naginterfaces.library.numdiff.sample

naginterfaces.library.numdiff.sample(x_0, hbase)

sample generates abscissae about a target abscissa $x_0$ for use in a subsequent call to rcomm().

For full information please refer to the NAG Library document for d04bb

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d04/d04bbf.html

Parameters

x_0float

The abscissa $x_0$ at which derivatives are required.

hbasefloat

The chosen step size $h$. If $h<10ϵ$, where $ϵ=\text{machine.precision}\left(\right)$, the default $h={ϵ}^{\left(1/4\right)}$ will be used.

Returns

xvalfloat, ndarray, shape $\left(21\right)$

The abscissae for passing to rcomm().

Notes

sample may be used to generate the necessary abscissae about a target abscissa $x_0$ for the calculation of derivatives using rcomm().

For a given $x_0$ and $h$, the abscissae correspond to the set $\{x_0,x_0\pm (2\text{j}-1)h\}$, for $\text{j}=1,2,\dots ,10$. These $21$ points will be returned in ascending order in $xval$. In particular, $xval\left[10\right]$ will be equal to $x_0$.

References

Lyness, J N and Moler, C B, 1969, Generalised Romberg methods for integrals of derivatives, Numer. Math. (14), 1–14