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

Constraint: $n \geq 0$ .
2: $x [n]$ – const double Input: On entry: the argument $x_{i}$ of the function, for $i = 1, 2, \dots, n$ .
3: $f [n]$ – double Output: On exit: $P (x_{i})$ , the function values.
4: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Because of its close relationship with

erfc

, the accuracy of this function is very similar to that in s15adc. If

ε

and

δ

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

| ε | ≃ | \frac{x e^{- \frac{1}{2} x^{2}}}{\sqrt{2 π} P (x)} δ |

so that the relative error in the argument,

x

, is amplified by a factor,

\frac{x e^{- \frac{1}{2} x^{2}}}{\sqrt{2 π} P (x)}

, in the result.

For

x

small and for

x

positive this factor is always less than

1

and accuracy is mainly limited by machine precision.

For large negative

x

the factor behaves like

\sim x^{2}

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^{- \frac{1}{2} x^{2}}}{\sqrt{2 π}} δ |

so absolute accuracy can be guaranteed for all

x

s15apc is not threaded in any implementation.

None.

This example reads values of x from a file, evaluates the function at each value of

x_{i}

and prints the results.

s15ap: FL CL CPP AD