naginterfaces.library.blast.zaxpby

naginterfaces.library.blast.zaxpby(alpha, x, beta, y)

zaxpby computes the sum of two scaled vectors, for complex scalars and vectors.

For full information please refer to the NAG Library document for f16gc

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f16/f16gcf.html

Parameters

alphacomplex

The scalar $\alpha$.

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

The $n$-element vector $x$.

If $\text{incx}<0$, $x_{\text{i}}$ must be stored in $x[(n-\text{i})\times \left|\text{incx}\right|]$, for $\text{i}=1,2,\dots ,n$.

If $n=0$, $x$ is not referenced.

betacomplex

The scalar $\beta$.

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

The $n$-element vector $y$.

If $\text{incy}>0$, $y_{\text{i}}$ must be stored in $y[(\text{i}-1)\times \text{incy}]$, for $\text{i}=1,2,\dots ,n$.

If $\text{incy}<0$, $y_{\text{i}}$ must be stored in $y[(n-\text{i})\times \left|\text{incy}\right|]$, for $\text{i}=1,2,\dots ,n$.

Intermediate elements of $y$ are not referenced.

Returns

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

The updated vector $y$ stored in the array elements used to supply the original vector $y$.

Intermediate elements of $y$ are unchanged.

Raises

NagValueError

(errno $-4$)

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

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

(errno $-7$)

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

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

Notes

zaxpby performs the operation

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

where $x$ and $y$ are $n$-element complex vectors, and $\alpha$ and $\beta$ are complex scalars. If $n$ is less than or equal to zero, or if $\alpha$ is equal to zero and $\beta$ is equal to $1$, this function returns immediately.

References

Basic Linear Algebra Subprograms Technical (BLAST) Forum, 2001, Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard, University of Tennessee, Knoxville, Tennessee, https://www.netlib.org/blas/blast-forum/blas-report.pdf