freealg.FreeForm.decompress#

FreeForm.decompress(size, x=None, method='newton', max_iter=500, step_size=0.1, tolerance=0.0001, plot=False, latex=False, save=False, plot_diagnostics=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{'newton', 'secant'}, default= 'newton': Root-finding method.
max_iter: int, default=500: Maximum number of root-finding method iterations.
step_size: float, default=0.1: Step size for Newton iterations.
tolerance: float, default=1e-4: Tolerance for the solution obtained by the Newton solver. Also used for the finite difference approximation to the derivative.
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.
plot_diagnosticsbool, default=False: Plots diagnostics including convergence and number of iterations of root finding method.

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 od 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