Arnoldi

• full name: tenpy.linalg.krylov_based.Arnoldi

• parent module: tenpy.linalg.krylov_based

• type: class

Inheritance Diagram

Methods

Arnoldi.__init__(H, psi0, options)
Arnoldi.iadd_prefactor_other(w, alpha, v)
Arnoldi.iscale_prefactor(w, scale)
Arnoldi.run()	Find the ground state of self.H.

class tenpy.linalg.krylov_based.Arnoldi(H, psi0, options)

Bases: 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 vector 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, [...]
reortho (from KrylovBased) in KrylovBased	For poorly conditioned matrices, one can quickly loose orthogonality of the [...]
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()

Find the ground state of self.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.