vbrmm, svbrmm, dvbrmm, cvbrmm, zvbrmm - variable block sparse row format matrix-matrix multiply
SUBROUTINE SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1), * BPNTRB(MB), BPNTRE(MB) REAL*4 ALPHA, BETA REAL*4 VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1), * BPNTRB(MB), BPNTRE(MB) REAL*8 ALPHA, BETA REAL*8 VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX*8 ALPHA, BETA COMPLEX*8 VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX*16 ALPHA, BETA COMPLEX*16 VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
C <- alpha op(A) B + beta C
where ALPHA and BETA are scalar, C and B are matrices, A is a matrix represented in variable 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 the 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 NNZ consisting of the block entries
of A where each block entry is a dense rectangular matrix
stored column by column.
NNZ is the total number of point entries in all nonzero
block entries of a matrix A.
INDX() integer array of length BNNZ+1 where BNNZ is the number of
block entries of a matrix A such that the I-th element of
INDX[] points to the location in VAL of the (1,1) element
of the I-th block entry.
BINDX() integer array of length BNNZ consisting of the block
column indices of the block entries of A where BNNZ is
the number block entries of a matrix A.
RPNTR() integer array of length MB+1 such that RPNTR(I)-RPNTR(1)+1
is the row index of the first point row in the I-th block
row.
RPNTR(MB+1) is set to M+RPNTR(1) where M is the number of
rows in matrix A.
Thus, the number of point rows in the I-th block row is
RPNTR(I+1)-RPNTR(I).
CPNTR() integer array of length KB+1 such that CPNTR(J)-CPNTR(1)+1
is the column index of the first point column in the J-th
block column. CPNTR(KB+1) is set to K+CPNTR(1) where K is
the number of columns in matrix A.
Thus, the number of point columns in the J-th block column
is CPNTR(J+1)-CPNTR(J).
BPNTRB() integer array of length MB such that BPNTRB(I)-BPNTRB(1)+1
points to location in BINDX of the first block entry of
the I-th block row of A.
BPNTRE() integer array of length MB such that BPNTRE(I)-BPNTRB(1)
points to location in BINDX of the last block entry of
the I-th block row of 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 variable block sparse row format (see for example Y.Saad, ``Iterative Methods for Sparse Linear Systems'', WPS, 1996). Its data structure consists of six array instead of the seven 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 array BINDX is used instead of two arrays BPNTRB and BPNTRE. To use the routine with this kind of variable block sparse row format the following calling sequence should be used SUBROUTINE SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2), * B, LDB, BETA, C, LDC, WORK, LWORK )