naginterfaces.library.interp.dim3_​scat_​shep_​eval

naginterfaces.library.interp.dim3_scat_shep_eval(x, y, z, f, iq, rq, u, v, w)

dim3_scat_shep_eval evaluates the three-dimensional interpolating function generated by dim3_scat_shep() and its first partial derivatives.

For full information please refer to the NAG Library document for e01th

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e01/e01thf.html

Parameters

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

$\text{m}$, $x$, $y$, $z$ and $f$ must be the same values as were supplied in the preceding call to dim3_scat_shep().

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

$\text{m}$, $x$, $y$, $z$ and $f$ must be the same values as were supplied in the preceding call to dim3_scat_shep().

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

$\text{m}$, $x$, $y$, $z$ and $f$ must be the same values as were supplied in the preceding call to dim3_scat_shep().

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

$\text{m}$, $x$, $y$, $z$ and $f$ must be the same values as were supplied in the preceding call to dim3_scat_shep().

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

Must be unchanged from the value returned from a previous call to dim3_scat_shep().

rqfloat, array-like, shape $(10\times m+7)$

Must be unchanged from the value returned from a previous call to dim3_scat_shep().

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

$u[\text{i}-1]$, $v[\text{i}-1]$, $w[\text{i}-1]$ must be set to the evaluation point $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, for $\text{i}=1,2,\dots ,n$.

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

$u[\text{i}-1]$, $v[\text{i}-1]$, $w[\text{i}-1]$ must be set to the evaluation point $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, for $\text{i}=1,2,\dots ,n$.

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

$u[\text{i}-1]$, $v[\text{i}-1]$, $w[\text{i}-1]$ must be set to the evaluation point $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, 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 $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, 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 dim3_scat_shep_eval returns with $errno$ = 3.

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

$qx[\text{i}-1]$, $qy[\text{i}-1]$, $qz[\text{i}-1]$ contains the value of the partial derivatives of the interpolant $Q(x,y,z)$ at $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, 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 $qx$, $qy$ and $qz$ are set to extrapolated approximations to the partial derivatives, and dim3_scat_shep_eval returns with $errno$ = 3.

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

$qx[\text{i}-1]$, $qy[\text{i}-1]$, $qz[\text{i}-1]$ contains the value of the partial derivatives of the interpolant $Q(x,y,z)$ at $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, 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 $qx$, $qy$ and $qz$ are set to extrapolated approximations to the partial derivatives, and dim3_scat_shep_eval returns with $errno$ = 3.

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

$qx[\text{i}-1]$, $qy[\text{i}-1]$, $qz[\text{i}-1]$ contains the value of the partial derivatives of the interpolant $Q(x,y,z)$ at $(u_{\text{i}},v_{\text{i}},w_{\text{i}})$, 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 $qx$, $qy$ and $qz$ are set to extrapolated approximations to the partial derivatives, and dim3_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: $m\ge 10$.

(errno $2$)

On entry, values in $rq$ appear to be invalid. Check that $rq$ has not been corrupted between calls to dim3_scat_shep() and dim3_scat_shep_eval.

(errno $2$)

On entry, values in $iq$ appear to be invalid. Check that $iq$ has not been corrupted between calls to dim3_scat_shep() and dim3_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

dim3_scat_shep_eval takes as input the interpolant $Q(x,y,z)$ of a set of scattered data points $(x_r,y_r,z_r,f_r)$, for $\text{r}=1,2,\dots ,m$, as computed by dim3_scat_shep(), and evaluates the interpolant and its first partial derivatives at the set of points $(u_i,v_i,w_i)$, for $\text{i}=1,2,\dots ,n$.

dim3_scat_shep_eval must only be called after a call to dim3_scat_shep().

This function is derived from the function QS3GRD described by Renka (1988).

References

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