bsrmm, sbsrmm, dbsrmm, cbsrmm, zbsrmm - block sparse row format matrix-matrix multiply
SUBROUTINE SBSRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB) REAL*4 ALPHA, BETA REAL*4 VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DBSRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB) REAL*8 ALPHA, BETA REAL*8 VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CBSRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB) COMPLEX*8 ALPHA, BETA COMPLEX*8 VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZBSRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB) COMPLEX*16 ALPHA, BETA COMPLEX*16 VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where: BNNZ = BPNTRE(MB)-BPNTRB(1)
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 row 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 A 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 column indices of the block entries of A.
BPNTRB() integer array of length MB such that BPNTRB(J)-BPNTRB(1)+1 points to location in BINDX of the first block entry of the J-th block row of A.
BPNTRE() integer array of length MB such that BPNTRE(J)-BPNTRB(1) points to location in BINDX of the last block entry of the J-th block row 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/
It is known that there exits another representation of the block sparse row 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 row 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 row format the following calling sequence should be used
CALL SBSRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, IA, IA(2), LB, * B, LDB, BETA, C, LDC, WORK, LWORK )
=cut