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

Chapter 3 Basic Matrix Operations 317
Solve triangular system STPSV/DTPSV/CTPSV/ZTPSV
Notes These subprograms conform to specifications of the Level 2 BLAS.
The subprograms do not check for singularity of matrix A. A is singular if
diag = ’N’ or ’n’ and some a
ii
= 0. This condition causes a division by zero to
occur. Therefore, the program must detect singularity and take appropriate
action to avoid a problem before calling any of these subprograms.
If an error in the arguments is detected, the subprograms call error handler
XERBLA, which writes an error message onto the standard error file and
terminates execution. The standard version of XERBLA (refer to the end of this
chapter) can be replaced with a user-supplied version to change the error
procedure. Error conditions are:
uplo ≠ ’L’ or ’l’ or ’U’ or ’u’
trans ≠ ’N’ or ’n’ or ’T’ or ’t’ or ’C’ or ’c’
diag ≠ ’N’ or ’n’ or ’U’ or ’u’
n < 0
incx = 0
Actual character arguments in a subroutine call can be longer than the
corresponding dummy arguments. Therefore, readability of the CALL
statement may be improved by coding the trans argument as ’NORMAL’ or
’NONTRANS’ for ’N’, ’TRANSPOSE’ for ’T’, or ’CTRANS’ for ’C’. Refer to
“Example 2.”
Example 1 Perform REAL*4 forward elimination using a 75-by-75 unit-diagonal,
lower-triangular real matrix stored in packed form in an array AP of dimension
5500, and x is a real vector 75 elements long stored in an array X of dimension
100.
CHARACTER*1 UPLO,TRANS,DIAG
INTEGER*4 N,INCX
REAL*4 AP(5500),X(100)
UPLO = ’L’
TRANS = ’N’
DIAG = ’U’
N = 75
INCX = 1
CALL STPSV (UPLO,TRANS,DIAG,N,AP,X,INCX)
Example 2 Perform REAL*4 back substitution using a 75-by-75 nonunit-diagonal,
upper-triangular real matrix stored in packed form in an array AP of dimension
5500, and x is a real vector 75 elements long stored in an array X of dimension
100.
INTEGER*4 N
REAL*4 AP(5500),X(100)
N = 75
CALL STPSV (’UPPER’,’NONTRANS’,’NONUNIT’,N,AP,X,1)