logistic_curve

sofia_redux.toolkit.resampling.logistic_curve(x, x0=0.0, k=1.0, a=0.0, c=1.0, q=1.0, b=1.0, v=1.0)

Evaluate the generalized logistic function.

The generalized logistic function is given as:

\[f(x) = A + \frac{K - A} {\left( C + Q e^{-B(x - x_0)} \right)^{1/\nu}}\]

Taken from Wikipedia contributors. (2020, June 11). Generalised logistic function. In Wikipedia, The Free Encyclopedia. Retrieved 23:51, July 6, 2020, from https://en.wikipedia.org/w/index.php?title=Generalised_logistic_function&oldid=961965809

Parameters:

xint or float or numpy.ndarray (shape)

The independent variable.

x0int or float or numpy.ndarray (shape), optional

An offset applied to x.

kint or float or numpy.ndarray (shape), optional

The upper asymptote when c is one.

aint or float or numpy.ndarray (shape), optional

The lower asymptote.

cint or float or numpy.ndarray (shape), optional

Typically takes a value of 1. Otherwise, the upper asymptote is a + ((k - a) / c^(1/v)).

qint or float or numpy.ndarray (shape), optional

Related to the value of f(0).

bint or float or numpy.ndarray (shape), optional

The growth rate.

vint or float or numpy.ndarray (shape), optional

Must be greater than zero. Affects near which asymptote the maximum growth occurs.

Returns:

resultfloat or numpy.ndarray (shape)

The logistic function evaluated at x.