eigs_lanczos

Performs an iterative eigenvalue calculation building eigenvectors using the Lanczos algorithm

JuliaC++C++ (explicit state initialization)

function eigs_lanczos(
    ops::OpSum,
    block::Block;
    neigvals::Int64 = 1,
    precision::Float64 = 1e-12,
    max_iterations::Int64 = 1000,
    force_complex::Bool = false,
    deflation_tol::Float64 = 1e-7,
    random_seed::Int64 = 42,
)

eigs_lanczos_result_t
eigs_lanczos(OpSum const &ops, Block const &block, int64_t neigvals = 1,
            double precision = 1e-12, int64_t max_iterations = 1000,
            bool force_complex = false, double deflation_tol = 1e-7,
            int64_t random_seed = 42);

eigs_lanczos_result_t 
eigs_lanczos(OpSum const &ops, Block const &block,
            State const &state, int64_t neigenvalues = 1,
            double precision = 1e-12, int64_t max_iterations = 1000,
            bool force_complex = false);

Parameters

Name	Description	Default
ops	OpSum defining the bonds of the operator
block	block on which the operator is defined
neigvals	number of eigenvalues to converge	1
precision	accuracy of the computed ground state	1e-12
max_iterations	maximum number of iterations	1000
force_complex	whether or not computation should be forced to have complex arithmetic	false
deflation_tol	tolerance for deflation, i.e. breakdown of Lanczos due to Krylow space exhaustion	1e-7
random_seed	random seed for setting up the initial vector	42

Returns

A struct with the following entries

Entry	Description
alphas	diagonal elements of the tridiagonal matrix
betas	off-diagonal elements of the tridiagonal matrix
eigenvalues	the computed Ritz eigenvalues of the tridiagonal matrix
eigenvectors	State of shape $D \times $`neigvals` holding all low-lying eigenvalues up to `neigvals`
niterations	number of iterations performed
criterion	string denoting the reason why the algorithm stopped