void GB_transpose_ix // transpose the pattern and values of a matrix
(
int64_t *Rp, // size m+1, input: row pointers, shifted on output
int64_t *Ri, // size cnz, output column indices
GB_void *Rx, // size cnz, output numerical values, type R_type
const GrB_Type R_type, // type of output R (do typecasting into R)
const GrB_Matrix A // input matrix
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
ASSERT (A != NULL) ;
ASSERT (R_type != NULL) ;
ASSERT (Rp != NULL && Ri != NULL && Rx != NULL) ;
ASSERT (GB_Type_compatible (A->type, R_type)) ;
ASSERT (!GB_ZOMBIES (A)) ;
//--------------------------------------------------------------------------
// get the input matrix
//--------------------------------------------------------------------------
const int64_t *Ai = A->i ;
const GB_void *Ax = A->x ;
//--------------------------------------------------------------------------
// define the worker for the switch factory
//--------------------------------------------------------------------------
#define GB_WORKER(rtype,atype) \
{ \
rtype *rx = (rtype *) Rx ; \
atype *ax = (atype *) Ax ; \
GB_for_each_vector (A) \
{ \
GB_for_each_entry (j, p, pend) \
{ \
int64_t q = Rp [Ai [p]]++ ; \
Ri [q] = j ; \
/* rx [q] = ax [p], type casting */ \
GB_CAST (rx [q], ax [p]) ; \
} \
} \
return ; \
}
//--------------------------------------------------------------------------
// launch the switch factory
//--------------------------------------------------------------------------
// The switch factory cannot be disabled by #ifndef GBCOMPACT
// because the generic worker does no typecasting.
// switch factory for two types, controlled by code1 and code2
GB_Type_code code1 = R_type->code ; // defines rtype
GB_Type_code code2 = A->type->code ; // defines atype
ASSERT (code1 <= GB_UDT_code) ;
ASSERT (code2 <= GB_UDT_code) ;
#include "GB_2type_template.c"
//--------------------------------------------------------------------------
// generic worker
//--------------------------------------------------------------------------
// the switch factory handles all built-in types; user-defined types
// fall through the switch factory to here, which can never be
// typecasted. Because the generic worker does no typecasting, the
// switch factory cannot be disabled.
ASSERT (A->type == R_type && A->type->code > GB_FP64_code) ;
int64_t asize = A->type->size ;
GB_for_each_vector (A)
{
GB_for_each_entry (j, p, pend)
{
int64_t q = Rp [Ai [p]]++ ;
Ri [q] = j ;
memcpy (Rx +(q*asize), Ax +(p*asize), asize) ;
}
}
GrB_Info GB_emult // C = A.*B
(
GrB_Matrix *Chandle, // output matrix (unallocated on input)
const GrB_Type ctype, // type of output matrix C
const bool C_is_csc, // format of output matrix C
const GrB_Matrix A, // input A matrix
const GrB_Matrix B, // input B matrix
const GrB_BinaryOp op, // op to perform C = op (A,B)
GB_Context Context
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
ASSERT (Chandle != NULL) ;
ASSERT_OK (GB_check (A, "A for C=A.*B", GB0)) ;
ASSERT_OK (GB_check (B, "B for C=A.*B", GB0)) ;
ASSERT (!GB_PENDING (A)) ; ASSERT (!GB_ZOMBIES (A)) ;
ASSERT (!GB_PENDING (B)) ; ASSERT (!GB_ZOMBIES (B)) ;
ASSERT_OK (GB_check (op, "op for C=A.*B", GB0)) ;
ASSERT (A->vdim == A->vdim && B->vlen == A->vlen) ;
ASSERT (GB_Type_compatible (ctype, op->ztype)) ;
ASSERT (GB_Type_compatible (A->type, op->xtype)) ;
ASSERT (GB_Type_compatible (B->type, op->ytype)) ;
(*Chandle) = NULL ;
//--------------------------------------------------------------------------
// allocate the output matrix C
//--------------------------------------------------------------------------
// C is hypersparse if A or B are hypersparse (contrast with GB_add)
bool C_is_hyper = (A->is_hyper || B->is_hyper) && (A->vdim > 1) ;
// [ allocate the result C; C->p is malloc'd
// worst case nnz (C) is min (nnz (A), nnz (B))
GrB_Info info ;
GrB_Matrix C = NULL ; // allocate a new header for C
GB_CREATE (&C, ctype, A->vlen, A->vdim, GB_Ap_malloc, C_is_csc,
GB_SAME_HYPER_AS (C_is_hyper), B->hyper_ratio,
GB_IMIN (A->nvec_nonempty, B->nvec_nonempty),
GB_IMIN (GB_NNZ (A), GB_NNZ (B)), true) ;
if (info != GrB_SUCCESS)
{
return (info) ;
}
//--------------------------------------------------------------------------
// get functions and type sizes
//--------------------------------------------------------------------------
GB_cast_function cast_A_to_X, cast_B_to_Y, cast_Z_to_C ;
cast_A_to_X = GB_cast_factory (op->xtype->code, A->type->code) ;
cast_B_to_Y = GB_cast_factory (op->ytype->code, B->type->code) ;
cast_Z_to_C = GB_cast_factory (C->type->code, op->ztype->code) ;
// If types are user-defined, the cast* function is just
// GB_copy_user_user, which requires the size of the type. No typecast is
// done.
GxB_binary_function fmult = op->function ;
size_t xsize = op->xtype->size ;
size_t ysize = op->ytype->size ;
size_t zsize = op->ztype->size ;
size_t asize = A->type->size ;
size_t bsize = B->type->size ;
size_t csize = C->type->size ;
// no typecasting needed if all the types match the operator
bool nocasting =
(A->type->code == op->xtype->code) &&
(B->type->code == op->ytype->code) &&
(C->type->code == op->ztype->code) ;
// scalar workspace
char xwork [nocasting ? 1 : xsize] ;
char ywork [nocasting ? 1 : ysize] ;
char zwork [nocasting ? 1 : zsize] ;
//--------------------------------------------------------------------------
// C = A .* B, where .*+ is defined by z=fmult(x,y)
//--------------------------------------------------------------------------
int64_t *Ci = C->i ;
GB_void *Cx = C->x ;
int64_t jlast, cnz, cnz_last ;
GB_jstartup (C, &jlast, &cnz, &cnz_last) ;
const int64_t *Ai = A->i, *Bi = B->i ;
const GB_void *Ax = A->x, *Bx = B->x ;
GB_for_each_vector2 (A, B)
{
//----------------------------------------------------------------------
// get the next column, A (:,j) and B (:j)
//----------------------------------------------------------------------
int64_t GBI2_initj (Iter, j, pa, pa_end, pb, pb_end) ;
int64_t ajnz = pa_end - pa ;
int64_t bjnz = pb_end - pb ;
//----------------------------------------------------------------------
// compute C (:,j): pattern is the set intersection
//----------------------------------------------------------------------
if (ajnz == 0 || bjnz == 0)
{
// one or both columns are empty; set intersection is empty
;
}
else if (Ai [pa_end-1] < Bi [pb])
{
// all entries in A are in lower row indices than all the
// entries in B; set intersection is empty
;
}
else if (Bi [pb_end-1] < Ai [pa])
{
// all entries in B are in lower row indices than all the
// entries in A; set intersection is empty
;
}
else if (ajnz > 256 * bjnz)
{
//------------------------------------------------------------------
// A (:,j) has many more nonzeros than B (:,j)
//------------------------------------------------------------------
for ( ; pa < pa_end && pb < pb_end ; )
{
int64_t ia = Ai [pa] ;
int64_t ib = Bi [pb] ;
if (ia < ib)
{
// A (ia,j) appears before B (ib,j)
// discard all entries A (ia:ib-1,j)
int64_t pleft = pa + 1 ;
int64_t pright = pa_end ;
GB_BINARY_TRIM_SEARCH (ib, Ai, pleft, pright) ;
ASSERT (pleft > pa) ;
pa = pleft ;
}
else if (ia > ib)
{
// B (ib,j) appears before A (ia,j)
pb++ ;
}
else // ia == ib
{
// A (i,j) and B (i,j) match
GB_EMULT ;
}
}
}
else if (bjnz > 256 * ajnz)
{
//------------------------------------------------------------------
// B (:,j) has many more nonzeros than A (:,j)
//------------------------------------------------------------------
for ( ; pa < pa_end && pb < pb_end ; )
{
int64_t ia = Ai [pa] ;
int64_t ib = Bi [pb] ;
if (ia < ib)
{
// A (ia,j) appears before B (ib,j)
pa++ ;
}
else if (ia > ib)
{
// B (ib,j) appears before A (ia,j)
// discard all entries B (ib:ia-1,j)
int64_t pleft = pb + 1 ;
int64_t pright = pb_end ;
GB_BINARY_TRIM_SEARCH (ia, Bi, pleft, pright) ;
ASSERT (pleft > pb) ;
pb = pleft ;
}
else // ia == ib
{
// A (i,j) and B (i,j) match
GB_EMULT ;
}
}
}
else
{
//------------------------------------------------------------------
// A (:,j) and B (:,j) have about the same number of entries
//------------------------------------------------------------------
for ( ; pa < pa_end && pb < pb_end ; )
{
int64_t ia = Ai [pa] ;
int64_t ib = Bi [pb] ;
if (ia < ib)
{
// A (ia,j) appears before B (ib,j)
pa++ ;
}
else if (ia > ib)
{
// B (ib,j) appears before A (ia,j)
pb++ ;
}
else // ia == ib
{
// A (i,j) and B (i,j) match
GB_EMULT ;
}
}
}
//----------------------------------------------------------------------
// finalize C(:,j)
//----------------------------------------------------------------------
// this cannot fail since C->plen is the upper bound: min of the
// non-empty vectors of A and B
info = GB_jappend (C, j, &jlast, cnz, &cnz_last, Context) ;
ASSERT (info == GrB_SUCCESS) ;
#if 0
// if it could fail, do this:
if (info != GrB_SUCCESS) { GB_MATRIX_FREE (&C) ; return (info) ; }
#endif
}
GrB_Info GB_wait // finish all pending computations
(
GrB_Matrix A, // matrix with pending computations
GB_Context Context
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
ASSERT (A != NULL) ;
// The matrix A might have pending operations but not be in the queue.
// GB_check expects the matrix to be in the queue. As a result, GB_check
// can report an inconsistency, and thus this assert must be made
// with a negative pr.
ASSERT_OK (GB_check (A, "A to wait", GB_FLIP (GB0))) ;
//--------------------------------------------------------------------------
// delete zombies
//--------------------------------------------------------------------------
// A zombie is an entry A(i,j) in the matrix that as been marked for
// deletion, but hasn't been deleted yet. It is marked by "negating"
// replacing its index i with GB_FLIP(i). Zombies are simple to delete via
// an in-place algorithm. No memory is allocated so this step always
// succeeds. Pending tuples are ignored, so A can have pending tuples.
GrB_Info info = GrB_SUCCESS ;
int64_t anz = GB_NNZ (A) ;
int64_t anz_orig = anz ;
int64_t anzmax_orig = A->nzmax ;
ASSERT (anz_orig <= anzmax_orig) ;
int64_t nzombies = A->nzombies ;
if (nzombies > 0)
{
// There are zombies that will now be deleted.
ASSERT (GB_ZOMBIES_OK (A)) ;
ASSERT (GB_ZOMBIES (A)) ;
// This step tolerates pending tuples
// since pending tuples and zombies do not intersect
ASSERT (GB_PENDING_OK (A)) ;
//----------------------------------------------------------------------
// zombies exist in the matrix: delete them all
//----------------------------------------------------------------------
// compare with the pruning phase of GB_resize
#define GB_PRUNE if (GB_IS_ZOMBIE (i)) continue ;
#include "GB_prune_inplace.c"
//----------------------------------------------------------------------
// all zombies have been deleted
//----------------------------------------------------------------------
// exactly A->nzombies have been deleted from A
ASSERT (A->nzombies == (anz_orig - anz)) ;
// at least one zombie has been deleted
ASSERT (anz < anz_orig) ;
// no more zombies; pending tuples may still exist
A->nzombies = 0 ;
ASSERT (GB_PENDING_OK (A)) ;
// A->nvec_nonempty has been updated
ASSERT (A->nvec_nonempty == GB_nvec_nonempty (A)) ;
}
ASSERT (anz == GB_NNZ (A)) ;
//--------------------------------------------------------------------------
// check for pending tuples
//--------------------------------------------------------------------------
// all the zombies are gone
ASSERT (!GB_ZOMBIES (A)) ;
if (!GB_PENDING (A))
{
// nothing more to do; remove the matrix from the queue
ASSERT (!GB_PENDING (A)) ;
GB_CRITICAL (GB_queue_remove (A)) ;
ASSERT (!(A->enqueued)) ;
// trim any significant extra space from the matrix, but allow for some
// future insertions. do not increase the size of the matrix;
// zombies have been deleted but no pending tuples added. This is
// guaranteed not to fail.
ASSERT (anz <= anz_orig) ;
info = GB_ix_resize (A, anz, Context) ;
ASSERT (info == GrB_SUCCESS) ;
// conform A to its desired hypersparsity
return (GB_to_hyper_conform (A, Context)) ;
}
// There are pending tuples that will now be assembled.
ASSERT (GB_PENDING (A)) ;
//--------------------------------------------------------------------------
// construct a new hypersparse matrix T with just the pending tuples
//--------------------------------------------------------------------------
// If anz > 0, T is always hypersparse. Otherwise T can be returned as
// non-hypersparse, and it is then transplanted as-is into the final A.
// T has the same type as A->type, which can differ from the type of the
// pending tuples, A->type_pending. This is OK since build process
// assembles the tuples in the order they were inserted into the matrix.
// The A->operator_pending can be NULL (an implicit SECOND function), or it
// can be any accum operator. The z=accum(x,y) operator can have any
// types, and it does not have to be associative.
GrB_Matrix T ;
info = GB_builder (&T, A->type, A->vlen, A->vdim, A->is_csc,
&(A->i_pending), &(A->j_pending), A->sorted_pending, A->s_pending,
A->n_pending, A->max_n_pending, A->operator_pending,
A->type_pending->code, Context) ;
//--------------------------------------------------------------------------
// free pending tuples
//--------------------------------------------------------------------------
// The tuples have been converted to T, which is more compact, and
// duplicates have been removed.
// This work needs to be done even if the builder fails.
// GB_builder frees A->j_pending. If successful, A->i_pending is now T->i.
// Otherwise A->i_pending is freed. In both cases, it has been set to NULL.
ASSERT (A->i_pending == NULL && A->j_pending == NULL) ;
// pending tuples are now free; so A->s_pending can be freed as well
// FUTURE: GB_builder could modify A->s_pending in place to save memory,
// but it can't do that for the user's S array for GrB_*_build.
GB_pending_free (A) ;
//--------------------------------------------------------------------------
// remove the matrix from the queue
//--------------------------------------------------------------------------
ASSERT (!GB_PENDING (A)) ;
ASSERT (!GB_ZOMBIES (A)) ;
GB_CRITICAL (GB_queue_remove (A)) ;
// No pending operations on A, and A is not in the queue, so GB_check can
// now see the conditions it expects.
ASSERT (!(A->enqueued)) ;
ASSERT_OK (GB_check (A, "A after moving pending tuples to T", GB0)) ;
//--------------------------------------------------------------------------
// check the status of the builder
//--------------------------------------------------------------------------
// Finally check the status of the builder. The pending tuples, just freed
// above, must be freed whether or not the builder is succesful.
if (info != GrB_SUCCESS)
{
// out of memory
GB_CONTENT_FREE (A) ;
ASSERT (T == NULL) ;
return (info) ;
}
ASSERT_OK (GB_check (T, "T = matrix of pending tuples", GB0)) ;
ASSERT (!GB_PENDING (T)) ;
ASSERT (!GB_ZOMBIES (T)) ;
ASSERT (GB_NNZ (T) > 0) ;
ASSERT (T->is_hyper) ;
ASSERT (T->nvec == T->nvec_nonempty) ;
//--------------------------------------------------------------------------
// check for quick transplant
//--------------------------------------------------------------------------
if (anz == 0)
{
// A has no entries so just transplant T into A, then free T and
// conform A to its desired hypersparsity.
return (GB_transplant_conform (A, A->type, &T, Context)) ;
}
//--------------------------------------------------------------------------
// reallocate A to hold the tuples
//--------------------------------------------------------------------------
// make A->nzmax larger to accomodate future tuples, but only
// allocate new space if the old A->nzmax is insufficient.
int64_t anz_new = anz + GB_NNZ (T) ; // must have at least this space
info = GB_ix_resize (A, anz_new, Context) ;
if (info != GrB_SUCCESS)
{
// out of memory
GB_MATRIX_FREE (&T) ;
return (info) ;
}
//--------------------------------------------------------------------------
// if A is hypersparse, ensure A->plen is sufficient for A=A+T
//--------------------------------------------------------------------------
// If anz > 0, T is hypersparse, even if A is a GrB_Vector
ASSERT (T->is_hyper) ;
// No addition is done since the nonzero patterns of A and T are disjoint.
int64_t *restrict Ah = A->h ;
int64_t *restrict Ap = A->p ;
int64_t *restrict Ai = A->i ;
GB_void *restrict Ax = A->x ;
int64_t anvec = A->nvec ;
int64_t anvec_new = anvec ;
const int64_t *restrict Th = T->h ;
const int64_t *restrict Tp = T->p ;
const int64_t *restrict Ti = T->i ;
const GB_void *restrict Tx = T->x ;
int64_t tnvec = T->nvec ;
int64_t ak, tk ;
if (A->is_hyper)
{
// 2-way merge of A->h and T->h
for (ak = 0, tk = 0 ; ak < anvec && tk < tnvec ; )
{
int64_t ja = Ah [ak] ;
int64_t jt = Th [tk] ;
if (jt == ja)
{
// vector jt appears in both A and T
ak++ ;
tk++ ;
}
else if (ja < jt)
{
// vector ja appears in A but not T
ak++ ;
}
else // jt < ja
{
// vector jt appears in T but not A
tk++ ;
anvec_new++ ;
}
}
// count the vectors not yet seen in T
if (tk < tnvec)
{
anvec_new += (tnvec - tk) ;
}
// reallocate A->p and A->h, if needed
if (anvec_new > A->plen)
{
if (GB_to_nonhyper_test (A, anvec_new, A->vdim))
{
// convert to non-hypersparse if anvec_new will become too large
info = GB_to_nonhyper (A, Context) ;
}
else
{
// increase the size of A->p and A->h. The size must be at
// least anvec_new, but add some slack for future growth.
int64_t aplen_new = 2 * (anvec_new + 1) ;
aplen_new = GB_IMIN (aplen_new, A->vdim) ;
info = GB_hyper_realloc (A, aplen_new, Context) ;
}
if (info != GrB_SUCCESS)
{
// out of memory; all content of A has been freed
ASSERT (A->magic == GB_MAGIC2) ;
GB_MATRIX_FREE (&T) ;
return (info) ;
}
Ah = A->h ;
Ap = A->p ;
}
}
ASSERT_OK (GB_check (A, "A after increasing A->h", GB0)) ;
ASSERT_OK (GB_check (T, "T to fold in", GB0)) ;
//--------------------------------------------------------------------------
// A = A + T ; in place by folding in the tuples in reverse order
//--------------------------------------------------------------------------
// Merge in the tuples into each vector, in reverse order. Note that Ap
// [k+1] or Ap [j+1] is changed during the iteration. The bottom of the
// new A is treated like a stack, where entries are placed on top of the Ai
// and Ax stack, and vector indices are placed on top of the Ah stack
// if A is hypersparse.
// T is always hypersparse, even if A and T are typecasted GrB_Vector
// objects. A can be non-hypersparse or hypersparse. If A is hypersparse
// then this step does not take O(A->vdim) time. It takes at most
// O(nnz(Z)+nnz(A)) time, regardless of the vector dimension of A and T,
// A->vdim and T->vdim.
bool A_is_hyper = A->is_hyper ;
int64_t asize = A->type->size ;
// pdest points to the top of the stack at the end of the A matrix;
// this is also the total number of nonzeros in A+T. Since the stack
// is empty, pdest points to one past the position where the last entry
// in A will appear.
int64_t pdest = anz_new ;
// pdest-1 must be within the size of A->i and A->x
ASSERT (pdest <= A->nzmax) ;
tk = tnvec - 1 ;
// ak_dest points to the top of the hyperlist stack, also currently empty.
int64_t ak_dest ;
if (A_is_hyper)
{
// Ah [ak] is the rightmost non-empty vector in the hypersparse A.
// It will be moved to Ah [anvec_new-1].
ak = A->nvec - 1 ;
ak_dest = anvec_new ;
}
else
{
// ak is the rightmost vector in the non-hypersparse A
ak = A->vdim - 1 ;
ak_dest = A->vdim ;
ASSERT (A->nvec == A->vdim) ;
}
// count the number of non-empty vectors (again, if hypersparse, but for
// the first time if non-hypersparse)
anvec_new = A->nvec_nonempty ;
// while T has non-empty vectors
while (tk >= 0)
{
// When T is exhausted, the while loop can stop. Let j1 be the
// leftmost non-empty vector of the hypersparse T. A(:,0:j1-1) is
// not affected by the merge. Only vectors A(:,j1:n-1) need to be
// shifted (where n == A->vdim).
// If the vectors of A are exhausted, ak becomes -1 and stays there.
ASSERT (ak >= -1) ;
//----------------------------------------------------------------------
// get vectors A(:,j) and T(:,j)
//----------------------------------------------------------------------
int64_t j, ja, jt, pa, pa_end, pt, pt_end ;
if (A_is_hyper)
{
// get the next non-empty vector ja in the prior hypersparse A
ja = (ak >= 0) ? Ah [ak] : -1 ;
}
else
{
// ja always appears in the non-hypersparse A
ja = ak ;
}
// jt is the next non-empty vector in the hypersparse T
jt = Th [tk] ;
ASSERT (jt >= 0) ;
ASSERT (ja >= -1) ;
if (ja == jt)
{
// vector j appears in both A(:,j) and T(:,j)
ASSERT (ak >= 0) ;
j = ja ;
pa_end = Ap [ak ] - 1 ;
pa = Ap [ak+1] - 1 ;
pt_end = Tp [tk ] - 1 ;
pt = Tp [tk+1] - 1 ;
}
else if (ja > jt)
{
// vector j appears in A(:,j) but not T(:,j)
ASSERT (ak >= 0) ;
j = ja ;
pa_end = Ap [ak ] - 1 ;
pa = Ap [ak+1] - 1 ;
pt_end = -1 ;
pt = -1 ;
}
else // jt > ja
{
// vector j appears in T(:,j) but not A(:,j)
ASSERT (ak >= -1) ;
j = jt ;
pa_end = -1 ;
pa = -1 ;
pt_end = Tp [tk ] - 1 ;
pt = Tp [tk+1] - 1 ;
}
ASSERT (j >= 0 && j < A->vdim) ;
// A (:,j) is in Ai,Ax [pa_end+1 ... pa]
// T (:,j) is in Ti,Tx [pt_end+1 ... pt]
//----------------------------------------------------------------------
// count the number of non-empty vectors in the new A
//----------------------------------------------------------------------
if (!(pa > pa_end) && (pt > pt_end))
{
// A(:,j) is empty but T(:,j) is not; count one more non-empty
// vector in A
anvec_new++ ;
}
//----------------------------------------------------------------------
// log the new end of A(:,j)
//----------------------------------------------------------------------
// get the next free slot on the hyperlist stack
ASSERT (ak < ak_dest) ;
ASSERT (GB_IMPLIES (!A_is_hyper, ak_dest == ak+1)) ;
--ak_dest ;
ASSERT (ak <= ak_dest) ;
ASSERT (ak_dest >= 0) ;
if (A_is_hyper)
{
// push j onto the stack for the new hyperlist for A
Ah [ak_dest] = j ;
}
ASSERT (GB_IMPLIES (!A_is_hyper, ak_dest == ak && j == ak)) ;
Ap [ak_dest+1] = pdest ;
//----------------------------------------------------------------------
// merge while entries exist in both A (:,j) and T (:,j) (reverse order)
//----------------------------------------------------------------------
while (pa > pa_end && pt > pt_end)
{
// entries exist in both A (:,j) and T (:,j); take the biggest one
int64_t ia = Ai [pa] ;
int64_t it = Ti [pt] ;
// no entries are both in A and T
ASSERT (ia != it) ;
// get next free slot on the top of the stack of the entries of A
--pdest ;
ASSERT (pa < pdest) ;
if (ia > it)
{
// push Ai,Ax [pa] onto the stack
Ai [pdest] = ia ;
// Ax [pdest] = Ax [pa]
memcpy (Ax +(pdest*asize), Ax +(pa*asize), asize) ;
--pa ;
}
else // it > ia
{
// push Ti,Tx [pt] onto the stack
ASSERT (it > ia) ;
Ai [pdest] = it ;
// Ax [pdest] = Tx [pt]
memcpy (Ax +(pdest*asize), Tx +(pt*asize), asize) ;
--pt ;
}
}
//----------------------------------------------------------------------
// merge the remainder
//----------------------------------------------------------------------
// Either A (:,j) or T (:,j) is exhausted; but the other one can have
// entries that still need to be shifted down.
// FUTURE: can use two memmove's here, for Ai and Ax, with no while
// loop, since the source and destination can overlap
while (pa > pa_end)
{
// entries still exist in A (:,j); shift downwards
int64_t ia = Ai [pa] ;
// get next free slot on the top of the stack of the entries of A
--pdest ;
ASSERT (pa <= pdest) ;
// push Ai,Ax [pa] onto the stack
if (pa != pdest)
{
Ai [pdest] = ia ;
// Ax [pdest] = Ax [pa]
memcpy (Ax +(pdest*asize), Ax +(pa*asize), asize) ;
}
--pa ;
}
// FUTURE: can use two memcpy's here, for Ai and Ax, with no while loop
while (pt > pt_end)
{
// entries still exist in T (:,j); shift downwards
int64_t it = Ti [pt] ;
// get next free slot on the top of the stack of the entries of A
--pdest ;
// push Ti,Tx [pt] onto the stack
Ai [pdest] = it ;
// Ax [pdest] = Tx [pt]
memcpy (Ax +(pdest*asize), Tx +(pt*asize), asize) ;
--pt ;
}
//----------------------------------------------------------------------
// advance to the next vector (right to left)
//----------------------------------------------------------------------
if (ja == jt)
{
// vector j appears in both A(:,j) and T(:,j)
--ak ;
--tk ;
}
else if (ja > jt)
{
// vector j appears in A(:,j) but not T(:,j)
--ak ;
}
else // jt > ja
{
// vector j appears in T(:,j) but not A(:,j)
--tk ;
}
}
// update the count of non-empty vectors in A
A->nvec_nonempty = anvec_new ;
// all vectors have been merged into A
if (A->is_hyper)
{
A->nvec = A->nvec_nonempty ;
}
// end condition: no need to log the end of A(:,-1) since Ap[0]=0
// already holds.
ASSERT (Ap [0] == 0) ;
//--------------------------------------------------------------------------
// tuples have now been assembled into the matrix
//--------------------------------------------------------------------------
GB_MATRIX_FREE (&T) ;
ASSERT_OK (GB_check (A, "A after assembling pending tuples", GB0)) ;
// conform A to its desired hypersparsity
return (GB_to_hyper_conform (A, Context)) ;
}
GrB_Info GB_AxB_meta // C<M>=A*B meta algorithm
(
GrB_Matrix *Chandle, // output matrix C
const bool C_is_csc, // desired CSR/CSC format of C
GrB_Matrix *MT_handle, // return MT = M' to caller, if computed
const GrB_Matrix M_in, // mask for C<M> (not complemented)
const GrB_Matrix A_in, // input matrix
const GrB_Matrix B_in, // input matrix
const GrB_Semiring semiring, // semiring that defines C=A*B
bool A_transpose, // if true, use A', else A
bool B_transpose, // if true, use B', else B
bool flipxy, // if true, do z=fmult(b,a) vs fmult(a,b)
bool *mask_applied, // if true, mask was applied
const GrB_Desc_Value AxB_method,// for auto vs user selection of methods
GrB_Desc_Value *AxB_method_used,// method selected
GB_Sauna *Sauna_Handle, // handle to sparse accumulator
GB_Context Context
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
ASSERT_OK_OR_NULL (GB_check (M_in, "M for meta A*B", GB0)) ;
ASSERT_OK (GB_check (A_in, "A_in for meta A*B", GB0)) ;
ASSERT_OK (GB_check (B_in, "B_in for meta A*B", GB0)) ;
ASSERT (!GB_PENDING (M_in)) ; ASSERT (!GB_ZOMBIES (M_in)) ;
ASSERT (!GB_PENDING (A_in)) ; ASSERT (!GB_ZOMBIES (A_in)) ;
ASSERT (!GB_PENDING (B_in)) ; ASSERT (!GB_ZOMBIES (B_in)) ;
ASSERT_OK (GB_check (semiring, "semiring for numeric A*B", GB0)) ;
ASSERT (mask_applied != NULL) ;
ASSERT (AxB_method_used != NULL) ;
ASSERT (Sauna_Handle != NULL) ;
(*Chandle) = NULL ;
if (MT_handle != NULL)
{
(*MT_handle) = NULL ;
}
GrB_Info info ;
GrB_Matrix AT = NULL ;
GrB_Matrix BT = NULL ;
GrB_Matrix MT = NULL ;
(*mask_applied) = false ;
(*AxB_method_used) = GxB_DEFAULT ;
//--------------------------------------------------------------------------
// handle the CSR/CSC formats of C, M, A, and B
//--------------------------------------------------------------------------
// On input, A and/or B can be transposed, and all four matrices can be in
// either CSR or CSC format, in any combination. This gives a total of 64
// possible combinations. However, a CSR matrix that is transposed is just
// the same as a non-transposed CSC matrix.
// Use transpose to handle the CSR/CSC format. If C is desired in CSR
// format, treat it as if it were in format CSC but transposed.
bool C_transpose = !C_is_csc ;
// If the mask is not present, then treat it as having the same CSR/CSC
// format as C.
bool M_is_csc = (M_in == NULL) ? C_is_csc : M_in->is_csc ;
// Treat M just like C. If M is in CSR format, treat it as if it were CSC
// but transposed, since there are no descriptors that transpose C or M.
bool M_transpose = !M_is_csc ;
// A can be transposed, and can also be in CSR or CSC format. If A is in
// CSR, treat it as A' in CSC, and if A' is in CSR, treat it as A in CSC.
if (!A_in->is_csc)
{
// Flip the sense of A_transpose
A_transpose = !A_transpose ;
}
// B is treated just like A
if (!B_in->is_csc)
{
// Flip the sense of A_transpose
B_transpose = !B_transpose ;
}
// Now all matrices C, M_in, A_in, and B_in, can be treated as if they
// were all in CSC format, except any of them can be transposed. There
// are now 16 cases to handle, where M, A, and B are M_in, A_in, and
// B_in and all matrices are CSR/CSC agnostic, and where C has not yet
// been created.
// C <M > = A * B
// C <M'> = A * B
// C'<M > = A * B
// C'<M'> = A * B
// C <M > = A * B'
// C <M'> = A * B'
// C'<M > = A * B'
// C'<M'> = A * B'
// C <M > = A' * B
// C <M'> = A' * B
// C'<M > = A' * B
// C'<M'> = A' * B
// C <M > = A' * B'
// C <M'> = A' * B'
// C'<M > = A' * B'
// C'<M'> = A' * B'
//--------------------------------------------------------------------------
// swap_rule: remove the tranpose of C
//--------------------------------------------------------------------------
// It is also possible to compute and return C' from this function, and to
// set C->is_csc as the negation of the desired format C_is_csc. This
// ensures that GB_accum_mask will transpose C when this function is done.
// FUTURE: give user control over the swap_rule. Any test here will work,
// with no other changes to the code below. The decision will only affect
// the performance, not the result.
bool swap_rule = (C_transpose) ;
GrB_Matrix A, B ;
bool atrans, btrans ;
if (swap_rule)
{
// Replace C'=A*B with C=B'*A', and so on. Swap A and B and transose
// them, transpose M, negate flipxy, and transpose M and C.
A = B_in ; atrans = !B_transpose ;
B = A_in ; btrans = !A_transpose ;
flipxy = !flipxy ;
M_transpose = !M_transpose ;
C_transpose = !C_transpose ;
}
else
{
// use the input matrices as-is
A = A_in ; atrans = A_transpose ;
B = B_in ; btrans = B_transpose ;
}
// Assuming the swap_rule == C_transpose, C no longer needs to be
// transposed, but the following assertion only holds if swap_rule ==
// C_transpose.
ASSERT (!C_transpose) ;
ASSERT_OK (GB_check (A, "final A for A*B", GB0)) ;
ASSERT_OK (GB_check (B, "final B for A*B", GB0)) ;
//--------------------------------------------------------------------------
// explicitly transpose the mask
//--------------------------------------------------------------------------
// all uses of GB_transpose below:
// transpose: typecast, no op, not in place
GrB_Matrix M ;
if (M_transpose && M_in != NULL)
{
// MT = M_in' also typecasting to boolean. It is not freed here
// unless an error occurs, but is returned to the caller.
GB_OK (GB_transpose (&MT, GrB_BOOL, C_is_csc, M_in, NULL, Context)) ;
M = MT ;
}
else
{
// M_in can be used as-is; it may be NULL
M = M_in ;
}
ASSERT_OK_OR_NULL (GB_check (M, "final M for A*B", GB0)) ;
//--------------------------------------------------------------------------
// typecast A and B when transposing them, if needed
//--------------------------------------------------------------------------
GrB_Type atype_required, btype_required ;
if (flipxy)
{
// A is passed as y, and B as x, in z = mult(x,y)
atype_required = semiring->multiply->ytype ;
btype_required = semiring->multiply->xtype ;
}
else
{
// A is passed as x, and B as y, in z = mult(x,y)
atype_required = semiring->multiply->xtype ;
btype_required = semiring->multiply->ytype ;
}
//--------------------------------------------------------------------------
// select the algorithm
//--------------------------------------------------------------------------
if (atrans)
{
//----------------------------------------------------------------------
// C<M> = A'*B' or A'*B
//----------------------------------------------------------------------
// explicitly transpose B
if (btrans)
{
// B = B'
GB_OK (GB_transpose (&BT, btype_required, true, B, NULL, Context)) ;
B = BT ;
}
//----------------------------------------------------------------------
// C<M> = A'*B
//----------------------------------------------------------------------
// A'*B is being computed: use the dot product without computing A'
// or use the saxpy (heap or gather/scatter) method
// If the mask is present, only entries for which M(i,j)=1 are
// computed, which makes this method very efficient when the mask is
// very sparse (triangle counting, for example). Each entry C(i,j) for
// which M(i,j)=1 is computed via a dot product, C(i,j) =
// A(:,i)'*B(:,j). If the mask is not present, the dot-product method
// is very slow in general, and thus the saxpy method is usually used
// instead (via gather/scatter or heap).
bool use_adotb ;
if (AxB_method == GxB_DEFAULT)
{
// auto selection for A'*B
if (M != NULL)
{
// C<M> = A'*B always uses the dot product method
use_adotb = true ;
}
else if (A->vdim == 1 || B->vdim == 1)
{
// C=A'*B uses dot product method if C is a 1-by-n or n-by-1
use_adotb = true ;
}
else
{
// when C is a matrix, C=A'*B uses the dot product method if A
// or B are dense, since the dot product method requires no
// workspace in that case and can exploit dense vectors of A
// and/or B.
GrB_Index bnzmax, anzmax ;
bool A_is_dense = GB_Index_multiply (&anzmax, A->vlen, A->vdim)
&& (anzmax == GB_NNZ (A)) ;
bool B_is_dense = GB_Index_multiply (&bnzmax, B->vlen, B->vdim)
&& (bnzmax == GB_NNZ (B)) ;
use_adotb = A_is_dense || B_is_dense ;
}
}
else
{
// user selection for A'*B
use_adotb = (AxB_method == GxB_AxB_DOT) ;
}
if (use_adotb)
{
// C<M> = A'*B via dot product method
(*AxB_method_used) = GxB_AxB_DOT ;
GB_OK (GB_AxB_dot (Chandle, M, A, B, semiring, flipxy, Context)) ;
}
else
{
// C<M> = A'*B via saxpy: gather/scatter or heap method
GB_OK (GB_transpose (&AT, atype_required, true, A, NULL, Context)) ;
GB_OK (GB_AxB_saxpy (Chandle, M, AT, B, semiring, flipxy,
AxB_method, AxB_method_used, Sauna_Handle, Context)) ;
}
}
else if (btrans)
{
//----------------------------------------------------------------------
// C<M> = A*B'
//----------------------------------------------------------------------
if (AxB_method == GxB_AxB_DOT)
{
// C<M> = A*B' via dot product
(*AxB_method_used) = GxB_AxB_DOT ;
GB_OK (GB_transpose (&AT, atype_required, true, A, NULL, Context)) ;
GB_OK (GB_transpose (&BT, btype_required, true, B, NULL, Context)) ;
GB_OK (GB_AxB_dot (Chandle, M, AT, BT, semiring, flipxy, Context)) ;
}
else
{
// C<M> = A*B' via saxpy: gather/scatter or heap method
GB_OK (GB_transpose (&BT, btype_required, true, B, NULL, Context)) ;
GB_OK (GB_AxB_saxpy (Chandle, M, A, BT, semiring, flipxy,
AxB_method, AxB_method_used, Sauna_Handle, Context)) ;
}
}
else
{
//----------------------------------------------------------------------
// C<M> = A*B
//----------------------------------------------------------------------
if (AxB_method == GxB_AxB_DOT)
{
// C<M> = A*B via dot product
(*AxB_method_used) = GxB_AxB_DOT ;
GB_OK (GB_transpose (&AT, atype_required, true, A, NULL, Context)) ;
GB_OK (GB_AxB_dot (Chandle, M, AT, B, semiring, flipxy, Context)) ;
}
else
{
// C<M> = A*B via saxpy: gather/scatter or heap method
GB_OK (GB_AxB_saxpy (Chandle, M, A, B, semiring, flipxy,
AxB_method, AxB_method_used, Sauna_Handle, Context)) ;
}
}
//--------------------------------------------------------------------------
// handle C_transpose and assign the CSR/CSC format
//--------------------------------------------------------------------------
// If C_transpose is true, then C' has been computed. In this case, negate
// the desired C_is_csc so that GB_accum_mask transposes the result before
// applying the accum operator and/or writing the result back to the user's
// C. If swap_rule == C_transpose, then C_transpose is always false here,
// but this could change in the future. The following code will adapt to
// any swap_rule, so it does not change if the swap_rule changes.
GrB_Matrix C = (*Chandle) ;
ASSERT (C != NULL) ;
C->is_csc = C_transpose ? !C_is_csc : C_is_csc ;
//--------------------------------------------------------------------------
// free workspace and return result
//--------------------------------------------------------------------------
GB_MATRIX_FREE (&AT) ;
GB_MATRIX_FREE (&BT) ;
ASSERT_OK (GB_check (C, "C output for all C=A*B", GB0)) ;
ASSERT_OK_OR_NULL (GB_check (MT, "MT if computed", GB0)) ;
(*mask_applied) = (M != NULL) ;
if (MT_handle != NULL)
{
// return MT to the caller, if computed and the caller wants it
(*MT_handle) = MT ;
}
else
{
// otherwise, free it
GB_MATRIX_FREE (&MT) ;
}
return (GrB_SUCCESS) ;
}
