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.