NAG Library Routine Document
F07WXF (ZTFTRI) computes the inverse of a complex triangular matrix stored in Rectangular Full Packed (RFP) format.
The RFP storage format is described in Section 3.3.3
in the F07 Chapter Introduction.
||TRANSR, UPLO, DIAG|
The routine may be called by its
F07WXF (ZTFTRI) forms the inverse of a complex triangular matrix , stored using RFP format. 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
- 1: TRANSR – CHARACTER(1)Input
: 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.
- 2: UPLO – CHARACTER(1)Input
: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
- 3: 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 .
- 4: N – INTEGERInput
On entry: , the order of the matrix .
- 5: A() – COMPLEX (KIND=nag_wp) arrayInput/Output
On entry: the by triangular matrix , stored in RFP format.
On exit: is overwritten by , in the same storage format as .
- 6: 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 real floating point operations is approximately .
The real analogue of this routine is F07WKF (DTFTRI)
This example computes the inverse of the matrix
and is stored using RFP format.
9.1 Program Text
Program Text (f07wxfe.f90)
9.2 Program Data
Program Data (f07wxfe.d)
9.3 Program Results
Program Results (f07wxfe.r)