naginterfaces.library.blast.zamin_​val

naginterfaces.library.blast.zamin_val(x)

zamin_val computes, with respect to absolute value, the smallest component of a complex vector, along with the index of that component.

For full information please refer to the NAG Library document for f16jt

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f16/f16jtf.html

Parameters

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.

Returns

kint

Note: this argument represents an array index; the value returned will be base-1.

$k$, the index, from the set $\{1,2,\dots ,n\}$, of the smallest component of $x$ with respect to absolute value. If $n\le 0$ on input then $k$ is returned as $0$.

rfloat

$r$, the smallest component of $x$ with respect to absolute value. If $n\le 0$ on input then $r$ is returned as $0.0$.

Raises

NagValueError

(errno $-3$)

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

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

Notes

zamin_val computes, with respect to absolute value, the smallest component, $r$, of an $n$-element complex vector $x$, and determines the smallest index, $k$, such that

$$r=\left|Re\left(x_k\right)\right|+\left|Im\left(x_k\right)\right|={min}_j\left|Re\left(x_j\right)\right|+\left|Im\left(x_j\right)\right|\text{.}$$

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