quimb.tensor.belief_propagation.l1bp

Classes

L1BP

Lazy 1-norm belief propagation. BP is run between groups of tensors

Functions

contract_l1bp(tn[, max_iterations, tol, site_tags, ...])

Estimate the contraction of tn using lazy 1-norm belief propagation.

Module Contents

class quimb.tensor.belief_propagation.l1bp.L1BP(tn, site_tags=None, *, damping=0.0, update='sequential', normalize=None, distance=None, local_convergence=True, optimize='auto-hq', message_init_function=None, contract_every=None, inplace=False, **contract_opts)

Bases: quimb.tensor.belief_propagation.bp_common.BeliefPropagationCommon

Lazy 1-norm belief propagation. BP is run between groups of tensors defined by site_tags. The message updates are lazy contractions.

Parameters:

  • tn (TensorNetwork) – The tensor network to run BP on.

  • site_tags (sequence of str, optional) – The tags identifying the sites in tn, each tag forms a region, which should not overlap. If the tensor network is structured, then these are inferred automatically.

  • damping (float or callable, optional) – The damping factor to apply to messages. This simply mixes some part of the old message into the new one, with the final message being damping * old + (1 - damping) * new. This makes convergence more reliable but slower.

  • update ({'sequential', 'parallel'}, optional) – Whether to update messages sequentially (newly computed messages are immediately used for other updates in the same iteration round) or in parallel (all messages are comptued using messages from the previous round only). Sequential generally helps convergence but parallel can possibly converge to differnt solutions.

  • normalize ({'L1', 'L2', 'L2phased', 'Linf', callable}, optional) – How to normalize messages after each update. If None choose automatically. If a callable, it should take a message and return the normalized message. If a string, it should be one of ‘L1’, ‘L2’, ‘L2phased’, ‘Linf’ for the corresponding norms. ‘L2phased’ is like ‘L2’ but also normalizes the phase of the message, by default used for complex dtypes.

  • distance ({'L1', 'L2', 'L2phased', 'Linf', 'cosine', callable}, optional) – How to compute the distance between messages to check for convergence. If None choose automatically. If a callable, it should take two messages and return the distance. If a string, it should be one of ‘L1’, ‘L2’, ‘L2phased’, ‘Linf’, or ‘cosine’ for the corresponding norms. ‘L2phased’ is like ‘L2’ but also normalizes the phases of the messages, by default used for complex dtypes if phased normalization is not already being used.

  • local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.

  • optimize (str or PathOptimizer, optional) – The path optimizer to use when contracting the messages.

  • contract_every (int, optional) – If not None, ‘contract’ (via BP) the tensor network every contract_every iterations. The resulting values are stored in zvals at corresponding points zval_its.

  • inplace (bool, optional) – Whether to perform any operations inplace on the input tensor network.

  • contract_opts – Other options supplied to cotengra.array_contract.

local_convergence = True
optimize = 'auto-hq'
contract_opts
touched
messages
contraction_tns
iterate(tol=5e-06)

Perform a single iteration of belief propagation. Subclasses should implement this method, returning either max_mdiff or a dictionary containing max_mdiff and any other relevant information:

{

“nconv”: nconv, “ncheck”: ncheck, “max_mdiff”: max_mdiff,

}

contract(strip_exponent=False, check_zero=True)

Contract the tensor network and return the resulting value.

normalize_message_pairs()

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).

quimb.tensor.belief_propagation.l1bp.contract_l1bp(tn, max_iterations=1000, tol=5e-06, site_tags=None, damping=0.0, update='sequential', diis=False, local_convergence=True, optimize='auto-hq', strip_exponent=False, info=None, progbar=False, **contract_opts)

Estimate the contraction of tn using lazy 1-norm belief propagation.

Parameters:

  • tn (TensorNetwork) – The tensor network to contract.

  • max_iterations (int, optional) – The maximum number of iterations to perform.

  • tol (float, optional) – The convergence tolerance for messages.

  • site_tags (sequence of str, optional) – The tags identifying the sites in tn, each tag forms a region. If the tensor network is structured, then these are inferred automatically.

  • damping (float, optional) – The damping parameter to use, defaults to no damping.

  • update ({'parallel', 'sequential'}, optional) – Whether to update all messages in parallel or sequentially.

  • local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.

  • optimize (str or PathOptimizer, optional) – The path optimizer to use when contracting the messages.

  • progbar (bool, optional) – Whether to show a progress bar.

  • 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.

  • contract_opts – Other options supplied to cotengra.array_contract.