The Logistic Function

Utilities for working with the Logistic Function.

Functions
template<typename floatT >
floatT	mx::math::func::logistic_param (floatT x, floatT thalf)
	Return the logistic function parameter for a specified rise time.
template<typename floatT >
floatT	mx::math::func::logistic (floatT t, floatT t0=0, floatT a=1)
	Return the value of the logistic function.

Function Documentation

logistic()

template<typename floatT >

floatT mx::math::func::logistic	(	floatT	t,
		floatT	t0 = 0,
		floatT	a = 1
	)

Return the value of the logistic function.

The logistic function is

\[ f(t) = \frac{1}{1 + e^{-a(t-t_0)}} \]

Parameters

t	[input] the argument.
t0	[input] [optional] the center of the curve, defaults to 0.
a	[input] [optional] the exponent parameter, defaults to 1.

Returns

the value of the logistic function at t

Template Parameters

floatT

is the floating point type of the arguments and the returned value.

Definition at line 81 of file logistic.hpp.

References mx::math::six_fifths().

logistic_param()

template<typename floatT >

floatT mx::math::func::logistic_param	(	floatT	x,
		floatT	thalf
	)

Return the logistic function parameter for a specified rise time.

The logistic function is

\[ f(t) = \frac{1}{1 + e^{-a(t-t_0)}} \]

The parameter \( a \) controls how fast the function rises. Here it is specified by the value \( f(t_{1/2}) = x\), where \( 0 < x < 1 \).

Returns

the value of a

Template Parameters

floatT

is the floating point type of the arguments and the returned value.

Parameters

[in]	x	the value at which the rise time is specified.
[in]	thalf	half the rise time, or the time after 0 when f(t) = x.

Definition at line 57 of file logistic.hpp.

References mx::math::six_fifths().