NAG FL Interface
f06rjf (dlantr)

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.

$\mathbf{norm}=\text{'F'}$ 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: $\mathbf{uplo}$ – Character(1) Input

On entry: specifies whether $A$ is upper or lower trapezoidal.

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

$A$ is upper trapezoidal.

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

$A$ is lower trapezoidal.

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

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

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\text{'N'}$

The diagonal elements are stored explicitly.

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

The diagonal elements are assumed to be $1$, and are not referenced.

Constraint: $\mathbf{diag}=\text{'N'}$ or $\text{'U'}$.

4: $\mathbf{m}$ – Integer Input

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

When $\mathbf{m}=0$, f06rjf is set to zero.

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

5: $\mathbf{n}$ – Integer Input

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

When $\mathbf{n}=0$, f06rjf is set to zero.

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

6: $\mathbf{a}(\mathbf{lda},*)$ – Real (Kind=nag_wp) array Input

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

On entry: the $m\times n$ trapezoidal matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$, $A$ is upper trapezoidal and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, $A$ is lower trapezoidal and the elements of the array above the diagonal are not referenced.
• If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

7: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f06rjf is called.

Constraint: $\mathbf{lda}\ge \max (1,\mathbf{m})$.

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

Note: the dimension of the array work must be at least $\max (1,\mathbf{m},\mathbf{n})$ 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