quimb.experimental.belief_propagation.d1bp¶

Belief propagation for standard tensor networks. This:

assumes no hyper indices, only standard bonds.
assumes a single (‘dense’) tensor per site
works directly on the ‘1-norm’ i.e. scalar tensor network

This is the simplest version of belief propagation, and is useful for simple investigations.

Classes¶

D1BP

Dense (as in one tensor per site) 1-norm (as in for 'classical' systems)

Functions¶

`initialize_messages`(tn[, fill_fn])
`contract_d1bp`(tn[, max_iterations, tol, damping, ...])	Estimate the contraction of standard tensor network `tn` using dense

Module Contents¶

quimb.experimental.belief_propagation.d1bp.initialize_messages(tn, fill_fn=None)¶

class quimb.experimental.belief_propagation.d1bp.D1BP(tn, messages=None, damping=0.0, update='sequential', local_convergence=True, message_init_function=None)¶

Bases: quimb.experimental.belief_propagation.bp_common.BeliefPropagationCommon

Dense (as in one tensor per site) 1-norm (as in for ‘classical’ systems) belief propagation algorithm. Allows message reuse. This version assumes no hyper indices (i.e. a standard tensor network). This is the simplest version of belief propagation.

Parameters:

tn (TensorNetwork) – The tensor network to run BP on.
messages (dict[(str, int), array_like], optional) – The initial messages to use, effectively defaults to all ones if not specified.
damping (float, optional) – The damping factor to use, 0.0 means no damping.
update ({'sequential', 'parallel'}, optional) – Whether to update messages sequentially or in parallel.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
fill_fn (callable, optional) – If specified, use this function to fill in the initial messages.

tn¶

The target tensor network.

Type:: TensorNetwork

messages¶

The current messages. The key is a tuple of the index and tensor id that the message is being sent to.

Type:: dict[(str, int), array_like]

key_pairs¶

A dictionary mapping the key of a message to the key of the message propagating in the opposite direction.

Type:: dict[(str, int), (str, int)]

tn¶

damping¶

local_convergence¶

update¶

backend¶

_abs¶

_sum¶

_normalize¶

_distance¶

touched¶

key_pairs¶

iterate(tol=5e-06)¶

normalize_messages()¶: Normalize all messages such that for each bond <m_i|m_j> = 1 and <m_i|m_i> = <m_j|m_j> (but in general != 1).

get_gauged_tn()¶: Gauge the original TN by inserting the BP-approximated transfer matrix eigenvectors, which may be complex. The BP-contraction of this gauged network is then simply the product of zeroth entries of each tensor.

contract(strip_exponent=False)¶

quimb.experimental.belief_propagation.d1bp.contract_d1bp(tn, max_iterations=1000, tol=5e-06, damping=0.0, update='sequential', local_convergence=True, strip_exponent=False, info=None, progbar=False, **contract_opts)¶

Estimate the contraction of standard tensor network tn using dense 1-norm belief propagation.

Parameters:

tn (TensorNetwork) – The tensor network to contract, it should have no dangling or hyper indices.
max_iterations (int, optional) – The maximum number of iterations to run for.
tol (float, optional) – The convergence tolerance for messages.
damping (float, optional) – The damping parameter to use, defaults to no damping.
update ({'sequential', 'parallel'}, optional) – Whether to update messages sequentially or in parallel.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
strip_exponent (bool, optional) – Whether to strip the exponent from the final result. If True then the returned result is (mantissa, exponent).
info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.
progbar (bool, optional) – Whether to show a progress bar.