__all__ = ['krylovsolve']
from .. import QobjEvo
from .sesolve import SESolver
[docs]def krylovsolve(
H, psi0, tlist, krylov_dim, e_ops=None, args=None, options=None
):
"""
Schrodinger equation evolution of a state vector for time independent
Hamiltonians using Krylov method.
Evolve the state vector ("psi0") finding an approximation for the time
evolution operator of Hamiltonian ("H") by obtaining the projection of
the time evolution operator on a set of small dimensional Krylov
subspaces (m << dim(H)).
The output is either the state vector or unitary matrix at arbitrary points
in time (`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values. e_ops cannot be used in conjunction
with solving the Schrodinger operator equation
Parameters
----------
H : :obj:`.Qobj`, :obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format.
System Hamiltonian as a Qobj or QobjEvo for time-dependent
Hamiltonians. List of [:obj:`.Qobj`, :obj:`.Coefficient`] or callable
that can be made into :obj:`.QobjEvo` are also accepted.
psi0 : :class:`.Qobj`
Initial state vector (ket)
tlist : *list* / *array*
list of times for :math:`t`.
krylov_dim: int
Dimension of Krylov approximation subspaces used for the time
evolution approximation.
e_ops : :class:`.Qobj`, callable, or list, optional
Single operator or list of operators for which to evaluate
expectation values or callable or list of callable.
Callable signature must be, `f(t: float, state: Qobj)`.
See :func:`~qutip.core.expect.expect` for more detail of operator
expectation.
args : dict, optional
dictionary of parameters for time-dependent Hamiltonians
options : dict, optional
Dictionary of options for the solver.
- | store_final_state : bool
| Whether or not to store the final state of the evolution in the
result class.
- | store_states : bool, None
| Whether or not to store the state vectors or density matrices.
On `None` the states will be saved if no expectation operators are
given.
- | normalize_output : bool
| Normalize output state to hide ODE numerical errors.
- | progress_bar : str {'text', 'enhanced', 'tqdm', ''}
| How to present the solver progress.
'tqdm' uses the python module of the same name and raise an error
if not installed. Empty string or False will disable the bar.
- | progress_kwargs : dict
| kwargs to pass to the progress_bar. Qutip's bars use `chunk_size`.
- | atol: float
| Absolute tolerance of the ODE integrator.
- | nsteps : int
| Maximum number of (internally defined) steps allowed in one
``tlist`` step.
- | min_step, max_step : float
| Miniumum and maximum lenght of one internal step.
- | always_compute_step: bool
| If True, the step lenght is computed each time a new Krylov
subspace is computed. Otherwise it is computed only once when
creating the integrator.
- | sub_system_tol: float
| Tolerance to detect an happy breakdown. An happy breakdown happens
when the initial ket is in a subspace of the Hamiltonian smaller
than ``krylov_dim``.
Returns
-------
result: :class:`.Result`
An instance of the class :class:`.Result`, which contains
a *list of array* ``result.expect`` of expectation values for the times
specified by ``tlist``, and/or a *list* ``result.states`` of state
vectors or density matrices corresponding to the times in ``tlist`` [if
``e_ops`` is an empty list of ``store_states=True`` in options].
"""
H = QobjEvo(H, args=args, tlist=tlist)
options = options or {}
options["method"] = "krylov"
options["krylov_dim"] = krylov_dim
solver = SESolver(H, options=options)
return solver.run(psi0, tlist, e_ops=e_ops)