naginterfaces.library.blast.ddot

naginterfaces.library.blast.ddot(conj, alpha, x, beta, y, r)

ddot updates a scalar by a scaled dot product of two real vectors.

For full information please refer to the NAG Library document for f16ea

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f16/f16eaf.html

Parameters

conjint

$conj$ is not referenced and need not be set. The presence of this argument in the BLAST standard is for consistency with the interface of the complex variant of this function.

alphafloat

The scalar $\alpha$.

xfloat, 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 $\alpha =0.0$ or $n=0$, $x$ is not referenced.

betafloat

The scalar $\beta$.

yfloat, 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.

If $\alpha =0.0$ or $n=0$, $y$ is not referenced.

rfloat

The initial value, $r$, to be updated. If $\beta =0.0$, $r$ need not be set on entry.

Returns

rfloat

The value $r$, scaled by $\beta$ and updated by the scaled dot product of $x$ and $y$.

Raises

NagValueError

(errno $-5$)

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

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

(errno $-8$)

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

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

Notes

ddot performs the operation

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

where $x$ and $y$ are $n$-element real vectors, and $r$, $\alpha$ and $\beta$ real scalars. If $n$ is less than zero, or, if $\beta$ is equal to one and either $\alpha$ or $n$ is equal to zero, 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