NAG Library Function Document
nag_ztftri (f07wxc)
1
Purpose
nag_ztftri (f07wxc) computes the inverse of a complex triangular matrix stored in Rectangular Full Packed (RFP) format.
2
Specification
#include <nag.h> |
#include <nagf07.h> |
void |
nag_ztftri (Nag_OrderType order,
Nag_RFP_Store transr,
Nag_UploType uplo,
Nag_DiagType diag,
Integer n,
Complex ar[],
NagError *fail) |
|
3
Description
nag_ztftri (f07wxc) 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 Chapter Introduction.
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
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
5
Arguments
- 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 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint:
or .
- 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.
Constraint:
or .
- 3:
– Nag_UploTypeInput
-
On entry: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
Constraint:
or .
- 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 .
Constraint:
or .
- 5:
– IntegerInput
-
On entry: , the order of the matrix .
Constraint:
.
- 6:
– ComplexInput/Output
-
On entry: the upper or lower triangular part (as specified by
uplo) of the
by
Hermitian 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 .
- 7:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
- NE_INTERNAL_ERROR
-
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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
- NE_SINGULAR
-
Diagonal element of is exactly zero.
is singular its inverse cannot be computed.
7
Accuracy
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
See
Du Croz and Higham (1992).
8
Parallelism and Performance
nag_ztftri (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 .
The real analogue of this function is
nag_dtftri (f07wkc).
10
Example
This example computes the inverse of the matrix
, where
and is stored using RFP format.
10.1
Program Text
Program Text (f07wxce.c)
10.2
Program Data
Program Data (f07wxce.d)
10.3
Program Results
Program Results (f07wxce.r)