Sign function
From Biocrawler, the free encyclopedia.
In mathematics and especially in computer science, the sign function is a logical function which extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function. The sign function is often represented as sgn and can be defined thus:
Any real number can be expressed as the product of its absolute value and its sign function:
From equation (1) it follows that
but equation (2) is indeterminate when x is set to zero.
The signum function is the derivative of the absolute value function (up to the indeterminacy at zero):
Also, the derivative of the signum function is two times the Dirac delta function,
The signum function is related to the Heaviside step function h0.5(x) thus
- sgnx = 2h0.5(x) − 1,
where the 0.5 subscript of the step function means that h0.5(0) = 0.5.
