NAG CL Interface
f16ubc (zgb_​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.

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

The Frobenius (or Euclidean) norm.

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

The $\infty$-norm.

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

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

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

3: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of rows of the matrix $A$.

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

4: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of columns of the matrix $A$.

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

5: $\mathbf{kl}$ – Integer Input

On entry: $k_l$, the number of subdiagonals within the band of $A$.

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

6: $\mathbf{ku}$ – Integer Input

On entry: $k_u$, the number of superdiagonals within the band of $A$.

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

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

Note: the dimension, dim, of the array ab must be at least

• $\max \left(1,\mathbf{pdab}\times \mathbf{n}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{m}\times \mathbf{pdab}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $m$ by $n$ band matrix $A$.

This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements $A_{ij}$, for row $i=1,\dots ,m$ and column $j=\max \left(1,i-k_l\right),\dots ,\min \left(n,i+k_u\right)$, depends on the order argument as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[\left(j-1\right)\times \mathbf{pdab}+\mathbf{ku}+i-j\right]$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[\left(i-1\right)\times \mathbf{pdab}+\mathbf{kl}+j-i\right]$.

8: $\mathbf{pdab}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) of the matrix $A$ in the array ab.

Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

9: $\mathbf{r}$ – double * Output

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

10: $\mathbf{fail}$ – 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, $\mathbf{kl}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{kl}\ge 0$.

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

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

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

NE_INT_3

On entry, $\mathbf{pdab}=〈\mathit{\text{value}}〉$, $\mathbf{kl}=〈\mathit{\text{value}}〉$, $\mathbf{ku}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

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