Cases prefixed with W are classified as warnings and
do not generate an error of type NAG:error_n. See nag_issue_warnings.
The function has been called with an argument that is larger in magnitude than ; the default result returned is zero.
The function has been called with an argument that is too close (as determined using the relative tolerance ) to an odd multiple of , at which the function is infinite; the function returns a value with the correct sign but a more or less arbitrary but large magnitude (see Accuracy).
An unexpected error has been triggered by this routine. Please
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.
If and are the relative errors in the argument and result respectively, then in principle
That is a relative error in the argument, , is amplified by at least a factor in the result.
Similarly if is the absolute error in the result this is given by
The equalities should hold if is greater than the machine precision ( is a result of data errors etc.) but if is simply the round-off error in the machine it is possible that internal calculation rounding will lose an extra figure.
The graphs below show the behaviour of these amplification factors.
In the principal range it is possible to preserve relative accuracy even near the zero of at but at the other zeros only absolute accuracy is possible. Near the infinities of both the relative and absolute errors become infinite and the function must fail (error ).
If is odd and the function could not return better than two figures and in all probability would produce a result that was in error in its most significant figure. Therefore the function fails and it returns the value
which is the value of the tangent at the nearest argument for which a valid call could be made.
Accuracy is also unavoidably lost if the function is called with a large argument. If the function fails (error ) and returns zero.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
fprintf('s07aa example results\n\n');
x = [-2.0 -0.5 1.0 3.0 1.5708];
n = size(x,2);
result = x;
[result(j), ifail] = s07aa(x(j));
disp(' x tan(x)');
s07aa example results
PDF version (NAG web site, 64-bit version, 64-bit version)