NAG Library Routine Document

f16rbf (dgb_norm)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{inorm}$ – IntegerInput

On entry: specifies the value to be returned. The integer codes shown below can be replaced by the equivalent named constants of the form NAG_?_NORM. These named constants are available via the nag_library module and are also used in the example program for clarity.

$\mathbf{inorm}=171$ (NAG_ONE_NORM)

The $1$-norm.

$\mathbf{inorm}=173$ (NAG_TWO_NORM)

The $2$-norm of a row or column vector.

$\mathbf{inorm}=174$ (NAG_FROBENIUS_NORM)

The Frobenius (or Euclidean) norm.

$\mathbf{inorm}=175$ (NAG_INF_NORM)

The $\infty$-norm.

$\mathbf{inorm}=177$ (NAG_MAX_NORM)

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

Constraints:

• $\mathbf{inorm}=171$, $173$, $174$, $175$ or $177$;
• if $\mathbf{inorm}=173$, $\mathbf{m}=1$ or $\mathbf{n}=1$.

2:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $A$. If $\mathbf{m}\le 0$ on input, f16rbf returns $0$.

3:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $A$. If $\mathbf{n}\le 0$ on input, f16rbf returns $0$.

4:     $\mathbf{kl}$ – IntegerInput

On entry: $k_l$, the number of subdiagonals within the band of $A$. If $\mathbf{kl}\le 0$ on input, f16rbf returns $0$.

5:     $\mathbf{ku}$ – IntegerInput

On entry: $k_u$, the number of superdiagonals within the band of $A$. If $\mathbf{ku}\le 0$ on input, f16rbf returns $0$.

6:     $\mathbf{ab}\left(\mathbf{ldab},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array ab must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $m$ 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

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

7:     $\mathbf{ldab}$ – IntegerInput

On entry: the first dimension of the array ab as declared in the (sub)program from which f16rbf is called.

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

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f16rbfe.f90)

10.2

Program Data

Program Data (f16rbfe.d)

10.3

Program Results

Program Results (f16rbfe.r)