Source code for netket.hilbert.discrete_hilbert

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from typing import Optional, Union
from collections.abc import Iterator
from textwrap import dedent
from functools import reduce

import numpy as np

from netket.utils.types import Array
from netket.errors import HilbertIndexingDuringTracingError, concrete_or_error

from .abstract_hilbert import AbstractHilbert

max_states = np.iinfo(np.int32).max
"""int: Maximum number of states that can be indexed"""


def _is_indexable(shape):
    """
    Returns whether a discrete Hilbert space of shape `shape` is
    indexable (i.e., its total number of states is below the maximum).
    """
    log_max = np.log(max_states)
    return np.sum(np.log(shape)) <= log_max


[docs] class DiscreteHilbert(AbstractHilbert): """Abstract class for an hilbert space defined on a lattice. This class defines the common interface that can be used to interact with hilbert spaces on lattices. """
[docs] def __init__(self, shape: tuple[int, ...]): """ Initializes a discrete Hilbert space with a basis of given shape. Args: shape: The local dimension of the Hilbert space for each degree of freedom. """ self._shape = tuple(shape) super().__init__()
@property def shape(self) -> tuple[int, ...]: r"""The size of the hilbert space on every site.""" return self._shape @property def constrained(self) -> bool: r"""The hilbert space does not contains `prod(hilbert.shape)` basis states. Typical constraints are population constraints (such as fixed number of bosons, fixed magnetization...) which ensure that only a subset of the total unconstrained space is populated. Typically, objects defined in the constrained space cannot be converted to QuTiP or other formats. """ raise NotImplementedError( # pragma: no cover dedent( f""" `constrained` is not implemented for discrete hilbert space {type(self)}. """ ) ) @property def is_finite(self) -> bool: r"""Whether the local hilbert space is finite.""" raise NotImplementedError( # pragma: no cover dedent( f""" `is_finite` is not implemented for discrete hilbert space {type(self)}. """ ) ) @property def n_states(self) -> int: r"""The total dimension of the many-body Hilbert space. Throws an exception iff the space is not indexable.""" raise NotImplementedError( # pragma: no cover dedent( f""" `n_states` is not implemented for discrete hilbert space {type(self)}. """ ) )
[docs] def size_at_index(self, i: int) -> int: r"""Size of the local degrees of freedom for the i-th variable. Args: i: The index of the desired site Returns: The number of degrees of freedom at that site """ return self.shape[i] # pragma: no cover
[docs] def states_at_index(self, i: int) -> Optional[list[float]]: r"""A list of discrete local quantum numbers at the site i. If the local states are infinitely many, None is returned. Args: i: The index of the desired site. Returns: A list of values or None if there are infinitely many. """ raise NotImplementedError() # pragma: no cover
[docs] def numbers_to_states(self, numbers: Union[int, np.ndarray]) -> np.ndarray: r"""Returns the quantum numbers corresponding to the n-th basis state for input n. `n` is an array of integer indices such that :code:`numbers[k]=Index(states[k])`. Throws an exception iff the space is not indexable. Args: numbers (numpy.array): Batch of input numbers to be converted into arrays of quantum numbers. """ numbers = concrete_or_error( np.asarray, numbers, HilbertIndexingDuringTracingError ) numbers_r = np.asarray(np.reshape(numbers, -1)) if np.any(numbers >= self.n_states): raise ValueError("numbers outside the range of allowed states") out = self._numbers_to_states(numbers_r) return out.reshape((*numbers.shape, self.size))
[docs] def states_to_numbers(self, states: np.ndarray) -> Union[int, np.ndarray]: r"""Returns the basis state number corresponding to given quantum states. The states are given in a batch, such that states[k] has shape (hilbert.size). Throws an exception iff the space is not indexable. Args: states: Batch of states to be converted into the corresponding integers. Returns: numpy.darray: Array of integers corresponding to states. """ if states.shape[-1] != self.size: raise ValueError( f"Size of this state ({states.shape[-1]}) not" f"corresponding to this hilbert space {self.size}" ) states = concrete_or_error( np.asarray, states, HilbertIndexingDuringTracingError ) states_r = np.asarray(np.reshape(states, (-1, states.shape[-1]))) out = self._states_to_numbers(states_r) if states.ndim == 1: return out[0] else: return out.reshape(states.shape[:-1])
[docs] def states(self) -> Iterator[np.ndarray]: r"""Returns an iterator over all valid configurations of the Hilbert space. Throws an exception iff the space is not indexable. Iterating over all states with this method is typically inefficient, and ```all_states``` should be preferred. """ for i in range(self.n_states): yield self.numbers_to_states(i).reshape(-1)
[docs] def all_states(self) -> np.ndarray: r"""Returns all valid states of the Hilbert space. Throws an exception if the space is not indexable. Returns: A (n_states x size) batch of states. this corresponds to the pre-allocated array if it was passed. """ numbers = np.arange(0, self.n_states, dtype=np.int64) return self.numbers_to_states(numbers)
[docs] def states_to_local_indices(self, x: Array): r"""Returns a tensor with the same shape of `x`, where all local values are converted to indices in the range `0...self.shape[i]`. This function is guaranteed to be jax-jittable. For the `Fock` space this returns `x`, but for other hilbert spaces such as `Spin` this returns an array of indices. .. warning:: This function is experimental. Use at your own risk. Args: x: a tensor containing samples from this hilbert space Returns: a tensor containing integer indices into the local hilbert """ raise NotImplementedError( "states_to_local_indices(self, x) is not " f"implemented for Hilbert space {self} of type {type(self)}" )
@property def is_indexable(self) -> bool: """Whether the space can be indexed with an integer""" if not self.is_finite: return False return _is_indexable(self.shape) def __mul__(self, other: "DiscreteHilbert"): if type(self) == type(other): res = self._mul_sametype_(other) if res is not NotImplemented: return res if isinstance(other, DiscreteHilbert): from .tensor_hilbert_discrete import TensorDiscreteHilbert return TensorDiscreteHilbert(self, other) elif isinstance(other, AbstractHilbert): from .tensor_hilbert import TensorGenericHilbert return TensorGenericHilbert(self, other) return NotImplemented def __pow__(self, n): return reduce(lambda x, y: x * y, [self for _ in range(n)])