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 routine.

Accuracy

Let

δ

and

ε

be the relative errors in the argument and result respectively.

δ

is considerably greater than the machine precision (i.e., if

δ

is due to data errors etc.), then

ε

and

δ

are approximately related by:

ε ≃ |\frac{x (1 - 2 x F (x))}{F (x)}| δ .

The following graph shows the behaviour of the error amplification factor

|\frac{x (1 - 2 x F (x))}{F (x)}|

Figure 1

However if

δ

is of the same order as machine precision, then rounding errors could make

ε

somewhat larger than the above relation indicates. In fact

ε

will be largely independent of

x

δ

, but will be of the order of a few times the machine precision.

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: s15af_example

function s15af_example


fprintf('s15af example results\n\n');

x = [-2   -0.5   1   1.5   2  5  10];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s15af(x(j));
end

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

s15af example results

      x           F(x)
  -2.000e+00  -3.013e-01
  -5.000e-01  -4.244e-01
   1.000e+00   5.381e-01
   1.500e+00   4.282e-01
   2.000e+00   3.013e-01
   5.000e+00   1.021e-01
   1.000e+01   5.025e-02

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

Chapter Contents

Chapter Introduction

NAG Toolbox