DUfzddlmZmZddlmZddlmZddlZddl Z ddl Z ddl Z ddl m Z ddl mZmZddlZd d ZdS) )partialreduce)Pool)addN)linalg)split partitionư>皙?c|}tj|}||}g} d} d} | } |dz} |}|dz}||||z}d|z }tj||}d}|}|}d}d}|dkrt dd ||krz|dz }d}|}t | dz|z|}||krW|dz }|dkr/||z }|}tj||}n ||z }|||zz}||||z|z||zz}|tj||z }||z} || z}!t|!|kr<|dkrn| dk}"tj|||"z | |"z }#||#| zz}nt |!|kr5|!|k}"tj|||"z | |"z }#||#| zz}n?|!}|||zz }|}||z }tj||}||kW||z}||||z}d|z }tj||}|}||dzz }||z }$|}tj|}%| }&| |$z} | |&dzzdkrt | | |&dzz} t t| | | |%z } |dkrt d |||%fzd | |%t d |fzd ||kztj t|}'||'|<|'tj | fS) aR A balancing algorithm for symmetric matrices X = BNEWT(A) attempts to find a vector X such that diag(X)*A*diag(X) is close to doubly stochastic. A must be symmetric and nonnegative. Parameters ---------- matvec : callable Linear operator that returns the matrix-vector product with x mask : 1D array of bool Mask of good bins tol : float Error tolerance x0 : 1D array Initial guess delta : float How close balancing vectors can get to the edge of the positive cone Delta : float How far balancing vectors can get from the edge of the positive cone We use a relative measure on the size of elements. Returns ------- x : 1D array balancing weights res : float residual error, measured by norm(diag(x)*A*x - e) Ng?r g?rz it in. it resT)flushz %3d %6d %.3ezMatrix-vector products = %6d) sumnponescopydotprintmaxminsqrtappendzeroslenarray)(matvecmasktolx0deltaDeltaflneresgetamaxetastop_tolxrtvrkrho_km1rho_km2routroldMVPikyinnertolZpbetawalphaapynewidxgammaratres_normeta_ox_fulls( V/var/www/html/software/conda/lib/python3.11/site-packages/cooltools/sandbox/balance.pybnewtrGsD  A  A z VVXX C A F CSyH A B FF1dOOA QBfRnnGG D D C A Qww oT**** )) Q  FFHHqD("--  FAAvvFFFHH&Q--(qLFF1q5$'''!a%/AbfQll*EBr6D4yyE!!A::1f#"S'9:: N4yyE!!Ul#"S'9:: N AeaiBGQAfRmmGK  N E q$  U&R.. q1u Tk74==#g  c ! !c1 +,,C#c6""Hx$788 77 "aH%55T B B B B 8 ,v5TBBBBI ))LXc$ii FF4L 28C==  )r Nr r r) functoolsrr multiprocessroperatorrnumpyrpandash5py scipy.sparsercooler.parallelrr coolerrGrHrFrSs%%%%%%%% ,,,,,,,, G!G!G!G!G!G!rH