NAG Library Routine Document

f06waf (dlansf)

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

On entry: specifies whether the RFP representation of $A$ is normal or transposed.

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

The matrix $A$ is stored in normal RFP format.

$\mathbf{transr}=\text{'T'}$

The matrix $A$ is stored in transposed RFP format.

Constraint: $\mathbf{transr}=\text{'N'}$ or $\text{'T'}$.

3:     $\mathbf{uplo}$ – 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 $\text{'L'}$.

4:     $\mathbf{n}$ – IntegerInput

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

When $\mathbf{n}=0$, f06waf (dlansf) returns zero.

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

5:     $\mathbf{a}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the upper or lower triangular part (as specified by uplo) of the $n$ by $n$ symmetric matrix $A$, in either normal or transposed RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction.

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

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

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f06wafe.f90)

10.2

Program Data

Program Data (f06wafe.d)

10.3

Program Results

Program Results (f06wafe.r)