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: $F (x_{i})$ , 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

Let

δ

and

ε

be the relative errors in the argument and result respectively.

δ

is considerably greater than the machine precision (i.e., if

δ

is due to data errors etc.), then

ε

and

δ

are approximately related by:

ε ≃ | \frac{x (1 - 2 x F (x))}{F (x)} | δ .

The following graph shows the behaviour of the error amplification factor

| \frac{x (1 - 2 x F (x))}{F (x)} |

Figure 1

However, if

δ

is of the same order as machine precision, then rounding errors could make

ε

somewhat larger than the above relation indicates. In fact

ε

will be largely independent of

x

δ

, but will be of the order of a few times the machine precision.

s15atc 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_{i}

and prints the results.

s15at: FL CL CPP AD