NAG Library Function Document

nag_zpftri (f07wwc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – 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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. 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: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{transr}$ – Nag_RFP_StoreInput

On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

$\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$

The matrix $A$ is stored in normal RFP format.

$\mathbf{transr}=\mathrm{Nag\_RFP\_ConjTrans}$

The conjugate transpose of the RFP representation of the matrix $A$ is stored.

Constraint: $\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$ or $\mathrm{Nag\_RFP\_ConjTrans}$.

3:    $\mathbf{uplo}$ – Nag_UploTypeInput

On entry: specifies how $A$ has been factorized.

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

$A=U^{\mathrm{H}}U$, where $U$ is upper triangular.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

$A=L{L}^{\mathrm{H}}$, where $L$ is lower triangular.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

5:    $\mathbf{ar}\left[\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right]$ – ComplexInput/Output

On entry: the Cholesky factorization of $A$ stored in RFP format, as returned by nag_zpftrf (f07wrc).

On exit: the factorization is overwritten by the $n$ by $n$ matrix $A^{-1}$ stored in RFP format.

6:    $\mathbf{fail}$ – 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 $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

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_MAT_NOT_POS_DEF

The leading minor of order $〈\mathit{\text{value}}〉$ is not positive definite and the factorization could not be completed. Hence $A$ itself is not positive definite. This may indicate an error in forming the matrix $A$. There is no function specifically designed to invert a Hermitian matrix stored in RFP format which is not positive definite; the matrix must be treated as a full Hermitian matrix, by calling nag_zhetri (f07mwc).

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07wwce.c)

10.2

Program Data

Program Data (f07wwce.d)

10.3

Program Results

Program Results (f07wwce.r)