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 aii = 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)

Chapter 3 Basic Matrix Operations 317