naginterfaces.library.dot.complex_​prec

naginterfaces.library.dot.complex_prec(a, b, cx, sw)

complex_prec calculates the value of a complex scalar product using basic precision or additional precision and adds it to a complex initial value.

For full information please refer to the NAG Library document for x03ab

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/x03/x03abf.html

Parameters

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

The elements of the first vector.

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

The elements of the second vector.

cxcomplex

The initial value $c$.

swbool

The precision to be used in the calculation.

$sw=True$

additional precision.

$sw=False$

basic precision.

Returns

dxcomplex

The result $d$.

Raises

NagValueError

(errno $1$)

On entry, $\text{istepb}=⟨value⟩$.

Constraint: $\text{istepb}>0$.

(errno $1$)

On entry, $\text{istepa}=⟨value⟩$.

Constraint: $\text{istepa}>0$.

(errno $2$)

On entry, $\text{isizeb}=⟨value⟩$, $n=⟨value⟩$ and $\text{istepb}=⟨value⟩$.

Constraint: $\text{isizeb}\ge (n-1)\times \text{istepb}+1$.

(errno $2$)

On entry, $\text{isizea}=⟨value⟩$, $n=⟨value⟩$ and $\text{istepa}=⟨value⟩$.

Constraint: $\text{isizea}\ge (n-1)\times \text{istepa}+1$.

Notes

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

complex_prec calculates the scalar product of two complex vectors and adds it to an initial value $c$ to give a correctly rounded result $d$:

$$d=c+\sum _{i=1}^n{a}_i{b}_i\text{.}$$

If $n<1$, $d=c$.

The vector elements $a_i$ and $b_i$ are stored in selected elements of the one-dimensional array arguments $a$ and $b$.

The products are accumulated in basic precision or additional precision depending on the argument $sw$.

This function has been designed primarily for use as an auxiliary function by other functions in the NAG Library, especially those in the modules on Linear Algebra.