NAG CL Interface
f07gtc (zppequ)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

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 3.1.3 in the Introduction to the NAG Library CL Interface 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_UploType Input

On entry: indicates whether the upper or lower triangular part of $A$ is stored in the array ap, as follows:

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

The upper triangle of $A$ is stored.

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

The lower triangle of $A$ is stored.

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

3: $\mathbf{n}$ – Integer Input

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

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

4: $\mathbf{ap}\left[\mathit{dim}\right]$ – const Complex Input

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 $n$ Hermitian 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 $i\ge j$.

Only the elements of ap corresponding to the diagonal elements $A$ are referenced.

5: $\mathbf{s}\left[\mathbf{n}\right]$ – double Output

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, s contains the diagonal elements of the scaling matrix $S$.

6: $\mathbf{scond}$ – double * Output

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, scond contains the ratio of the smallest value of s to the largest value of s. If $\mathbf{scond}\ge 0.1$ and amax is neither too large nor too small, it is not worth scaling by $S$.

7: $\mathbf{amax}$ – double * Output

On exit: $\max \left|a_{ij}\right|$. If amax is very close to overflow or underflow, the matrix $A$ should be scaled.

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

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_MAT_NOT_POS_DEF

The $〈\mathit{\text{value}}〉$th diagonal element of $A$ is not positive (and hence $A$ cannot be positive definite).

NE_NO_LICENCE

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.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results