quimb.tensor.belief_propagation.l2bp

Classes

L2BP

Lazy (as in multiple uncontracted tensors per site) 2-norm (as in for

Functions

_identity(x)

contract_l2bp(tn[, site_tags, damping, update, ...])

Estimate the norm squared of tn using lazy belief propagation.

compress_l2bp(tn, max_bond[, cutoff, cutoff_mode, ...])

Compress tn using lazy belief propagation, producing a tensor

Module Contents

quimb.tensor.belief_propagation.l2bp._identity(x)
class quimb.tensor.belief_propagation.l2bp.L2BP(tn, site_tags=None, *, damping=0.0, update='sequential', normalize=None, distance=None, symmetrize=True, local_convergence=True, optimize='auto-hq', contract_every=None, inplace=False, **contract_opts)

Bases: quimb.tensor.belief_propagation.bp_common.BeliefPropagationCommon

Lazy (as in multiple uncontracted tensors per site) 2-norm (as in for wavefunctions and operators) belief propagation.

Parameters:

  • tn (TensorNetwork) – The tensor network to form the 2-norm of and 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.

  • symmetrize (bool or callable, optional) – Whether to symmetrize the messages, i.e. for each message ensure that it is hermitian with respect to its bra and ket indices. If a callable it should take a message and return the symmetrized message.

  • 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
property symmetrize
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,

}

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). This is different to normalizing each message.

contract(strip_exponent=False, check_zero=True)

Estimate the contraction of the norm squared using the current messages.

partial_trace(site, normalized=True, optimize='auto-hq')
compress(tn, max_bond=None, cutoff=5e-06, cutoff_mode='rsum2', renorm=0, lazy=False)

Compress the state tn, assumed to matched this L2BP instance, using the messages stored.

quimb.tensor.belief_propagation.l2bp.contract_l2bp(tn, site_tags=None, damping=0.0, update='sequential', local_convergence=True, optimize='auto-hq', max_iterations=1000, tol=5e-06, strip_exponent=False, info=None, progbar=False, **contract_opts)

Estimate the norm squared of tn using lazy belief propagation.

Parameters:

  • tn (TensorNetwork) – The tensor network to estimate the norm squared of.

  • site_tags (sequence of str, optional) – The tags identifying the sites in tn, each tag forms a region.

  • 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 contraction strategy to use.

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

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

  • 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.

  • contract_opts – Other options supplied to cotengra.array_contract.

quimb.tensor.belief_propagation.l2bp.compress_l2bp(tn, max_bond, cutoff=0.0, cutoff_mode='rsum2', max_iterations=1000, tol=5e-06, site_tags=None, damping=0.0, update='sequential', local_convergence=True, optimize='auto-hq', lazy=False, inplace=False, info=None, progbar=False, **contract_opts)

Compress tn using lazy belief propagation, producing a tensor network with a single tensor per site.

Parameters:

  • tn (TensorNetwork) – The tensor network to form the 2-norm of, run BP on and then compress.

  • max_bond (int) – The maximum bond dimension to compress to.

  • cutoff (float, optional) – The cutoff to use when compressing.

  • cutoff_mode (int, optional) – The cutoff mode to use when compressing.

  • 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.

  • lazy (bool, optional) – Whether to perform the compression lazily, i.e. to leave the computed compression projectors uncontracted.

  • inplace (bool, optional) – Whether to perform the compression inplace.

  • info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.

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

  • contract_opts – Other options supplied to cotengra.array_contract.

Return type:

TensorNetwork