NAG Library Routine Document

E01RBF

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 parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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:

$IFAIL = 1$: The value of X corresponds to a pole of $R (x)$ or is so close that an overflow is likely to ensue.

See Section 7 in E01RAF.

The time taken by E01RBF is approximately proportional to

m

This example reads in the parameters

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