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

332 HP MLIB User’s Guide
STRSV/DTRSV/CTRSV/ZTRSV Solve triangular system
Name STRSV/DTRSV/CTRSV/ZTRSV
Solve triangular system
Purpose Given an n-by-n upper- or lower-triangular matrix A and an n-vector x, these
subprograms overwrite x with the solution y to the system of linear equations
Ay = x. This is the forward elimination or back substitution step of Gaussian
elimination. Optionally, A can be replaced by A
T
, the transpose of A, or by A*,
the conjugate transpose of A. Specifically, these subprograms compute
where A
−T
is the inverse of the transpose of A, and is the inverse of the
conjugate transpose of A.
These subprograms are more primitive than the LAPACK linear equation
solvers. As such, they are intended to supplement but not replace them, serving
instead as building blocks in constructing optimized linear algebra software. In
fact, many of the LAPACK subprograms have been recoded to call these
subprograms.
Refer to “F_STRSV/F_DTRSV/F_CTRSV/F_ZTRSV” on page 417 for details of
the equivalent BLAS Standard subprograms.
Matrix
Storage
For these subprograms, you supply A in a two-dimensional array large enough
to hold a square matrix. The other triangle of the array is not referenced. If A
has an unstored unit diagonal (see input argument diag), then the diagonal
elements of the array also are not referenced.
Usage VECLIB:
CHARACTER*1 uplo, trans, diag
INTEGER*4 n, lda, incx
REAL*4 a(lda, n), x(lenx)
CALL STRSV(uplo, trans, diag, n, a, lda, x, incx)
CHARACTER*1 uplo, trans, diag
INTEGER*4 n, lda, incx
REAL*8 a(lda, n), x(lenx)
CALL DTRSV(uplo, trans, diag, n, a, lda, x, incx)
CHARACTER*1 uplo, trans, diag
INTEGER*4 n, lda, incx
COMPLEX*8 a(lda, n), x(lenx)
CALL CTRSV(uplo, trans, diag, n, a, lda, x, incx)
xA
1–
x← xA
T–
x← and xA
*–
x,←,,
A
*–