naginterfaces.library.interp.dimn_​scat_​shep_​eval¶

naginterfaces.library.interp.dimn_scat_shep_eval(x, f, iq, rq, xe)[source]

dimn_scat_shep_eval evaluates the multidimensional interpolating function generated by dimn_scat_shep() and its first partial derivatives.

For full information please refer to the NAG Library document for e01zn

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/e01/e01znf.html

Parameters
xfloat, array-like, shape

Note: the th ordinate of the point is stored in .

Must be the same array supplied as argument in the preceding call to dimn_scat_shep(). It must remain unchanged between calls.

ffloat, array-like, shape

Must be the same array supplied as argument in the preceding call to dimn_scat_shep(). It must remain unchanged between calls.

iqint, array-like, shape

Must be the same array returned as argument in the preceding call to dimn_scat_shep(). It must remain unchanged between calls.

rqfloat, array-like, shape

Must be the same array returned as argument in the preceding call to dimn_scat_shep(). It must remain unchanged between calls.

xefloat, array-like, shape

Note: the th ordinate of the point is stored in .

must be set to the evaluation point , for .

Returns
qfloat, ndarray, shape

contains the value of the interpolant, at , for . If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in are set to an extrapolated approximation, and dimn_scat_shep_eval returns with = 3.

qxfloat, ndarray, shape

contains the value of the partial derivatives with respect to the th independent variable (dimension) of the interpolant at , for , and for each of the partial derivatives . If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in are set to extrapolated approximations to the partial derivatives, and dimn_scat_shep_eval returns with = 3.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, exceeds the largest machine integer.

and .

(errno )

On entry, .

Constraint: .

(errno )

On entry, values in appear to be invalid. Check that has not been corrupted between calls to dimn_scat_shep() and dimn_scat_shep_eval.

(errno )

On entry, values in appear to be invalid. Check that has not been corrupted between calls to dimn_scat_shep() and dimn_scat_shep_eval.

Warns
NagAlgorithmicWarning
(errno )

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

Notes

dimn_scat_shep_eval takes as input the interpolant , of a set of scattered data points , for , as computed by dimn_scat_shep(), and evaluates the interpolant and its first partial derivatives at the set of points , for .

dimn_scat_shep_eval must only be called after a call to dimn_scat_shep().

dimn_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