naginterfaces.library.sparse.direct_​real_​gen_​norm

naginterfaces.library.sparse.direct_real_gen_norm(norm, n, icolzp, irowix, a)

direct_real_gen_norm computes the $1$-norm, the $\infty$-norm or the maximum absolute value of the elements of a real, square, sparse matrix which is held in compressed column (Harwell–Boeing) format.

For full information please refer to the NAG Library document for f11ml

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f11/f11mlf.html

Parameters

normstr, length 1

Specifies the value to be returned in $anorm$.

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

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

$norm=\text{'I'}$

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

$norm=\text{'M'}$

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

nint

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

icolzpint, array-like, shape $(n+1)$

The new column index array of sparse matrix $A$. See the F11 Introduction.

irowixint, array-like, shape $\left(\text{asize}\right)$

The row index array of sparse matrix $A$. See the F11 Introduction.

afloat, array-like, shape $\left(\text{asize}\right)$

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

Returns

anormfloat

The computed quantity relating the matrix.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $1$)

On entry, $norm=⟨value⟩$.

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

Notes

direct_real_gen_norm computes various quantities relating to norms of a real, sparse $n\times n$ matrix $A$ presented in compressed column (Harwell–Boeing) format.