phf@SrSSKJrJrJr SSKJr SSKJr SSKJ r J r J r J r SSK Jr Sr\"0S S 9S 5rS r\"0S S 9S 5rS!SjrSrSrSr\"0S S 9S5rSrSrSrSrSr"SS\5r\"5rS"Sjr\RAS5S"Sj5r!\RAS5S"Sj5r"\RAS5S"S j5r#g )#z& Functions for generating partitions. )chain permutationsproduct)config)cache) Bipartition KPartitionPart Tripartition)Registryc## [U5nU(dg[U5S:XaU/v gUSn[USS5H7n[U5Hup4USUU/U-/-X#S-S-v M U//U-v M9 g7f)zGenerate all set partitions of a collection. Example: >>> list(partitions(range(3))) # doctest: +NORMALIZE_WHITESPACE [[[0, 1, 2]], [[0], [1, 2]], [[0, 1], [2]], [[1], [0, 2]], [[0], [1], [2]]] Nrr)listlen partitions enumerate) collectionfirstsmallernsubsets I/home/james-whalen/.local/lib/python3.13/site-packages/pyphi/partition.pyrrsj!J  :!l qMEjn-"7+IA"1+%6!1 22WqST]B B,wi'!!.sA8A:N)rmaxmemc/nUS::aU$[SUS- -5H^n///n[U5HnX$- S-nX5RU5 M UR[US5[US545 M` U$)aBReturn indices for undirected bipartitions of a sequence. Args: N (int): The length of the sequence. Returns: list: A list of tuples containing the indices for each of the two parts. Example: >>> N = 3 >>> bipartition_indices(N) [((), (0, 1, 2)), ((0,), (1, 2)), ((1,), (0, 2)), ((0, 1), (2,))] rr)rangeappendtuple)Nresultipartrbits rbipartition_indicesr$.s FAv 1q1u: BxqA6Q,C I  Q   uT!W~uT!W~67  Mc ^[[T55VVs/sH/up[U4SjU55[U4SjU554PM1 snn$s snnf)a-Return a list of bipartitions for a sequence. Args: a (Iterable): The sequence to partition. Returns: list[tuple[tuple]]: A list of tuples containing each of the two partitions. Example: >>> bipartition((1,2,3)) [((), (1, 2, 3)), ((1,), (2, 3)), ((2,), (1, 3)), ((1, 2), (3,))] c3.># UH nTUv M g7fN.0r!seqs r bipartition..Z-9a3q69c3.># UH nTUv M g7fr(r)r+jr,s rr-r.[r/r0)r$rr)r, part0_idx part1_idxs` r bipartitionr6LsX )>> N = 3 >>> directed_bipartition_indices(N) # doctest: +NORMALIZE_WHITESPACE [((), (0, 1, 2)), ((0,), (1, 2)), ((1,), (0, 2)), ((0, 1), (2,)), ((2,), (0, 1)), ((0, 2), (1,)), ((1, 2), (0,)), ((0, 1, 2), ())] N)r$)rindicesidxs rdirected_bipartition_indicesr;_s7."!$G 4R4=9=C$B$i=9 999s,c ^[[T55VVs/sH/up#[U4SjU55[U4SjU554PM1 nnnU(aUSS$U$s snnf)aReturn a list of directed bipartitions for a sequence. Args: seq (Iterable): The sequence to partition. Returns: list[tuple[tuple]]: A list of tuples containing each of the two parts. Example: >>> directed_bipartition((1, 2, 3)) # doctest: +NORMALIZE_WHITESPACE [((), (1, 2, 3)), ((1,), (2, 3)), ((2,), (1, 3)), ((1, 2), (3,)), ((3,), (1, 2)), ((1, 3), (2,)), ((2, 3), (1,)), ((1, 2, 3), ())] c3.># UH nTUv M g7fr(r)r*s rr-'directed_bipartition..s)y!s1vyr0c3.># UH nTUv M g7fr(r)r2s rr-r>s0KAQr0rr8)r;rr)r, nontrivialr4r5 bipartitionss` rdirected_bipartitionrB{sl.%AS$J$J I )y) )50K0K+KL$JAb!! s6A c## [U5n[U5H upU4[USUXS-S-54v M" g7f)z4Generate bipartitions where one part is of length 1.Nr)rrr)r,r!elts rbipartition_of_onerEsC s)CC.vuS!WsE8}4566!s<>c#2# UH nUSSS2v M g7f)z#Reverse the elements of a sequence.Nr8r))r,rDs rreverse_elementsrGs$B$iscT[[U55n[U[U55$)aGenerate directed bipartitions where one part is of length 1. Args: seq (Iterable): The sequence to partition. Returns: list[tuple[tuple]]: A list of tuples containing each of the two partitions. Example: >>> partitions = directed_bipartition_of_one((1, 2, 3)) >>> list(partitions) # doctest: +NORMALIZE_WHITESPACE [((1,), (2, 3)), ((2,), (1, 3)), ((3,), (1, 2)), ((2, 3), (1,)), ((1, 3), (2,)), ((1, 2), (3,))] )rrErrG)r,rAs rdirected_bipartition_of_onerIs'(*3/0L / = >>r%c/nUS::aU$/SQn[X S9HPn////n[U5HupVXFRU5 M UR[SU555 MR U$)a:Return indices for directed tripartitions of a sequence. Args: N (int): The length of the sequence. Returns: list[tuple]: A list of tuples containing the indices for each partition. Example: >>> N = 1 >>> directed_tripartition_indices(N) [((0,), (), ()), ((), (0,), ()), ((), (), (0,))] r)rrr)repeatc38# UHn[U5v M g7fr()r)r+ps rr-0directed_tripartition_indices..s3dE!HHds)rrrr)rr basekeyr"r!locations rdirected_tripartition_indicesrRst FAv Dt&B|$S>KA N ! !! $*  e3d334 ' Mr%c#^# [[T55HFupn[U4SjU55[U4SjU55[U4SjU554v MH g7f)aGenerator over all directed tripartitions of a sequence. Args: seq (Iterable): a sequence. Yields: tuple[tuple]: A tripartition of ``seq``. Example: >>> seq = (2, 5) >>> list(directed_tripartition(seq)) # doctest: +NORMALIZE_WHITESPACE [((2, 5), (), ()), ((2,), (5,), ()), ((2,), (), (5,)), ((5,), (2,), ()), ((), (2, 5), ()), ((), (2,), (5,)), ((5,), (), (2,)), ((), (5,), (2,)), ((), (), (2, 5))] c3.># UH nTUv M g7fr(r)r*s rr-(directed_tripartition..'QSVQr0c3.># UH nTUv M g7fr(r)r2s rr-rUrVr0c3.># UH nTUv M g7fr(r))r+kr,s rr-rUrVr0N)rRrr)r,abcs` rdirected_tripartitionr]sS,1S:a'Q'''Q'''Q'') );sA A#c[U5Vs/sHn/PM nn[U5HnXQUS-RX65 M U$s snf)Nr)rr)rrZrYrr!psr3s r_visitr`sLAh h"hB  1X QU8 JM* I s A c ## US:Xa[X4XV5v O%[US- US- X-S-X4XV5HnUv M XS-:Xa@US- X@'[X4XV5v XAS:a"XAS- XA'[X4XV5v XAS:aM!ggXS-:aX-S-S:Xa US- XAS- 'OUS- X@'XAU-S-S:Xa[XS- SX4XV5HnUv M O[XS- SX4XV5HnUv M XAS:a[XAS- XA'XAU-S-S:Xa[XS- SX4XV5HnUv M O[XS- SX4XV5HnUv M XAS:aMZggg7f)Nrrrr`_f_bmunusigmarrZrYrvs rrcrc s QwQ1))BFBFRZ1$4aAJAGK !V|QQ1))eaiEAIAEq- -eai 1f J! q QA1fIFAE EEMQ ! #FAqQ;<FAqQ;<eaiEAIAE "a'BQ1?AG@BQ1?AG@ eai sA?ECEEc ## XS-:XaBXAUS- :a$[X4XV5v XAS-XA'XAUS- :aM$[X4XV5v SX@'OXS-:aXAU-S-S:Xa[XS- SX4XV5HnUv M O[XS- SX4XV5HnUv M XAUS- :a]XAS-XA'XAU-S-S:Xa[XS- SX4XV5HnUv M O[XS- SX4XV5HnUv M XAUS- :aM]X-S-S:XaSXAS- 'OSX@'US:Xa[X4XV5v g[US- US- X-S-X4XV5HnUv M g7f)Nrrrrbres rrdrd,s !V|eb1fnq- -EAIAEeb1fnQ1)) 1f EEMQ ! #FAqQ;<FAqQ;<eb1fnEAIAE "a'BQ1?AG@BQ1?AG@ eb1fn J! q A1fIAE QwQ1))BFBFRZ1$4aAJAGKs6ECEAEc [U5n[U5nUS:XdUS:a/$US:XaU//$S/US--n[SUS-5HnUS- X2U- U-'M [XSX#X5$)zGenerate all ``k``-partitions of a collection. Example: >>> list(k_partitions(range(3), 2)) [[[0, 1], [2]], [[0], [1, 2]], [[0, 2], [1]]] rr)rrrrc)rrYrrZr3s r k_partitionsrlOsj!J JA AvQ Av ~ q1u A 1a!e_1ua%!)  aAqQ ++r%c\rSrSrSrSrSrg)PartitionRegistryiha!Storage for partition schemes registered with PyPhi. Users can define custom partitions: Examples: >>> @partition_types.register('NONE') # doctest: +SKIP ... def no_partitions(mechanism, purview): ... return [] And use them by setting ``config.PARTITION_TYPE = 'NONE'`` rr)N)__name__ __module__ __qualname____firstlineno____doc__desc__static_attributes__r)r%rrnrnhs  Dr%rncB[[RnU"XU5$)z^Return a generator over all mechanism-purview partitions, based on the current configuration. )partition_typesrPARTITION_TYPE) mechanismpurview node_labelsfuncs rmip_partitionsr}zs! 600 1D  K 00r%BIc ## [U5n[U5n[X45H^upVUS(d US(dMUS(d US(dM1[[ USUS5[ USUS5US9v M` g7f)u=Return an generator of all |small_phi| bipartitions of a mechanism over a purview. Excludes all bipartitions where one half is entirely empty, *e.g*:: A ∅ ─── ✕ ─── B ∅ is not valid, but :: A ∅ ─── ✕ ─── ∅ B is. Args: mechanism (tuple[int]): The mechanism to partition purview (tuple[int]): The purview to partition Yields: Bipartition: Where each bipartition is:: bipart[0].mechanism bipart[1].mechanism ─────────────────── ✕ ─────────────────── bipart[0].purview bipart[1].purview Example: >>> mechanism = (0,) >>> purview = (2, 3) >>> for partition in mip_bipartitions(mechanism, purview): ... print(partition, '\n') # doctest: +NORMALIZE_WHITESPACE ∅ 0 ─── ✕ ─── 2 3 ∅ 0 ─── ✕ ─── 3 2 ∅ 0 ─── ✕ ─── 2,3 ∅ rrr{N)r6rBrr r )ryrzr{ numerators denominatorsrds rmip_bipartitionsrs|^Y'J'0L 1 aDAaDDqtqttd1Q41.QqT1Q40@*57 72s9BB2BTRIc #^ # [U5n[U5n[5nSn[U[ X455Hupx[ [ USUS5[ USUS5[ SUS5US9R5n Sm U 4Sjn U "U 5(aMdX;dMkURU 5 U v M g 7f) uReturn an iterator over all wedge partitions. These are partitions which strictly split the mechanism and allow a subset of the purview to be split into a third partition, e.g.:: A B ∅ ─── ✕ ─── ✕ ─── B C D See |PARTITION_TYPE| in |config| for more information. Args: mechanism (tuple[int]): A mechanism. purview (tuple[int]): A purview. Yields: Tripartition: all unique tripartitions of this mechanism and purview. cUupUS=(d US=(aK US=(d US=(a3 US=(a US=(d US(+=(d US(+$)z2Return whether the factoring should be considered.rrr)) factoring numerator denominators rvalidwedge_partitions..validsi"+ q\ +[^ ! q\ +[^ !l+y| Q  Q   r%rrr)rrc@UR=(d UR$)z!Check that the part is not empty.ryrz)r"s rnonempty"wedge_partitions..nonemptys>>1T\\ 1r%c >USUS4USUS4USUS4/nUH_up#T"U5(dMT"U5(dM#URUR-S:XdURUR-S:XdM_ g g)uCheck if the tripartition can be transformed into a causally equivalent partition by combing two of its parts; e.g., A/∅ × B/∅ × ∅/CD is equivalent to AB/∅ × ∅/CD so we don't include it. rrrr)TFr)tripartpairsxyrs r compressible&wedge_partitions..compressibles WQZ(WQZ(WQZ(E QKKHQKKq{{2b8QYY."4  r%N) r6r]setfilterrr r normalizeadd) ryrzr{rryieldedrrrrrrs @rwedge_partitionsrs(Y'J(1LeG  ugj?@ 1qt  1qt  QqTN#  )+  2 "G$$)? KK MAAsBC C'CALLc#~# [U5GHnUR/5 [U5n[[U5U5n[ SUS-5HnXF- n[ X5HnUV s/sHn [ U 5PM nn URS/U-5 [[U55Hun [UU 5V V s/sH#up[[ U 5[ U 55PM% n n n U SRU:XaU SR(aMh[U SU06v Mw M M GM! gs sn fs sn n f7f)aReturn all possible partitions of a mechanism and purview. Partitions can consist of any number of parts. Args: mechanism (tuple[int]): A mechanism. purview (tuple[int]): A purview. Yields: KPartition: A partition of this mechanism and purview into ``k`` parts. rr)rr{N)rrrminrrlrextendrrzipr ryrzr )ryrzr{mechanism_partitionn_mechanism_partsmax_purview_partitionn_purview_partsn_emptypurview_partition_listpurview_permutationmrMpartss rall_partitionsrsK *)4""2& 34 #CL2C D$Q(=(ABO'9G%1'%K!2C%E2C&+5\2C"%E"(("8,/$%67,9' %((;(;%=%=DAU1XuQx0%=Qx))Y658;K;K $eEEE,9&L C 5%EsA)D=+D2 =D==*D7'AD=)Fr()$rs itertoolsrrrrrmodelsr r r r registryr rr$r6r;rBrErGrIrRr]r`rcrdrlrnrwr}registerrrrr)r%rrs, 32??"8R:G&R::6B7 ?0R<)B F F,2  $%1$47 47n% D!DN% (F!(Fr%