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

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W $ifail = 1$: The function has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of $\cosh x$ at the nearest valid argument.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

δ

and

ε

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

ε ≃ x \tanh x \times δ .

That is, the relative error in the argument,

x

, is amplified by a factor, at least

x \tanh x

. The equality should hold if

δ

is greater than the machine precision (

δ

is due to data errors etc.) but if

δ

is simply a result of round-off in the machine representation of

x

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

The behaviour of the error amplification factor is shown by the following graph:

Figure 1

It should be noted that near

x = 0

where this amplification factor tends to zero the accuracy will be limited eventually by the machine precision. Also for

|x| \geq 2

ε \sim x δ = Δ

where

Δ

is the absolute error in the argument

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: s10ac_example

function s10ac_example


fprintf('s10ac example results\n\n');

x = [-10   -0.5     0    0.5     25];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s10ac(x(j));
end

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

s10ac example results

      x        cosh(x)
  -1.000e+01   1.101e+04
  -5.000e-01   1.128e+00
   0.000e+00   1.000e+00
   5.000e-01   1.128e+00
   2.500e+01   3.600e+10

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

Chapter Contents

Chapter Introduction

NAG Toolbox