LanczosGroundState¶

full name: tenpy.linalg.krylov_based.LanczosGroundState
parent module: tenpy.linalg.krylov_based
type: class

Inheritance Diagram

Methods

`LanczosGroundState.__init__`(H, psi0, options)
`LanczosGroundState.run`()	Find the ground state of H.

class tenpy.linalg.krylov_based.LanczosGroundState(H, psi0, options, orthogonal_to=[])[source]¶

Bases: KrylovBased

Lanczos algorithm to find the ground state.

Assumes that H is hermitian.

Deprecated since version 0.6.0: Renamed attribute params to options.

Deprecated since version 0.6.0: Going to remove the orthogonal_to argument. Instead, replace H with OrthogonalNpcLinearOperator(H, orthogonal_to) using the OrthogonalNpcLinearOperator.

Options

config LanczosGroundState¶

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 [...]
E_tol	Stop if energy difference per step < `E_tol`
min_gap (from KrylovBased) in KrylovBased	Lower cutoff for the gap estimate used in the P_tol criterion.
N_cache	The maximum number of `psi` to keep in memory during the first iteration. [...]
N_max (from KrylovBased) in KrylovBased	Maximum number of steps to perform.
N_min (from KrylovBased) in KrylovBased	Minimum number of steps to perform.
P_tol (from KrylovBased) in KrylovBased	Tolerance for the error estimate from the Ritz Residual, [...]
reortho	For poorly conditioned matrices, one can quickly loose orthogonality of the [...]

option E_tol: float¶: Stop if energy difference per step < E_tol

option N_cache: int¶: The maximum number of psi to keep in memory during the first iteration. By default, we keep all states (up to N_max). Set this to a number >= 2 if you are short on memory. The penalty is that one needs another Lanczos iteration to determine the ground state in the end, i.e., runtime is large.

option reortho: bool¶: For poorly conditioned matrices, one can quickly loose orthogonality of the generated Krylov basis. If reortho is True, we re-orthogonalize against all the vectors kept in cache to avoid that problem.

run()[source]¶

Find the ground state of H.

Returns

E0 (float) – Ground state energy (estimate).
psi0 (Array) – Ground state vector (estimate).
N (int) – Used dimension of the Krylov space, i.e., how many iterations where performed.