MaximiseBilinearForm #219
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MaximiseBilinearForm #219
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This PR adds a solver which, given a
bilinearformnetwork <x|A|y>and some partitioning of the network, optimises|y>to maximize<x|A|y> * conj(<x|A|y>) / <y|y>)and then returns<x|A|y>and<y|.One-site and two-site sweeping is available. Currently, an "orthogonal" algorithm is supported where
yis kept in the orthogonal gauge to do the optimization. A "biorthogonal" version of the algorithm will be supported once biorthogonal gauging routines likegauge_walkare added to the library.The assertions that
<x|A|y>forms a tree under partitioning and that|y>is a tree are made - although these can can be lifted in the future and the fitting done for general networks under the BP approximation with appropriate definitions of theupdaterandsequencefunctions.With this PR, the ability to fit
ITensorNetworksof fairly general structure down to some desired tensor networkywhich forms a tree is doable in a cost efficient manner. This will be the workhorse for the incomingBoundaryMPSCachetype but the code here also generalizes thetruncate(tn::AbstractTTN)function and offers a cost effective alternative to the code insrc/contract_approx/.@mtfishman and @emstoudenmire The solver here (in
src/formnetworks/maximise_bilinearformnetwork.jl) is based on the idea of doing some sort of alternating update style procedure so it would be good to discuss how that can fit within the re-write ofalternating_updateTests are added.