naginterfaces.library.fit.dim2_​spline_​evalm

naginterfaces.library.fit.dim2_spline_evalm(x, y, lamda, mu, c)[source]

dim2_spline_evalm calculates values of a bicubic spline from its B-spline representation. The spline is evaluated at all points on a rectangular grid.

For full information please refer to the NAG Library document for e02df

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/e02/e02dff.html

Parameters
xfloat, array-like, shape

and must contain , for , and , for , respectively. These are the and coordinates that define the rectangular grid of points at which values of the spline are required.

yfloat, array-like, shape

and must contain , for , and , for , respectively. These are the and coordinates that define the rectangular grid of points at which values of the spline are required.

lamdafloat, array-like, shape

and must contain the complete sets of knots and associated with the and variables respectively.

mufloat, array-like, shape

and must contain the complete sets of knots and associated with the and variables respectively.

cfloat, array-like, shape

must contain the coefficient described in Notes, for , for .

Returns
fffloat, ndarray, shape

contains the value of the spline at the point , for , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the knots in are not in nondecreasing order.

(errno )

On entry, the knots in are not in nondecreasing order.

(errno )

On entry, is violated.

(errno )

On entry, is violated.

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_spline_evalm calculates values of the bicubic spline on a rectangular grid of points in the - plane, from its augmented knot sets and and from the coefficients , for , for , in its B-spline representation

Here and denote normalized cubic B-splines, the former defined on the knots to and the latter on the knots to .

The points in the grid are defined by coordinates , for , along the axis, and coordinates , for , along the axis.

This function may be used to calculate values of a bicubic spline given in the form produced by interp.dim2_spline_grid, dim2_spline_panel(), dim2_spline_grid() and dim2_spline_sctr(). It is derived from the function B2VRE in Anthony et al. (1982).

References

Anthony, G T, Cox, M G and Hayes, J G, 1982, DASL – Data Approximation Subroutine Library, National Physical Laboratory

Cox, M G, 1978, The numerical evaluation of a spline from its B-spline representation, J. Inst. Math. Appl. (21), 135–143