Logistic Roots

logistic_roots(first_constant, second_constant, third_constant, precision=4)

Calculates the roots of a logistic function

Parameters

  • first_constant (int or float) – Carrying capacity of the original logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • second_constant (int or float) – Growth rate of the original logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • third_constant (int or float) – Value of the sigmoid’s midpoint of the original logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

  • TypeError – First three arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

roots – List of the x-coordinates of all of the x-intercepts of the original function; if the function never crosses the x-axis, then it will return a list of None

Return type

list of float

See also

logistic_equation(), logistic_derivatives(), logistic_integral(), logistic_model()

Notes

  • Standard form of a logistic function: \(f(x) = \frac{a}{1 + \text{e}^{-b\cdot(x - c)}}\)

  • Logistic formula: \(x = \varnothing\)

Examples

Import logistic_roots function from regressions library
>>> from regressions.analyses.roots.logistic import logistic_roots
Calculate the roots of a logistic function with coefficients 2, 3, and 5
>>> roots_first = logistic_roots(2, 3, 5)
>>> print(roots_first)
[None]
Calculate the roots of a logistic function with coefficients 100, 5, and 11
>>> roots_second = logistic_roots(100, 5, 11)
>>> print(roots_second)
[None]
Calculate the roots of a logistic function with all inputs set to 0
>>> roots_zeroes = logistic_roots(0, 0, 0)
>>> print(roots_zeroes)
[None]