NAG FL Interface
f07wxf computes the inverse of a complex triangular matrix stored in Rectangular Full Packed (RFP) format.
|Integer, Intent (In)
|Integer, Intent (Out)
|Complex (Kind=nag_wp), Intent (Inout)
|Character (1), Intent (In)
||transr, uplo, diag
The routine may be called by the names f07wxf, nagf_lapacklin_ztftri or its LAPACK name ztftri.
forms the inverse of a complex triangular matrix
, stored using RFP format.
The RFP storage format is described in Section 3.3.3
in the F07
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
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2
: specifies whether the normal RFP representation of
or its conjugate transpose is stored.
- The matrix is stored in normal RFP format.
- The conjugate transpose of the RFP representation of the matrix is stored.
: 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 .
– Complex (Kind=nag_wp) array
: the upper or lower triangular part (as specified by uplo
) of the
, in either normal or transposed RFP format (as specified by transr
). The storage format is described in detail in Section 3.3.3
in the F07
On exit: is overwritten by , in the same storage format as .
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.
Diagonal element of 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
f07wxf 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 real floating-point operations is approximately .
The real analogue of this routine is f07wkf
This example computes the inverse of the matrix
and is stored using RFP format.