1: $n$ – Integer Input: On entry: $n$ , the number of points.

Constraint: $n \geq 0$ .
2: $x (n)$ – Real (Kind=nag_wp) array Input: On entry: the argument $x_{i}$ of the function, for $i = 1, 2, \dots, n$ .
3: $f (n)$ – Real (Kind=nag_wp) array Output: On exit: $Q (x_{i})$ , the function values.
4: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. 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:

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Because of its close relationship with

erfc

the accuracy of this routine is very similar to that in s15adf. If

ε

and

δ

are the relative errors in result and argument, respectively, then in principle they are related by

| ε | ≃ | \frac{x e^{- x^{2} / 2}}{\sqrt{2 π} Q (x)} δ | .

For

x

negative or small positive this factor is always less than

1

and accuracy is mainly limited by machine precision. For large positive

x

we find

ε \sim x^{2} δ

and hence to a certain extent relative accuracy is unavoidably lost. However, the absolute error in the result,

E

, is given by

| E | ≃ | \frac{x e^{- x^{2} / 2}}{\sqrt{2 π}} δ |

and since this factor is always less than one absolute accuracy can be guaranteed for all

x

Background information to multithreading can be found in the Multithreading documentation.

s15aqf is not threaded in any implementation.

None.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

s15aq: FL CL CPP AD PY MB