NAG Toolbox: nag_sparse_direct_real_gen_norm (f11ml)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{norm\_p}$ – string (length ≥ 1)

Specifies the value to be returned in anorm.

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

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

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

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

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

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

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

2:     $\mathrm{n}$ – int64int32nag_int scalar

$n$, the order of the matrix $A$.

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

3:     $\mathrm{icolzp}\left(:\right)$ – int64int32nag_int array

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

$\mathbf{icolzp}\left(i\right)$ contains the index in $A$ of the start of a new column. See Compressed column storage (CCS) format in the F11 Chapter Introduction.

4:     $\mathrm{irowix}\left(:\right)$ – int64int32nag_int array

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 $A$

The row index array of sparse matrix $A$.

5:     $\mathrm{a}\left(:\right)$ – double array

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 $A$

The array of nonzero values in the sparse matrix $A$.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{anorm}$ – double scalar

The computed quantity relating the matrix.

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

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

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

   $\mathbf{ifail}=-99$

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

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f11ml_example

function f11ml_example


fprintf('f11ml example results\n\n');

% Norms of sparse A
n      = int64(5);
icolzp = [int64(1); 3; 5;  7; 9; 12];
irowix = [int64(1); 3; 1;  5; 2;  3;  2; 4; 3; 4; 5];
a      = [        2;  4; 1; -2; 1;  1; -1; 1; 1; 2; 3];

% Calculate 1-norm
norm_p = '1';
[anorm, ifail] = f11ml( ...
                        norm_p, n, icolzp, irowix, a);
fprintf('One-norm      = %7.3f\n', anorm);

% Calculate Maximum
norm_p = 'M';
[anorm, ifail] = f11ml( ...
                        norm_p, n, icolzp, irowix, a);
fprintf('Max           = %7.3f\n', anorm);

% Calculate I-norm
norm_p = 'I';
[anorm, ifail] = f11ml( ...
                        norm_p, n, icolzp, irowix, a);
fprintf('Infinity-norm = %7.3f\n', anorm);

f11ml example results

One-norm      =   6.000
Max           =   4.000
Infinity-norm =   6.000