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.