NAG Library Routine Document

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:     $\mathbf{m}$ – IntegerInput

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:     $\mathbf{n}$ – IntegerInput

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:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) arrayInput

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

On entry: the $m$ by $n$ 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:     $\mathbf{lda}$ – IntegerInput

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

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

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

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

6

Error Indicators and Warnings

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Accuracy

8

Parallelism and Performance

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Further Comments

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Example