naginterfaces.library.interp.dim2_​scat_​shep_​eval

naginterfaces.library.interp.dim2_scat_shep_eval(x, y, f, iq, rq, u, v)

dim2_scat_shep_eval evaluates the two-dimensional interpolating function generated by dim2_scat_shep() and its first partial derivatives.

For full information please refer to the NAG Library document for e01sh

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/e01/e01shf.html

Parameters

xfloat, array-like, shape $\left(m\right)$

$\text{m}$, $x$, $y$ and $f$ must be the same values as were supplied in the preceding call to dim2_scat_shep().

yfloat, array-like, shape $\left(m\right)$

$\text{m}$, $x$, $y$ and $f$ must be the same values as were supplied in the preceding call to dim2_scat_shep().

ffloat, array-like, shape $\left(m\right)$

$\text{m}$, $x$, $y$ and $f$ must be the same values as were supplied in the preceding call to dim2_scat_shep().

iqint, array-like, shape $(2\times m+1)$

Must be unchanged from the value returned from a previous call to dim2_scat_shep().

rqfloat, array-like, shape $(6\times m+5)$

Must be unchanged from the value returned from a previous call to dim2_scat_shep().

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

The evaluation points $(u_{\text{i}},v_{\text{i}})$, for $\text{i}=1,2,\dots ,n$.

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

The evaluation points $(u_{\text{i}},v_{\text{i}})$, for $\text{i}=1,2,\dots ,n$.

Returns

qfloat, ndarray, shape $\left(n\right)$

The values of the interpolant at $(u_{\text{i}},v_{\text{i}})$, for $\text{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in $q$ are set to an extrapolated approximation, and dim2_scat_shep_eval returns with $errno$ = 3.

qxfloat, ndarray, shape $\left(n\right)$

The values of the partial derivatives of the interpolant $Q(x,y)$ at $(u_{\text{i}},v_{\text{i}})$, for $\text{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in $qx$ and $qy$ are set to extrapolated approximations to the partial derivatives, and dim2_scat_shep_eval returns with $errno$ = 3.

qyfloat, ndarray, shape $\left(n\right)$

The values of the partial derivatives of the interpolant $Q(x,y)$ at $(u_{\text{i}},v_{\text{i}})$, for $\text{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in $qx$ and $qy$ are set to extrapolated approximations to the partial derivatives, and dim2_scat_shep_eval returns with $errno$ = 3.

Raises

NagValueError

(errno $1$)

On entry, $\text{lrq}$ is too small: $\text{lrq}=⟨value⟩$.

(errno $1$)

On entry, $\text{liq}$ is too small: $\text{liq}=⟨value⟩$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 6$.

(errno $2$)

On entry, values in $rq$ appear to be invalid. Check that $rq$ has not been corrupted between calls to dim2_scat_shep() and dim2_scat_shep_eval.

(errno $2$)

On entry, values in $iq$ appear to be invalid. Check that $iq$ has not been corrupted between calls to dim2_scat_shep() and dim2_scat_shep_eval.

Warns

NagAlgorithmicWarning

(errno $3$)

On entry, at least one evaluation point lies outside the region of definition of the interpolant. At such points the corresponding values in $q$ and $qx$ contain extrapolated approximations. Points should be evaluated one by one to identify extrapolated values.

Notes

dim2_scat_shep_eval takes as input the interpolant $Q(x,y)$ of a set of scattered data points $(x_r,y_r,f_r)$, for $\text{r}=1,2,\dots ,m$, as computed by dim2_scat_shep(), and evaluates the interpolant and its first partial derivatives at the set of points $(u_i,v_i)$, for $\text{i}=1,2,\dots ,n$.

dim2_scat_shep_eval must only be called after a call to dim2_scat_shep().

This function is derived from the function QS2GRD described by Renka (1988).

References

Renka, R J, 1988, Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data, ACM Trans. Math. Software (14), 149–150