NAG FL Interface
f07ujf computes the inverse of a real triangular matrix, using packed storage.
|Integer, Intent (In)
|Integer, Intent (Out)
|Real (Kind=nag_wp), Intent (Inout)
|Character (1), Intent (In)
The routine may be called by the names f07ujf, nagf_lapacklin_dtptri or its LAPACK name dtptri.
f07ujf forms the inverse of a real triangular matrix , using packed storage. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19
: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
: indicates whether
is a nonunit or unit triangular matrix.
- is a nonunit triangular matrix.
- is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .
On entry: , the order of the matrix .
– Real (Kind=nag_wp) array
the dimension of the array ap
must be at least
, packed by columns.
- if , the upper triangle of must be stored with element in for ;
- if , the lower triangle of must be stored with element in for .
If , the diagonal elements of are assumed to be , and are not referenced; the same storage scheme is used whether or ‘U’.
On exit: is overwritten by , using the same storage format as described above.
unless the routine detects an error (see Section 6
Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
Element of the diagonal is exactly zero.
is singular its inverse cannot be computed.
The computed inverse
is a modest linear function of
is the machine precision
Note that a similar bound for cannot be guaranteed, although it is almost always satisfied.
The computed inverse satisfies the forward error bound
See Du Croz and Higham (1992)
Parallelism and Performance
f07ujf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction
for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note
for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately .
The complex analogue of this routine is f07uwf
This example computes the inverse of the matrix
using packed storage.