freealg.FreeForm.decompress#

FreeForm.decompress(size, x=None, max_iter=500, eigvals=True, tolerance=1e-09, plot=False, latex=False, save=False)#

Free decompression of spectral density.

Parameters:

sizeint: Size of the decompressed matrix.
xnumpy.array, default=None: Positions where density to be evaluated at. If None, an interval slightly larger than the support interval will be used.
max_iter: int, default=500: Maximum number of secant method iterations.
eigvals: bool, default=True: Return estimated (sampled) eigenvalues as well as the density.
tolerance: float, default=1e-9: Tolerance for the solution obtained by the Newton solver. Also used for the finite difference approximation to the derivative.
seedint, default=None: Seed for random number generator. Used for QMC sampling.
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:

xnumpy.array: Locations where the spectral density is estimated
rhonumpy.array: Estimated spectral density at locations x
eigsnumpy.array: Estimated eigenvalues as low-discrepancy samples of the estimated spectral density. Only returns if eigvals=True.