csrmm, scsrmm, dcsrmm, ccsrmm, zcsrmm - compressed sparse row format matrix-matrix multiply
SUBROUTINE SCSRMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) REAL*4 ALPHA, BETA REAL*4 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DCSRMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) REAL*8 ALPHA, BETA REAL*8 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CCSRMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) COMPLEX*8 ALPHA, BETA COMPLEX*8 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZCSRMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) COMPLEX*16 ALPHA, BETA COMPLEX*16 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(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 compressed 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 is real.
M Number of rows in matrix A
N Number of columns in matrix C
K Number of 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 nonzero
entries of A.
INDX() integer array of length NNZ consisting of the
column indices of nonzero entries of A.
PNTRB() integer array of length M such that PNTRB(J)-PNTRB(1)+1
points to location in VAL of the first nonzero element
in row J.
PNTRE() integer array of length M such that PNTRE(J)-PNTRB(1)
points to location in VAL of the last nonzero element
in row J.
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 compressed 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 row in the arrays VAL and INDX is used instead of two arrays PNTRB and PNTRE. To use the routine with this kind of compressed sparse row format the following calling sequence should be used SUBROUTINE SCSRMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, INDX, IA, IA(2), B, LDB, BETA, * C, LDC, WORK, LWORK )