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

None.

Accuracy

δ

and

ε

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

|ε| ≃ |\frac{x}{\sqrt{1 + x^{2}} arcsinh x} δ| .

That is, the relative error in the argument,

x

, is amplified by a factor at least

\frac{x}{\sqrt{1 + x^{2}} arcsinh x}

, in the result.

The equality should 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 it is possible that an extra figure may be lost in internal calculation round-off.

The behaviour of the amplification factor is shown in the following graph:

Figure 1

It should be noted that this factor is always less than or equal to one. For large

x

we have the absolute error in the result,

E

, in principle, given by

E \sim δ .

This means that eventually accuracy is 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: s11ab_example

function s11ab_example


fprintf('s11ab example results\n\n');

x = [-2    -0.5    1     6];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s11ab(x(j));
end

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

s11ab example results

      x        arcsinh(x)
  -2.000e+00  -1.444e+00
  -5.000e-01  -4.812e-01
   1.000e+00   8.814e-01
   6.000e+00   2.492e+00

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

Chapter Contents

Chapter Introduction

NAG Toolbox