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

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

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://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/e01/e01sbf.html

Parameters
xfloat, array-like, shape

must be unchanged from the previous call of dim2_scat()

yfloat, array-like, shape

must be unchanged from the previous call of dim2_scat()

ffloat, array-like, shape

must be unchanged from the previous call of dim2_scat()

triangint, array-like, shape

must be unchanged from the previous call of dim2_scat()

must be unchanged from the previous call of dim2_scat()

pxfloat

The point at which the interpolant is to be evaluated.

pyfloat

The point 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 . On the first call to dim2_scat_eval, must be set to . For efficiency on subsequent calls to dim2_scat_eval an updated value of as returned by dim2_scat_eval may be supplied instead. An input value outside the range will be treated as .

Returns
istint

The index of one of the vertices of the triangle containing the point .

pffloat

The value of the interpolant evaluated at the point .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

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

Warns
NagAlgorithmicWarning
(errno )

Warning – the evaluation point lies outside the triangulation boundary. The returned value was computed by extrapolation.

Notes

dim2_scat_eval takes as input the arguments defining the interpolant of a set of scattered data points , for , as computed by dim2_scat(), and evaluates the interpolant at the point .

If is equal to for some value of , the returned value will be equal to .

If is not equal to for any , the derivatives in will be used to compute the interpolant. A triangle is sought which contains the point , and the vertices of the triangle along with the partial derivatives and values at the vertices are used to compute the value . If the point lies outside the triangulation defined by the input arguments, the returned value is obtained by extrapolation. In this case, the interpolating function 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 interpolation method, Rocky Mountain J. Math. (14), 223–237