is the maximum number of decimal digits that can be accurately represented for the particular implementation (see nag_machine_decimal_digits (x02be)).

For

|x| \geq x_{hi}

there is a danger of setting underflow in

erfc (x)

. For

x \geq x_{hi}

, nag_specfun_erf_real (s15ae) returns

\erf (x) = 1

; for

x \leq - x_{hi}

it returns

\erf (x) = - 1

References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637

Parameters

Compulsory Input Parameters

1: $x$ – double scalar: The argument $x$ of the function.

Optional Input Parameters

None.

Output Parameters

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 nag_specfun_erf_real (s15ae). The argument ifail has been included for consistency with other functions in this chapter.

Accuracy

See Accuracy in nag_specfun_erfc_real (s15ad).

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: s15ae_example

function s15ae_example


fprintf('s15ae example results\n\n');

x = [-6   -4.5    -1    1     4.5   6];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s15ae(x(j));
end

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

s15ae example results

      x          erf(x)
  -6.000e+00  -1.000e+00
  -4.500e+00  -1.000e+00
  -1.000e+00  -8.427e-01
   1.000e+00   8.427e-01
   4.500e+00   1.000e+00
   6.000e+00   1.000e+00

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

Chapter Contents

Chapter Introduction

NAG Toolbox