dyson_equalizer.plots module#

The dyson_equalizer.plots module provides functions to create useful plots

dyson_equalizer.plots.plot_mp_density(eigs: ndarray, gamma: float, show_only_significant: int = None, matrix_label: str = 'X', ax: Axes | None = None) → None[source]#

Plots the density of eigenvalues of the covariance matrix and compares to the Marchenko-Pastur distribution

This function assumes the input are the eigenvalues of a covariance matrix of a random matrix whose entries have variance 1. These eigenvalues follow the Marchenko-Pastur distribution.

Parameters:

eigs: (n) numpy.array: The array of eigenvalues (e.g. of a covariance matrix) to plot
gamma: float: The ratio between the dimensions of the matrix (between 0 and 1)
show_only_significant: int, optional: Set this value to show only a small number of significant eigenvalues (defaults to None) This option is useful is some of the signal eigenvalues are much bigger than the noise.
matrix_label: str, optional: The name of the matrix that will be used as label (defaults to X)
ax: plt.Axes, optional: A matplotlib Axes object. If none is provided, a new figure is created.

See also

dyson_equalizer.algorithm.marchenko_pastur

Examples

We generate a random matrix X of size (100, 1000) and show that the eigenvalues of the covariance matrix Y = ¹⁄ₙXXᵀ follow a Marchenko-Pastur distribution.

import numpy as np
from dyson_equalizer.plots import plot_mp_density

m, n = 100, 1000
X = np.random.normal(size=(m, n))
Y = X @ X.T / n
eigs = sorted(np.linalg.eigvals(Y), reverse=True)

plot_mp_density(eigs, gamma=m/n)

(Source code, png, hires.png, pdf)

../_images/dyson_equalizer-plots-1.png — Eigenvalues plot of a random matrix#

dyson_equalizer.plots.plot_mp_eigenvalues(eigs: ndarray, gamma: float, eigenvalues_to_show: int = 100, log_y: bool = True, matrix_label: str = 'X', ax: Axes | None = None) → None[source]#

Plots the eigenvalues of the covariance matrix and compares to the Marchenko-Pastur threshold

This function assumes the input are the eigenvalues of a covariance matrix of a random matrix whose entries have variance 1. These eigenvalues follow the Marchenko-Pastur distribution.

Parameters:

eigs: (n) numpy.array: The array of eigenvalues (e.g. of a covariance matrix) to plot
gamma: float: The ratio between the dimensions of the matrix (between 0 and 1)
eigenvalues_to_show: int, optional: The number of eigenvalues to show in the plot (defaults to 100)
log_y: bool, optional: Whether the y-axis should be logarithmic (defaults to True)
matrix_label: str, optional: The name of the matrix that will be used as label (defaults to X)
ax: plt.Axes, optional: A matplotlib Axes object. If none is provided, a new figure is created.