The routine may be called by the names f07wkf, nagf_lapacklin_dtftri or its LAPACK name dtftri.
f07wkf forms the inverse of a real triangular matrix , stored using RFP format.
The RFP storage format is described in Section 3.3.3 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: – Character(1)Input
On entry: specifies whether the RFP representation of is normal or transposed.
The matrix is stored in normal RFP format.
The matrix is stored in transposed RFP format.
2: – Character(1)Input
On entry: specifies whether is upper or lower triangular.
is upper triangular.
is lower triangular.
3: – Character(1)Input
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 .
4: – IntegerInput
On entry: , the order of the matrix .
5: – Real (Kind=nag_wp) arrayInput/Output
On entry: the upper or lower triangular part (as specified by uplo) of the symmetric matrix , 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 Chapter Introduction.
On exit: is overwritten by , in the same storage format as .
6: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error 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 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
f07wkf 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 floating-point operations is approximately .