin;
  PetscValidPointer(C);

  PetscValidHeaderSpecific(A,MAT_COOKIE);
  PetscValidType(A);
  MatPreallocated(A);
  if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  PetscValidHeaderSpecific(B,MAT_COOKIE);
  PetscValidType(B);
  MatPreallocated(B);
  if (!B->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  if (B->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",B->M,A->N);

  ierr = PetscStrcpy(funct,"MatMatMult_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,A->type_name);CHKERRQ(ierr);
  ierr = PetscStrcat(funct,B->type_name);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,funct,(PetscVoidFunction)&mult);CHKERRQ(ierr);
  if (!mult) SETERRQ2(PETSC_ERR_SUP,
                         "C=A*B not implemented for A of type %s and B of type %s",
                         A->type_name,B->type_name);
  ierr = (*mult)(A,B,C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
int MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B, Mat *C) {
  int ierr;
  char symfunct[80],numfunct[80],types[80];
  int (*symbolic)(Mat,Mat,Mat*),(*numeric)(Mat,Mat,Mat);

  PetscFunctionBegin;
  ierr = PetscStrcpy(types,A->type_name);CHKERRQ(ierr);
  ierr = PetscStrcat(types,B->type_name);CHKERRQ(ierr);
  ierr = PetscStrcpy(symfunct,"MatMatMultSymbolic_");CHKERRQ(ierr);
  ierr = PetscStrcat(symfunct,types);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,symfunct,(PetscVoidFunction)&symbolic);CHKERRQ(ierr);
  if (!symbolic) SETERRQ2(PETSC_ERR_SUP,
                         "C=A*B not implemented for A of type %s and B of type %s",
                         A->type_name,B->type_name);
  ierr = PetscStrcpy(numfunct,"MatMatMultNumeric_");CHKERRQ(ierr);
  ierr = PetscStrcat(numfunct,types);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,numfunct,(PetscVoidFunction)&numeric);CHKERRQ(ierr);
  if (!numeric) SETERRQ2(PETSC_ERR_SUP,
                         "C=A*B not implemented for A of type %s and B of type %s",
                         A->type_name,B->type_name);
  ierr = PetscLogEventBegin(logkey_matmatmult,A,B,0,0);CHKERRQ(ierr);
  ierr = (*symbolic)(A,B,C);CHKERRQ(ierr);
  ierr = (*numeric)(A,B,*C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(logkey_matmatmult,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultSymbolic"
/*@
   MatMatMultSymbolic - Performs construction, preallocation, and computes the ij structure
   of the matrix-matrix product C=A*B.  Call this routine before calling MatMatMultNumeric().

   Collective on Mat

   Input Parameters:
+  A - the left matrix
-  B - the right matrix

   Output Parameters:
.  C - the matrix containing the ij structure of product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for SeqAIJ type matrices.

   Level: intermediate

.seealso: MatMatMult(),MatMatMultNumeric()
@*/
int MatMatMultSymbolic(Mat A,Mat B,Mat *C) {
  /* Perhaps this "interface" routine should be moved into the interface directory.*/
  /* To facilitate implementations with varying types, QueryFunction is used.*/
  /* It is assumed that implementations will be composed as "MatMatMultSymbolic_<type of A><type of B>". */
  int ierr;
  char funct[80];
  int (*symbolic)(Mat,Mat,Mat *);

  PetscFunctionBegin;
  PetscValidPointer(C);

  PetscValidHeaderSpecific(A,MAT_COOKIE);
  PetscValidType(A);
  MatPreallocated(A);
  if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  PetscValidHeaderSpecific(B,MAT_COOKIE);
  PetscValidType(B);
  MatPreallocated(B);
  if (!B->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  if (B->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",B->M,A->N);

  ierr = PetscStrcpy(funct,"MatMatMultSymbolic_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,A->type_name);CHKERRQ(ierr);
  ierr = PetscStrcat(funct,B->type_name);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,funct,(PetscVoidFunction)&symbolic);CHKERRQ(ierr);
  if (!symbolic) SETERRQ2(PETSC_ERR_SUP,
                         "C=A*B not implemented for A of type %s and B of type %s",
                         A->type_name,B->type_name);
  ierr = (*symbolic)(A,B,C);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "MatMatMult_Symbolic_SeqAIJ_SeqAIJ"
int MatMatMult_Symbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat *C)
{
  int            ierr;
  FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
  int            *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj;
  int            *ci,*cj,*lnk,idx0,idx,bcol;
  int            am=A->M,bn=B->N,bm=B->M;
  int            i,j,k,anzi,brow,bnzj,cnzi;
  MatScalar      *ca;

  PetscFunctionBegin;
  /* Start timers */
  ierr = PetscLogEventBegin(logkey_matmatmult_symbolic,A,B,0,0);CHKERRQ(ierr);

  /* Set up */
  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr = PetscMalloc(((am+1)+1)*sizeof(int),&ci);CHKERRQ(ierr);
  ci[0] = 0;
  
  ierr = PetscMalloc((bn+1)*sizeof(int),&lnk);CHKERRQ(ierr);
  for (i=0; i<bn; i++) lnk[i] = -1;

  /* Initial FreeSpace size is nnz(B)=4*bi[bm] */
  ierr = GetMoreSpace(4*bi[bm],&free_space);CHKERRQ(ierr);
  current_space = free_space;

  /* Determine symbolic info for each row of the product: */
  for (i=0;i<am;i++) {
    anzi = ai[i+1] - ai[i];
    cnzi = 0;
    lnk[bn] = bn;
    for (j=0;j<anzi;j++) {
      brow = *aj++;
      bnzj = bi[brow+1] - bi[brow];
      bjj  = bj + bi[brow];
      idx  = bn;
      for (k=0;k<bnzj;k++) {
        bcol = bjj[k];
        if (lnk[bcol] == -1) { /* new col */   
          if (k>0) idx = bjj[k-1];   
          do { 
            idx0 = idx;
            idx  = lnk[idx0];
          } while (bcol > idx);           
          lnk[idx0] = bcol;
          lnk[bcol] = idx;
          cnzi++;
        }
      }
    }

    /* 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) {
      printf("...%d -th row, double space ...\n",i);
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, and zero out denserow and lnk */
    idx = bn;
    for (j=0; j<cnzi; j++){
      idx0 = idx;
      idx  = lnk[idx0];     
      *current_space->array++ = idx; 
      lnk[idx0] = -1;
    }
    lnk[idx] = -1;

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

    ci[i+1] = ci[i] + cnzi;
  }

  /* 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 = PetscMalloc((ci[am]+1)*sizeof(int),&cj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree(lnk);CHKERRQ(ierr);
    
  /* Allocate space for ca */
  ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
  ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
  
  /* put together the new matrix */
  ierr = MatCreateSeqAIJWithArrays(A->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
  c = (Mat_SeqAIJ *)((*C)->data);
  c->freedata = PETSC_TRUE;
  c->nonew    = 0;

  ierr = PetscLogEventEnd(logkey_matmatmult_symbolic,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultNumeric"
/*@
   MatMatMultNumeric - Performs the numeric matrix-matrix product.
   Call this routine after first calling MatMatMultSymbolic().

   Collective on Mat

   Input Parameters:
+  A - the left matrix
-  B - the right matrix

   Output Parameters:
.  C - the product matrix, whose ij structure was defined from MatMatMultSymbolic().

   Notes:
   C must have been created with MatMatMultSymbolic.

   This routine is currently only implemented for SeqAIJ type matrices.

   Level: intermediate

.seealso: MatMatMult(),MatMatMultSymbolic()
@*/
int MatMatMultNumeric(Mat A,Mat B,Mat C){
  /* Perhaps this "interface" routine should be moved into the interface directory.*/
  /* To facilitate implementations with varying types, QueryFunction is used.*/
  /* It is assumed that implementations will be composed as "MatMatMultNumeric_<type of A><type of B>". */
  int ierr;
  char funct[80];
  int (*numeric)(Mat,Mat,Mat);

  PetscFunctionBegin;

  PetscValidHeaderSpecific(A,MAT_COOKIE);
  PetscValidType(A);
  MatPreallocated(A);
  if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  PetscValidHeaderSpecific(B,MAT_COOKIE);
  PetscValidType(B);
  MatPreallocated(B);
  if (!B->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  PetscValidHeaderSpecific(C,MAT_COOKIE);
  PetscValidType(C);
  MatPreallocated(C);
  if (!C->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (C->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix"); 

  if (B->N!=C->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",B->N,C->N);
  if (B->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",B->M,A->N);
  if (A->M!=C->M) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",A->M,C->M);

  /* Query A for ApplyPtAP implementation based on types of P */
  ierr = PetscStrcpy(funct,"MatMatMultNumeric_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,A->type_name);CHKERRQ(ierr);
  ierr = PetscStrcat(funct,B->type_name);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,funct,(PetscVoidFunction)&numeric);CHKERRQ(ierr);
  if (!numeric) SETERRQ2(PETSC_ERR_SUP,
                         "C=A*B not implemented for A of type %s and B of type %s",
                         A->type_name,B->type_name);
  ierr = (*numeric)(A,B,C);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "MatMatMult_Numeric_SeqAIJ_SeqAIJ"
int MatMatMult_Numeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
{
  int        ierr,flops=0;
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
  Mat_SeqAIJ *b = (Mat_SeqAIJ *)B->data;
  Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
  int        *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
  int        am=A->M,cn=C->N;
  int        i,j,k,anzi,bnzi,cnzi,brow;
  MatScalar  *aa=a->a,*ba=b->a,*baj,*ca=c->a,*temp;

  PetscFunctionBegin;  

  /* Start timers */
  ierr = PetscLogEventBegin(logkey_matmatmult_numeric,A,B,C,0);CHKERRQ(ierr);

  /* Allocate temp accumulation space to avoid searching for nonzero columns in C */
  ierr = PetscMalloc((cn+1)*sizeof(MatScalar),&temp);CHKERRQ(ierr);
  ierr = PetscMemzero(temp,cn*sizeof(MatScalar));CHKERRQ(ierr);
  /* Traverse A row-wise. */
  /* Build the ith row in C by summing over nonzero columns in A, */
  /* the rows of B corresponding to nonzeros of A. */
  for (i=0;i<am;i++) {
    anzi = ai[i+1] - ai[i];
    for (j=0;j<anzi;j++) {
      brow = *aj++;
      bnzi = bi[brow+1] - bi[brow];
      bjj  = bj + bi[brow];
      baj  = ba + bi[brow];
      for (k=0;k<bnzi;k++) {
        temp[bjj[k]] += (*aa)*baj[k];
      }
      flops += 2*bnzi;
      aa++;
    }
    /* Store row back into C, and re-zero temp */
    cnzi = ci[i+1] - ci[i];
    for (j=0;j<cnzi;j++) {
      ca[j] = temp[cj[j]];
      temp[cj[j]] = 0.0;
    }
    ca += cnzi;
    cj += cnzi;
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
                         
  /* Free temp */
  ierr = PetscFree(temp);CHKERRQ(ierr);
  ierr = PetscLogFlops(flops);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(logkey_matmatmult_numeric,A,B,C,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "RegisterMatMatMultRoutines_Private"
int RegisterMatMatMultRoutines_Private(Mat A) {
  int ierr;

  PetscFunctionBegin;
  if (!logkey_matmatmult) {
    ierr = PetscLogEventRegister(&logkey_matmatmult,"MatMatMult",MAT_COOKIE);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMatMult_seqaijseqaij",
                                           "MatMatMult_SeqAIJ_SeqAIJ",
                                           MatMatMult_SeqAIJ_SeqAIJ);CHKERRQ(ierr);
  if (!logkey_matmatmult_symbolic) {
    ierr = PetscLogEventRegister(&logkey_matmatmult_symbolic,"MatMatMult_Symbolic",MAT_COOKIE);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMatMultSymbolic_seqaijseqaij",
                                           "MatMatMult_Symbolic_SeqAIJ_SeqAIJ",
                                           MatMatMult_Symbolic_SeqAIJ_SeqAIJ);CHKERRQ(ierr);
  if (!logkey_matmatmult_numeric) {
    ierr = PetscLogEventRegister(&logkey_matmatmult_numeric,"MatMatMult_Numeric",MAT_COOKIE);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMatMultNumeric_seqaijseqaij",
                                           "MatMatMult_Numeric_SeqAIJ_SeqAIJ",
                                           MatMatMult_Numeric_SeqAIJ_SeqAIJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}