# contract¶

tenpy.algorithms.network_contractor.contract(tensor_list, tensor_names=None, leg_contractions=None, open_legs=None, sequence=None)[source]

Contract a network of tensors.

Based on the MatLab function ncon.m as described in arXiv:1402.0939.

Parameters
• tensor_list (list of Array) – The tensors to be contracted.

• leg_contractions (list of [n1, l1, n2, l2]) – A list of contraction instructions. An entry of leg_contractions has the form [n1, l1, n2, l2], where n1, n2 are entries of tensor_names and each identify an Array in tensor_list. l1, l2 are leg labels of the corresponding Array. The instruction implies to contract leg l1 of tensor n1 with leg l2 of tensor n2.

• open_legs (list of [n1, l1, l]) – A list of instructions for “open” (uncontracted) legs. [n1, l1, l] implies that leg l1 of tensor n1 is not contracted and is labelled l in the result.

• tensor_names (list of str) – A list of names for each tensor, to be used in leg_contractions and open_legs. The default value is list(range(len(tensor_list))), so that the tensor “names” are 0, 1, 2, ....

• sequence (list of int) – The order in which the leg_contractions are to be performed. An entry of network_contractor.outer_product indicates performing an outer product. This corresponds to the zero-in-sequence convention of arXiv:1304.6112

Returns

result – The number or tensor resulting from the contraction.

Return type

Array | complex