naginterfaces.library.interp.dim2_​scat_​eval

naginterfaces.library.interp.dim2_scat_eval(x, y, f, triang, grads, px, py, ist=1)

dim2_scat_eval evaluates at a given point the two-dimensional interpolant function computed by dim2_scat().

For full information please refer to the NAG Library document for e01sb

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/e01/e01sbf.html

Parameters

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

$x$ must be unchanged from the previous call of dim2_scat()

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

$y$ must be unchanged from the previous call of dim2_scat()

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

$f$ must be unchanged from the previous call of dim2_scat()

triangint, array-like, shape $(7\times m)$

$triang$ must be unchanged from the previous call of dim2_scat()

gradsfloat, array-like, shape $(2,m)$

$grads$ must be unchanged from the previous call of dim2_scat()

pxfloat

The point $(px,py)$ at which the interpolant is to be evaluated.

pyfloat

The point $(px,py)$ at which the interpolant is to be evaluated.

istint, optional

The index of the starting node in the search for a triangle containing the point $(px,py)$. On the first call to dim2_scat_eval, $ist$ must be set to $1$. For efficiency on subsequent calls to dim2_scat_eval an updated value of $ist$ as returned by dim2_scat_eval may be supplied instead. An input value outside the range $1\le ist\le m$ will be treated as $1$.

Returns

istint

The index of one of the vertices of the triangle containing the point $(px,py)$.

pffloat

The value of the interpolant evaluated at the point $(px,py)$.

Raises

NagValueError

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 3$.

(errno $2$)

On entry, $triang$ does not contain a valid data point triangulation; $triang$ may have been corrupted since the call to dim2_scat().

Warns

NagAlgorithmicWarning

(errno $3$)

Warning – the evaluation point $(⟨value⟩,⟨value⟩)$ lies outside the triangulation boundary. The returned value was computed by extrapolation.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

dim2_scat_eval takes as input the arguments defining the interpolant $F(x,y)$ 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(), and evaluates the interpolant at the point $(px,py)$.

If $(px,py)$ is equal to $(x_r,y_r)$ for some value of $r$, the returned value will be equal to $f_r$.

If $(px,py)$ is not equal to $(x_r,y_r)$ for any $r$, the derivatives in $grads$ will be used to compute the interpolant. A triangle is sought which contains the point $(px,py)$, and the vertices of the triangle along with the partial derivatives and $f_r$ values at the vertices are used to compute the value $F(px,py)$. If the point $(px,py)$ lies outside the triangulation defined by the input arguments, the returned value is obtained by extrapolation. In this case, the interpolating function $f$ is extended linearly beyond the triangulation boundary. The method is described in more detail in Renka and Cline (1984) and the code is derived from Renka (1984).

dim2_scat_eval must only be called after a call to dim2_scat().

References

Renka, R L, 1984, Algorithm 624: triangulation and interpolation of arbitrarily distributed points in the plane, ACM Trans. Math. Software (10), 440–442

Renka, R L and Cline, A K, 1984, A triangle-based $C^1$ interpolation method, Rocky Mountain J. Math. (14), 223–237