Arnoldi

Inheritance Diagram

Inheritance diagram of tenpy.linalg.lanczos.Arnoldi

Methods

Arnoldi.__init__(H, psi0, options)

Arnoldi.run()

Find the ground state of H.

class tenpy.linalg.lanczos.Arnoldi(H, psi0, options)[source]

Bases: tenpy.linalg.lanczos.KrylovBased

Arnoldi method for diagonalizing square, non-hermitian/symmetric matrices.

Generalization of LanczosGroundState, allowing general, square matrices.

Options

config Arnoldi
option summary

cutoff (from KrylovBased) in KrylovBased

Cutoff to abort if the norm of the new krylov vecotr is too small. [...]

E_shift (from KrylovBased) in KrylovBased

Shift the energy (=eigenvalues) by that amount *during* the Lanczos run by [...]

min_gap (from KrylovBased) in KrylovBased

Lower cutoff for the gap estimate used in the P_tol criterion.

N_max (from KrylovBased) in KrylovBased

Maximum number of steps to perform.

N_min (from KrylovBased) in KrylovBased

Minimum number of steps to perform.

num_ev

Number of eigenvectors to look for/return in `run`.

P_tol (from KrylovBased) in KrylovBased

Tolerance for the error estimate from the Ritz Residual, [...]

which

Determines which (extremal) eigenvalues to look for, name [...]

option which: 'LM' | 'LR' | 'SR'

Determines which (extremal) eigenvalues to look for, name largest magnitude (in absolute value, 'LM'), or largest or smallest real part ('LR' and 'SR', respectively).

option num_ev: int

Number of eigenvectors to look for/return in run.

run()[source]

Find the ground state of H.

Returns

  • E0s (numpy array) – Best eigenvalue estimates, Arnoldi.num_ev entries, sorted according to Arnoldi.which.

  • psis (list of Array) – Corresponding best eigenvectors (estimates).

  • N (int) – Used dimension of the Krylov space, i.e., how many iterations where performed.