freealg.AlgebraicForm.decompress#

AlgebraicForm.decompress(size, x=None, method='moc', min_n_times=10, newton_opt={'armijo': 0.0001, 'max_iter': 50, 'min_lam': 1e-06, 'sweep': True, 'tol': 1e-12, 'w_min': 1e-14}, plot=False, latex=False, save=False, verbose=False)#

Free decompression of spectral density.

Parameters:

sizeint or array_like

Size(s) of the decompressed matrix. This can be a scalar or an array of sizes. For each matrix size in size array, a density is produced.

xnumpy.array, default=None

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

method{'moc', 'coeffs'`}, default= ``'moc'

Method of decompression:

'moc': Method of characteristics with Newton iterations.
'coeffs': Evolving polynomial coefficients directly.

min_n_timesint, default=10

Minimum number of inner sizes to evolve.

newton_optdict

A dictionary of settings to pass to Newton iteration solver.

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.

verbosebool, default=False

If True, it prints verbose be bugging information.

Returns:

rhonumpy.array or numpy.ndarray

Estimated spectral density at locations x. rho can be a 1D or 2D array output:

If size is a scalar, rho is a 1D array of the same size as x.
If size is an array of size n, rho is a 2D array with n rows, where each row corresponds to decompression to a size. Number of columns of rho is the same as the size of x.

xnumpy.array

Locations where the spectral density is estimated