pade_eval evaluates a rational function at a user-supplied point, given the numerator and denominator coefficients.

For full information please refer to the NAG Library document for e02rb

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/e02/e02rbf.html

Parameters
afloat, array-like, shape

, for , must contain the value of the coefficient in the numerator of the rational function.

bfloat, array-like, shape

, for , must contain the value of the coefficient in the denominator of the rational function.

xfloat

The point at which the rational function is to be evaluated.

Returns
ansfloat

The result of evaluating the rational function at the given point .

Raises
NagValueError
(errno )

Evaluation at or near a pole.

(errno )

The first entries in are zero: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

Given a real value and the coefficients , for and , for , pade_eval evaluates the rational function

using nested multiplication (see Conte and de Boor (1965)).

A particular use of pade_eval is to compute values of the Padé approximants determined by pade_app().

References

Conte, S D and de Boor, C, 1965, Elementary Numerical Analysis, McGraw–Hill

Peters, G and Wilkinson, J H, 1971, Practical problems arising in the solution of polynomial equations, J. Inst. Maths. Applics. (8), 16–35