freealg.AlgebraicForm.density

AlgebraicForm.density(x=None, eta=0.0002, ac_only=False, plot=False, latex=False, save=False)

Evaluate spectral density of the fitted spectral curve.

Parameters:

xnumpy.array, default=None

Positions where density to be evaluated at. If None, an interval slightly larger than the support interval will be used.

etafloat, default=2e-4

A small number to be used for approximating the local behavior of atom with a mollifier of scale eta.

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.

Returns:

rhonumpy.array

Density at locations x.

See also

hilbert

stieltjes

Notes

In the density plot (assuming plot=True), the solid curve shows the absolutely-continuous part of the spectral density. If the density has atom(s), they are shown as an arrow, where the hight of the arrow is proportional to its mass, and can be read from the right ordinate of the plot.

Examples

>>> # Create a distribution with two bulks
>>> from freealg.distributions import CompoundFreePoisson
>>> cfp = CompoundFreePoisson(t=[2.0,  5.5], w=[0.75, 0.25],
...                           lam=0.1)

>>> # Create AlgebraicForm and fit the distribution
>>> from freealg import AlgebraicForm
>>> af = AlgebraicForm(cfp)
>>> af.fit(deg_m=3, deg_z=1)

>>> # Plot the density of the fitted spectral curve
>>> import numpy
>>> x = numpy.linspace(0, 8, 1000)
>>> rho = af.density(x, plot=True)