freealg.distributions.CompoundFreePoisson.density

CompoundFreePoisson.density(x=None, eta=0.0002, max_iter=100, tol=1e-12, ac_only=True, plot=False, latex=False, save=False, eig=None)

Density of distribution.

Parameters:

xnumpy.array, default=None

The locations where density is evaluated at. If None, an interval slightly larger than the supp interval of the spectral density is used.

rhonumpy.array, default=None

Density. If None, it will be computed.

etafloat, default=2e-4

The offset \(\eta\) from the real axis where the density is evaluated using Plemelj formula at \(z = x + i \eta\).

max_iterint, default=100

Maximum number of Newton iterations to solve for the Stieltjes root.

tolfloat, default=1e-12

Tolerance for Newton iterations to solve for the Stieltjes root.

ac_onlybool, default=True

If True, it returns the absolutely-continuous part of density.

plotbool, default=False

If True, density is plotted.

latexbool, default=False

If True, the plot is rendered using LaTeX. This option is relevant only if plot=True.

savebool, default=False

If not False, the plot is saved. If a string is given, it is assumed to the save filename (with the file extension). This option is relevant only if plot=True.

eignumpy.array, default=None

A collection of eigenvalues to compare to via histogram. This option is relevant only if plot=True.

Returns:

rhonumpy.array

Density.