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 $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface 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:

$ifail = 1$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .

$ifail = - 99$: 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

8 Parallelism and Performance

s15aqf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

Interfaces: FL CL AD

NAG FL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s15aq: FL CL AD

NAG FL Interfaces15aqf (compcdf_​normal_​vector)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
s15aqf (compcdf_normal_vector)