Misc Module¶

The misc module contains commonly used functions.

misc.two_d_gaussian(span, amplitude, mu_x, mu_y, sigma_x, sigma_y, theta, baseline)¶: 2D Gaussian distribution

\begin{gather*} f(x,y) = \text{baseline} + A \exp \left [ -(x-\mu_x)^2 - 2b ( x-\mu_x)( y-\mu_y) - c(y-\mu_y)^2 \right ] \\ a = \frac{\cos^2\theta}{2\sigma_x^2} + \frac{\sin^2\theta}{2\sigma_y^2} \\ b = -\frac{\sin 2\theta}{4\sigma_x^2} + \frac{\sin 2\theta}{4\sigma_y^2} \\ a = \frac{\sin^2\theta}{2\sigma_x^2} + \frac{\cos^2\theta}{2\sigma_y^2} \end{gather*}

misc.super_gauss_function(x, baseline, amplitude, mean, sigma, power)¶: Higher order Gaussian

\[f(x) = \text{baseline} + A \exp \left [ \left ( \frac{x-\mu_x}{ 2\sigma^2_x}\right)^p\right]\]

misc.mundane_gauss_function(x, baseline, amplitude, mean, sigma)¶: Gaussian distribution

\[f(x) = \text{baseline} + A \exp \left [ \frac{x-\mu_x}{ 2\sigma^2_x}\right]\]

misc.skewnormal(x, loc, scale, shape, amplitude, baseline)¶: skewnormal distribution

\begin{gather*} f(x) = \text{baseline} + \frac{2A}{\text{scale}} \phi(t) \Phi(\alpha t) \\ \phi(x) = \frac{1}{\sqrt{2 \pi}} e^{- \frac{t^2}{2}} \\ \Phi(x) = \frac{1}{2} \left [1+ \text{erf} \left( \frac{t}{ \sqrt{2}} \right) \right ] \\ t \to \frac{x-\text{location}}{\text{scale}} \end{gather*}