naginterfaces.library.interp.dim1_​everett¶

naginterfaces.library.interp.dim1_everett(p, a)[source]

dim1_everett interpolates a function of one variable at a given point from a table of function values evaluated at equidistant points, using Everett’s formula.

For full information please refer to the NAG Library document for e01ab

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/e01/e01abf.html

Parameters
pfloat

The point at which the interpolated function value is required, i.e., with .

afloat, array-like, shape

must be set to the function value , for .

Returns
afloat, ndarray, shape

The contents of are unspecified.

gfloat, ndarray, shape

The array contains

 y0 in g[0] y1 in g[1] δ2ry0 in g[2r] δ2ry1 in g[2r+1], for r=1,2,…,n−1.

The interpolated function value is stored in .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

dim1_everett interpolates a function of one variable at a given point

where and is the interval of differencing, from a table of values and where . The formula used is that of Fröberg (1970), neglecting the remainder term:

The values of and are stored on exit from the function in addition to the interpolated function value .

References

Fröberg, C E, 1970, Introduction to Numerical Analysis, Addison–Wesley