Contents
sbscmm - block sparse column matrix-matrix multiply
SUBROUTINE SBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, MB, N, KB, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
REAL ALPHA, BETA
REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE SBSCMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, KB, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER*8 BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
REAL ALPHA, BETA
REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where: BNNZ = BPNTRE(KB)-BPNTRB(1)
F95 INTERFACE
SUBROUTINE BSCMM( TRANSA, MB, [N], KB, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, KB, LB
INTEGER, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL
REAL, DIMENSION(:, :) :: B, C
SUBROUTINE BSCMM_64( TRANSA, MB, [N], KB, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, KB, LB
INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL
REAL, DIMENSION(:, :) :: B, C
C <- alpha op(A) B + beta C
where ALPHA and BETA are scalar, C and B are dense matrices,
A is a matrix represented in block sparse column format and
op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
( ' indicates matrix transpose)
TRANSA Indicates how to operate with the sparse matrix
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.
MB Number of block rows in matrix A
N Number of columns in matrix C
KB Number of block columns in matrix A
ALPHA Scalar parameter
DESCRA() 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 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() scalar array of length LB*LB*BNNZ consisting of
the block entries stored column-major within each
dense block.
BINDX() integer array of length BNNZ consisting of the
block row indices of the block entries of A.
BPNTRB() integer array of length KB such that
BPNTRB(J)-BPNTRB(1)+1 points to location in BINDX
of the first block entry of the J-th block column
of A.
BPNTRE() integer array of length KB such that
BPNTRE(J)-BPNTRB(1) points to location in BINDX
of the last block entry of the J-th block column
of A.
LB dimension of dense blocks composing A.
B() rectangular array with first dimension LDB.
LDB leading dimension of B
BETA Scalar parameter
C() rectangular array with first dimension LDC.
LDC leading dimension of C
WORK() scratch array of length LWORK. WORK is not
referenced in the current version.
LWORK length of WORK array. LWORK is not referenced
in the current version.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
"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
It is known that there exists another representation of the
block sparse column format (see for example Y.Saad,
"Iterative Methods for Sparse Linear Systems", WPS, 1996).
Its data structure consists of three array instead of the
four used in the current implementation. The main
difference is that only one array, IA, containing the
pointers to the beginning of each block column in the arrays
VAL and BINDX is used instead of two arrays BPNTRB and
BPNTRE. To use the routine with this kind of block sparse
column format the following calling sequence should be used
CALL SBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, BINDX, IA, IA(2), LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )