skymm, sskymm, dskymm, cskymm, zskymm - Skyline format matrix-matrix multiply
SUBROUTINE SSKYMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), REAL*4 ALPHA, BETA REAL*4 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DSKYMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), REAL*8 ALPHA, BETA REAL*8 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CSKYMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), COMPLEX*8 ALPHA, BETA COMPLEX*8 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DSKYMM( TRANSA, M, N, K, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, K, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), COMPLEX*16 ALPHA, BETA COMPLEX*16 VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTR(M+1)-PNTR(1) (upper triangular) NNZ = PNTR(K+1)-PNTR(1) (lower triangular) PNTR() size = (M+1) (upper triangular) PNTR() size = (K+1) (lower triangular)
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 skyline 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 (NOT SUPPORTED) 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() array contain the nonzeros of A in skyline profile form. Row-oriented if DESCRA(2) = 1 (lower triangular), column oriented if DESCRA(2) = 2 (upper triangular).
PNTR() integer array of length M+1 (lower triangular) or K+1 (upper triangular) such that PNTR(I)-PNTR(1)+1 points to the location in VAL of the first element of the skyline profile in row (column) I.
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/
The SKY data structure is not supported for a general matrix structure (DESCRA(1)=0).