NAG Library Routine Document
F07UJF (DTPTRI) computes the inverse of a real triangular matrix, using packed storage.
The routine may be called by its
F07UJF (DTPTRI) 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
- 1: UPLO – CHARACTER(1)Input
: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
- 2: DIAG – CHARACTER(1)Input
: 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 .
- 3: N – INTEGERInput
On entry: , the order of the matrix .
- 4: AP() – REAL (KIND=nag_wp) arrayInput/Output
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.
- 5: INFO – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
If , the th parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.
If , is exactly zero; is singular and 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)
The total number of floating point operations is approximately .
The complex analogue of this routine is F07UWF (ZTPTRI)
This example computes the inverse of the matrix
using packed storage.
9.1 Program Text
Program Text (f07ujfe.f90)
9.2 Program Data
Program Data (f07ujfe.d)
9.3 Program Results
Program Results (f07ujfe.r)