LanczosGroundState

Inheritance Diagram

Inheritance diagram of tenpy.linalg.krylov_based.LanczosGroundState

Methods

LanczosGroundState.__init__(H, psi0, options)

LanczosGroundState.iadd_prefactor_other(w, ...)

LanczosGroundState.iscale_prefactor(w, scale)

LanczosGroundState.run()

Find the ground state of H.
class tenpy.linalg.krylov_based.LanczosGroundState(H, psi0, options)[source]

Bases: KrylovBased

Lanczos algorithm to find the ground state.

Assumes that H is hermitian.

Options

config LanczosGroundState
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 [...]

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 (from KrylovBased) in KrylovBased

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.

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.