# 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.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
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from typing import Optional
import jax
import numpy as np
from jax import numpy as jnp
from netket.graph import AbstractGraph
from .base import MetropolisRule
[docs]
class ExchangeRule(MetropolisRule):
r"""
A Rule exchanging the state on a random couple of sites, chosen from a list of
possible couples (clusters).
This rule acts on two local degree of freedom :math:`s_i` and :math:`s_j`,
and proposes a new state: :math:`s_1 \dots s^\prime_i \dots s^\prime_j \dots s_N`,
where in general :math:`s^\prime_i \neq s_i` and :math:`s^\prime_j \neq s_j`.
The sites :math:`i` and :math:`j` are also chosen to be within a maximum graph
distance of :math:`d_{\mathrm{max}}`.
The transition probability associated to this sampler can
be decomposed into two steps:
1. A pair of indices :math:`i,j = 1\dots N`, and such
that :math:`\mathrm{dist}(i,j) \leq d_{\mathrm{max}}`,
is chosen with uniform probability.
2. The sites are exchanged, i.e. :math:`s^\prime_i = s_j` and :math:`s^\prime_j = s_i`.
Notice that this sampling method generates random permutations of the quantum
numbers, thus global quantities such as the sum of the local quantum numbers
are conserved during the sampling.
This scheme should be used then only when sampling in a
region where :math:`\sum_i s_i = \mathrm{constant}` is needed,
otherwise the sampling would be strongly not ergodic.
"""
clusters: jax.Array
r"""2-Dimensional tensor :math:`T_{i,j}` of shape
:math:`N_\text{clusters}\times 2` where the first dimension
runs over the list of 2-site clusters and the second dimension
runs over the 2 sites of those clusters.
The Exchange rule will swap the two sites of a random row of this
matrix at every Metropolis step.
"""
[docs]
def __init__(
self,
*,
clusters: Optional[list[tuple[int, int]]] = None,
graph: Optional[AbstractGraph] = None,
d_max: int = 1,
):
r"""
Constructs the Exchange Rule.
You can pass either a list of clusters or a netket graph object to
determine the clusters to exchange.
Args:
clusters: The list of clusters that can be exchanged. This should be
a list of 2-tuples containing two integers. Every tuple is an edge,
or cluster of sites to be exchanged.
graph: A graph, from which the edges determine the clusters
that can be exchanged.
d_max: Only valid if a graph is passed in. The maximum distance
between two sites
"""
if clusters is None and graph is not None:
clusters = compute_clusters(graph, d_max)
elif not (clusters is not None and graph is None):
raise ValueError(
"""You must either provide the list of exchange-clusters or a netket graph, from
which clusters will be computed using the maximum distance d_max. """
)
self.clusters = jnp.array(clusters)
[docs]
def transition(rule, sampler, machine, parameters, state, key, σ):
n_chains = σ.shape[0]
# pick a random cluster
cluster_id = jax.random.randint(
key, shape=(n_chains,), minval=0, maxval=rule.clusters.shape[0]
)
def scalar_update_fun(σ, cluster):
# sites to be exchanged,
si = rule.clusters[cluster, 0]
sj = rule.clusters[cluster, 1]
σp = σ.at[si].set(σ[sj])
return σp.at[sj].set(σ[si])
return (
jax.vmap(scalar_update_fun, in_axes=(0, 0), out_axes=0)(σ, cluster_id),
None,
)
def __repr__(self):
return f"ExchangeRule(# of clusters: {len(self.clusters)})"
def compute_clusters(graph: AbstractGraph, d_max: int):
"""
Given a netket graph and a maximum distance, computes all clusters.
If `d_max = 1` this is equivalent to taking the edges of the graph.
Then adds next-nearest neighbors and so on.
"""
clusters = []
distances = np.asarray(graph.distances())
size = distances.shape[0]
for i in range(size):
for j in range(i + 1, size):
if distances[i][j] <= d_max:
clusters.append((i, j))
res_clusters = np.empty((len(clusters), 2), dtype=np.int64)
for i, cluster in enumerate(clusters):
res_clusters[i] = np.asarray(cluster)
return res_clusters
