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

406 HP MLIB User’s Guide
F_STPSV/F_DTPSV/F_CTPSV/F_ZTPSV Triangular packed solve
Name F_STPSV/F_DTPSV/F_CTPSV/F_ZTPSV
Triangular packed solve
Purpose F_xTPSV solves one of the following equations:
where x is a vector and the matrix T is a unit, non-unit, upper, or lower
triangular packed matrix. T
−T
is the inverse of the transpose of T, and is
the inverse of the conjugate transpose of T.
Refer to “STPSV/DTPSV/CTPSV/ZTPSV” on page 313 for details of the HP
MLIB legacy BLAS triangular-solve subprograms, and a description of packed
storage for a triangular matrix.
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
INTEGER*4 DIAG, INCX, N, TRANS, UPLO
REAL*4 ALPHA, AP( * ), X( * )
SUBROUTINE F_STPSV (UPLO, TRANS, DIAG, N, ALPHA, AP, X, INCX)
INTEGER*4 DIAG, INCX, N, TRANS, UPLO
REAL*8 ALPHA, AP( * ), X( * )
SUBROUTINE F_DTPSV (UPLO, TRANS, DIAG, N, ALPHA, AP, X, INCX)
INTEGER*4 DIAG, INCX, N, TRANS, UPLO
COMPLEX*8 ALPHA, AP( * ), X( * )
SUBROUTINE F_CTPSV (UPLO, TRANS, DIAG, N, ALPHA, AP, X, INCX)
INTEGER*4 DIAG, INCX, N, TRANS, UPLO
COMPLEX*16 ALPHA, AP( * ), X( * )
SUBROUTINE F_ZTPSV (UPLO, TRANS, DIAG, N, ALPHA, AP, X, INCX)
VECLIB8
INTEGER*8 DIAG, INCX, N, TRANS, UPLO
REAL*4 ALPHA, AP( * ), X( * )
SUBROUTINE F_STPSV (UPLO, TRANS, DIAG, N, ALPHA, AP, X, INCX)
x αT
1–
x←
x αT
T–
x←
x αT
*–
x←
T
*–