NAG CL Interface
s15aqc (compcdf_​normal_​vector)

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1 Purpose

s15aqc returns an array of values of the complement of the cumulative Normal distribution function, Q(x).

2 Specification

#include <nag.h>
void  s15aqc (Integer n, const double x[], double f[], NagError *fail)
The function may be called by the names: s15aqc, nag_specfun_compcdf_normal_vector or nag_cumul_normal_complem_vector.

3 Description

s15aqc evaluates approximate values for the complement of the cumulative Normal distribution function
Q(x) = 12π x e-u2/2 du ,  
for an array of arguments xi, for i=1,2,,n.
The function is based on the fact that
Q(x) = 12 erfc(x2)  
and it calls s15adc to obtain the necessary value of erfc, the complementary error function.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: n Integer Input
On entry: n, the number of points.
Constraint: n0.
2: x[n] const double Input
On entry: the argument xi of the function, for i=1,2,,n.
3: f[n] double Output
On exit: Q(xi), 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: n0.
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, then in principle they are related by
|ε| | x e -x2/2 2πQ(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 εx2δ and hence to a certain extent relative accuracy is unavoidably lost. However, the absolute error in the result, E, is given by
|E| | x e -x2/2 2π δ|  
and since this factor is always less than one absolute accuracy can be guaranteed for all x.

8 Parallelism and Performance

s15aqc 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.

10.1 Program Text

Program Text (s15aqce.c)

10.2 Program Data

Program Data (s15aqce.d)

10.3 Program Results

Program Results (s15aqce.r)