e01 Chapter Contents
e01 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_1d_ratnl_eval (e01rbc)

## 1  Purpose

nag_1d_ratnl_eval (e01rbc) evaluates continued fractions of the form produced by nag_1d_ratnl_interp (e01rac).

## 2  Specification

 #include #include
 void nag_1d_ratnl_eval (Integer m, const double a[], const double u[], double x, double *f, NagError *fail)

## 3  Description

nag_1d_ratnl_eval (e01rbc) evaluates the continued fraction
 $Rx=a1+Rmx$
where
 $Rix=am-i+ 2x-um-i+ 1 1+Ri- 1x , for ​ i=m,m- 1,…,2.$
and
 $R1x=0$
for a prescribed value of $x$. nag_1d_ratnl_eval (e01rbc) is intended to be used to evaluate the continued fraction representation (of an interpolatory rational function) produced by nag_1d_ratnl_interp (e01rac).

## 4  References

Graves–Morris P R and Hopkins T R (1981) Reliable rational interpolation Numer. Math. 36 111–128

## 5  Arguments

1:     mIntegerInput
On entry: $m$, the number of terms in the continued fraction.
Constraint: ${\mathbf{m}}\ge 1$.
2:     a[m]const doubleInput
On entry: ${\mathbf{a}}\left[\mathit{j}-1\right]$ must be set to the value of the parameter ${a}_{\mathit{j}}$ in the continued fraction, for $\mathit{j}=1,2,\dots ,m$.
3:     u[m]const doubleInput
On entry: ${\mathbf{u}}\left[\mathit{j}-1\right]$ must be set to the value of the parameter ${u}_{\mathit{j}}$ in the continued fraction, for $\mathit{j}=1,2,\dots ,m-1$. (The element ${\mathbf{u}}\left[m-1\right]$ is not used).
4:     xdoubleInput
On entry: the value of $x$ at which the continued fraction is to be evaluated.
5:     fdouble *Output
On exit: the value of the continued fraction corresponding to the value of $x$.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_POLE_PRESENT
x corresponds to a pole of $R\left(x\right)$, or is very close. ${\mathbf{x}}=〈\mathit{\text{value}}〉$.

## 7  Accuracy

See Section 7 in nag_1d_ratnl_interp (e01rac).

The time taken by nag_1d_ratnl_eval (e01rbc) is approximately proportional to $m$.

## 9  Example

This example reads in the arguments ${a}_{j}$ and ${u}_{j}$ of a continued fraction (as determined by the example for nag_1d_ratnl_interp (e01rac)) and evaluates the continued fraction at a point $x$.

### 9.1  Program Text

Program Text (e01rbce.c)

### 9.2  Program Data

Program Data (e01rbce.d)

### 9.3  Program Results

Program Results (e01rbce.r)