naginterfaces.library.interp.dim1_​aitken

naginterfaces.library.interp.dim1_aitken(a, b, x)[source]

dim1_aitken interpolates a function of one variable at a given point from a table of function values evaluated at equidistant or non-equidistant points , for , using Aitken’s technique of successive linear interpolations.

For full information please refer to the NAG Library document for e01aa

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/e01/e01aaf.html

Parameters
afloat, array-like, shape

must contain the -component of the th data point, , for .

bfloat, array-like, shape

must contain the -component (function value) of the th data point, , for .

xfloat

The point at which the interpolation is required. Note that may lie outside the interval defined by the minimum and maximum values in , in which case an extrapolated value will be computed; extrapolated results should be treated with considerable caution since there is no information on the behaviour of the function outside the defined interval.

Returns
afloat, ndarray, shape

contains the value , for .

bfloat, ndarray, shape

The contents of are unspecified.

cfloat, ndarray, shape

contain the first set of linear interpolations,

contain the second set of linear interpolations,

contain the third set of linear interpolations,

contains the interpolated function value at the point .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

Notes

dim1_aitken interpolates a function of one variable at a given point from a table of values and , for using Aitken’s method (see Fröberg (1970)). The intermediate values of linear interpolations are stored to enable an estimate of the accuracy of the results to be made.

References

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