Contents
cbcomm - block coordinate matrix-matrix multiply
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(int transa, int mb, int n, int kb, complex
*alpha, int *descra, complex *val, int *bindx, int *bjndx,
int bnnz, int lb, complex *b, int ldb, complex *beta,
complex *c, int ldc);
void cbcomm_64(long transa, long mb, long n, long kb,
complex *alpha, long *descra, complex *val, long *bindx,
long *bjndx, long bnnz, long lb, complex *b, long ldb,
complex *beta, complex *c, long ldc);
cbcomm 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.
TRANSA(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)
Libsunperf SPARSE BLAS is fully parallel and compatible
with NIST FORTRAN 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 representation. 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 complex 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 representation are used;
2. the diagonal blocks which are referenced in the sparse
matrix representation 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) .