U -eS@slddlZddlZGdddZGdddZGdddeZGdd d eZGd d d ZGd d d ZdS)Nc@szeZdZdddZddZddd Zd d Zd d ZddZddZ ddZ ddZ ddZ d ddZ ddZddZdS)!ComplexFNcCs||_||_||_d|_d|_g|_t||||||_|j||d|rPd|_ n| |j g|jd |j |j |_d|_|g|_|j d|j ddS)Nr)symmetry)dimboundsrgenZ perm_cycleH VertexCacheVn_cubegeneration_cycle add_centroidappendC0homology_group_rankhgrZhgrd graph_mapZ performance)selfrfunc func_argsrrg_consZg_argsrrg/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/scipy/optimize/_shgo_lib/triangulation.py__init__s&   zComplex.__init__cCs|jSN)r rrrr__call__0szComplex.__call__c Csttj|td}||_ttj|td}||_t|}t|}|g}|rtddd|j |_ |j |j |d} | | |||j |j |nFtdd|||_ |j |j ||j |j |g} || |||rtd| D] } | qdS)zm Generate the simplicial triangulation of the N-D hypercube containing 2**n vertices ZdtyperzInitial hyper cube:N)listnpzerosintoriginZonessupremumtupleSimplexrr add_vertexr perm_symmetryCellpermprint print_out) rrrprintoutr"r#Z origintupleZ supremumtuple x_parentsi_s i_parentsvrrrr 3s, zComplex.n_cubec st|}fddt|jD}|D]}t}||t|}d||<t|} |j|j| |j| |j||D]} |j| |j| qt|} | || || |q$dS)Ncsg|]}|kr|qSrr).0xr/rr \sz Complex.perm..r) r$rangercopyrrr&r connectr)) rr/r-xixi_tZ iter_rangeiZ i2_parentsxi2xi2_tx_ip x_parents2rr3rr)Ws     z Complex.permc Cst|}t|}d||<t|}|j|j||j||j||D]}|j||j|qNt|}|||d7}||jkrdS||||dSNr) r$r6rr&r r7rrr') rr.r-r8r9r;r<r=r>rrrr'us    zComplex.perm_symmetrycCstt|jt|jd|_|j|jt |j|j|j_|jt |j |jt |j|D]&}|jt |j |jt |j qnd|_ dS)znSplit the central edge between the origin and supremum of a cell and add the new vertex to the complex@TN)rrarrayr"r#centroidrr&r r$ disconnectr7r2centroid_addedrr0rrrrs " $zComplex.add_centroidcCs|jr0tjd|jdd|jdgtd|_n tjd|jd|jgtd|_|jD]"}|jD]}d|j|j |j f<qdqZdS)Nrr) rDrr rr!Z structureZHCrnnindex)rr0v2rrr incidences  zComplex.incidencecCsdd|D|_dS)z Make a list of size 2**n + 1 where an entry is a vertex incidence, each list element contains a list of indexes corresponding to that entries neighborscSsg|]}dd|jDqS)cSsg|] }|jqSr)rH)r1rIrrrr4sz0Complex.graph_map...)rGr1r0rrrr4sz%Complex.graph_map..N)rgraphrrrrrszComplex.graph_mapc Cst|j}t|d}z|j|Wn tk rF|jgYnXg}t|ddD]*\}}t|j}||||||j q^t|j D]4\}} ||krq| D]} || || qq||j k r~|S)zSSubgenerate a cell `C_i` of generation `gen` and homology group rank `hgr`.rN) r$rBlenr IndexErrorr enumerater2construct_hypercubehg_nrLrCr) rZC_irZ origin_newZcentroid_indexZH_newr:r0r# connectionsjrrrsub_generate_cells(   zComplex.sub_generate_cellcCsrd}zB|j|jD]0}|jr0|||jdq|||jdqWntk r^d}YnX|jd7_|S)zV Run sub_generate_cell for every cell in the current complex self.gen FrT)r rrsplit_simplex_symmetryrUrO)rZ no_splitscrrrsplit_generations zComplex.split_generationcCsNt|}t|}t||||}t||d|_g} t|ddD]R\} } t| j} ||| } || }| |}t|}||j || |qL||j |j| |jt|j D]0\} }|D]"}|j | |  |j | |qq|r:t dt d|t d||D]} | q*|j| ||S)z Build a hypercube with triangulations symmetric to C0. Parameters ---------- origin : vec supremum : vec (tuple) gen : generation hgr : parent homology group rank g?NrMzA sub hyper cube with:z origin: {}z supremum: {})rrAr(r$rBrPrr2r&r rrLr7r*formatr+r )rr"r#rrr,Zv_oZv_sZC_newV_newr:r0Zv_xZ sub_cell_t1Z sub_cell_t2ZvecrSrTrrrrQs4      "  zComplex.construct_hypercubec Csz|j|Wn tk r.|jgYnX|}|dj}|dj}|jtt|t|d}|j||j||ddD]}| |j|jqt ||j |j |j }||d|||ddD]}||qt ||j |j |j } | || j d|ddD]}| |q"t|ddD],\} }| |j krd| |n | |qD| |d|j|||j|| dS)aI Split a hypersimplex S into two sub simplices by building a hyperplane which connects to a new vertex on an edge (the longest edge in dim = {2, 3}) and every other vertex in the simplex that is not connected to the edge being split. This function utilizes the knowledge that the problem is specified with symmetric constraints The longest edge is tracked by an ordering of the vertices in every simplices, the edge between first and second vertex is the longest edge to be split in the next iteration. rrMr@Nr)r rOrr2r r$rrArCr7r%rRr rr&rP) rSrsZfirstxZlastxrZr0ZS_new_lZS_new_ukrrrrV,s<  "     zComplex.split_simplex_symmetryc CsPddlm}|jdkr4||jD]}|D]t}|D]f}|jdkr^tj|jt d}nZtj|jt d}t t |jD]:}|||j|d|j|d|j|d||<q|| |dg|dgdg}g}|j D]} |jdkrtj| jt d} n\tj| jt d} t t |jD]<}| ||j|d|j|d|j|d| |<q || d|| d||d||dq| ||qsz2VertexGroup.homology_group_rank..)rRsumrerrrrrs zVertexGroup.homology_group_rankcCs|jdkr|j|j|_|jS)zt Returns the difference between the current homology group of the cell and its parent group N)rprRroZhgdrrrrhomology_group_differentials z'VertexGroup.homology_group_differentialcCsdS)z Returns the number of stationary points theoretically contained in the cell based information currently known about the cell Nrrrrrpolytopial_sperner_lemmasz$VertexGroup.polytopial_sperner_lemmacCs|D] }|qdS)z3 Print the current cell to console N)r+rErrrr+s zVertexGroup.print_outN) rjrkrlrrr&rrtrur+rrrrrms   rmcs eZdZdZfddZZS)r(zR Contains a cell that is symmetric to the initial hypercube triangulation cs$t||||_||_d|_dSr)superrr"r#rB)rrnror"r# __class__rrrsz Cell.__init__rjrkrl__doc__r __classcell__rrrwrr(sr(cs eZdZdZfddZZS)r%zq Contains a simplex that is symmetric to the initial symmetry constrained hypersimplex triangulation cs$t|||d|d|_dSr?)rvrr )rrnror rrwrrrszSimplex.__init__ryrrrwrr% sr%c@s>eZdZdddZddZddZd d Zd d Zd dZdS)VertexNrc Cs||_t||_tj|td} |dk rTt|D]$\} \} } | | | | | | | <q.| |_|dk rd|_|dk rt ||D].\} }| |jf|dkrztj |_ d|_qqz|jr|| f||_ |dk r||_ nt |_ d|_d|_|dk r||_dS)NrTgF)r2rsorderrrArcrPrffeasiblezipinffrGsetZfval check_minrH)rr2rrrr g_cons_argsrGrHrfr:ZlbZubgargsrrrrs0 zVertex.__init__cCs t|jSr)hashr2rrrr__hash__;szVertex.__hash__cCsN||k rJ||jkrJ|j||j||r>d|_d|_d|_d|_dS)NFT)rGaddrq_minrrErrrr7>s  zVertex.connectcCs2||jkr.|j||j|d|_d|_dS)NT)rGremoverrErrrrCKs    zVertex.disconnectcs,jr&tfddjD_d_jS)zACheck whether this vertex is strictly less than all its neighborsc3s|]}j|jkVqdSr)rrKrrrrrUsz#Vertex.minimiser..F)rallrGrrrrrrqRszVertex.minimisercCsLtd|jd}|jD]}|d|j7}qt|td|jdS)Nz Vertex: {}z Connections: z{} z Order = {})r*rYr2rGr})rZconstrvcrrrr+Zs  zVertex.print_out)NNrNrNN) rjrkrlrrr7rCrqr+rrrrr|s % r|c@s eZdZdddZd ddZdS) r rNTcCs>i|_||_||_||_||_||_d|_d|_|r:d|_dS)NrrM) cacherrrrrnfevsizerH)rrrrrrindexedrrrreszVertexCache.__init__c Csz |j|WStk r|rR|jd7_t||j|j|j|j|j|jd}nt||j|j|j|j|jd}||j|<|jdk r|jdk r|j r|j d7_ |j d7_ q|j d7_ n|j d7_ |j d7_ |j|YSXdS)Nr)rrrrrrH)rrrrr) rKeyErrorrHr|rrrrrr~rr)rr2rZxvalrrr __getitem__ts8    zVertexCache.__getitem__)rNNrT)T)rjrkrlrrrrrrr ds  r ) numpyrr6rrmr(r%r|r rrrrsD5 O