API Reference#

Free Forms#

The following classes core implementations defining the free objects.

`freealg.FreeForm`(A[, support, delta, dtype])	Free probability for large matrices.
`freealg.AlgebraicForm`(A[, support, delta, dtype])	Algebraic surrogate for ensemble models.
`freealg.GeometricForm`(A[, support, delta, dtype])	Geometric object representing Riemann surface for ensemble models.

The followings are the free version of some of the common linalg functions.

`freealg.eigvalsh`(A[, size, psd, seed, plot])	Estimate the eigenvalues of a matrix.
`freealg.cond`(A[, size, seed])	Estimate the condition number of a Hermitian positive-definite matrix.
`freealg.norm`(A[, size, order, seed])	Estimate the Schatten norm of a Hermitian matrix.
`freealg.trace`(A[, N, p, seed])	Estimate the trace of a power of a Hermitian matrix.
`freealg.slogdet`(A[, size, seed])	Estimate the sign and logarithm of the determinant of a Hermitian matrix.

The following functions are utilities for distributions.

`freealg.supp`(eigs[, method, k, p])	Estimates the support of the eigenvalue density.
`freealg.sample`(x, rho, num_pts[, method, seed])	Low-discrepancy sampling from density estimate.
`freealg.submatrix`(matrix, size[, paired, seed])	Randomly sample a submatrix from a larger matrix.
`freealg.kde`(eig, xs, lam_m, lam_p, h[, ...])	Kernel density estimation of eigenvalues.

The following classes define classical random ensembles.

`freealg.distributions.MarchenkoPastur`(lam[, ...])	Marchenko-Pastur distribution.
`freealg.distributions.Wigner`(r)	Wigner semicircle distribution.
`freealg.distributions.KestenMcKay`(d)	Kesten-McKay distribution.
`freealg.distributions.Wachter`(a, b)	Wachter distribution.
`freealg.distributions.Meixner`(a, b, c)	Meixner distribution.
`freealg.distributions.ChiralBlock`(alpha, beta, c)	Twisted chiral block model.
`freealg.distributions.DeformedWigner`(t, w[, ...])	Deformed Wiger distribution
`freealg.distributions.DeformedMarchenkoPastur`(t, w)	Deformed Marchenko-Pastur distribution
`freealg.distributions.CompoundFreePoisson`(t, ...)	Compound free Poisson distribution
`freealg.distributions.FreeLevy`(t, w, lam[, ...])	Free Levy distribution
`freealg.distributions.FussCatalan`([p])	Fuss-Catalan (a.k.a.

Function utilities for visualizing of real and complex functions.

`freealg.visualization.domain_coloring`(c[, ...])	Convert complex field c to RGB via HSV domain coloring.
`freealg.visualization.glue_branches`(z, m1, m2)	m12 is the mixing of m1 and m2 where it contains m1 on C^+ and m2 on C^-.
`freealg.visualization.hist`(array[, bins, m, ...])	Histogram (optionally ASH-smoothed) with detected multi-interval support and atom-centered bins.
`freealg.visualization.auto_bins`(array[, ...])	Automatic choice for the number of bins for the histogram of an array.