freealg.distributions.ChiralBlock

class freealg.distributions.ChiralBlock(alpha, beta, c)

Twisted chiral block model.

Parameters:

alphafloat

The parameter \(\alpha\). See notes below.

betafloat

The parameter \(\beta\). See notes below.

cfloat

Ratio parameter \(c = p / n\). See notes below. It must be > 0.

Notes

The chiral block model corresponds to the bipartite biregular graph with the matrix

\[ \begin{align}\begin{aligned}\begin{split}\mathbf{A} = \begin{bmatrix} \alpha \mathbf{I} & \mathbf{X} \\ \mathbf{A}^{\intercal} & \beta \mathbf{I}\end{split}\\\end{bmatrix},\end{aligned}\end{align} \]

where \(\mathbf{X} \in \mathbb{R}^{p \times n}\), and \(c = p / n \in (0, \infty)\).

Methods

density([x, eta, ac_only, plot, latex, ...])	Density of distribution.
stieltjes(z[, alt_branch])	Stieltjes transform
support()	Support
sample(size[, x_min, x_max, method, seed, ...])	Sample from distribution.
matrix(size[, seed])	Generate matrix with the spectral density of the distribution.

roots	Roots of polynomial implicitly representing Stieltjes transform
poly	Polynomial coefficients implicitly representing the Stieltjes