The function may be called by the names: f07wxc, nag_lapacklin_ztftri or nag_ztftri.
f07wxc forms the inverse of a complex triangular matrix , stored using RFP format.
The RFP storage format is described in Section 3.4.3 in the F07 Chapter Introduction.
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. Software37, 2
1: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – Nag_RFP_StoreInput
On entry: 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.
3: – Nag_UploTypeInput
On entry: specifies whether is upper or lower triangular.
is upper triangular.
is lower triangular.
4: – Nag_DiagTypeInput
On entry: 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 .
5: – IntegerInput
On entry: , the order of the matrix .
6: – ComplexInput/Output
On entry: the upper or lower triangular part (as specified by uplo) of the Hermitian matrix , in either normal or transposed RFP format (as specified by transr). The storage format is described in detail in Section 3.4.3 in the F07 Chapter Introduction.
On exit: is overwritten by , in the same storage format as .
7: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
Diagonal element of is exactly zero.
is singular its inverse cannot be computed.
The computed inverse satisfies
where is a modest linear function of , and 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
Background information to multithreading can be found in the Multithreading documentation.
f07wxc 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 function. 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 .