naginterfaces.library.blas.dsbmv

naginterfaces.library.blas.dsbmv(uplo, k, alpha, a, x, beta, y=None)

dsbmv computes the matrix-vector product for a real symmetric band matrix.

For full information please refer to the NAG Library document for f06pd

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06pdf.html

Parameters

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 $A$.

alphafloat

The scalar $\alpha$.

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

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

xfloat, array-like, shape $\left(n\right)$

The $n$-element vector $x$.

betafloat

The scalar $\beta$.

yNone or float, array-like, shape $\left(n\right)$, optional

The $n$-element vector $y$, if $beta=0.0$ $y$ need not be set.

Returns

yfloat, ndarray, shape $\left(n\right)$

The updated vector $y$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $uplo$.

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

(errno $2$)

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

Constraint: $n\ge 0$.

(errno $3$)

On entry, error in parameter $k$.

Constraint: $k\ge 0$.

(errno $8$)

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

Constraint: $\text{incx}\ne 0$.

(errno $11$)

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

Constraint: $\text{incy}\ne 0$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

dsbmv performs the matrix-vector operation

$$y\leftarrow \alpha Ax+\beta y\text{,}$$

where $A$ is an $n\times n$ real symmetric band matrix with $k$ subdiagonals and $k$ superdiagonals, $x$ and $y$ are $n$-element real vectors, and $\alpha$ and $\beta$ are real scalars.