tbplas.DiagSolver

class tbplas.DiagSolver(model: Any, overlap: Any = None, enable_mpi: bool = False, echo_details: bool = True)

Base class for solvers based on exact diagonalization.

NOTE: we declare the type of ‘model’ and ‘overlap’ to be ‘Any’ for duck typing.

__model

model for which properties will be calculated

Type:: ‘PrimitiveCell’ or ‘Sample’ instance

__overlap

container for holding overlaps for primitive cells with non-orthogonal orbitals

Type:: ‘Overlap’ instance

__h_mat

dense Hamiltonian matrix

Type:: (num_orb, num_orb) complex128 array

__s_mat

dense overlap matrix for the general eigenvalue problem

Type:: (num_orb, num_orb) complex128 array

__init__(model: Any, overlap: Any = None, enable_mpi: bool = False, echo_details: bool = True) → None

Parameters:

model – primitive cell or sample under study
overlap – container for overlaps between orbitals
enable_mpi – whether to enable MPI-based parallelization
echo_details – whether to output parallelization details

Methods

`__init__`(model[, overlap, enable_mpi, ...])	param model: primitive cell or sample under study
`all_average`(data_local)	Average results over random samples broadcast to all process.
`all_reduce`(data_local)	Reduce local data and broadcast to all processes.
`average`(data_local)	Average results over random samples and store results to master process.
`barrier`()	Wrapper for self.comm.Barrier.
`bcast`(data_local)	Broadcast data from master to other processes.
`calc_bands`(k_points[, convention, solver, ...])	Calculate band structure along given k_path.
`calc_dos`(k_points[, e_min, e_max, e_step, ...])	Calculate density of states for given energy range and step.
`calc_states`(k_points[, convention, solver, ...])	Calculate energies and wave functions on k-points.
`dist_bound`(n_max)	Same as dist_range, but returns the lower and upper bounds.
`dist_list`(raw_list[, algorithm])	Distribute a list over processes.
`dist_range`(n_max)	Distribute range(n_max) over processes.
`log`([event, fmt])	Log the date and time of event.
`print`([text])	Print text on master process.
`reduce`(data_local)	Reduce local data to master process.

Attributes

`is_master`	Determine whether this is the master process.
`lat_vec`	Get the lattice vectors of the model.
`model_is_pc`	Check if the model is a primitive cell.
`mpi_enabled`	Determine whether MPI is enabled.
`num_orb`	Get the number of orbitals in the model.
`rank`	Interface for the '__rank' attribute.
`recip_lat_vec`	Get the reciprocal lattice vectors of the model in 1/nm.
`size`	Interface for the '__size' attribute.

__init__(model: Any, overlap: Any = None, enable_mpi: bool = False, echo_details: bool = True) → None

Parameters:

model – primitive cell or sample under study
overlap – container for overlaps between orbitals
enable_mpi – whether to enable MPI-based parallelization
echo_details – whether to output parallelization details

all_average(data_local: ndarray) → ndarray

Average results over random samples broadcast to all process.

Parameters:: data_local – local results on each process
Returns:: averaged data from data_local

all_reduce(data_local: ndarray) → ndarray

Reduce local data and broadcast to all processes.

Parameters:: data_local – local results on each process
Returns:: summed data from data_local

average(data_local: ndarray) → ndarray

Average results over random samples and store results to master process.

Parameters:: data_local – local results on each process
Returns:: averaged data from data_local

barrier() → None: Wrapper for self.comm.Barrier.

bcast(data_local: ndarray) → None

Broadcast data from master to other processes.

Parameters:: data_local – local results on each process
Returns:: None

calc_bands(k_points: ndarray, convention: int = 1, solver: str = 'lapack', orbital_indices: Union[Iterable[int], ndarray] = None, **kwargs) → namedtuple

Calculate band structure along given k_path.

The result is a named tuple with the following attributes: k_len: (num_kpt,) float64 array, length of k-path bands: (num_kpt, num_bands) float64 array, band structure proj: (num_kpt, num_bands) float64 array, projection on selected orbitals

Parameters:

k_points – (num_kpt, 3) float64 array FRACTIONAL coordinates of the k-points
convention – convention for setting up the Hamiltonian
solver – solver type, should be “lapack” or “arpack”
orbital_indices – indices of orbitals for evaluating projection, take all orbitals into consideration if no orbitals are specified
kwargs – arguments for the arpack solver

Returns:

k_len, band structure and projection packed in named tuple

Raises:

ValueError – if solver is neither lapack nor arpack

calc_dos(k_points: ndarray, e_min: float = None, e_max: float = None, e_step: float = 0.05, sigma: float = 0.05, basis: str = 'Gaussian', g_s: int = 1, **kwargs) → Tuple[ndarray, ndarray]

Calculate density of states for given energy range and step.

Parameters:

k_points – (num_kpt, 3) float64 array FRACTIONAL coordinates of k-points
e_min – lower bound of the energy range in eV
e_max – upper hound of the energy range in eV
e_step – energy step in eV
sigma – broadening parameter in eV
basis – basis function to approximate the Delta function
g_s – spin degeneracy
kwargs – arguments for ‘calc_bands’

Returns:

(energies, dos) energies: (num_grid,) float64 array energy grid corresponding to e_min, e_max and e_step dos: (num_grid,) float64 array density of states in states/eV

Raises:

ValueError – if basis is neither Gaussian nor Lorentzian, or the solver is neither lapack nor arpack

calc_states(k_points: ndarray, convention: int = 1, solver: str = 'lapack', all_reduce: bool = True, **kwargs) → Tuple[ndarray, ndarray]

Calculate energies and wave functions on k-points.

Parameters:

k_points – (num_kpt, 3) float64 array FRACTIONAL coordinates of the k-points
convention – convention for setting up the Hamiltonian
solver – solver type, should be “lapack” or “arpack”
all_reduce – whether to call MPI_Allreduce to synchronize the results on each process
kwargs – arguments for the arpack solver

Returns:

(bands, states) bands: (num_kpt, num_bands) float64 array energies on the k-points states: (num_kpt, num_bands, num_orb) complex128 array wave functions on the k-points, each ROW of states[i_k] is a wave function

Raises:

ValueError – if solver is neither lapack nor arpack

dist_bound(n_max: int) → Tuple[int, int]

Same as dist_range, but returns the lower and upper bounds. Both of the bounds are close, i.e. [i_min, i_max].

Parameters:: n_max – upper bound of range
Returns:: lower and upper bounds of subrange assigned to this process

dist_list(raw_list: List[Any], algorithm: str = 'range') → List[Any]

Distribute a list over processes.

Parameters:

raw_list – raw list to distribute
algorithm – distribution algorithm, should be either “remainder” or “range”

Returns:

sublist assigned to this process

dist_range(n_max: int) → range

Distribute range(n_max) over processes.

Parameters:: n_max – upper bound of the range
Returns:: subrange assigned to this process

log(event: str = '', fmt: str = '%x %X') → None

Log the date and time of event.

Parameters:

event – notice of the event
fmt – date and time format

Returns:

None.

print(text: str = '') → None

Print text on master process.

NOTE: flush=True is essential for some MPI implementations, e.g. MPICH3.

Parameters:: text – text to print
Returns:: None

reduce(data_local: ndarray) → ndarray

Reduce local data to master process.

Parameters:: data_local – local results on each process
Returns:: summed data from data_local

__weakref__: list of weak references to the object (if defined)

property is_master: bool: Determine whether this is the master process.

property lat_vec: ndarray

Get the lattice vectors of the model.

Returns:: (3, 3) float64 array lattice vectors of in nm

property model_is_pc: bool

Check if the model is a primitive cell.

Returns:: whether the model is a primitive cell

property mpi_enabled: bool: Determine whether MPI is enabled.

property num_orb: int

Get the number of orbitals in the model.

Returns:: number of orbitals

property rank: int

Interface for the ‘__rank’ attribute.

Returns:: rank of this MPI process

property recip_lat_vec: ndarray

Get the reciprocal lattice vectors of the model in 1/nm.

Returns:: (3, 3) float64 array reciprocal lattice vectors of in nm

property size: int

Interface for the ‘__size’ attribute.

Returns:: number of MPI processes