NAG FL Interface
f06ref (dlansb)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{norm}$ – Character(1) Input

On entry: specifies the value to be returned.

$\mathbf{norm}=\text{'1'}$ or $\text{'O'}$

The $1$-norm.

$\mathbf{norm}=\text{'I'}$

The $\infty$-norm (= the $1$-norm for a symmetric matrix).

$\mathbf{norm}=\text{'F'}$ or $\text{'E'}$

The Frobenius (or Euclidean) norm.

$\mathbf{norm}=\text{'M'}$

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

Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.

2: $\mathbf{uplo}$ – Character(1) Input

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

$\mathbf{uplo}=\text{'U'}$

The upper triangular part of $A$ is stored.

$\mathbf{uplo}=\text{'L'}$

The lower triangular part of $A$ is stored.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

3: $\mathbf{n}$ – Integer Input

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

When $\mathbf{n}=0$, f06ref returns zero.

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

4: $\mathbf{k}$ – Integer Input

On entry: $k$, the number of subdiagonals or superdiagonals of the matrix $A$.

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

5: $\mathbf{ab}(\mathbf{ldab},*)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array ab must be at least $\mathbf{n}$.

On entry: the $n\times n$ symmetric band matrix $A$.

The matrix is stored in rows $1$ to $k+1$, more precisely,

• if $\mathbf{uplo}=\text{'U'}$, the elements of the upper triangle of $A$ within the band must be stored with element $A_{ij}$ in $\mathbf{ab}(k+1+i-j,j)\text{ for }\max (1,j-k)\le i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the elements of the lower triangle of $A$ within the band must be stored with element $A_{ij}$ in $\mathbf{ab}(1+i-j,j)\text{ for }j\le i\le \min (n,j+k)\text{.}$

6: $\mathbf{ldab}$ – Integer Input

On entry: the first dimension of the array ab as declared in the (sub)program from which f06ref is called.

Constraint: $\mathbf{ldab}\ge \mathbf{k}+1$.

7: $\mathbf{work}\left(*\right)$ – Real (Kind=nag_wp) array Workspace

Note: the dimension of the array work must be at least $\max (1,\mathbf{n})$ if $\mathbf{norm}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$, and at least $1$ otherwise.

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example