NAG Library Routine Document

F06RBF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{NORM}$ – 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.

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

The Frobenius (or Euclidean) norm.

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

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

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

2:     $\mathrm{N}$ – INTEGERInput

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

When $\mathbf{N}=0$, F06RBF returns zero.

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

3:     $\mathrm{KL}$ – INTEGERInput

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

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

4:     $\mathrm{KU}$ – INTEGERInput

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

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

5:     $\mathrm{AB}\left(\mathbf{LDAB},*\right)$ – REAL (KIND=nag_wp) arrayInput

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

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

The matrix is stored in rows $1$ to $k_l+k_u+1$, more precisely, the element $A_{ij}$ must be stored in

$$\mathbf{AB}\left(k_u+1+i-j,j\right)\text{\hspace{1em} for }\max \left(1,j-k_u\right)\le i\le \min \left(n,j+k_l\right)\text{.}$$

6:     $\mathrm{LDAB}$ – INTEGERInput

On entry: the first dimension of the array AB as declared in the (sub)program from which F06RBF is called.

Constraint: $\mathbf{LDAB}\ge \mathbf{KL}+\mathbf{KU}+1$.

7:     $\mathrm{WORK}\left(*\right)$ – REAL (KIND=nag_wp) arrayWorkspace

Note: the dimension of the array WORK must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{NORM}=\text{'I'}$, and at least $1$ otherwise.

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example