naginterfaces.library.blas.dzssq

naginterfaces.library.blas.dzssq(x, scal, sumsq)

dzssq updates the Euclidean norm of complex vector in scaled form.

For full information please refer to the NAG Library document for f06kj

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06kjf.html

Parameters

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

The $n$-element vector $x$.

scalfloat

The scaling factor $\alpha$. On the first call to dzssq $scal=0.0$.

sumsqfloat

The scaled sum of squares $\xi$. On the first call to dzssq $sumsq=1.0$.

Returns

scalfloat

The updated scaling factor $\tilde{\alpha }={max}_i(\alpha ,\left|Re\left(x_i\right)\right|,\left|Im\left(x_i\right)\right|)$.

sumsqfloat

The updated scaled sum of squares $\tilde{\xi }$, satisfying: $1\le \tilde{\xi }\le \xi +2n$.

Raises

NagValueError

(errno $3$)

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

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

(errno $4$)

On entry, error in parameter $scal$.

Constraint: $scal\ge 0$.

(errno $5$)

On entry, error in parameter $sumsq$.

Constraint: $sumsq\ge 1$.

Notes

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

Given an $n$-element complex vector $x$, and real scalars $\alpha$ and $\xi$, dzssq returns updated values $\tilde{\alpha }$ and $\tilde{\xi }$ such that

$${\tilde{\alpha }}^2\tilde{\xi }={\left|x_1\right|}^2+{\left|x_2\right|}^2+\cdots +{\left|x_n\right|}^2+{\alpha }^2\xi \text{.}$$

dzssq is designed for use in the safe computation of the Euclidean norm of a complex vector, without unnecessary overflow or destructive underflow. An initial call to dzssq (with $\xi =1$ and $\alpha =0$) may be followed by further calls to dzssq and finally a call to dnorm() to complete the computation. Multiple calls of dzssq may be needed if the elements of the vector cannot all be accessed in a single array $x$.