naginterfaces.library.interp.dim4_​scat_​shep_​eval

naginterfaces.library.interp.dim4_scat_shep_eval(x, f, iq, rq, xe)

dim4_scat_shep_eval evaluates the four-dimensional interpolating function generated by dim4_scat_shep() and its first partial derivatives.

For full information please refer to the NAG Library document for e01tl

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/e01/e01tlf.html

Parameters

xfloat, array-like, shape $(4,m)$

Note: the coordinates of $x_r$ are stored in $x[0,r-1]\dots x[3,r-1]$.

Must be the same array supplied as argument $\text{x}$ in the preceding call to dim4_scat_shep(). It must remain unchanged between calls.

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

Must be the same array supplied as argument $\text{f}$ in the preceding call to dim4_scat_shep(). It must remain unchanged between calls.

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

Must be the same array returned as argument $\text{iq}$ in the preceding call to dim4_scat_shep(). It must remain unchanged between calls.

rqfloat, array-like, shape $(15\times m+9)$

Must be the same array returned as argument $\text{rq}$ in the preceding call to dim4_scat_shep(). It must remain unchanged between calls.

xefloat, array-like, shape $(4,n)$

$xe[0,\text{r}-1],\dots ,xe[3,\text{r}-1]$ must be set to the evaluation point $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

Returns

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

$q[\text{i}-1]$ contains the value of the interpolant, at $x_{\text{i}}$, 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 dim4_scat_shep_eval returns with $errno$ = 3.

qxfloat, ndarray, shape $(4,n)$

$qx[j-1,i-1]$ contains the value of the partial derivatives with respect to $x_j$ of the interpolant $Q\left(x\right)$ at $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$, and for each of the four partial derivatives $j=1,2,3,4$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in $qx$ are set to extrapolated approximations to the partial derivatives, and dim4_scat_shep_eval returns with $errno$ = 3.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 16$.

(errno $2$)

On entry, values in $rq$ appear to be invalid. Check that $rq$ has not been corrupted between calls to dim4_scat_shep() and dim4_scat_shep_eval.

(errno $2$)

On entry, values in $iq$ appear to be invalid. Check that $iq$ has not been corrupted between calls to dim4_scat_shep() and dim4_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

dim4_scat_shep_eval takes as input the interpolant $Q\left(x\right)$, $x\in R^4$ of a set of scattered data points $(x_{\text{r}},f_{\text{r}})$, for $\text{r}=1,2,\dots ,m$, as computed by dim4_scat_shep(), and evaluates the interpolant and its first partial derivatives at the set of points $x_i$, for $\text{i}=1,2,\dots ,n$.

dim4_scat_shep_eval must only be called after a call to dim4_scat_shep().

dim4_scat_shep_eval is derived from the new implementation of QS3GRD described by Renka (1988). It uses the modification for high-dimensional interpolation described by Berry and Minser (1999).

References

Berry, M W, Minser, K S, 1999, Algorithm 798: high-dimensional interpolation using the modified Shepard method, ACM Trans. Math. Software (25), 353–366

Renka, R J, 1988, Algorithm 661: QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data, ACM Trans. Math. Software (14), 151–152