NAG Library Function Document

nag_ztptri (f07uwc)

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 2.3.1.3 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:    $\mathbf{uplo}$ – Nag_UploTypeInput

On entry: specifies whether $A$ is upper or lower triangular.

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

$A$ is upper triangular.

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

$A$ is lower triangular.

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

3:    $\mathbf{diag}$ – Nag_DiagTypeInput

On entry: indicates whether $A$ is a nonunit or unit triangular matrix.

$\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$

$A$ is a nonunit triangular matrix.

$\mathbf{diag}=\mathrm{Nag\_UnitDiag}$

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

Constraint: $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathrm{Nag\_UnitDiag}$.

4:    $\mathbf{n}$ – IntegerInput

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

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

5:    $\mathbf{ap}\left[\mathit{dim}\right]$ – ComplexInput/Output

Note: the dimension, dim, of the array ap must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$.

On entry: the $n$ by $n$ triangular matrix $A$, packed by rows or columns.

The storage of elements $A_{ij}$ depends on the order and uplo arguments as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(j-1\right)\times j/2+i-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(2n-j\right)\times \left(j-1\right)/2+i-1\right]$, for $i\ge j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(2n-i\right)\times \left(i-1\right)/2+j-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(i-1\right)\times i/2+j-1\right]$, for $i\ge j$.

If $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$, the diagonal elements of $\mathrm{AP}$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$.

On exit: $A$ is overwritten by $A^{-1}$, using the same storage format as described above.

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 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.

An unexpected error has been triggered by this function. Please contact NAG.
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

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero. $A$ is singular its inverse cannot be computed.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f07uwce.c)

10.2  Program Data

Program Data (f07uwce.d)

10.3  Program Results

Program Results (f07uwce.r)