NAG Library Routine Document

S15AFF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     X – REAL (KIND=nag_wp)Input

On entry: the argument $x$ of the function.

2:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. 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 $-1\text{ or }1$ 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 $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

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

6  Error Indicators and Warnings

7  Accuracy

If $\delta$ is considerably greater than the machine precision (i.e., if $\delta$ is due to data errors etc.), then $\epsilon$ and $\delta$ are approximately related by:

$$\epsilon \simeq \left|\frac{x\left(1-2xF\left(x\right)\right)}{F\left(x\right)}\right|\delta \text{.}$$

The following graph shows the behaviour of the error amplification factor $\left|\frac{x\left(1-2xF\left(x\right)\right)}{F\left(x\right)}\right|$:

Figure 1

However if $\delta$ is of the same order as machine precision, then rounding errors could make $\epsilon$ somewhat larger than the above relation indicates. In fact $\epsilon$ will be largely independent of $x$ or $\delta$, but will be of the order of a few times the machine precision.

8  Further Comments

9  Example

9.1  Program Text

Program Text (s15affe.f90)

9.2  Program Data

Program Data (s15affe.d)

9.3  Program Results

Program Results (s15affe.r)