freealg.distributions.Wachter.stieltjes#

Wachter.stieltjes(x=None, y=None, plot=False, on_disk=False, latex=False, save=False)#

Stieltjes transform of distribution.

Parameters:

xnumpy.array, default=None: The x axis of the grid where the Stieltjes transform is evaluated. If None, an interval slightly larger than the support interval of the spectral density is used.
ynumpy.array, default=None: The y axis of the grid where the Stieltjes transform is evaluated. If None, a grid on the interval [-1, 1] is used.
plotbool, default=False: If True, Stieltjes transform is plotted.
on_diskbool, default=False: If True, the Stieltjes transform is mapped on unit disk. This option relevant only if plot=True.
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:

Examples

>>> from freealg.distributions import Wachter
>>> wa = Wachter(2, 3)
>>> m1, m2 = wa.stieltjes(plot=True)

Plot on unit disk using Cayley transform:

>>> m1, m2 = wa.stieltjes(plot=True, on_disk=True)