NAG FL Interface
f07uwf (ztptri)

1 Purpose

f07uwf computes the inverse of a complex triangular matrix, using packed storage.

2 Specification

Fortran Interface
Subroutine f07uwf ( uplo, diag, n, ap, info)
Integer, Intent (In) :: n
Integer, Intent (Out) :: info
Complex (Kind=nag_wp), Intent (Inout) :: ap(*)
Character (1), Intent (In) :: uplo, diag
C Header Interface
#include <nag.h>
void  f07uwf_ (const char *uplo, const char *diag, const Integer *n, Complex ap[], Integer *info, const Charlen length_uplo, const Charlen length_diag)
The routine may be called by the names f07uwf, nagf_lapacklin_ztptri or its LAPACK name ztptri.

3 Description

f07uwf forms the inverse of a complex triangular matrix A, using packed storage. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.

4 References

Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19

5 Arguments

1: uplo Character(1) Input
On entry: specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: uplo='U' or 'L'.
2: diag Character(1) Input
On entry: indicates whether A is a nonunit or unit triangular matrix.
A is a nonunit triangular matrix.
A is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be 1.
Constraint: diag='N' or 'U'.
3: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
4: ap* Complex (Kind=nag_wp) array Input/Output
Note: the dimension of the array ap must be at least max1,n×n+1/2.
On entry: the n by n triangular matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A must be stored with element Aij in api+jj-1/2 for ij;
  • if uplo='L', the lower triangle of A must be stored with element Aij in api+2n-jj-1/2 for ij.
If diag='U', the diagonal elements of A are assumed to be 1, and are not referenced; the same storage scheme is used whether diag='N' or ‘U’.
On exit: A is overwritten by A-1, using the same storage format as described above.
5: info Integer Output
On exit: info=0 unless the routine detects an error (see Section 6).

6 Error Indicators and Warnings

If info=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.
Element value of the diagonal is exactly zero. A is singular its inverse cannot be computed.

7 Accuracy

The computed inverse X satisfies
XA-IcnεXA ,  
where cn is a modest linear function of n, and ε is the machine precision.
Note that a similar bound for AX-I cannot be guaranteed, although it is almost always satisfied.
The computed inverse satisfies the forward error bound
X-A-1cnεA-1AX .  
See Du Croz and Higham (1992).

8 Parallelism and Performance

f07uwf 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.

9 Further Comments

The total number of real floating-point operations is approximately 43n3.
The real analogue of this routine is f07ujf.

10 Example

This example computes the inverse of the matrix A, where
A= 4.78+4.56i 0.00+0.00i 0.00+0.00i 0.00+0.00i 2.00-0.30i -4.11+1.25i 0.00+0.00i 0.00+0.00i 2.89-1.34i 2.36-4.25i 4.15+0.80i 0.00+0.00i -1.89+1.15i 0.04-3.69i -0.02+0.46i 0.33-0.26i ,  
using packed storage.

10.1 Program Text

Program Text (f07uwfe.f90)

10.2 Program Data

Program Data (f07uwfe.d)

10.3 Program Results

Program Results (f07uwfe.r)