sl_gauss

trace.sl_gauss(A, n=150, deg=20, pdf='rademacher', rng='pcg', seed=-1, orth=0, num_threads=0)

Stochastic Gaussian quadrature approximation.

Computes a set of sample nodes and weights for the degree-k orthogonal polynomial approximating the cumulative spectral measure of A. This function can be used to approximate the spectral density of A, or to approximate the spectral sum of any function applied to the spectrum of A.

Parameters

Name	Type	Description	Default
A	ndarray, sparray, or LinearOperator	real symmetric operator.	required
n	int	Number of random vectors to sample for the quadrature estimate.	150
deg	int	Degree of the quadrature approximation.	20
rng	‘splitmix64’, ’xoshiro256**‘, ’pcg64’, ‘lcg64’, ‘mt64’	Random number generator to use (PCG64 by default).	'splitmix64'
seed	int	Seed to initialize the rng entropy source. Set seed > -1 for reproducibility.	-1
pdf	‘rademacher’, ‘normal’	Choice of zero-centered distribution to sample random vectors from.	'rademacher'
orth	int	Number of additional Lanczos vectors to orthogonalize against when building the Krylov basis.	0
num_threads	int	Number of threads to use to parallelize the computation. Setting num_threads < 1 to let OpenMP decide.	0

Returns

Type	Description
float	Estimate of the trace of the matrix function f(A).
(dict, optional)	If ‘info = True’, additional information about the computation.