rb_decay#
- rb_decay(x, y, b=0.5)[source]#
Get base of exponential decay function which is assumed to be close to 1.
This assumes following model:
\[y(x) = a \alpha^x + b.\]To estimate the base of decay function \(\alpha\), we consider
\[y'(x) = y(x) - b = a \alpha^x,\]and thus,
\[y'(x+dx) = a \alpha^x \alpha^dx.\]By considering the ratio of y values at \(x+dx\) to \(x\),
\[ry = \frac{a \alpha^x \alpha^dx}{a \alpha^x} = \alpha^dx.\]From this relationship, we can estimate \(\alpha\) as
\[\alpha = ry^\frac{1}{dx}.\]- Parameters:
x (ndarray) â Array of x values.
y (ndarray) â Array of y values.
b (float) â Asymptote of decay function.
- Returns:
Base of decay function.
- Return type:
float