i5zdZddlZddlZddlZddlmZddlmZddlm Z ddlm Z ej Gdd e Z Gd d e ZGd d e ZGdde ZGddeZGdde ZGdde ZGdde ZdddddddZGdde ZdS)z Core Topology Objects --- :mod:`MDAnalysis.core.topologyobjects` ================================================================ The building blocks for MDAnalysis' description of topology N)mdamath)cached)util) distancesceZdZdZdZddZedZedZedZ ed Z ed Z d Z d Z d ZdZdZdZdZdZdZdS)TopologyObjectaBase class for all Topology items. Defines the behaviour by which Bonds/Angles/etc in MDAnalysis should behave. .. versionadded:: 0.9.0 .. versionchanged:: 0.10.0 All TopologyObject now keep track of if they were guessed or not via the ``is_guessed`` managed property. .. versionadded:: 0.11.0 Added the `value` method to return the size of the object .. versionchanged:: 2.6.0 Updated Atom ID representation order to match that of AtomGroup indices )_ix_ubtype _bondtype_guessedorderNFcL||_||_||_||_||_dS)aCreate a topology object Parameters ---------- ix : numpy array indices of the Atoms universe : MDAnalysis.Universe type : optional Type of the bond guessed : optional If the Bond is guessed N)r r r rr)selfixuniversetypeguessedrs i/srv/www/vhosts/g4struct/public_html/venv/lib/python3.11/site-packages/MDAnalysis/core/topologyobjects.py__init__zTopologyObject.__init__<s+  c0|jj|jS)zAtoms within this Bond)r atomsr rs rrzTopologyObject.atomsOsw}TX&&rc|jS)zRTuple of indices describing this object .. versionadded:: 0.10.0 )r rs rindiceszTopologyObject.indicesTs xrc|jSNr rs rrzTopologyObject.universe\ wrcP|j|jSt|jjS)zType of the bond as a tuple Note ---- When comparing types, it is important to consider the reverse of the type too, i.e.:: a.type == b.type or a.type == b.type[::-1] )r tuplertypesrs rrzTopologyObject.type`s' > %> !)** *rc*t|jSr)boolrrs r is_guessedzTopologyObject.is_guessedqsDM"""rcRt|jt|jfSr)hashr r#rrs r__hash__zTopologyObject.__hash__us!TWeDL112333rcd|jjdd|jDS)z8Return representation in same order of AtomGroup indicesz<{cname} between: {conts}>, c8g|]}d|S)zAtom {0})format).0is r z+TopologyObject.__repr__..|s&HHHaZ..q11HHHr)cnameconts)r. __class____name__joinrrs r__repr__zTopologyObject.__repr__xsG+22.)))HH4<HHHII3   rc||jvS)z8Check whether an atom is in this :class:`TopologyObject`rrothers r __contains__zTopologyObject.__contains__s ""rc|j|jksdStj|j|jp'tj|jddd|jS)z/Check whether two bonds have identical contentsFN)rnp array_equalrr:s r__eq__zTopologyObject.__eq__sU}..5~dlEM:: bn L2  ? ?  rc||k Srr:s r__ne__zTopologyObject.__ne__5=  rcVt|jt|jkSr)r#rr:s r__lt__zTopologyObject.__lt__s!T\""U5=%9%999rc|j|S)z%Can retrieve a given Atom from withinr9ritems r __getitem__zTopologyObject.__getitem__sz$rc*t|jSr)iterrrs r__iter__zTopologyObject.__iter__sDJrc*t|jSr)lenr rs r__len__zTopologyObject.__len__s48}}r)NFN)r5 __module__ __qualname____doc__ __slots__rpropertyrrrrr'r*r7r<rArDrGrKrNrQrCrrr r )sH  II&''X'XX++X+ ##X#444   ###   !!!:::      rr c(eZdZdZdZdZddZeZdS)BondaA bond between two :class:`~MDAnalysis.core.groups.Atom` instances. Two :class:`Bond` instances can be compared with the ``==`` and ``!=`` operators. A bond is equal to another if the same atom numbers are connected and they have the same bond order. The ordering of the two atom numbers is ignored as is the fact that a bond was guessed. The presence of a particular atom can also be queried:: >>> Atom in Bond will return either ``True`` or ``False``. .. versionchanged:: 0.9.0 Now a subclass of :class:`TopologyObject`. Changed class to use :attr:`__slots__` and stores atoms in :attr:`atoms` attribute. bondc||jdkr |jdS||jdkr |jdStd)zBond.partner(Atom) Returns ------- the other :class:`~MDAnalysis.core.groups.Atom` in this bond rUnrecognised Atomr ValueErrorratoms rpartnerz Bond.partnersM 4:a= :a= TZ] " ":a= 011 1rTcz|r |jjnd}tj|dj|dj|S)zLength of the bond. .. versionchanged:: 0.11.0 Added pbc keyword .. versionchanged:: 0.19.0 Changed default of pbc to True Nrr[r dimensionsr calc_bondspositionrpbcboxs rlengthz Bond.lengths;+.7dm&&4#DG$4d1g6FLLLrNT)r5rRrSrTr rarjvaluerCrrrXrXsM& E 2 2 2 M M M M EEErrXc"eZdZdZdZddZeZdS)Anglea)An angle between three :class:`~MDAnalysis.core.groups.Atom` instances. Atom 2 is the apex of the angle .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Now a subclass of :class:`TopologyObject`; now uses :attr:`__slots__` and stores atoms in :attr:`atoms` attribute angleTc|r |jjnd}tjt j|dj|dj|dj|S)aReturns the angle in degrees of this Angle. Angle between atoms 0 and 2 with apex at 1:: 2 / / 1------0 Note ---- The numerical precision is typically not better than 4 decimals (and is only tested to 3 decimals). .. versionadded:: 0.9.0 .. versionchanged:: 0.17.0 Fixed angles close to 180 giving NaN .. versionchanged:: 0.19.0 Added pbc keyword, default True Nrr[r)rrdr?rad2degr calc_anglesrfrgs rroz Angle.anglesZ*+.7dm&&4z  !Q $q'"2DG4Dc     rNrk)r5rRrSrTr rorlrCrrrnrns: E    : EEErrnc"eZdZdZdZddZeZdS)DihedralaDihedral (dihedral angle) between four :class:`~MDAnalysis.core.groups.Atom` instances. The dihedral is defined as the angle between the planes formed by Atoms (1, 2, 3) and (2, 3, 4). .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Now a subclass of :class:`TopologyObject`; now uses :attr:`__slots__` and stores atoms in :attr:`atoms` attribute. .. versionchanged:: 0.11.0 Renamed to Dihedral (was Torsion) dihedralTc |r |jjnd}|j\}}}}tjt j|j|j|j|j|S)aCalculate the dihedral angle in degrees. Dihedral angle around axis connecting atoms 1 and 2 (i.e. the angle between the planes spanned by atoms (0,1,2) and (1,2,3)):: 3 | 1-----2 / 0 Note ---- The numerical precision is typically not better than 4 decimals (and is only tested to 3 decimals). .. versionadded:: 0.9.0 .. versionchanged:: 0.19.0 Added pbc keyword, default True N)rrdrr?rqrcalc_dihedralsrf)rrhriABCDs rruzDihedral.dihedrals^,+.7dm&&4Z 1az  $ AJ AJ     rNrk)r5rRrSrTr rurlrCrrrtrts:   E    > EEErrtceZdZdZdZdZdS)ImproperDihedrala Improper Dihedral (improper dihedral angle) between four :class:`~MDAnalysis.core.groups.Atom` instances. MDAnalysis treats the improper dihedral angle as the angle between the planes formed by Atoms (1, 2, 3) and (2, 3, 4). .. warning:: Definitions of Atom ordering in improper dihedrals can change. Check the definitions here against your software. .. versionadded:: 0.9.0 .. versionchanged:: 0.11.0 Renamed to ImproperDihedral (was Improper_Torsion) improperc*|S)zImproper dihedral angle in degrees. Note ---- The numerical precision is typically not better than 4 decimals (and is only tested to 3 decimals). )rurs rr~zImproperDihedral.improperFs}}rN)r5rRrSrTr r~rCrrr}r}2s4" Err}c(eZdZdZdZdZddZeZdS) UreyBradleya'A Urey-Bradley angle between two :class:`~MDAnalysis.core.groups.Atom` instances. Two :class:`UreyBradley` instances can be compared with the ``==`` and ``!=`` operators. A UreyBradley angle is equal to another if the same atom numbers are involved. .. versionadded:: 1.0.0 ureybradleyc||jdkr |jdS||jdkr |jdStd)zUreyBradley.partner(Atom) Returns ------- the other :class:`~MDAnalysis.core.groups.Atom` in this interaction rr[r\r]r_s rrazUreyBradley.partner\sM 4:a= :a= TZ] " ":a= 011 1rTcz|r |jjnd}tj|dj|dj|S)zDistance between the atoms.Nrr[rcrgs rdistancezUreyBradley.distancejs9*-7dm&&4#DG$4d1g6FLLLrNrk)r5rRrSrTr rarrlrCrrrrQsM E 2 2 2MMMM EEErrceZdZdZdZdS)CMapz Coupled-torsion correction map term between five :class:`~MDAnalysis.core.groups.Atom` instances. .. versionadded:: 1.0.0 cmapN)r5rRrSrTr rCrrrrrs EEErrcXeZdZdZdZdZedZdZdZ dZ dZ d Z d Z d S) TopologyDictaA customised dictionary designed for sorting the bonds, angles and dihedrals present in a group of atoms. Usage:: topologydict = TopologyDict(members) TopologyDicts are also built lazily from a :class:`TopologyGroup.topDict` attribute. The :class:`TopologyDict` collects all the selected topology type from the atoms and categorises them according to the types of the atoms within. A :class:`TopologyGroup` containing all of a given bond type can be made by querying with the appropriate key. The keys to the :class:`TopologyDict` are a tuple of the atom types that the bond represents and can be viewed using the :meth:`keys` method. For example, from a system containing pure ethanol :: >>> td = u.bonds.topDict >>> td.keys() [('C', 'C'), ('C', 'H'), ('O', 'H'), ('C', 'O')] >>> td['C', 'O'] < TopologyGroup containing 912 bonds > .. Note:: The key for a bond is taken from the type attribute of the atoms. Getting and setting types of bonds is done smartly, so a C-C-H angle is considered identical to a H-C-C angle. Duplicate entries are automatically removed upon creation and combination of different Dicts. This means a bond between atoms 1 and 2 will only ever appear once in a dict despite both atoms 1 and 2 having the bond in their :attr:`bond` attribute. Two :class:`TopologyDict` instances can be combined using addition and it will not create any duplicate bonds in the process. Arguments --------- members : A list of :class:`TopologyObject` instances .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Changed initialisation to use a list of :class:`TopologyObject` instances instead of list of atoms; now used from within :class:`TopologyGroup` instead of accessed from :class:`AtomGroup`. ct|tstdt|_|j|_|j|_|D];}|j} |j|xx|gz cc<!#t$r|g|j|<Y8wxYw|jrUtt|j dtr| dSdSdS)Nz%Can only construct from TopologyGroupr) isinstance TopologyGroup TypeErrordictrr r toptyperKeyErrorlistkeysr# _removeDupes)r topologygroupbr s rrzTopologyDict.__init__s-77 ECDD DFF ($*  ' 'AFE ' %   QC'     ' ' '$%3 %    ' 9 D)9)9$:$:1$=uEE            sA33B  B ct}|jD]D}|ddd|vr|j|||< ||dddxx|j|z cc<E||_dS)zoSorts through contents and makes sure that there are no duplicate keys (through type reversal) Nr>r)rnewdictks rrzTopologyDict._removeDupess&& 1 1ATTrT7g%%!Yq\ $$B$   DIaL0     rc|jSrr rs rrzTopologyDict.universer!rcNt|jS)z>Returns the number of types of bond in the topology dictionary)rPrrrs rrQzTopologyDict.__len__s49>>##$$$rc4|jS)z8Returns a list of the different types of available bonds)rrrs rrzTopologyDict.keyssy~~rc*t|jS)z%Iterator over keys in this dictionary)rMrrs rrNzTopologyDict.__iter__sDIrcTdt||jS)Nz(numr)r.rPrrs rr7zTopologyDict.__repr__s-9@@D  A   rc||vrg||jvr|j|}n|j|ddd}tjd|D}t||j|jSt |)zfReturns a TopologyGroup matching the criteria if possible, otherwise returns ``None`` Nr>cg|] }|j SrCr)r/ss rr1z,TopologyDict.__getitem__..s:::1QY:::rr )rr?vstackrr rr)rkey selectionbixs rrKzTopologyDict.__getitem__s $;;di IcN  Ic$$B$i0 ):: :::;;C dgT\BBB B3-- rc8||jvp|ddd|jvS)z Returns boolean on whether a given type exists within this dictionary For topology groups the key (1,2,3) is considered the same as (3,2,1) Nr>rr:s rr<zTopologyDict.__contains__s'  !=U44R4[DI%==rN)r5rRrSrTrrrVrrQrrNr7rKr<rCrrrr}s88t   2 X%%%         >>>>>rr)rYrrorur~rcZeZdZdZ ddZedZdZeZdZ ee ddZ d Z ed Z d ZeZd Zd ZdZdZdZdZdZdZedZedZedZedZdZddddZd dZd!dZd!dZ dS)"raA container for a groups of bonds. All bonds of a certain types can be retrieved from within the :class:`TopologyGroup` by querying with a tuple of types:: tg2 = tg.select_bonds([key]) Where *key* describes the desired bond as a tuple of the involved :class:`~MDAnalysis.core.groups.Atom` types, as defined by the .type Atom attribute). A list of available keys can be displayed using the :meth:`types` method. Alternatively, all the bonds which are in a given :class:`~MDAnalysis.core.groups.AtomGroup` can be extracted using :meth:`atomgroup_intersection`:: tg2 = tg.atomgroup_intersection(ag) This allows the keyword *strict* to be given, which forces all members of all bonds to be inside the AtomGroup passed to it. Finally, a TopologyGroup can be sliced similarly to AtomGroups:: tg2 = tg[5:10] The :meth:`bonds`, :meth:`angles` and :meth:`dihedrals` methods offer a "shortcut" to the Cython distance calculation functions in :class:`MDAnalysis.lib.distances`. TopologyGroups can be combined with TopologyGroups of the same bond type (ie can combine two angle containing TopologyGroups). .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Overhauled completely: (1) Added internal :class:`TopologyDict` accessible by the :attr:`topDict` attribute. (2) :meth:`selectBonds` allows the :attr:`topDict` to be queried with tuple of types. (3) Added :meth:`atomgroup_intersection` to allow bonds which are in a given :class:`AtomGroup` to be retrieved. .. versionchanged:: 0.10.0 Added :func:`from_indices` constructor, allowing class to be created from indices. Can now create empty Group. Renamed :meth:`dump_contents` to :meth:`to_indices` .. versionchanged:: 0.11.0 Added `values` method to return the size of each object in this group Deprecated selectBonds method in favour of select_bonds .. versionchanged:: 0.19.0 Empty TopologyGroup now returns correctly shaped empty array via indices property and to_indices() .. versionchanged::1.0.0 ``type``, ``guessed``, and ``order`` are no longer reshaped to arrays with an extra dimension Nc:|%ddddt|d_nK|tvr|_n:tddtt j|}t|}|t jd|}|t jd|}n9|dus|d urt j||}nt j|t }|t jd|}|dkrytj |d \}} |_ || _ || _|| _fd t!j jd D_nkt jg_ t jg_ t jg_t jg_g__t+_dS)NrYroru)rrrrz"Unsupported btype, use one of '{}'r,TFdtype) return_indexcHg|]}jjdd|fSr)r_bix)r/r0rrs rr1z*TopologyGroup.__init__..s>tyA/rr[)rPr _BTYPE_TO_SHAPEr^r.r6r?asarrayrepeatr&r unique_rowsr _bondtypesr_orderrangeshape_agsarrayr r_cache) rbondidxrr rrrnbondsuniquniq_idxs ` ` rrzTopologyGroup.__init__Qs =$J??GAJDJJo % %DJJ6$))O4455  *W%%W <9T6**D ?if--GG __5 0 0i00GGj555G =IdF++E A::!-gDIIIND(DI"8nDO#H-DM/DKtyq122DII  DI hrllDOHRLLDM(2,,DKDIff rc|jS)zThe Universe that we belong tor rs rrzTopologyGroup.universes wrc|j|S)zRetrieves a selection from this topology group based on types. .. seeAlso :meth:`types` .. versionadded 0.9.0 )topDict)rrs r select_bondszTopologyGroup.select_bondss|I&&rcNt|jS)z]Return a list of the bond types in this TopologyGroup .. versionadded 0.9.0 )rrrrs rr$zTopologyGroup.typess DL%%''(((rrc t|S)a! Returns the TopologyDict for this topology group. This is used for the select_bonds method when fetching a certain type of bond. This is a cached property so will be generated the first time it is accessed. .. versionadded 0.9.0 )rrs rrzTopologyGroup.topDictsD!!!rc |s|S|ddr tjn tj}|jfd|jjD}||d}||S)aRetrieve all bonds from within this TopologyGroup that are within the AtomGroup which is passed. Parameters ---------- ag : AtomGroup The `:class:~MDAnalysis.core.groups.AtomGroup` to intersect with. strict : bool Only retrieve bonds which are completely contained within the AtomGroup. [``False``] .. versionadded:: 0.9.0 strictFc:g|]}tj|SrC)r?isin)r/colatom_idxs rr1z8TopologyGroup.atomgroup_intersection..s%>>>3X&&>>>rr)axis)getr?allanyrrT)ragkwargsfuncseenmaskrs @ratomgroup_intersectionz$TopologyGroup.atomgroup_intersectionsz" K He44@rvv"&:?>>>$)+>>>tDq!!!Dzrc||s4t|j}tjd|ftjS|jS)zvall bond indices See Also -------- to_indices : function that just returns `indices` rr)rr r?zerosint32r)rrs rrzTopologyGroup.indicess; #DJ/E8QJbh777 79 rc|jS)aReturn a data structure with atom indices describing the bonds. This format should be identical to the original contents of the entries in universe._topology. Note that because bonds are sorted as they are initialised, the order that atoms are defined in each entry might be reversed. Returns ------- indices : tuple A tuple of tuples which define the contents of this TopologyGroup in terms of the atom numbers. (0 based index within u.atoms) .. versionadded:: 0.9.0 .. versionchanged:: 0.10.0 Renamed from "dump_contents" to "to_indices" rrs r to_indiceszTopologyGroup.to_indicess (|rc&|jjdS)z%Number of bonds in the topology groupr)rrrs rrQzTopologyGroup.__len__syq!!rc jt|ttfs/tdt ||s|S|st|trvt|jdddf|j|jtj |j gtj |j gtj |j gSt|j|j|j|j|j|jS|j|jkstdt|trttj|j|jdddfg|j|jtj|jtj |j ggtj|jtj |j ggtj|jtj |j ggSttj|j|jg|j|jtj|j|jgtj|j|jgtj|j|jgS)zCombine two TopologyGroups together. Can combined two TopologyGroup of the same type, or add a single TopologyObject to a TopologyGroup. zJCan only combine TopologyObject or TopologyGroup to TopologyGroup, not {0}Nr rrrz6Cannot add different types of TopologyObjects together)rr rrr.rrrr r?rr r'rrrr concatenater:s r__add__zTopologyGroup.__add__s%.-!@AA 6$u++&&  K2 %00 $M$'*N+5?"344He&6%788(EK=11 %MN+)!N, ;$*,,O%00 $NDL%-aaa2H#IJJM*"(EO3D*E*EFN%2B1C(D(DE.bh }&=&=>     %NDL%-#@AAM*%:J(KLLNDM5>+JKK.$+u|)DEE rc t|tjrsttt t ttd|j }||j ||j |j ||j ||j|S||j ||j |j |j ||j ||j|S)zReturns a particular bond as single object or a subset of this TopologyGroup as another TopologyGroup .. versionchanged:: 0.10.0 Allows indexing via boolean numpy array )rYrorur~rr)rrrr)rnumbersIntegralrXrnrtr}rrr rr rrrr4)rrJoutclasss rrKzTopologyGroup.__getitem__Hs dG, - - $,* jH8 $_T* d+k$'  >> $j_T* d+k$' " rc|j|jvS)z+Tests if this TopologyGroup contains a bond)rrrIs rr<zTopologyGroup.__contains__ks|ty((rcTdt||jS)Nz(r)r.rPr rs rr7zTopologyGroup.__repr__os-9@@D  A   rc@tj|j|jS)z,Test if contents of TopologyGroups are equal)r?r@rr:s rrAzTopologyGroup.__eq__ts~dlEM:::rc||k SrrCr:s rrDzTopologyGroup.__ne__xrErc*t|dk S)Nr)rPrs r __nonzero__zTopologyGroup.__nonzero__{st99>!!rc|jdS)z3The first atom in each TopologyObject in this Grouprrrs ratom1zTopologyGroup.atom1~y|rc|jdS)z4The second atom in each TopologyObject in this Groupr[rrs ratom2zTopologyGroup.atom2rrc |jdS#t$r1t|j}d|jd|d}t|dwxYw)z3The third atom in each TopologyObject in this GrouprTopologyGroup of s only has  vertical AtomGroupsNr IndexErrorrr rnverterrmsgs ratom3zTopologyGroup.atom3u /9Q<  / / /#DJ/E'DJ''5''' V$$$ .  / ;A c |jdS#t$r1t|j}d|jd|d}t|dwxYw)z4The fourth atom in each TopologyObject in this GrouprrrrNrrs ratom4zTopologyGroup.atom4rrc |jdkr |jdi|S|jdkr |jdi|S|jdkr |jdi|S|jdkr |jdi|SdS)abReturn the size of each object in this Group :Keywords: *pbc* apply periodic boundary conditions when calculating distance [``False``] *result* allows a predefined results array to be used, note that this will be overwritten .. versionadded:: 0.11.0 rYrorur~NrC)r bondsangles dihedrals)rrs rvalueszTopologyGroup.valuess :  4:'''' ' Z7 " "4;(((( ( Z: % %!4>++F++ + Z: % %!4>++F++ +& %rF)resultrhcFtfd|Ds(d|}td|d|s,tjt tj}|sdnjdj}djD}||||dS)Nc3.K|]}j|kVdSrr)r/r rs r z8TopologyGroup._calc_connection_values..s*;;54:&;;;;;;rz' or 'zTopologyGroup is not of type ''rcg|] }|j SrC) positions)r/rs rr1z9TopologyGroup._calc_connection_values..s666bR\666r)rir ) rr6rr?rrPfloat64rrd)rrr rhbtypesstrbtyperirs` r_calc_connection_valuesz%TopologyGroup._calc_connection_valuess;;;;F;;;;; J}}V,,HHXHHHII I 5Xc$ii44F:dd49Q<#:66DI666 tYC7777rcH|tjd||S)asCalculates the distance between all bonds in this TopologyGroup :Keywords: *pbc* apply periodic boundary conditions when calculating distance [False] *result* allows a predefined results array to be used, note that this will be overwritten Uses cython implementation rYrhr )rrre)rrhr s rrzTopologyGroup.bondss-++  &c&,   rcH|tjd||S)aCalculates the angle in radians formed between a bond between atoms 1 and 2 and a bond between atoms 2 & 3 Parameters ---------- result : array_like allows a predefined results array to be used, note that this will be overwritten pbc : bool apply periodic boundary conditions when calculating angles [``False``] this is important when connecting vectors between atoms might require minimum image convention Returns ------- angles : ndarray .. versionchanged :: 0.9.0 Added *pbc* option (default ``False``) ror)rrrrrr rhs rrzTopologyGroup.angless-,++  !7F,   rcJ|tjdd||S)aCalculate the dihedral angle in radians for this topology group. Defined as the angle between a plane formed by atoms 1, 2 and 3 and a plane formed by atoms 2, 3 and 4. Parameters ---------- result : array_like allows a predefined results array to be used, note that this will be overwritten pbc : bool apply periodic boundary conditions when calculating angles [``False``] this is important when connecting vectors between atoms might require minimum image convention Returns ------- angles : ndarray .. versionchanged:: 0.9.0 Added *pbc* option (default ``False``) rur~r)rrrwrs rrzTopologyGroup.dihedralss30++  $   ,   r)NNNN)FN)NF)!r5rRrSrTrrVrr selectBondsr$rrrrr dump_contentsrQrrKr<r7rArDrrrrrrrrrrrCrrrrsE55v <<<<|X'''K))) VF^^ " "^X "   D  X ,M"""CCCJ!!!F)))   ;;;!!!"""XX / /X / / /X /,,,,=Ae88888    "    4      rr)rTrnumpyr? functoolslibrlib.utilrrrtotal_orderingobjectr rXrnrtr}rrrrrrCrrr!sN0 oooooVoood11111>111h)))))N)))X22222~222lx>.B>O>O>O>O>O>6O>O>O>f   t t t t t Ft t t t t r