NAG CL Interface
s15asc (erf_​real_​vector)

1 Purpose

s15asc returns an array of values of the error function erfx

2 Specification

#include <nag.h>
void  s15asc (Integer n, const double x[], double f[], NagError *fail)
The function may be called by the names: s15asc, nag_specfun_erf_real_vector or nag_erf_vector.

3 Description

s15asc calculates approximate values for the error function
erfx = 2π 0x e-t2 dt = 1-erfcx ,  
for an array of arguments xi, for i=1,2,,n.
Let x^ be the root of the equation erfcx-erfx=0 (then x^0.46875). For xx^ the value of erfx is based on the following rational Chebyshev expansion for erfx:
erfx xR,m x2 ,  
where R,m denotes a rational function of degree in the numerator and m in the denominator.
For x>x^ the value of erfx is based on a rational Chebyshev expansion for erfcx: for x^<x4 the value is based on the expansion
erfcx ex2 R,m x ;  
and for x>4 it is based on the expansion
erfcx ex2 x 1π + 1x2 R,m 1/x2 .  
For each expansion, the specific values of and m are selected to be minimal such that the maximum relative error in the expansion is of the order 10-d, where d is the maximum number of decimal digits that can be accurately represented for the particular implementation (see X02BEC).
For xxhi there is a danger of setting underflow in erfcx (the value of xhi is given in the Users' Note for your implementation). For xxhi, s15asc returns erfx=1; for x-xhi it returns erfx=-1.

4 References

NIST Digital Library of Mathematical Functions
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637

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: erfxi, 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

See Section 7 in s15arc.

8 Parallelism and Performance

s15asc is not threaded in any implementation.

9 Further Comments

None.

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 (s15asce.c)

10.2 Program Data

Program Data (s15asce.d)

10.3 Program Results

Program Results (s15asce.r)