rb_decay

rb_decay(x, y, b=0.5)

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

$$y^{\prime }(x)=y(x)-b=a{\alpha }^x,$$

and thus,

$$y^{\prime }(x+dx)=a{\alpha }^x{\alpha }^{d}x.$$

By considering the ratio of y values at $x+dx$ to $x$,

$$ry=\frac{a{\alpha }^x{\alpha }^{d}x}{a{\alpha }^x}={\alpha }^{d}x.$$

From this relationship, we can estimate $\alpha$ as

$$\alpha =r{y}^{\frac{1}{dx}}.$$

Parameters:

• x (ndarray) – Array of x values.

• y (ndarray) – Array of y values.

• b (float) – Asymptote of decay function.

Returns:

Base of decay function.

Return type:

float