gwkokab.utils.math

Functions

beta_dist_concentrations_to_mean_variance(...)	Let \(\alpha\) and \(\beta\) be the shape parameters of a beta
beta_dist_mean_variance_to_concentrations(...)	Let \(\mu\) and \(\sigma^2\) be the mean and variance of a beta
cumtrapz(→ jaxtyping.Array)	Calculate the cumulative trapezoidal integration of y with respect to x.
logsubexp(→ jaxtyping.ArrayLike)	Compute \(\log(\exp(a) - \exp(b))\) in a numerically stable way.
truncnorm_logpdf(→ jaxtyping.ArrayLike)	Compute the log probability density function of a truncated normal distribution.

Module Contents

gwkokab.utils.math.beta_dist_concentrations_to_mean_variance(alpha: jaxtyping.ArrayLike, beta: jaxtyping.ArrayLike, loc: jaxtyping.ArrayLike = 0.0, scale: jaxtyping.ArrayLike = 1.0) → Tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

Let \(\alpha\) and \(\beta\) be the shape parameters of a beta distribution, \(a\) being the location and \(b\) being the scale. This function returns the mean and variance of the distribution. Then concentrations are given by:

\[\mu = a+b\frac{\alpha}{\alpha + \beta}\qquad \sigma^2 = b^2\frac{\alpha \beta}{(\alpha + \beta)^2 (\alpha + \beta + 1)}\]

Parameters:

• alpha (ArrayLike) – The shape parameter \(\alpha\).

• beta (ArrayLike) – The shape parameter \(\beta\).

• loc (ArrayLike) – The location \(a\) of the beta distribution.

• scale (ArrayLike) – The scale \(b\) of the beta distribution.

Returns:

The mean \(\mu\) and variance \(\sigma^2\) of the beta distribution.

Return type:

Tuple[ArrayLike, ArrayLike]

gwkokab.utils.math.beta_dist_mean_variance_to_concentrations(mean: jaxtyping.ArrayLike, variance: jaxtyping.ArrayLike, loc: jaxtyping.ArrayLike = 0.0, scale: jaxtyping.ArrayLike = 1.0) → Tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

Let \(\mu\) and \(\sigma^2\) be the mean and variance of a beta distribution, \(a\) being the location and \(b\) being the scale. This function returns the shape parameters \(\alpha\) and \(\beta\) of the distribution. Then concentrations are given by:

\[\alpha = -\frac{\mu-a}{b} \left(\left(\frac{\mu-a}{\sigma}\right)\left(\frac{\mu-a-b}{\sigma}\right)+1\right)\qquad \beta = \alpha\left(\frac{b}{\mu-a}-1\right)\]

Parameters:

• mean (ArrayLike) – The mean \(\mu\) of the beta distribution.

• variance (ArrayLike) – The variance \(\sigma^2\) of the beta distribution.

• loc (ArrayLike) – The location \(a\) of the beta distribution.

• scale (ArrayLike) – The scale \(b\) of the beta distribution.

Returns:

The shape parameters \(\alpha\) and \(\beta\) of the beta distribution.

Return type:

Tuple[ArrayLike, ArrayLike]

gwkokab.utils.math.cumtrapz(y: jaxtyping.Array, x: jaxtyping.Array) → jaxtyping.Array

Calculate the cumulative trapezoidal integration of y with respect to x.

Parameters:

• y (Array) – array to integrate

• x (Array) – array to integrate over

Returns:

The result of the cumulative trapezoidal integration of y with respect to x.

Return type:

Array

gwkokab.utils.math.logsubexp(a: jaxtyping.ArrayLike, b: jaxtyping.ArrayLike) → jaxtyping.ArrayLike

Compute \(\log(\exp(a) - \exp(b))\) in a numerically stable way.

Parameters:

• a (ArrayLike) – input array

• b (ArrayLike) – input array

Returns:

The value of \(\log(\exp(a) - \exp(b))\).

Return type:

ArrayLike

gwkokab.utils.math.truncnorm_logpdf(xx: jaxtyping.ArrayLike, loc: jaxtyping.ArrayLike, scale: jaxtyping.ArrayLike, low: jaxtyping.ArrayLike, high: jaxtyping.ArrayLike) → jaxtyping.ArrayLike

Compute the log probability density function of a truncated normal distribution.

Parameters:

• xx (ArrayLike) – The input array.

• loc (ArrayLike) – The mean of the distribution.

• scale (ArrayLike) – The standard deviation of the distribution.

• low (ArrayLike) – The lower bound of the distribution.

• high (ArrayLike) – The upper bound of the distribution.

Returns:

The log probability density function of the truncated normal distribution.

Return type:

ArrayLike