naginterfaces.library.fit.pade_​eval

naginterfaces.library.fit.pade_eval(a, b, x)

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://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e02/e02rbf.html

Parameters

afloat, array-like, shape $\left(\text{ia}\right)$

$a\left[\text{j}\right]$, for $\text{j}=1,2,\dots ,l+1$, must contain the value of the coefficient $a_{\text{j}}$ in the numerator of the rational function.

bfloat, array-like, shape $\left(\text{ib}\right)$

$b\left[\text{k}\right]$, for $\text{k}=1,2,\dots ,m+1$, must contain the value of the coefficient $b_k$ in the denominator of the rational function.

xfloat

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

Returns

ansfloat

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

Raises

NagValueError

(errno $1$)

Evaluation at or near a pole.

(errno $2$)

The first $\text{ib}$ entries in $b$ are zero: $\text{ib}=⟨value⟩$.

(errno $2$)

On entry, $\text{ib}=⟨value⟩$.

Constraint: $\text{ib}\ge 1$.

(errno $2$)

On entry, $\text{ia}=⟨value⟩$.

Constraint: $\text{ia}\ge 1$.

Notes

Given a real value $x$ and the coefficients $a_j$, for $\text{j}=0,1,\dots ,l$ and $b_k$, for $\text{k}=0,1,\dots ,m$, pade_eval evaluates the rational function

$$\frac{{\sum }_{j=0}^l{a}_j{x}^j}{{\sum }_{k=0}^m{b}_k{x}^k}\text{.}$$

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