_MhRdZdZgdZddlZddlmZddlZddlm Z dd l m Z dd l m Z mZmZmZmZmZmZdd lmZmZmZmZdd lmZmZdd lmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'ddl(Z(GddeeZ)dZ*dZ+dZ,dZ-ddZ.dZ/Gdde)eZ0Gdde e)Z1dS)z2 A sparse matrix in COOrdinate or 'triplet' formatzrestructuredtext en) coo_array coo_matrixisspmatrix_cooN)warn)copy_if_needed)spmatrix) coo_tocsr coo_todensecoo_todense_nd coo_matvec coo_matvec_ndcoo_matmat_densecoo_matmat_dense_nd)issparseSparseEfficiencyWarning_spbasesparray) _data_matrix _minmax_mixin) upcast_char to_nativeisshapegetdtypegetdatadowncast_intp_indexget_index_dtype check_shapecheck_reshape_kwargs isscalarlikeisdenseceZdZdZeddZd2dddZedZej d Zed Z e j d Z d Z e j j e _ d3d Ze jj e_ d3dZe jj e_ dZd4dZe jj e_ d5dZe jj e_ d6dZe jj e_ d7dZd7dZd7dZd7dZe jj e_ d7dZe jj e_ d7dZe jj e_ d8dZejj e_ dZd9dZd5dZd Zd!Z d"Z!d#Z"d$Z#d%Z$d&Z%d'Z&d(Z'd)Z(d*Z)d+Z*d:d-Z+d.Z,d/Z-d0Z.d7d1Z/dS); _coo_basecoor ANFmaxprintcp  tj|||stt|trt ||jrt||j|_| t|j t|t}t fdtt|jD|_t!jg||_d|_n[ |\}}n)#t(t*f$r} t)d| d} ~ wwxYw|At-d |Drt+d t d |D}t||j|_| |t|jd  t  fd |D|_t1|||_d|_nbt3|r|j|jkrr~t d|jD|_|jt|||_t|j|j|_|j|_n|} t | j|_| jt|| d|_t| j|j|_d|_n=t!j|} t|t<s7t!j| } | j dkrt)d| j dt| j|j|_|;t||j|jkrd|d|j} t+| | t|j| !}t fd|D|_t1| |||_d|_t|jdkr#t d|jD|_|"dS)Nr'allow_ndmaxval)defaultc3DK|]}tjgVdSdtypeNnparray).0_ idx_dtypes Q/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/sparse/_coo.py z%_coo_base.__init__..(sN$G$G)*%'HRy$A$A$A$G$G$G$G$G$Gr1Tzinvalid input formatc3<K|]}t|dkVdS)rNlenr6idxs r9r:z%_coo_base.__init__..3s,;;S3s88q=;;;;;;r;z4cannot infer dimensions from zero sized index arraysc3hK|]-}tjtj|dzV.dSr N)operatorindexr4maxr?s r9r:z%_coo_base.__init__..6sM"5"5&)#+."="="A"5"5"5"5"5"5r;)r-check_contentsc3FK|]}tj|VdS)copyr2Nr3)r6r@rIr8s r9r:z%_coo_base.__init__..<sH$8$8),%'HSt9$M$M$M$8$8$8$8$8$8r;rHFc3>K|]}|VdSNrIr?s r9r:z%_coo_base.__init__..Cs*'J'Js 'J'J'J'J'J'Jr;rLrz!expected 2D array or matrix, not Dzinconsistent shapes: z != c3FK|]}|dVdSFrLN)astype)r6r@ index_dtypes r9r:z%_coo_base.__init__..]sG$8$8),%(JJ{J$G$G$8$8$8$8$8$8r;c3XK|]%}|tjdV&dSrO)rPr4int64r?s r9r:z%_coo_base.__init__..cs4XXS 28% @ @XXXXXXr;)#r__init__r isinstancetupler _allow_ndr_shape_get_index_dtyperErfloatranger>coordsr4r5datahas_canonical_format TypeError ValueErroranyshaperrformatrPtocooasarrayr atleast_2dndimnonzero_check)selfarg1rbr2rIr( data_dtypeobjr\er%Mmessager8rQs ` @@r9rTz_coo_base.__init__sdD8<<<< "!D dE " "= 1tdn555 2)$HHH  11T[9I9I1JJ %eU;;; #$G$G$G$G.3C 4D4D.E.E$G$G$GGG HRz::: ,0))C"&KC!:.CCC#$:;;BC=;;F;;;;;?(*>???!"5"5-3"5"5"555E)%$.III  11&9"R"R"RDK040ID--**,,C"' "3"3DK #0D0D5 Q QDI"-ci$."Q"Q"QDK05D--Jt$$!$00W a((Av{{'(UAF(U(U(UVVV)!'DNKKK $"54>BBBdkQQ"R%"R"RT["R"R(111"333t{;K;K3LL #$8$8$8$806$8$8$888 #AfIDFFF ,0) t{  a  XXDKXXXXXDK s DD9$D44D9c|jdkr |jdStj|j}|d|S)Nr F)write)rgr\r4 zeros_likecolsetflags)rjresults r9rowz _coo_base.rowgsC 9q==;r? "tx((e$$$ r;c|jdkrtdtj||jdj}|jdd|fz|jddz|_dS)Nrz8cannot set row attribute of a 1-dimensional sparse arrayrrr1)rgr`r4rer\r2)rjnew_rows r9rxz _coo_base.rowpsf 9q==WXX X*WDKO,ABBBk#2#&'3dk"##6FF r;c|jdS)Nrzr\)rjs r9ruz _coo_base.colws{2r;ctj||jdj}|jdd|fz|_dS)Nrzr1)r4rer\r2)rjnew_cols r9ruz _coo_base.col{s<*WDKO,ABBBk#2#&'3 r;c t||j|j}t|\}}||jkr|r|S|St |j|j|}t|dkr=|dkrt||d}n7t||dddd}ntj |||}| |jt| t fd |D}|r|j}n|j}|||f|d S) Nr*orderrCr rrzr,c3DK|]}tj|VdSr0r4re)r6cor8s r9r:z$_coo_base.reshape..s2PPr2:b :::PPPPPPr;FrbrI)rrbrWr rI _ravel_coordsr\r>divmodr4 unravel_indexrYrErVr] __class__) rjargskwargsrbrrI flat_coords new_coordsnew_datar8s @r9reshapez_coo_base.reshapesWD$*t~FFF*622 t DJ   yy{{" $DK5III u::??||#Kq:: #Kq::44R4@ )+uEJJJJ))$+c%jj)II PPPPZPPPPP   !y~~''HHyH~~x4E~NNNr;c||dkr|jdkrt|jtfd|jDrt d|jjdkstd|jDrt dt S|dkr ||jz }||jkrt dtjt|jd|z |j d|z S) Nrr c3>K|]}t|kVdSrKr=)r6r@nnzs r9r:z$_coo_base._getnnz..s-::s3s88s?::::::r;z3all index and data arrays must have the same lengthc3,K|]}|jdkVdSrB)rgr?s r9r:z$_coo_base._getnnz..s()O)OC#(a-)O)O)O)O)O)Or;z'coordinates and data arrays must be 1-Daxis out of bounds minlength) rgr>r]rar\r`intr4bincountrrb)rjaxisrs @r9_getnnzz_coo_base._getnnzs .sF55!$Js)<<<555555r;rzaxis z index z exceeds matrix dimension znegative axis z index: N)rgr>r\r` enumerater2kindrnamerYrErbrVrr]rmin)rjrr@r8s @r9riz_coo_base._checks 9DK(( ( (M$' $4$4MMAEMMNN N  ,, # #FAsy~$$PAPPsy~PPP !####))$+c$*oo)NN 5555(, 55555 di(( 8a<<#DK00 N N37799 1 --$&IQ&I&Iswwyy&I&I9=A&I&IJJJ7799q==$%La%L%L%L%LMMM! < N Nr;c|tjddd}nttrlt |drt |jkrt dt t|jkrt dn|dkrt dtfd|D}tfd|D} j |f|| S) Nrz__len__z"axes don't match matrix dimensionszrepeated axis in transpose)r rzoSparse matrices do not support an 'axes' parameter because swapping dimensions is the only logical permutation.c32K|]}j|VdSrK)rXr6rrjs r9r:z&_coo_base.transpose..s)<.s)==1 A======r;r) r[rgrUrhasattrr>r`setrVrr])rjaxesrIpermuted_shapepermuted_coordss` r9 transposez_coo_base.transposes& <##DDbD)DD g & & :4++ Gs4yyDI/E/E !EFFF3t99~~** !=>>>+ V^^9:: :<<<.s*MM(#sC#IMMMMMMr;c g|] \}}||k Srr)r6r@sizes r9 z$_coo_base.resize..s-***(sDd ***r;c3(K|] }|V dSrKrr6r@rs r9r:z#_coo_base.resize..s'#E#E#CI#E#E#E#E#E#Er;)rrWrgr`r>rr\rbmathprodr4rr]rXrrazip logical_andreduceallrV)rjrbrmax_size tmp_shapetmp is_truncatingrs @r9resizez_coo_base.resizesEDN;;; 9q===>> > u::>>@AA A u:: ! !' TZ@@Ky''H*;yy+A5IIDK )8),DIDK F u:: ! ! OSZZ!^O,$)c%jj012  ,,y))C*[c%jj[1DK)KSZZK0DKMMc$*e6L6LMMMMM  ,>((**,/ U,C,C***D88:: ,##E#E#E#E#E#E#EEE  IdO  r;c |||}t|jj}|s|jjst d|jdkrWttj dg|j |j|j d|j | d|n |jdkrH|j\}}t|||j |j|j|j | d|n|r5tjdtj|jdd}nFtjtj|jddddddddd}tj|j }t||j |j||j | d|||jS)Nz&Output array must be C or F contiguousr rArrz)_process_toarray_argsrflags f_contiguous c_contiguousr`rgr r4r5rr\r]ravelrbr rxruappendcumprod concatenater) rjroutBfortranroNstridesr\s r9toarrayz_coo_base.toarrays  & &uc 2 2ag*++ Gqw3 GEFF F 9>> 28QC==$(DI;q>49aggcllG M M M M Y!^^:DAq 1dh$(DI g / / / / O)Arz$*SbS/'B'BCC)BJtz!""~ddd/C$D$DTTrT$JANN^DK00F 7DHdi!49aggcllG E E Eyy$$$r;cX|jdkrtd|jd|jdkr!||j|jSddlm}||j \}}}}||||f|}|j s| |S) aQConvert this array/matrix to Compressed Sparse Column format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_array >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsc() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) rz+Cannot convert. CSC format must be 2D. Got rMrr1r ) csc_arrayrb) rgr`r_csc_containerrbr2_cscr_coo_to_compressed_swapr^r)rjrIrindptrindicesr]rbxs r9tocscz_coo_base.tocsc:s( 9>>W49WWWXX X 8q==&&tz&DD D ' ' ' ' ' '+/+B+B9?+S+S (FGT5##T7F$;5#IIA, #  """Hr;cj|jdkrtd|jd|jdkr!||j|jSddlm}||j |}|\}}}}||||f|j }|j s| |S) aNConvert this array/matrix to Compressed Sparse Row format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_array >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsr() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) rz*Cannot convert. CSR must be 1D or 2D. Got rMrr1r ) csr_arrayrLr) rgr`r_csr_containerrbr2_csrrrrr^r) rjrIrarraysrrr]rbrs r9tocsrz_coo_base.tocsr[s( 9q==V$)VVVWW W 8q==&&tz&DD D ' ' ' ' ' ',,Y_4,HHF+1 (FGT5##T7F$;4:#NNA, #  """Hr;c ,||j\}}||jt|j|}|jdkr|r|jdn |jd}t|}tj d|g|}|r|j n|j } ||| |j fS||j\} } t| }| |d} | |d} tj |dz|}tj| |}tj|j |j} t!|||| | |j ||| ||| |j fS)z?convert (shape, coords, data) to (indptr, indices, data, shape)r,r rr1FrL) _shape_as_2drYr\rErrgrIr>r4r5r]rbrPempty empty_liker2r ) rjswaprIrorr8rrrr]majorminors r9rz_coo_base._coo_to_compressed}stD%&&1))$+c$(A>N>N)OO 9>>/3Gdk!n))+++QGg,,CXq#hi888F'+:49>>###D7D$*4 4tDK(( u%jj YU 33 YU 33!a%y111-Y777}TYdj999!QUE49fgtLLLwdj00r;c2|r|S|SrKrL)rjrIs r9rdz_coo_base.tocoos  99;; Kr;ct|jdkrtd|jd||j|jz }t j|d\}}t|dkr(tdt|dtd |j j d krt j d |j }nUt j t||jd zf|j }|j |||jf<|||f|jS)Nrz+Cannot convert. DIA format must be 2D. Got rMT)return_inversedzConstructing a DIA matrix with z diagonals is inefficientrr)rrr1r r)rgr`rrurxr4uniquer>rrr]rzerosr2rE_dia_containerrb)rjrIksdiagsdiag_idxr]s r9todiaz_coo_base.todias5 9>>W49WWWXX X  X )Bt<<<x u::   "3u::"""(Q 8 8 8 8 9>Q  8F$*555DD8SZZ)9:$*MMMD'+yD48# $""D%= "CCCr;cR|jdkrtd|jd|||j|j}|jdkr|jd}nt|j}tt||j |_ |S)Nrz*Cannot convert. DOK must be 1D or 2D. Got rMr1r r) rgr`r_dok_containerrbr2r\rdictr]_dict)rjrIdokr\s r9todokz_coo_base.todoks 9q==V$)VVVWW W !!$*DJ!?? 9>>[^FF$+&FVTY//00  r;rc d |jdkrtd|j\}}|| ks||kr tjd|jjStjt|t|dz|t|dz |j}|j |z|j k |j r|j }|j }nGt fd|jD}|||j \\}}}|||t|dz<|S)Nrz diagonal requires two dimensionsrr1c3(K|] }|V dSrKr)r6r@ diag_masks r9r:z%_coo_base.diagonal..s'??CY??????r;)rgr`rbr4rr]r2rrrErxrur^rVr\_sum_duplicates) rjkrowscolsdiagrxr]indsr7r s @r9diagonalz_coo_base.diagonals0 9>>?@@ @Z d ::d8ATY_555 5xD3q!99,dSAYY.>??"j***X\dh.  $ N(9%C9Y'DD????4;?????D!11$ )8LMMNHS!d $S3q!99_ r;c2|jdkrtd|j\}}|jrt|sdS|jj}|j|jz |k}|dkrt||z|}|jrt|t|}tj ||j|k}tj | | |z|} tj ||} nt|||z }|jrt|t|}tj ||j|k}tj ||} tj |||z|} |jr |d|} n"tj ||j} || dd<tj |j|| ftj |j|| ff|_ tj |j|| f|_d|_dS)Nrz*setting a diagonal requires two dimensionsrr1F)rgr`rbr>rxr2rurr4 logical_orarangerrr\r]r^) rjvaluesr rorr8 full_keep max_indexkeepr{rrs r9_setdiagz_coo_base._setdiags 9>>IJJ Jz1 ; s6{{  FHN Htx'1, q55AaC I{ 8 3v;;77 =DH ,ABBDiQBN)DDDGi ;;;GGAqs I{ 8 3v;;77 =DH ,ABBDi ;;;Gi1y= BBBG ; !jyj)HHx <<?? $)!!!r;Tc|rtd|jD}n|j}|||f|j|jS)zReturns a matrix with the same sparsity structure as self, but with different data. By default the index arrays are copied. c3>K|]}|VdSrKrLr?s r9r:z'_coo_base._with_data.. s*==#388::======r;)rbr2)rVr\rrbr2)rjr]rIr\s r9 _with_dataz_coo_base._with_datasS  !=======FF[F~~tVnDJdj~QQQr;c|jrdS||j|j}|\|_|_d|_dS)zeEliminate duplicate entries by adding them together This is an *in place* operation NT)r^r r\r])rjsummeds r9rz_coo_base.sum_duplicatessI  $  F%%dk49==!' TY$(!!!r;ct|dkr||fStj|dddtfd|D}|}tjd|Dtjdtfd|D}tj\}tj |t||j }||fS)Nrrzc3(K|] }|V dSrKr)r6r@rs r9r:z,_coo_base._sum_duplicates.."s'44cs5z444444r;c:g|]}|dd|ddkS)r Nrzrr?s r9rz-_coo_base._sum_duplicates..$s:, , , $'CGs3B3x , , , r;Tc3(K|] }|V dSrKr)r6r@ unique_masks r9r:z,_coo_base._sum_duplicates..(s(::Cs;'::::::r;r1) r>r4lexsortrVrrrrhaddreduceatrr2)rjr\r] unique_indsrr#s @@r9r z_coo_base._sum_duplicatess  t99>>4<  6$$B$<((4444V44444E{m**, , +1, , ,   ik22 ::::6:::::z+.. vt%8%E%ETZXXt|r;c|jdk|j|_tfd|jD|_dS)z[Remove zero entries from the array/matrix This is an *in place* operation rc3(K|] }|V dSrKrrs r9r:z,_coo_base.eliminate_zeros..4s'==#CI======r;N)r]rVr\)rjrs @r9eliminate_zerosz_coo_base.eliminate_zeros-sG yA~IdO ========= r;c <|j|jkr td|jd|jdt|jj|jj}t j||d}t|jj }|j dkrWtt jdg|j |j |j d|j|d|n |j d krH|j\}}t#|||j |j|j|j|d|n|r5t jdt j|jdd }nFt jt j|jddddd ddd d}t j|j }t||j |j ||j|d|||d S) NIncompatible shapes ( and rT)r2rIr rrrrzFrL)rbr`rr2charr4r5rrrrgr rr\r]rrr rxrurrr _container) rjotherr2rwrrorrr\s r9 _add_densez_coo_base._add_dense:s ;$* $ $TTZTTekTTTUU UDJOU[-=>>%u4888fl/00 9>> 28QC==$(DI;q>49fll36G6G R R R R Y!^^$DAq 1dh$(DI S))7 4 4 4 4 O)Arz$*SbS/'B'BCC)BJtz!""~ddd/C$D$DTTrT$JANN^DK00F 7DHdi!49fll3.?.? J J JvE222r;c|jdkr'||S|j|jkr t d|jd|jd||}t j|j|jf}tt j|j |j fd}|||f|j}|SNrr,r-rr )rr) rgr _add_sparserbr`rr4rr]rVr\rjr0rrrs r9r4z_coo_base._add_sparseRs 9q==::<<++E22 2 ;$* $ $TTZTTekTTTUU Uu%%>49ej"9::2>4; *EANNNOO NNHj1N D Dr;c|jdkr'||S|j|jkr t d|jd|jd||}t j|j|j f}tt j|j |j fd}t||f|j}|Sr3) rgr _sub_sparserbr`rr4rr]rVr\rr5s r9r7z_coo_base._sub_sparse_s 9q==::<<++E22 2 ;$* $ $TTZTTekTTTUU Uu%%>49uzk":;;2>4; *EANNNOO x,DJ ? ? ?r;c N|jdkr'tjtj|jddt |jj|jj}tj |j}tj tj |ddddddddddd}tj |j }t|jt!|j|||j||||jdd}|S|jdkr |jdnd}tj|t |jj|jj}|jdkr|j}|j}nD|jdkr"|j d}tj|}nt-d|jt/|j|||j||t1|t2r|dkr|dS|S)Nrrzr1r rz$coo_matvec not implemented for ndim=)rgr4rrrrbrr2r.r5rrrr\rrr>r]rrurxrtNotImplementedErrorrrUr) rjr0rwrbrr\ result_shaperurxs r9_matmul_vectorz_coo_base._matmul_vectorls 9q==Xdi 3B388$/ AQ$R$RTTTFHTZ((Ei 5":ddd+; < >(C(CC Y!^^+a.C-$$CC%BtyBBDD D 48S#ty%@@@ dG $ $ ):):!9  r;ct|r||S |j}n+#t$rt j|}|j}YnwxYwt t|ddt t|dddddz}||}|j}t t|ddt t|dddddz}|| |}|turtS|dks|dkrt|j}n\t t|jddt t|jdddddz}||S)Nrrrzr ) r! _mul_scalarrgAttributeErrorr4rerVr[r_matmul_dispatchNotImplemented)rjr0o_ndimpermtrs_ndimrets r9_rmatmul_dispatchz_coo_base._rmatmul_dispatchs    '##E** * $! $ $ $ 5)) $vss+,,uU6]]2335G"5M/N/NND&&BYFvss+,,uU6]]2335G"5M/N/NND..&&77;;Cn$$%%{{fkkSXU38__SbS122U5??233;OPTPTRTPT;U5V5VV==&& &s.%AAct|r||St|set|sVt j|}|jdkr|jtjkrtS |j n#t$r|}YnwxYw|jdkr |jdkrtj ||S|j d}d}|jtjurB|j |fkr||S|j |dfkrC||}|jg|j dddRS|jdkr%|d|d|j dd}t'||j d |krm|j dd }|j dd }||kr4 t j||n#t&$rt'd wxYw||St'|d |d|j d d t|r||St|r|jdk} |jdk} | r||j}| r"||j ddf}||j d kr#t'|d |d|j d d |jd ks |jd krX|j dd }|j dd }||kr4 t j||n#t&$rt'd wxYw||}| rL|t3|j dd t3|j ddz}| r"||j dd}|SdS)Nrrrzz)matmul: dimension mismatch with signaturer z (n,k=z),(k=z,)->(n,)rrz&Batch dimensions are not broadcastablez (n,..,k=z,..,m)->(n,..,m)r)r!multiplyrr"r4 asanyarrayrgr2object_r@rbr>rr?rndarrayr;rrr`broadcast_shapes_matmul_multivectorr=r_matmul_sparserV) rjr0other_ar err_prefixrwmsg batch_shape_A batch_shape_B self_is_1d other_is_1ds r9r?z_coo_base._matmul_dispatchsd    (=='' ' 75>> mE**G|q  W]bj%@%@&%  !     9q==UZ!^^+D%88 8 JrN@ ?bj ( ({qd""**5111{q!f$$,,U[[]];;%v~:tz#2#:::::zQ#KK1KK5;q>KKK oo%{2!## $ 3B3 % CRC 0  M11S+M=IIII%SSS()QRRRS//666 !UUAUUEKOUUU    +##E** * E??& aJ*/K 7||D$566 ; u{1~q&9::EKO## !UUAUUEKOUUU y1}} Q $ 3B3 % CRC 0  M11S+M=IIII%SSS()QRRRS((//F Bfl3B3.?(@(@(-fl233.?(@(@)ABB ; SbS(9::MM& & s*?B BB>GG."L88Mc t|jj|jj}|jdks |jdkr|jdkr|d|jd|}|t|jddt|jddzStj |jdd|jdd}||jddz}||jddz}| |}tj ||}||jddz|jddz}tj ||}t|jt|j|jdtj|tj|tj|j|j|d| |S|jdkr)|jd|jdf}|j}|j} n:|jdkr/|jdf}|jd}tj|} tj ||}t1|j|jd| ||j|d||t5| S) Nrr rrrrzr1rr)type)rr2r.rgrrbrMrVr4rL _broadcast_to broadcast_torrrr>r5rr\r]rrurxrtrviewrW) rjr0 result_dtyperwbroadcast_shape self_shape other_shaper:rurxs r9rMz_coo_base._matmul_multivectors"4:?EK4DEE 9>>UZ1__yA~~aA77KKERR~~eEK,<&=&=ekRTRURUFV@W@W&WXXX 1$*SbS/5;sPRsCSTTO(4:bcc?:J)EK,<>RSSAQQLXl,???F #dj//5;r? " 5 5rx 7M7M "t{ ; ; $ 5;;s+;+;V E E EM 9>> JqM5;q>:L(C(CC Y!^^!KN,L+a.C-$$C,l;;;5;r?CEKK$4$4f > > >{{U {,,,r;ct|st|s~t|sotj|}|jdkr5|jtjkr tdt|d |j n#t$r|}YnwxYw|jdkr4tj |s |jdkrtj||Stj |r||zSt|r||S|jdkrtd|jdkrL|jdkrA|j d|j dkr t#d|j d |j d ||zS|jd krL|jd krA|j d|j dkr t#d|j d |j d ||zS||S) aReturn the dot product of two arrays. Strictly speaking a dot product involves two vectors. But in the sense that an array with ndim >= 1 is a collection of vectors, the function computes the collection of dot products between each vector in the first array with each vector in the second array. The axis upon which the sum of products is performed is the last axis of the first array and the second to last axis of the second array. If the second array is 1-D, the last axis is used. Thus, if both arrays are 1-D, the inner product is returned. If both are 2-D, we have matrix multiplication. If `other` is 1-D, the sum product is taken along the last axis of each array. If `other` is N-D for N>=2, the sum product is over the last axis of the first array and the second-to-last axis of the second array. Parameters ---------- other : array_like (dense or sparse) Second array Returns ------- output : array (sparse or dense) The dot product of this array with `other`. It will be dense/sparse if `other` is dense/sparse. Examples -------- >>> import numpy as np >>> from scipy.sparse import coo_array >>> A = coo_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]]) >>> v = np.array([1, 0, -1]) >>> A.dot(v) array([ 1, -3, -1], dtype=int64) For 2-D arrays it is the matrix product: >>> A = coo_array([[1, 0], [0, 1]]) >>> B = coo_array([[4, 1], [2, 2]]) >>> A.dot(B).toarray() array([[4, 1], [2, 2]]) For 3-D arrays the shape extends unused axes by other unused axes. >>> A = coo_array(np.arange(3*4*5*6)).reshape((3,4,5,6)) >>> B = coo_array(np.arange(3*4*5*6)).reshape((5,4,6,3)) >>> A.dot(B).shape (3, 4, 5, 5, 4, 3) rz"dot argument not supported type: ''rr%z input must be a COO matrix/arrayr shapes r-z" are not aligned for inner productrz are not aligned for matmul)rr"r!r4rIrgr2rJr_rWrbr>isscalarrdot _dense_dotrcr` _sparse_dot)rjr0o_arrays r9rcz _coo_base.dot+s6j 75>> \%5H5H mE**G|q  W]bj%@%@ ST%[[ S S STTT  !     9q==bk%00=EJqLL;tU++ + ;u   %<  5>> +??5)) ) \U " ">?? ? Y!^^ az!} A.. "F4:"F"FEK"F"F"FGGG%<  Y!^^ az!} A.. "?4:"?"?EK"?"?"?@@@%< ##E** *sB BBc|jdk}|jdk}|r||j}|r"||jddf}|jd|jdkr t d|jd|jdt |j|j|jdz g}t |j|j|jdz g}|jdd}|jdd|jddz}tj||jdf}|jdtj|f} ||jdf} |jd|f} t|j | f|} t|j | f| } | | z }||z}||f}g}t|j|D]-\}}| tj||.t|j |f|}|r||dd}|r||dd}|S) Nr rrzrrrar- are not aligned for n-D dotr)rgrrrbr`_ravel_non_reduced_axesr\rrrr]rdrextendr4r)rjr0rTrUself_raveled_coordsother_raveled_coordsself_nonreduced_shapeother_nonreduced_shaperavel_coords_shape_selfravel_coords_shape_otherself_2d_coordsother_2d_coordsself_2dother_2drcombined_shapeshapes prod_coordscsprod_arrs r9rez_coo_base._sparse_dotsY!^ jAo   3<< 122D  7MM5;q>1"566E :b>U[_ , , "@4:"@"@EK"@"@"@AAA 6dk6:j49Q;-QQ6u|7<{UZPQ\N T T!% 3B3!&SbS!1EK4D!D$(9-B#C#CTZPR^"T$)KOTY?U5V5V#W -t{2? <+-ABTY79PQQej/:) rjr0rTrUnew_shape_selfnew_shape_otherr:rwrzs r9rdz_coo_base._dense_dotsY!^ jAo   3<< 122D  7MM5;q>1"566E :b>U[_ , , "@4:"@"@EK"@"@"@AAA JssOdc%+&6&6&:; ;djo M #dj//A"56Dz#2#SbS)99EK>,//  :'' QRR(899H  ;'' SbS(9::Hr;rcHts~tsotj}|jdkr5|jtjkr tdtd j n#t$r|YnwxYwtjj|\}}tfdt||Drtdtr||S||S)a Return the tensordot product with another array along the given axes. The tensordot differs from dot and matmul in that any axis can be chosen for each of the first and second array and the sum of the products is computed just like for matrix multiplication, only not just for the rows of the first times the columns of the second. It takes the dot product of the collection of vectors along the specified axes. Here we can even take the sum of the products along two or even more axes if desired. So, tensordot is a dot product computation applied to arrays of any dimension >= 1. It is like matmul but over arbitrary axes for each matrix. Given two tensors, `a` and `b`, and the desired axes specified as a 2-tuple/list/array containing two sequences of axis numbers, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s elements (components) over the axes specified by ``a_axes`` and ``b_axes``. The `axes` input can be a single non-negative integer, ``N``; if it is, then the last ``N`` dimensions of `a` and the first ``N`` dimensions of `b` are summed over. Parameters ---------- a, b : array_like Tensors to "dot". axes : int or (2,) array_like * integer_like If an int N, sum over the last N axes of `a` and the first N axes of `b` in order. The sizes of the corresponding axes must match. * (2,) array_like A 2-tuple of sequences of axes to be summed over, the first applying to `a`, the second to `b`. The sequences must be the same length. The shape of the corresponding axes must match between `a` and `b`. Returns ------- output : coo_array The tensor dot product of this array with `other`. It will be dense/sparse if `other` is dense/sparse. See Also -------- dot Examples -------- >>> import numpy as np >>> import scipy.sparse >>> A = scipy.sparse.coo_array([[[2, 3], [0, 0]], [[0, 1], [0, 5]]]) >>> A.shape (2, 2, 2) Integer axes N are shorthand for (range(-N, 0), range(0, N)): >>> A.tensordot(A, axes=1).toarray() array([[[[ 4, 9], [ 0, 15]], [[ 0, 0], [ 0, 0]]], [[[ 0, 1], [ 0, 5]], [[ 0, 5], [ 0, 25]]]]) >>> A.tensordot(A, axes=2).toarray() array([[ 4, 6], [ 0, 25]]) >>> A.tensordot(A, axes=3) array(39) Using tuple for axes: >>> a = scipy.sparse.coo_array(np.arange(60).reshape(3,4,5)) >>> b = np.arange(24).reshape(4,3,2) >>> c = a.tensordot(b, axes=([1,0],[0,1])) >>> c.shape (5, 2) >>> c array([[4400, 4730], [4532, 4874], [4664, 5018], [4796, 5162], [4928, 5306]]) rz#tensordot arg not supported type: 'r`c3VK|]#\}}j|j|kV$dSrKr)r6axbxr0rjs r9r:z&_coo_base.tensordot..CsL992rz"~R0999999r;z*sizes of the corresponding axes must match)r"rr4rIrgr2rJr_rWrbr> _process_axesrarr`_dense_tensordot_sparse_tensordot)rjr0r other_array axes_self axes_others`` r9 tensordotz_coo_base.tensordotsTru~~ $huoo $-..K1$$):bj)H)H Td5kk T T TUUU $ ! $ $ $# $!.diT J J : 99999 J77999 9 9 KIJJ J 5>> H(( :FF F))%JGG Gs6A>> B  B ctj}tj}tjj}t jfdDfdD}tjj}t jfdDfdD} t fdt|D} t fdt|D} tj | tj fdDf} tj fdDtj | f} ||f}| |f}tj |f| }tj |f| }||z }| | z}g}t|j| | fD]/\}}|r(|t j||0|gkrt!|j St|j |f| S) Nc*g|]}j|Srr}r6rrjs r9rz/_coo_base._sparse_tensordot..Vs 1 1 1T[_ 1 1 1r;c*g|]}j|Srrrs r9rz/_coo_base._sparse_tensordot..Vs3W3W3WrDJrN3W3W3Wr;c*g|]}j|Srr}r6ar0s r9rz/_coo_base._sparse_tensordot..Zs 1 1 1U\!_ 1 1 1r;c*g|]}j|Srrrs r9rz/_coo_base._sparse_tensordot..Zs3W3W3WqEKN3W3W3Wr;c3:K|]}|vj|VdSrKr)r6rrrjs r9r:z._coo_base._sparse_tensordot..]s?&6&6!#9!4!4'+jn!4!4!4!4&6&6r;c3:K|]}|vj|VdSrKr)r6rrr0s r9r:z._coo_base._sparse_tensordot.._s?'8'82"$J"6"6(-{2"6"6"6"6'8'8r;c*g|]}j|Srrrs r9rz/_coo_base._sparse_tensordot..ds*N*N*Nb4:b>*N*N*Nr;c*g|]}j|Srr)r6rr0s r9rz/_coo_base._sparse_tensordot..es.T.T.T2u{2.T.T.Tr;r)r>rbrir\r4ravel_multi_indexrVr[rrrr]rdrrjrsum)rjr0rr ndim_self ndim_otherself_non_red_coordsself_reduced_coordsother_non_red_coordsother_reduced_coordsrmrnrorprqrrrsrtrrur\rxrys```` r9rz_coo_base._sparse_tensordotMs OO %% 6dk4:6?AA 2 1 1 1 1y 1 1 13W3W3W3WY3W3W3WYY6u|U[7A C C!3 1 1 1 1j 1 1 13W3W3W3WJ3W3W3W  !&&6&6&6&6&6uY?O?O&6&6&6!6!6!&'8'8'8'8'8zARAR'8'8'8"8"8$(9-B#C#C $ *N*N*N*NI*N*N*N O O#Q$(I.T.T.T.T.T.T.T$U$U$(I.D$E$E$G ./BC/1EFTY79PQQej/:> !$)V,NCCCCr;ctj}tj}fdt|D}fdD}fd|D}fdt|D} fdD} fd| D} |z} | ddz| ddz} | t j| g|t j|R}g| ddt j| | ddR}||S)Ncg|]}|v| Srr)r6rrs r9rz._coo_base._dense_tensordot..s# V V V"IBUBUBUBUBUr;c*g|]}j|Srrr6ryrjs r9rz._coo_base._dense_tensordot..s???djm???r;c*g|]}j|Srrrs r9rz._coo_base._dense_tensordot..s!O!O!OA$*Q-!O!O!Or;cg|]}|v| Srr)r6rrs r9rz._coo_base._dense_tensordot..s-";";";%'z%9%9#%%9%9%9r;c*g|]}j|Srrr6ryr0s r9rz._coo_base._dense_tensordot..sBBB!u{1~BBBr;c*g|]}j|Srrrs r9rz._coo_base._dense_tensordot..s"R"R"Ra5;q>"R"R"Rr;rz) r>rbr[rr4rrrrc)rjr0rrrrnon_reduced_axes_selfreduced_shape_selfnon_reduced_shape_selfnon_reduced_axes_otherreduced_shape_othernon_reduced_shape_other permute_self permute_other reshape_self reshape_others```` r9rz_coo_base._dense_tensordots OO %% V V V VeI.>.> V V V????Y???!O!O!O!O9N!O!O!O";";";";uZ/@/@";";";BBBBzBBB"R"R"R"R;Q"R"R"R,y8 "3B3 '* 47Mbcc7R R ~~l++ UM22O/O;M1N1NOO 71#2#67 BU8V8V70577 ||L))--emmM.J.JKKKr;c@|jdkr |jdkrtj||S|j}|j}t j|dd|dd}t ||ddz}t ||ddz}||}||}t|} t|} | | z } t| g||jd|jdRS)a Perform sparse-sparse matrix multiplication for two n-D COO arrays. The method converts input n-D arrays to 2-D block array format, uses csr_matmat to multiply them, and then converts the result back to n-D COO array. Parameters: self (COO): The first n-D sparse array in COO format. other (COO): The second n-D sparse array in COO format. 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Parameters ---------- x object to check for being a coo matrix Returns ------- bool True if `x` is a coo matrix, False otherwise Examples -------- >>> from scipy.sparse import coo_array, coo_matrix, csr_matrix, isspmatrix_coo >>> isspmatrix_coo(coo_matrix([[5]])) True >>> isspmatrix_coo(coo_array([[5]])) False >>> isspmatrix_coo(csr_matrix([[5]])) False )rUr)rs r9rros. a $ $$r;ceZdZdZdS)ra  A sparse array in COOrdinate format. Also known as the 'ijv' or 'triplet' format. This can be instantiated in several ways: coo_array(D) where D is an ndarray coo_array(S) with another sparse array or matrix S (equivalent to S.tocoo()) coo_array(shape, [dtype]) to construct an empty sparse array with shape `shape` dtype is optional, defaulting to dtype='d'. coo_array((data, coords), [shape]) to construct from existing data and index arrays: 1. data[:] the entries of the sparse array, in any order 2. coords[i][:] the axis-i coordinates of the data entries Where ``A[coords] = data``, and coords is a tuple of index arrays. When shape is not specified, it is inferred from the index arrays. Attributes ---------- dtype : dtype Data type of the sparse array shape : tuple of integers Shape of the sparse array ndim : int Number of dimensions of the sparse array nnz size data COO format data array of the sparse array coords COO format tuple of index arrays has_canonical_format : bool Whether the matrix has sorted coordinates and no duplicates format T Notes ----- Sparse arrays can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Advantages of the COO format - facilitates fast conversion among sparse formats - permits duplicate entries (see example) - very fast conversion to and from CSR/CSC formats Disadvantages of the COO format - does not directly support: + arithmetic operations + slicing Intended Usage - COO is a fast format for constructing sparse arrays - Once a COO array has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations - By default when converting to CSR or CSC format, duplicate (i,j) entries will be summed together. This facilitates efficient construction of finite element matrices and the like. (see example) Canonical format - Entries and coordinates sorted by row, then column. - There are no duplicate entries (i.e. duplicate (i,j) locations) - Data arrays MAY have explicit zeros. Examples -------- >>> # Constructing an empty sparse array >>> import numpy as np >>> from scipy.sparse import coo_array >>> coo_array((3, 4), dtype=np.int8).toarray() array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> # Constructing a sparse array using ijv format >>> row = np.array([0, 3, 1, 0]) >>> col = np.array([0, 3, 1, 2]) >>> data = np.array([4, 5, 7, 9]) >>> coo_array((data, (row, col)), shape=(4, 4)).toarray() array([[4, 0, 9, 0], [0, 7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5]]) >>> # Constructing a sparse array with duplicate coordinates >>> row = np.array([0, 0, 1, 3, 1, 0, 0]) >>> col = np.array([0, 2, 1, 3, 1, 0, 0]) >>> data = np.array([1, 1, 1, 1, 1, 1, 1]) >>> coo = coo_array((data, (row, col)), shape=(4, 4)) >>> # Duplicate coordinates are maintained until implicitly or explicitly summed >>> np.max(coo.data) 1 >>> coo.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) N)rrrrrr;r9rrs"kkkkr;rceZdZdZdZdS)ra. A sparse matrix in COOrdinate format. Also known as the 'ijv' or 'triplet' format. This can be instantiated in several ways: coo_matrix(D) where D is a 2-D ndarray coo_matrix(S) with another sparse array or matrix S (equivalent to S.tocoo()) coo_matrix((M, N), [dtype]) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'. coo_matrix((data, (i, j)), [shape=(M, N)]) to construct from three arrays: 1. data[:] the entries of the matrix, in any order 2. i[:] the row indices of the matrix entries 3. j[:] the column indices of the matrix entries Where ``A[i[k], j[k]] = data[k]``. When shape is not specified, it is inferred from the index arrays Attributes ---------- dtype : dtype Data type of the matrix shape : 2-tuple Shape of the matrix ndim : int Number of dimensions (this is always 2) nnz size data COO format data array of the matrix row COO format row index array of the matrix col COO format column index array of the matrix has_canonical_format : bool Whether the matrix has sorted indices and no duplicates format T Notes ----- Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Advantages of the COO format - facilitates fast conversion among sparse formats - permits duplicate entries (see example) - very fast conversion to and from CSR/CSC formats Disadvantages of the COO format - does not directly support: + arithmetic operations + slicing Intended Usage - COO is a fast format for constructing sparse matrices - Once a COO matrix has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations - By default when converting to CSR or CSC format, duplicate (i,j) entries will be summed together. This facilitates efficient construction of finite element matrices and the like. (see example) Canonical format - Entries and coordinates sorted by row, then column. - There are no duplicate entries (i.e. duplicate (i,j) locations) - Data arrays MAY have explicit zeros. Examples -------- >>> # Constructing an empty matrix >>> import numpy as np >>> from scipy.sparse import coo_matrix >>> coo_matrix((3, 4), dtype=np.int8).toarray() array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> # Constructing a matrix using ijv format >>> row = np.array([0, 3, 1, 0]) >>> col = np.array([0, 3, 1, 2]) >>> data = np.array([4, 5, 7, 9]) >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray() array([[4, 0, 9, 0], [0, 7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5]]) >>> # Constructing a matrix with duplicate coordinates >>> row = np.array([0, 0, 1, 3, 1, 0, 0]) >>> col = np.array([0, 2, 1, 3, 1, 0, 0]) >>> data = np.array([1, 1, 1, 1, 1, 1, 1]) >>> coo = coo_matrix((data, (row, col)), shape=(4, 4)) >>> # Duplicate coordinates are maintained until implicitly or explicitly summed >>> np.max(coo.data) 1 >>> coo.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) cd|vr-|d|df|d<|j|dS)Nr\rxru)pop__dict__update)rjstates r9 __setstate__zcoo_matrix.__setstate__jsQ 5  %yy//51A1ABE(O U#####r;N)rrrrrrr;r9rrs0nn`$$$$$r;r)r)2r __docformat____all__rwarningsrnumpyr4 _lib._utilr_matrixr _sparsetoolsr r r rrrr_baserrrr_datarr_sputilsrrrrrrrrr r!r"rCr$rrrrirrrrrr;r9rs88% 7 7 7 ''''''000000000000000000GFFFFFFFFFFF........QQQQQQQQQQQQQQQQQQQQQQQQQQb<b<b<b<b< mb<b<b