NAG CL Interface
s15apc (cdf_​normal_​vector)

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1 Purpose

s15apc returns an array of values of the cumulative Normal distribution function, P(x).

2 Specification

#include <nag.h>
void  s15apc (Integer n, const double x[], double f[], NagError *fail)
The function may be called by the names: s15apc, nag_specfun_cdf_normal_vector or nag_cumul_normal_vector.

3 Description

s15apc evaluates approximate values of the cumulative Normal distribution function
P(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
P(x) = 12 erfc(-x2)  
and it calls s15adc to obtain a value of erfc for the appropriate argument.

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: P(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

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
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.
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| | x e -12 x2 2πP(x) δ|  
so that the relative error in the argument, x, is amplified by a factor, x e -12 x2 2πP(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 x2 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 -12 x2 2π δ|  
so absolute accuracy can be guaranteed for all x.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s15apc is not threaded in any implementation.

9 Further Comments


10 Example

This example reads values of x from a file, evaluates the function at each value of xi and prints the results.

10.1 Program Text

Program Text (s15apce.c)

10.2 Program Data

Program Data (s15apce.d)

10.3 Program Results

Program Results (s15apce.r)