cbcomm(3P) Sun Performance Library cbcomm(3P)NAMEcbcomm - block coordinate matrix-matrix multiply
SYNOPSIS
SUBROUTINE CBCOMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, BINDX, BJNDX, BNNZ, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB,
* LDB, LDC, LWORK
INTEGER BINDX(BNNZ), BJNDX(BNNZ)
COMPLEX ALPHA, BETA
COMPLEX VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CBCOMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, BINDX, BJNDX, BNNZ, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB,
* LDB, LDC, LWORK
INTEGER*8 BINDX(BNNZ), BJNDX(BNNZ)
COMPLEX ALPHA, BETA
COMPLEX VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE BCOMM(TRANSA,MB,[N],KB,ALPHA,DESCRA,VAL,BINDX, BJNDX,
* BNNZ, LB, B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, N, KB, BNNZ, LB
INTEGER, DIMENSION(:) :: DESCRA, BINDX, BJNDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL
COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE BCOMM_64(TRANSA,MB,[N],KB,ALPHA,DESCRA,VAL,BINDX, BJNDX,
* BNNZ, LB, B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, N, KB, BNNZ, LB
INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BJNDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL
COMPLEX, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void cbcomm (const int transa, const int mb, const int n, const int kb,
const floatcomplex* alpha, const int* descra, const floatcom‐
plex* val, const int* bindx, const int* bjndx, const int
bnnz, const int lb, const floatcomplex* b, const int ldb,
const floatcomplex* beta, floatcomplex* c, const int ldc);
void cbcomm_64 (const long transa, const long mb, const long n, const
long kb, const floatcomplex* alpha, const long* descra, const
floatcomplex* val, const long* bindx, const long* bjndx,
const long bnnz, const long lb, const floatcomplex* b, const
long ldb, const floatcomplex* beta, floatcomplex* c, const
long ldc);
DESCRIPTIONcbcomm performs one of the matrix-matrix operations
C <- alpha op(A) B + beta C
where op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )
( ' indicates matrix transpose),
A is an (mb*lb) by (kb*lb) sparse matrix represented in the block
coordinate format, alpha and beta are scalars, C and B are dense
matrices.
ARGUMENTSTRANSA(input) On entry, integer TRANSA specifies the form
of op( A ) to be used in the matrix
multiplication as follows:
0 : operate with matrix
1 : operate with transpose matrix
2 : operate with the conjugate transpose of matrix.
2 is equivalent to 1 if matrix is real.
Unchanged on exit.
MB(input) On entry, integer MB specifies the number of block rows
in the matrix A. Unchanged on exit.
N(input) On entry, integer N specifies the number of columns in
the matrix C. Unchanged on exit.
KB(input) On entry, integer KB specifies the number of block
columns in the matrix A. Unchanged on exit.
ALPHA(input) On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
DESCRA (input) Descriptor argument. Five element integer array:
DESCRA(1) matrix structure
0 : general
1 : symmetric (A=A')
2 : Hermitian (A= CONJG(A'))
3 : Triangular
4 : Skew(Anti)-Symmetric (A=-A')
5 : Diagonal
6 : Skew-Hermitian (A= -CONJG(A'))
DESCRA(2) upper/lower triangular indicator
1 : lower
2 : upper
DESCRA(3) main block diagonal type
0 : non-unit
1 : unit
DESCRA(4) Array base (NOT IMPLEMENTED)
0 : C/C++ compatible
1 : Fortran compatible
DESCRA(5) repeated indices? (NOT IMPLEMENTED)
0 : unknown
1 : no repeated indices
VAL(input) On entry, VAL is a scalar array of length
LB*LB*BNNZ consisting of the non-zero block
entries of A, in any order. Each block
is stored in standard column-major form.
Unchanged on exit.
BINDX(input) On entry, BINDX is an integer array of length BNNZ
consisting of the block row indices of the non-zero
block entries of A. Unchanged on exit.
BJNDX(input) On entry, BJNDX is an integer array of length BNNZ
consisting of the block column indices of the non-zero
block entries of A. Unchanged on exit.
BNNZ (input) On entry, integer BNNZ specifies the number of nonzero
block entries in A. Unchanged on exit.
LB (input) On entry, integer LB specifies the dimension of dense
blocks composing A. Unchanged on exit.
B (input) Array of DIMENSION ( LDB, N ).
Before entry with TRANSA = 0, the leading kb*lb by n
part of the array B must contain the matrix B, otherwise
the leading mb*lb by n part of the array B must contain the
matrix B. Unchanged on exit.
LDB (input) On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. Unchanged on exit.
BETA (input) On entry, BETA specifies the scalar beta. Unchanged on exit.
C(input/output) Array of DIMENSION ( LDC, N ).
Before entry with TRANSA = 0, the leading mb*lb by n
part of the array C must contain the matrix C, otherwise
the leading kb*lb by n part of the array C must contain the
matrix C. On exit, the array C is overwritten by the matrix
( alpha*op( A )* B + beta*C ).
LDC (input) On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. Unchanged on exit.
WORK (is not referenced in the current version)
LWORK (is not referenced in the current version)
SEE ALSO
Libsunperf SPARSE BLAS is fully parallel and compatible with NIST FOR‐
TRAN Sparse Blas but the sources are different. Libsunperf SPARSE BLAS
is free of bugs found in NIST FORTRAN Sparse Blas. Besides several new
features and routines are implemented.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
Based on the standard proposed in
"Document for the Basic Linear Algebra Subprograms (BLAS) Standard",
University of Tennessee, Knoxville, Tennessee, 1996:
http://www.netlib.org/utk/papers/sparse.ps
NOTES/BUGS
The all sparse blas matrix-matrix multiply routines for block entry
formats are designed so that if DESCRA(1)> 0, the routines check the
validity of each sparse block entry given in the sparse blas represen‐
tation. Block entries with incorrect indices are not used and no error
message related to the entries is issued.
The feature also provides a possibility to use just one sparse matrix
representation of a general block matrix A for computing matrix-matrix
multiply for another sparse matrix composed by block triangles and/or
the main block diagonal of A .
Assume that there is the sparse matrix representation of a general com‐
plex matrix A decomposed in the form
A = L + D + U
where L is the strictly block lower triangle of A, U is the strictly
block upper triangle of A, D is the block diagonal matrix. Let's I
denotes the identity matrix.
Then the correspondence between the first three values of DESCRA and
the result matrix for the sparse representation of A is
___________________________________________________________________
DESCRA(1)DESCRA(2)DESCRA(3) RESULT
___________________________________________________________________
1 1 0 alpha*op(L+D+L')*B+beta*C
1 1 1 alpha*op(L+I+L')*B+beta*C
1 2 0 alpha*op(U'+D+U)*B+beta*C
1 2 1 alpha*op(U'+I+U)*B+beta*C
2 1 0 alpha*op(L+D+conjg(L'))*B+beta*C
2 1 1 alpha*op(L+I+conjg(L'))*B+beta*C
2 2 0 alpha*op(conjg(U')+D+U)*B+beta*C
2 2 1 alpha*op(conjg(U')+I+U)*B+beta*C
3 1 1 alpha*op(L+I)*B+beta*C
3 1 0 alpha*op(L+D)*B+beta*C
3 2 1 alpha*op(U+I)*B+beta*C
3 2 0 alpha*op(U+D)*B+beta*C
4 1 0 or 1 alpha*op(L+D-L')*B+beta*C
4 2 0 or 1 alpha*op(U+D-U')*B+beta*C
5 1 or 2 0 alpha*op(D)*B+beta*C
5 1 or 2 1 alpha*B+beta*C
6 1 0 or 1 alpha*op(L+D-conjg(L'))*B+beta*C
6 2 0 or 1 alpha*op(U+D-conjg(U'))*B+beta*C
___________________________________________________________________
Remarks to the table:
1. the value of DESCRA(3) is simply ignored , if DESCRA(1)= 4 or 6 but
the diagonal blocks which are referenced in the sparse matrix represen‐
tation are used;
2. the diagonal blocks which are referenced in the sparse matrix rep‐
resentation are not used, if DESCRA(3)=1 and DESCRA(1)is one of 1, 2, 3
or 5;
3. if DESCRA(3) is not 1 and DESCRA(1) is one of 1,2, 4 or 6, the type
of D should correspond to the choosen value of DESCRA(1) .
3rd Berkeley Distribution 6 Mar 2009 cbcomm(3P)