NAG Library Routine Document

f11mlf (direct_real_gen_norm)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

On entry: specifies the value to be returned in anorm.

$\mathbf{norm}=\text{'1'}$ or $\text{'O'}$

The $1$-norm ${‖A‖}_1$ of the matrix is computed, that is ${\displaystyle \underset{1\le j\le n}{\max }}{\displaystyle \sum _{i=1}^n}\left|A_{ij}\right|$.

$\mathbf{norm}=\text{'I'}$

The $\infty$-norm ${‖A‖}_{\infty }$ of the matrix is computed, that is ${\displaystyle \underset{1\le i\le n}{\max }}{\displaystyle \sum _{j=1}^n}\left|A_{ij}\right|$.

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

The value ${\displaystyle \underset{1\le i,j\le n}{\max }}\left|A_{ij}\right|$ (not a norm).

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

2:     $\mathbf{anorm}$ – Real (Kind=nag_wp)Output

On exit: the computed quantity relating the matrix.

3:     $\mathbf{n}$ – IntegerInput

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

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

4:     $\mathbf{icolzp}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array icolzp must be at least $\mathbf{n}+1$.

On entry: $\mathbf{icolzp}\left(i\right)$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the F11 Chapter Introduction.

5:     $\mathbf{irowix}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array irowix must be at least $\mathbf{icolzp}\left(\mathbf{n}+1\right)-1$, the number of nonzeros of the sparse matrix $A$.

On entry: the row index array of sparse matrix $A$.

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

Note: the dimension of the array a must be at least $\mathbf{icolzp}\left(\mathbf{n}+1\right)-1$, the number of nonzeros of the sparse matrix $A$.

On entry: the array of nonzero values in the sparse matrix $A$.

7:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{norm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$ or $\text{'M'}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11mlfe.f90)

10.2

Program Data

Program Data (f11mlfe.d)

10.3

Program Results

Program Results (f11mlfe.r)