# Gamma#

class Gamma[source]#

Gamma response function with 3 parameters A, a, and n.

Parameters
• up (bool or None, optional) – indicates whether a positive stress will cause the head to go up (True, default) or down (False), if None the head can go both ways.

• meanstress (float) – mean value of the stress, used to set the initial value such that the final step times the mean stress equals 1

• cutoff (float) – proportion after which the step function is cut off. default is 0.999.

Notes

The impulse response function is:

$\theta(t) = At^{n-1} e^{-t/a} / (a^n Gamma(n))$

where A, a, and n are parameters. The Gamma function is equal to the Exponential function when n=1.

## Methods#

 __init__ block Method to return the block function. gain get_init_parameters Get initial parameters and bounds. get_t Internal method to determine the times at which to evaluate the step-response, from t=0. get_tmax Method to get the response time for a certain cutoff. impulse Method to return the impulse response function. step Method to return the step function.