skysm, sskysm, dskysm, cskysm, zskysm - Skyline format triangular solve
SUBROUTINE SSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), REAL*4 ALPHA, BETA REAL*4 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), REAL*8 ALPHA, BETA REAL*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 PNTR(*), COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(M), 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 C <- ALPHA D op(A) B + BETA C C <- ALPHA op(A) D B + BETA C
where ALPHA and BETA are scalar, C and B are m by n dense matrices, D is a diagonal scaling matrix, A is a unit, or non-unit, upper or lower triangular matrix represented in skyline format and op( A ) is one of
op( A ) = inv(A) or op( A ) = inv(A') or op( A ) =inv(conjg( A' )). (inv denotes matrix inverse, ' 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
UNITD Type of scaling: 1 : Identity matrix (argument DV[] is ignored) 2 : Scale on left (row scaling) 3 : Scale on right (column scaling)
DV() Array of length M containing the diagonal entries of the scaling diagonal matrix D.
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'))
Note: For the routine, DESCRA(1)=3 is only supported.
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. On exit, if LWORK = -1, WORK(1) returns the optimum LWORK.
LWORK length of WORK array. LWORK should be at least M.
For good performance, LWORK should generally be larger. For optimum performance on multiple processors, LWORK >=M*N_CPUS where N_CPUS is the maximum number of processors available to the program.
If LWORK=0, the routine is to allocate workspace needed.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimum size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.