HP MLIB User's Guide Vol. 1 7th Ed.

Chapter 4 Sparse BLAS Operations 525
Skyline format triangular solve SSKYSM/DSKYSM/CSKYSM/ZSKYSM
Name SSKYSM/DSKYSM/CSKYSM/ZSKYSM
Skyline format triangular solve
Purpose Skyline format triangular solve. Given a scalar α, an upper- or
lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms
compute either of the matrix solutions αA
–1
B, or αDA
–1
B, or αA
–1
DB, where D
is a diagonal matrix. The size of A is m-by-m. Optionally, A
–1
may be replaced
by A
–T
, or by A
–
*. Here, A
–T
is the transpose-inverse and A
–
* is the
conjugate-transpose-inverse of A. The solution matrix may be stored in the
result matrix C or optionally may be added to or subtracted from it. This is
handled in a convenient, but general way by two scalar arguments, α and β,
which are used as multipliers of the solution matrix and the result matrix.
Specifically, these subprograms compute matrix solutions of the form
Usage VECLIB:
SUBROUTINE SSKYSM
INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork
INTEGER*4 descra(*), pntr(*)
REAL*4 alpha, beta
REAL*4 val(*), b(ldb,*), c(ldc,*), work(*)
CALL SSKYSM (transa, m, n, unitd, dv, alpha, descra, val, pntr, b, ldb,
beta, c, ldc, work, lwork)
SUBROUTINE DSKYSM
INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork
INTEGER*4 descra(*), pntr(*)
REAL*8 alpha, beta
REAL*8 val(*), b(ldb,*), c(ldc,*), work(*)
CALL DSKYSM (transa, m, n, unitd, dv, alpha, descra, val, pntr, b, ldb,
beta, c, ldc, work, lwork)
SUBROUTINE CSKYSM
INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork
INTEGER*4 descra(*), pntr(*)
COMPLEX*8 alpha, beta
COMPLEX*8 val(*), b(ldb,*), c(ldc,*), work(*)
CALL CSKYSM (transa, m, n, unitd, dv, alpha, descra, val, pntr, b, ldb,
beta, c, ldc, work, lwork)
C ←αA
–1
B +βC
C ←αA
–T
B +βCC←αA
–
*B +βC
C ←αDA
–1
B +βC
C ←αDA
–T
B +βCC←αDA
–
*B +βC
C ←αA
–1
DB +βC
C ←αA
–T
DB +βCC←αA
–
*DB +βC