freealg.supp#

freealg.supp(eigs, method='asymp', k=None, p=0.001)#

Estimates the support of the eigenvalue density.

Parameters:

method{'range', 'asymp', 'jackknife', 'regression', 'interior', 'interior_smooth'}, default= 'asymp'

The method of support estimation:

'range': no estimation; the support is the range of the eigenvalues.
'asymp': assume the relative error in the min/max estimator is \(1/n\).
'jackknife': estimates the support using Quenouille’s [1] jackknife estimator. Fast and simple, more accurate than the range.
'regression': estimates the support by performing a regression under the assumption that the edge behavior is of square-root type. Often most accurate.
'interior': estimates a support assuming the range overestimates; uses quantiles \((p, 1-p)\).
'interior_smooth': same as 'interior' but using kernel density estimation, from [2].

kint, default = None

Number of extreme order statistics to use for method='regression'.

pfloat, default=0.001

The edges of the support of the distribution is detected by the \(p\)-quantile on the left and \((1-p)\)-quantile on the right where method='interior' or method='interior_smooth'. This value should be between 0 and 1, ideally a small number close to zero.

Returns:

lam_mfloat: Lower end of support interval \([\lambda_{-}, \lambda_{+}]\).
lam_pfloat: Upper end of support interval \([\lambda_{-}, \lambda_{+}]\).