Source code for netket.hilbert.tensor_hilbert
# Copyright 2021 The NetKet Authors - All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Optional, Union
from collections.abc import Iterable
from abc import ABC
import numpy as np
from .abstract_hilbert import AbstractHilbert
[docs]
class TensorHilbert(ABC):
r"""Abstract base class for the tensor product of several sub-spaces,
representing the space.
This class can also be used to construct the correct type of TensorHilbert
subclass given the input types: if all input types are Generic hilbert spaces,
`TensorGeneralHilbert` will be constructed, while if they all are `DiscreteHilbert`
a `TensorDiscreteHilbert` will be created.
In general you should not construct this object directly, but you should
simply multiply different hilbert spaces together. In this case, Python's
`*` operator will be interpreted as a tensor product.
This is an abstract mixing class that should be inherited from, together
with another class that inherits from `AbstractHilbert`.
"""
def __new__(cls, *args, **kwargs):
# This logic overrides the constructor, such that if someone tries to
# construct this class directly by calling `TensorHilbert(...)`
# it will construct either a DiscreteHilbert or TensorDiscreteHilbert
from .tensor_hilbert_discrete import TensorDiscreteHilbert, DiscreteHilbert
if cls is TensorHilbert:
if all(isinstance(hi, DiscreteHilbert) for hi in args):
cls = TensorDiscreteHilbert
else:
cls = TensorGenericHilbert
return super().__new__(cls)
[docs]
def __init__(self, hilb_spaces: Iterable[AbstractHilbert], *args, **kwargs):
r"""Constructs a tensor Hilbert space.
Args:
*hilb: An iterable object containing at least 1 hilbert space.
"""
# Flatten "TensorHilberts" found inside hilb_spaces
_hilb_spaces_flat = []
for hi in hilb_spaces:
if isinstance(hi, TensorHilbert):
_hilb_spaces_flat.extend(hi.subspaces)
else:
_hilb_spaces_flat.append(hi)
hilb_spaces = _hilb_spaces_flat
self._hilbert_spaces = tuple(hilb_spaces)
self._n_hilbert_spaces = len(hilb_spaces)
self._hilbert_i = np.concatenate(
[[i for _ in range(hi.size)] for (i, hi) in enumerate(hilb_spaces)]
)
self._sizes = tuple([hi.size for hi in hilb_spaces])
self._cum_sizes = np.cumsum(self._sizes)
self._cum_indices = np.concatenate([[0], self._cum_sizes])
self._size = sum(self._sizes)
self._delta_indices_i = np.array(
[self._cum_indices[i] for i in self._hilbert_i]
)
super().__init__(
*args, **kwargs
) # forwards all unused arguments so that this class is a mixin.
@property
def size(self) -> int:
return self._size
@property
def subspaces(self) -> tuple[AbstractHilbert, ...]:
"""Tuplec ontaining all the subspaces of this tensor product of
Hilbert spaces.
"""
return self._hilbert_spaces
def _sub_index(self, i: int) -> int:
"""Internal function computing the subspace index for the given site
i.
Arguments:
i: Index of a site in :math:`[0, N)`.
Returns:
The index `j` such that self.subspaces[j] is the Hilbert space
containing site `i`.
"""
for j, sz in enumerate(self._cum_sizes):
if i < sz:
return j
@property
def _attrs(self):
return self._hilbert_spaces
[docs]
def ptrace(self, sites: Union[int, list]) -> Optional[AbstractHilbert]:
if isinstance(sites, int):
sites = [sites]
sites = np.sort(sites)
for site in sites:
if site < 0 or site >= self.size:
raise ValueError(
f"Site {site} not in this hilbert space of site {self.size}"
)
Nsites = len(sites)
if self.size - Nsites == 0:
return None
else:
new_hilberts = []
sz = 0
for hilb in self._hilbert_spaces:
sites_this_hilb = (
sites[np.logical_and(sites >= sz, sites < sz + hilb.size)] - sz
)
if len(sites_this_hilb) == 0:
new_hilberts.append(hilb)
else:
ptraced_hilb = hilb.ptrace(sites_this_hilb)
if ptraced_hilb is not None:
new_hilberts.append(ptraced_hilb)
sz += hilb.size
if len(new_hilberts) == 0:
return None
elif len(new_hilberts) >= 1:
hilb = new_hilberts[0]
for h in new_hilberts[1:]:
hilb = hilb * h
return hilb
def __repr__(self):
if len(self._hilbert_spaces) == 1:
return f"{type(self).__name__}({self._hilbert_spaces[0]})"
_str = f"{self._hilbert_spaces[0]}"
for hi in self._hilbert_spaces[1:]:
_str += f"⊗{hi}"
return _str
def __mul__(self, other):
spaces_l = self._hilbert_spaces[:-1]
space_center_l = self._hilbert_spaces[-1]
if isinstance(other, TensorHilbert):
space_center_r = other._hilbert_spaces[0]
spaces_r = other._hilbert_spaces[1:]
else:
space_center_r = other
spaces_r = tuple()
# Attempt to 'merge' the two spaces at the interface.
spaces_center = space_center_l * space_center_r
if isinstance(spaces_center, TensorHilbert):
spaces_center = (space_center_l, space_center_r)
else:
spaces_center = (spaces_center,)
return TensorHilbert(*spaces_l, *spaces_center, *spaces_r)
class TensorGenericHilbert(TensorHilbert, AbstractHilbert):
def __init__(self, *hilb_spaces: AbstractHilbert):
if not all(isinstance(hi, AbstractHilbert) for hi in hilb_spaces):
raise TypeError(
"Arguments to TensorHilbert must all be subtypes of "
"AbstractHilbert. However the types are:\n\n"
f"{list(type(hi) for hi in hilb_spaces)}\n"
)
super().__init__(hilb_spaces)
