freealg.FreeForm.stieltjes#

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

Compute Stieltjes transform of the spectral density on a grid.

This function evaluates Stieltjes transform on an array of points, or over a 2D Cartesian grid on the complex plane.

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, 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:

m_pnumpy.ndarray: The Stieltjes transform on the principal branch.
m_mnumpy.ndarray: The Stieltjes transform continued to the secondary branch.