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_integral_sin (s13ad). The argument ifail has been included for consistency with other functions in this chapter.

Accuracy

δ

and

ε

are the relative errors in the argument and result, respectively, then in principle

|ε| ≃ |\frac{δ \sin x}{Si (x)}| .

The equality may hold if

δ

is greater than the machine precision (

δ

due to data errors etc.) but if

δ

is simply due to round-off in the machine representation, then since the factor relating

δ

ε

is always less than one, the accuracy will be limited by 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: s13ad_example

function s13ad_example


fprintf('s13ad example results\n\n');

x = [0:0.2:1];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s13ad(x(j));
end

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

s13ad_plot;



function s13ad_plot
x = [-12:0.1:12];
  for j=1:numel(x)
    [si(j), ifail] = s13ad(x(j));
  end

  fig1 = figure;
  plot(x,si);
  xlabel('x');
  ylabel('Si(x)');
  title('Sine Integral Si(x)');
  axis([-12 12 -2 2]);

s13ad example results

      x          Si(x)
   0.000e+00   0.000e+00
   2.000e-01   1.996e-01
   4.000e-01   3.965e-01
   6.000e-01   5.881e-01
   8.000e-01   7.721e-01
   1.000e+00   9.461e-01

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

Chapter Contents

Chapter Introduction

NAG Toolbox