naginterfaces.library.blas.zgbmv

naginterfaces.library.blas.zgbmv(trans, m, kl, ku, alpha, a, x, beta, y=None)

zgbmv computes the matrix-vector product for a complex general band matrix, its transpose or its conjugate transpose.

For full information please refer to the NAG Library document for f06sb

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06sbf.html

Parameters

transstr, length 1

Specifies the operation to be performed.

$trans=\text{'N'}$

$y\leftarrow \alpha Ax+\beta y$.

$trans=\text{'T'}$

$y\leftarrow \alpha A^{T}x+\beta y$.

$trans=\text{'C'}$

$y\leftarrow \alpha A^{H}x+\beta y$.

mint

$m$, the number of rows of the matrix $A$.

klint

$k_l$, the number of subdiagonals within the band of $A$.

kuint

$k_u$, the number of superdiagonals within the band of $A$.

alphacomplex

The scalar $\alpha$.

acomplex, array-like, shape $(kl+ku+1,n)$

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

xcomplex, array-like, shape $(:)$

Note: the required length for this argument is determined as follows: if $trans=\text{'N'}$: $n$; if $trans\text{in}(\text{'T'},\text{'C'})$: $m$; otherwise: $0$.

The vector $x$.

betacomplex

The scalar $\beta$.

yNone or complex, array-like, shape $(:)$, optional

Note: the required length for this argument is determined as follows: if $trans=\text{'N'}$: $m$; if $trans\text{in}(\text{'T'},\text{'C'})$: $n$; otherwise: $0$.

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

Returns

ycomplex, ndarray, shape $(:)$

The updated vector $y$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $trans$.

Constraint: $trans=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $2$)

On entry, error in parameter $m$.

Constraint: $m\ge 0$.

(errno $3$)

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

Constraint: $n\ge 0$.

(errno $4$)

On entry, error in parameter $kl$.

Constraint: $kl\ge 0$.

(errno $5$)

On entry, error in parameter $ku$.

Constraint: $ku\ge 0$.

(errno $10$)

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

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

(errno $13$)

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.

zgbmv performs one of the matrix-vector operations

$$y\leftarrow \alpha Ax+\beta y\text{,}y\leftarrow \alpha A^{T}x+\beta y\text{or}y\leftarrow \alpha A^{H}x+\beta y\text{,}$$

where $A$ is an $m\times n$ complex band matrix with $k_l$ subdiagonals and $k_u$ superdiagonals, $x$ and $y$ are complex vectors, and $\alpha$ and $\beta$ are complex scalars.

If $m=0$ or $n=0$, no operation is performed.