1: $result$ – double scalar: The result of the function.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

There are no failure exits from this function. The argument ifail is included for consistency with other functions in this chapter.

Accuracy

Because of its close relationship with

erfc

, the accuracy of this function is very similar to that in nag_specfun_erfc_real (s15ad). 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 one 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

Further Comments

None.

Example

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

Open in the MATLAB editor: s15ab_example

function s15ab_example


fprintf('s15ab example results\n\n');

x = [-20   -1     0    1    2    20];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s15ab(x(j));
end

disp('      x          P(x)');
fprintf('%12.3e%12.3e\n',[x; result]);

s15ab example results

      x          P(x)
  -2.000e+01   2.754e-89
  -1.000e+00   1.587e-01
   0.000e+00   5.000e-01
   1.000e+00   8.413e-01
   2.000e+00   9.772e-01
   2.000e+01   1.000e+00

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox