NAG CL Interface
f16ugc (zsp_​norm)

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: $\mathbf{norm}$ – Nag_NormType Input

On entry: specifies the value to be returned.

$\mathbf{norm}=\mathrm{Nag\_OneNorm}$

The $1$-norm.

$\mathbf{norm}=\mathrm{Nag\_InfNorm}$

The $\infty$-norm.

$\mathbf{norm}=\mathrm{Nag\_FrobeniusNorm}$

The Frobenius (or Euclidean) norm.

$\mathbf{norm}=\mathrm{Nag\_MaxNorm}$

The value ${\displaystyle \underset{i,j}{\max }}\left|a_{ij}\right|$ (not a norm).

Constraint: $\mathbf{norm}=\mathrm{Nag\_OneNorm}$, $\mathrm{Nag\_InfNorm}$, $\mathrm{Nag\_FrobeniusNorm}$ or $\mathrm{Nag\_MaxNorm}$.

3: $\mathbf{uplo}$ – Nag_UploType Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored.

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

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

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

4: $\mathbf{n}$ – Integer Input

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

If $n=0$, n is set to zero.

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

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

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

On entry: the $n\times n$ symmetric 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 $\mathbf{ap}\left[(j-1)\times j/2+i-1\right]$, for $i\le j$;

if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,

$A_{ij}$ is stored in $\mathbf{ap}\left[(2n-j)\times (j-1)/2+i-1\right]$, for $i\ge j$;

if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,

$A_{ij}$ is stored in $\mathbf{ap}\left[(2n-i)\times (i-1)/2+j-1\right]$, for $i\le j$;

if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,

$A_{ij}$ is stored in $\mathbf{ap}\left[(i-1)\times i/2+j-1\right]$, for $i\ge j$.

6: $\mathbf{r}$ – double * Output

On exit: the value of the norm specified by norm.

7: $\mathbf{fail}$ – 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_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