NAG Toolbox: nag_blast_dgb_norm (f16rb)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies the value to be returned.

$\mathbf{job}=\text{'O'}$

The $1$-norm.

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

The $2$-norm of a row or column vector.

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

The $\infty$-norm.

$\mathbf{job}=\text{'F'}$

The Frobenius (or Euclidean) norm.

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

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

Constraints:

• $\mathbf{job}=\text{'O'}$, $\text{'T'}$, $\text{'I'}$, $\text{'F'}$ or $\text{'M'}$;
• if $\mathbf{job}=\text{'T'}$, $\mathbf{m}=1$ or $\mathbf{n}=1$.

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

$m$, the number of rows of the matrix $A$. If $\mathbf{m}\le 0$ on input, nag_blast_dgb_norm (f16rb) returns $0$.

3:     $\mathrm{kl}$ – int64int32nag_int scalar

$k_l$, the number of subdiagonals within the band of $A$. If $\mathbf{kl}\le 0$ on input, nag_blast_dgb_norm (f16rb) returns $0$.

4:     $\mathrm{ku}$ – int64int32nag_int scalar

$k_u$, the number of superdiagonals within the band of $A$. If $\mathbf{ku}\le 0$ on input, nag_blast_dgb_norm (f16rb) returns $0$.

5:     $\mathrm{ab}\left(\mathit{ldab},:\right)$ – double array

The first dimension of the array ab must be at least $\mathbf{kl}+\mathbf{ku}+1$.

The second dimension of the array ab must be at least $\max \left(1,\mathbf{n}\right)$.

The $m$ by $n$ band matrix $A$.

The matrix is stored in rows $1$ to $k_l+k_u+1$, more precisely, the element $A_{ij}$ must be stored in

$$\mathbf{ab}\left(k_u+1+i-j,j\right)\text{\hspace{1em} for }\max \left(1,j-k_u\right)\le i\le \min \left(m,j+k_l\right)\text{.}$$

Optional Input Parameters

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

Default: the second dimension of the array ab.

$n$, the number of columns of the matrix $A$. If $\mathbf{n}\le 0$ on input, nag_blast_dgb_norm (f16rb) returns $0$.

Output Parameters

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

The result of the function.

Error Indicators and Warnings

Accuracy

Further Comments

Example

Open in the MATLAB editor: f16rb_example

function f16rb_example


fprintf('f16rb example results\n\n');

kl = int64(2);
ku = int64(2);
m  = int64(6);
a = [ 1, 1, 0, 0;
      2, 2, 2, 0;
      3, 3, 3, 3;
      0, 4, 4, 4;
      0, 0, 5, 5;
      0, 0, 0, 6];
ab = zeros(5, 6);
% Convert a to packed storage
[a, ab, ifail] = f01zc( ...
			'p', kl, ku, a, ab);

fprintf('\nNorms of banded matrix ab:\n\n');

r_one = f16rb('o', m, kl, ku, ab);
fprintf('One norm           = %9.4f\n', r_one);

r_inf = f16rb('i', m, kl, ku, ab);
fprintf('Infinity norm      = %9.4f\n', r_inf);

r_fro = f16rb('f', m, kl, ku, ab);
fprintf('Frobenious norm    = %9.4f\n', r_fro);

r_max = f16rb('m', m, kl, ku, ab);
fprintf('Maximum norm       = %9.4f\n', r_max);

f16rb example results


Norms of banded matrix ab:

One norm           =   18.0000
Infinity norm      =   12.0000
Frobenious norm    =   13.5647
Maximum norm       =    6.0000