naginterfaces.library.blas.dlansb

naginterfaces.library.blas.dlansb(norm, uplo, k, ab)

dlansb returns the value of the $1$-norm, the $\infty$-norm, the Frobenius norm, or the maximum absolute value of the elements of a real $n\times n$ symmetric band matrix.

For full information please refer to the NAG Library document for f06re

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06ref.html

Parameters

normstr, length 1

Specifies the value to be returned.

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

The $1$-norm.

$norm=\text{'I'}$

The $\infty$-norm (= the $1$-norm for a symmetric matrix).

$norm=\text{'F'}$ or $\text{'E'}$

The Frobenius (or Euclidean) norm.

$norm=\text{'M'}$

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

uplostr, length 1

Specifies whether the upper or lower triangular part of $A$ is stored.

$uplo=\text{'U'}$

The upper triangular part of $A$ is stored.

$uplo=\text{'L'}$

The lower triangular part of $A$ is stored.

kint

$k$, the number of subdiagonals or superdiagonals of the matrix $A$.

abfloat, array-like, shape $(k+1,n)$

The $n\times n$ symmetric band matrix $A$.

Returns

nrmfloat

The value of the $1$-norm, the $\infty$-norm, the Frobenius norm, or the maximum absolute value of the elements of the real $n\times n$ symmetric band matrix.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $norm$.

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

(errno $2$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $3$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $4$)

On entry, error in parameter $k$.

Constraint: $k\ge 0$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.