NAG Library Routine Document

1: $m$ – IntegerInput: On entry: $m$ , the number of terms in the continued fraction.

Constraint: $m \geq 1$ .
2: $a (m)$ – Real (Kind=nag_wp) arrayInput: On entry: $a (j)$ must be set to the value of the parameter $a_{j}$ in the continued fraction, for $j = 1, 2, \dots, m$ .
3: $u (m)$ – Real (Kind=nag_wp) arrayInput: On entry: $u (j)$ must be set to the value of the parameter $u_{j}$ in the continued fraction, for $j = 1, 2, \dots, m - 1$ . (The element $u (m)$ is not used).
4: $x$ – Real (Kind=nag_wp)Input: On entry: the value of $x$ at which the continued fraction is to be evaluated.
5: $f$ – Real (Kind=nag_wp)Output: On exit: the value of the continued fraction corresponding to the value of $x$ .
6: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: x corresponds to a pole of $R (x)$ , or is very close. $x = 〈value〉$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

See Section 7 in e01raf.

e01rbf is not threaded in any implementation.

The time taken by e01rbf is approximately proportional to

m

This example reads in the arguments

a_{j}

and

u_{j}

of a continued fraction (as determined by the example for e01raf) and evaluates the continued fraction at a point

x