freealg.eigh

freealg.eigh(A, N=None, psd=None, plots=False)

Estimate the eigenvalues of a matrix.

This function estimates the eigenvalues of the matrix \(\mathbf{A}\) or a larger matrix containing \(\mathbf{A}\) using free decompression.

Parameters:

Anumpy.ndarray

The symmetric real-valued matrix \(\mathbf{A}\) whose eigenvalues (or those of a matrix containing \(\mathbf{A}\)) are to be computed.

Nint, default=None

The size of the matrix containing \(\mathbf{A}\) to estimate eigenvalues of. If None, returns estimates of the eigenvalues of \(\mathbf{A}\) itself.

psdbool, default=None

Determines whether the matrix is positive-semidefinite (PSD; all eigenvalues are non-negative). If None, the matrix is considered PSD if all sampled eigenvalues are positive.

plotsbool, default=False

Print out all relevant plots for diagnosing eigenvalue accuracy.

Returns:

eigsnumpy.array

Eigenvalues of decompressed matrix

See also

cond

Notes

This is a convenience function for the freealg.FreeForm class with some effective defaults that work well for common random matrix ensembles. For improved performance and plotting utilites, consider fine-tuning parameters using the FreeForm class.

References

[1]

Reference.

Examples

>>> from freealg import cond
>>> from freealg.distributions import MarchenkoPastur

>>> mp = MarchenkoPastur(1/50)
>>> A = mp.matrix(3000)
>>> eigs = eigh(A)