(ph@SrSr/SQrSSKrSSKJr SSKrSSKJ r SS K J r SS K J r JrJrJrJrJrJr SS KJrJrJrJr SS KJrJr SS KJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r' SSK(r("SS\\5r)Sr*Sr+Sr,Sr-SSjr.Sr/"SS\)\5r0"SS\ \)5r1g)z1A 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 isscalarlikeisdensec\rSrSrSr\"SS5rS/SS.Sjjr\S5r \ RS 5r \S 5r \ RS 5r S r \ RR\ lS0S jr\ RR\lS0Sjr\ R R\lSrS1Sjr\ R$R\lS2Sjr\ R&R\lS3Sjr\ R(R\lS4SjrS4SjrS4SjrS4Sjr\ R0R\lS4Sjr\ R2R\lS4Sjr\ R4R\lS5Sjr\R6R\lSrS6SjrS2SjrSr Sr!Sr"S r#S!r$S"r%S#r&S$r'S%r(S&r)S'r*S(r+S7S)jr,S*r-S+r.S,r/S4S-jr0S.r1g)8 _coo_basecoor ANmaxprintc^^ ^[R"XUS9 T(d[m[U[5(Gae[ XR S9(a[XR S9UlUR[UR5S9m [U[S9n[ U 4Sj[[UR5555Ul[ R""/US9UlSUlGOUupxUc4[-S U55(a [+S 5e[ S U55n[X R S9UlURU[UR.5SS 9m [ UU 4S jU55Ul[1UTUS9UlSUlGOc[3U5(GaUR4UR4:XaT(a[ SUR55UlUR$R7[X155Ul[UR.UR S9UlUR&UlGOUR95n [ U R5UlU R$R7[X:5SS9Ul[U R.UR S9UlSUlGO3[ R:"U5n [U[<5(d?[ R>"U 5n U R@S:wa[)SU R@S35e[U R.UR S9UlUb>[X R S9UR:waSUSUR3n [+U 5eUR[UR5S9mU RC5n[ U4SjU55Ul[1XTUS9UlSUl[UR5S:a![ SUR55UlURE5 g![([*4an [)S5U eSn A ff=f)Nr(allow_ndmaxval)defaultc3N># UHn[R"/TS9v M g7fdtypeNnparray).0_ idx_dtypes D/var/www/html/venv/lib/python3.13/site-packages/scipy/sparse/_coo.py %_coo_base.__init__..(s$$G.E%'HHRy$A.E"%r2Tzinvalid input formatc3># UHn[U5S:Hv M g7f)rNlenr7idxs r:r;r<3s;FS3s8q=Fz4cannot infer dimensions from zero sized index arraysc3|# UH2n[R"[R"U55S-v M4 g7fr N)operatorindexr5maxrAs r:r;r<6s-"5-3c#+.."="A-3s:<)r.check_contentsc3P># UHn[R"UTTS9v M g7f)copyr3Nr4)r7rBrLr9s r:r;r<<s%$806%'HHSt9$M06s#&rKFc3@# UHoR5v M g7fNrLrAs r:r;r<Cs'Jks krOrz!expected 2D array or matrix, not Dzinconsistent shapes: z != c3D># UHnURTSS9v M g7fFrON)astype)r7rB index_dtypes r:r;r<]s%$806%(JJ{J$G06s c3\# UH"oR[RSS9v M$ g7frS)rTr5int64rAs r:r;r<csXKS 288% @Ks*,)#r__init__r isinstancetupler _allow_ndr_shape_get_index_dtyperHrfloatranger@coordsr5r6datahas_canonical_format TypeError ValueErroranyshaperrformatrTtocooasarrayr atleast_2dndimnonzero_check)selfarg1rfr3rLr) data_dtypeobjr`er&Mmessager9rUs ` @@r:rX_coo_base.__init__sd8<!D dE " "tnn5)$H  11T[[9I1J %eU; #$G.3C 4D.E$GG HHRz: ,0)C"&KC=;F;;;(*>??!"5-3"55E)%..I  11&9>"RDK040I0ID-**,C"' "3DK #0D5 QDI"-cii$.."QDK05D-JJt$!$00 a(Avv{'*KAFF8ST(UVV)!''DNNK $"5>>BdkkQ$9%T[[M"R(11"333t{{;K3L #$806$88 #AIDF ,0) t{{ a XDKKXXDK m":.C#$:;BCs6QQ0 Q++Q0cURS:aURS$[R"UR5nUR SS9 U$)Nr F)write)rkr`r5 zeros_likecolsetflags)rnresults r:row _coo_base.rowgs@ 99q=;;r? "txx(e$ cURS:a [S5e[R"XRSR S9nURSSU4-URSS-Ulg)Nrz8cannot set row attribute of a 1-dimensional sparse arrayrwr2)rkrdr5rir`r3)rnnew_rows r:r}r~ps^ 99q=WX X**WKKO,A,ABkk#2&'3dkk"#6FF rc URS$Nrr`)rns r:rz _coo_base.colws{{2rc[R"XRSRS9nURSSU4-Ulg)Nrr2)r5rir`r3)rnnew_cols r:rzr{s7**WKKO,A,ABkk#2&'3 rct^ [XRURS9n[U5upEX0R:XaU(aUR 5$U$[ UR URUS9n[U5S:Xa*US:Xa[XcS5nO*[XcS5SSS2nO[R"XcUS9nURUR [U5S9m [U 4S jU55nU(aURR 5nO URnURX4US S 9$) Nr+orderrCr rrr-c3N># UHn[R"UTS9v M g7fr1r5ri)r7cor9s r:r;$_coo_base.reshape..sPZr2::b :Zr=FrfrL)rrfr[r rL _ravel_coordsr`r@divmodr5 unravel_indexr]rHrZra __class__) rnargskwargsrfrrL flat_coords new_coordsnew_datar9s @r:reshape_coo_base.reshapesD**t~~F*62  JJ yy{" $DKK5I u:?|#Kq: #Kq:4R4@ ))+EJJ))$++c%j)I PZPP  yy~~'HyyH~~x4E~NNrc8^UbUS:XaURS:Xa[UR5m[U4SjUR55(a [ S5eURRS:wd![SUR55(a [ S5e[ T5$US:aXR- nXR:a [ S5e[R"[URSU- 5URSU- S9$) Nrr c3@># UHn[U5T:gv M g7frNr?)r7rBnnzs r:r;$_coo_base._getnnz..s:ks3s8s?ksz3all index and data arrays must have the same lengthc3># UHoRS:gv M g7frE)rkrAs r:r;rs)O;C((a-;rCz'coordinates and data arrays must be 1-Daxis out of bounds minlength) rkr@rarer`rdintr5bincountrrf)rnaxisrs @r:_getnnz_coo_base._getnnzs # UHn[R"UTS9v M g7fr1r)r7rBr9s r:r;#_coo_base._check..s#5(3JJs)<(3r=rzaxis z index z exceeds matrix dimension znegative axis z index: N)rkr@r`rd enumerater3kindrnamer]rHrfrZrrarmin)rnrrBr9s @r:rm_coo_base._checks 99DKK( ($$' $4#5[ MN N  ,FAyy~~$|A3&>syy~~>NaP !#- ))$++c$**o)N 5(, 55 dii( 88a<#DKK0779 1 -$uQCwswwykB99=A&IJJ779q=$~aS %LMM 1 rc^Uc[TR5SSS2nO[T[5(ac[ US5(a[ U5TR:wa [ S5e[ [U55TR:wa [ S5eOUS:wa [ S5e[U4SjU55n[U4SjU55nTRTRU4X2S 9$) Nr__len__z"axes don't match matrix dimensionszrepeated axis in transpose)r rzoSparse matrices do not support an 'axes' parameter because swapping dimensions is the only logical permutation.c3B># UHnTRUv M g7frN)r\r7rrns r:r;&_coo_base.transpose..s# UHnTRUv M g7frNrrs r:r;rs=1 Arr) r_rkrYrhasattrr@rdsetrZrra)rnaxesrLpermuted_shapepermuted_coordss` r: transpose_coo_base.transposes <#DbD)D g & &4++s4yDII/E !EFF3t9~* !=>>+ V^9: :.sM6L(#CI6Lsc3,># UH oTv M g7frNrr7rBrs r:r;rs#E#I)rr[rkrdr@rr`rfmathprodr5rrar\rrezip logical_andreduceallrZ) rnrfrmax_size tmp_shapetmp is_truncatingrBsizers @r:resize_coo_base.resizesENN; 99q==> > u:>@A A u: !' TZZ@Kyy'H**;y+A5IDK )8,DIK  u: ! OSZ!^,$))c%j012  ,,y)C**[c%j1DK))KSZ0DKMc$**e6LMM >>((,/ U,C*,Cys ,C*D88::##E#EE  IIdO  *sH< c dURX5n[URR5nU(d&URR(d [ S5eUR S:Xab[[R"S/5URUR URSURURS5U5 GOGUR S:XaWURupV[XVURUR UR"URURS5U5 OU(a9[R$"S[R&"URSS55nOD[R$"[R&"URSSSSS25SSS2S5n[R("UR5n[XpRUR XRURS5U5 UR+UR5$)Nz&Output array must be C or F contiguousr rArr)_process_toarray_argsrflags f_contiguous c_contiguousrdrkr r5r6rr`raravelrfr r}rzappendcumprod concatenater) rnroutBfortranrsNstridesr`s r:toarray_coo_base.toarrays}  & &u 2agg**+qww33EF F 99> 288QC=$((DII;;q>499aggclG M YY!^::DA dhh$((DII g /))Arzz$**Sb/'BC))BJJtzz!"~dd/C$DTrT$JAN^^DKK0F 7HHdii!99aggclG Eyy$$rcnURS:wa[SURS35eURS:Xa$URURUR S9$SSKJn URUR5up4pVURXTU4US9nUR(dUR5 U$) aConvert 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 rQrr2r ) csc_arrayrf) rkrdr_csc_containerrfr3_cscr_coo_to_compressed_swaprbr)rnrLrindptrindicesrarfxs r:tocsc_coo_base.tocsc:s( 99>J499+UVWX X 88q=&&tzz&D D '+/+B+B9??+S (FT##TF$;5#IA,,  "HrcURS:a[SURS35eURS:Xa$URURUR S9$SSKJn URURUS9nUupEpgURXeU4URS 9nUR(dUR5 U$) aConvert 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 rQrr2r ) csr_arrayrOr) rkrdr_csr_containerrfr3_csrrrrrbr) rnrLrarraysrrrarfrs r:tocsr_coo_base.tocsr[s( 99q=I$))TUVW W 88q=&&tzz&D D ',,Y__4,HF+1 (FT##TF$;4::#NA,,  "Hrc <U"UR5up4URUR[URU5S9nUR S:XaU(aURSR 5OURSn[U5n[R"SU/US9nU(aURR 5O URn XXR4$U"UR5up[U 5nU RUSS9n U RUSS9n [R"US-US9n[R"XS9n[R"URURS9n [!X4XzXRXU 5 XXR4$)z?convert (shape, coords, data) to (indptr, indices, data, shape)r-r rr2FrO) _shape_as_2dr]r`rHrrkrLr@r5r6rarfrTempty empty_liker3r ) rnswaprLrsrr9rrrramajorminors r:r_coo_base._coo_to_compressed}sGD%%&))$++c$((A>N)O 99>/3dkk!n))+QGg,CXXq#hi8F'+499>>#DD**4 4DKK( %j YU 3 YU 3!a%y1--7}}TYYdjj9!E99ftLjj00rc4U(aUR5$U$rNrO)rnrLs r:rh_coo_base.tocoos 99; KrcURS:wa[SURS35eUR5 URUR- n[ R "USS9up4[U5S:a[S[U5S3[SS 9 URRS :Xa [ R"S URS 9nO_[ R"[U5URR5S -4URS 9nURXTUR4'URXS4UR S9$)Nrz+Cannot convert. DIA format must be 2D. Got rQT)return_inversedzConstructing a DIA matrix with z diagonals is inefficientrr)rrr2r r)rkrdrrzr}r5uniquer@rrrarzerosr3rH_dia_containerrf)rnrLksdiagsdiag_idxras r:todia_coo_base.todias 99>J499+UVWX X  XX ))Bt< u:  23u:,?""(Q 8 99>>Q 88F$**5D88SZ)9:$**MD'+yyD488# $""D= "CCrcjURS:a[SURS35eUR5 URURUR S9nURS:XaUR SnO[UR 6n[[X0R55Ul U$)Nrz*Cannot convert. DOK must be 1D or 2D. Got rQr2r r) rkrdr_dok_containerrfr3r`rdictra_dict)rnrLdokr`s r:todok_coo_base.todoks 99q=I$))TUVW W !!$**DJJ!? 99>[[^F$++&FVYY/0  rc ^ URS:wa [S5eURup#X*::dX:a)[R"SUR R S9$[R"[U[US5-U[US5- 5UR S9nURU-UR:Hm UR(aURT nUR T nOB[U 4SjUR55nURXpR T 5uupXnXdU[US5-'U$)Nrz diagonal requires two dimensionsrr2c3,># UH oTv M g7frNr)r7rB diag_masks r:r;%_coo_base.diagonal..s?;CY;r)rkrdrfr5rrar3rrrHr}rzrbrZr`_sum_duplicates) rnkrowscolsdiagr}raindsr8r$s @r:diagonal_coo_base.diagonals 99>?@ @ZZ  :88ATYY__5 5xxD3q!9,dSAY.>?"jj*XX\dhh.  $ $((9%C99Y'D?4;;??D!11$ )8LMNHSd $S3q!9_ rcURS:wa [S5eURup4UR(a[U5(dgURR nUR UR- U:gnUS:a[X2-U5nUR(a[U[U55n[R"X`R U:5n[R"U*U*U-US9n [R"XuS9n O[X4U- 5nUR(a[U[U55n[R"X`RU:5n[R"XuS9n [R"X"U-US9n UR(aUSUn O"[R"XpR S9n XSS&[R"URUU 45[R"UR UU 454Ul [R"URUU 45UlSUlg)Nrz*setting a diagonal requires two dimensionsrr2F)rkrdrfr@r}r3rzrr5 logical_orarangerrr`rarb) rnvaluesr'rsrr9 full_keep max_indexkeeprrrs r:_setdiag_coo_base._setdiags 99>IJ Jzz ;;s6{{ HHNN HHtxx'1, q5AC I{{ 3v;7 ==HH ,ABDiiQBN)DGii ;GAs I{{ 3v;7 ==HH ,ABDii ;Giiy= BG ;;jy)Hxx ? $)!rcU(a[SUR55nO URnURX4URURS9$)z|Returns a matrix with the same sparsity structure as self, but with different data. By default the index arrays are copied. c3@# UHoR5v M g7frNrOrAs r:r;'_coo_base._with_data.. s=#88::rP)rfr3)rZr`rrfr3)rnrarLr`s r: _with_data_coo_base._with_datasC ===F[[F~~tnDJJdjj~QQrcUR(agURURUR5nUuUlUlSUlg)zUEliminate duplicate entries by adding them together This is an *in place* operation NT)rbr&r`ra)rnsummeds r:r_coo_base.sum_duplicatess@  $ $ %%dkk499=!' TY$(!rc ^^[U5S:XaX4$[R"USSS25m[U4SjU55nUTn[RR UVs/sH o3SSUSS:gPM sn5m[R "ST5m[U4SjU55n[R"T5un[RRU[U5URS9nX4$s snf)Nrrc3,># UH oTv M g7frNr)r7rBrs r:r;,_coo_base._sum_duplicates.."s4Vc5zVrr Tc3,># UH oTv M g7frNr)r7rB unique_masks r:r;rA(s:6C;'6rr2) r@r5lexsortrZr/rrrladdreduceatrr3)rnr`rarB unique_indsrrCs @@r:r&_coo_base._sum_duplicatess t9><  6$B$<(4V44E{mm**+1, +1CGs3Bx 6,  iik2 :6::zz+. vvt%8%ETZZX|, s(C<c^URS:gmURTUl[U4SjUR55Ulg)zKRemove zero entries from the array/matrix This is an *in place* operation rc3,># UH oTv M g7frNrrs r:r;,_coo_base.eliminate_zeros..4s=#IrN)rarZr`)rnrs @r:eliminate_zeros_coo_base.eliminate_zeros-s7 yyA~IIdO === rc URUR:wa&[SURSURS35e[URRURR5n[ R "XSS9n[URR5nURS:Xab[[ R "S/5URURURSURURS5U5 GOGURS :XaWUR upV[#XVURUR$UR&URURS5U5 OU(a9[ R("S[ R*"URSS 55nOD[ R("[ R*"URSSSSS 25SSS 2S5n[ R,"UR5n[XpRURXRURS5U5 UR/US S 9$) NIncompatible shapes ( and rT)r3rLr rrrrFrO)rfrdrr3charr5r6rrrrkr rr`rarrr r}rzrrr _container) rnotherr3r|rrsrrr`s r: _add_dense_coo_base._add_dense:s ;;$** $4TZZLekk]RSTU UDJJOOU[[-=-=>%48fll//0 99> 288QC=$((DII;;q>499fll36G R YY!^$$DA dhh$((DII S)7 4))Arzz$**Sb/'BC))BJJtzz!"~dd/C$DTrT$JAN^^DKK0F 7HHdii!99fll3.? JvE22rcURS:aUR5RU5$URUR:wa&[ SURSURS35eUR U5n[ R"URUR45n[[ R"URUR4SS95nUR X#4URS9nU$NrrOrPrr )rr) rkr _add_sparserfrdrr5rrarZr`rnrSrrrs r:rX_coo_base._add_sparseRs 99q=::<++E2 2 ;;$** $4TZZLekk]RSTU Uu%>>499ejj"9:2>>4;; *EANO NNH1N DrcURS:aUR5RU5$URUR:wa&[ SURSURS35eUR U5n[ R"URUR*45n[[ R"URUR4SS95n[X#4URS9nU$rW) rkr _sub_sparserfrdrr5rrarZr`rrYs r:r\_coo_base._sub_sparse_s 99q=::<++E2 2 ;;$** $4TZZLekk]RSTU Uu%>>499uzzk":;2>>4;; *EANO x,DJJ ?rc URS:Ga;[R"[R"UR SS5[ URRURR5S9n[R"UR 5n[R"[R"USSSSS25SSS2SSS5n[R"UR5n[UR[!UR 5XEUR"X5 UR%UR SS5nU$URS:aUR SOSn[R"U[ URRURR5S9nURS:XaUR&nUR(nONURS:Xa&URSn[R*"U5nO[-SUR35e[/URXUR"X5 [1U[25(a US:XaUS$U$)Nrrr2r rz$coo_matvec not implemented for ndim=)rkr5rrrrfrr3rQr6rrrr`rrr@rarrzr}ryNotImplementedErrorrrYr) rnrSr|rfrr` result_shaperzr}s r:_matmul_vector_coo_base._matmul_vectorls 99q=XXdii 3B8$/ AQAQ$RTFHHTZZ(Eii 5":dd+; ((C((C YY!^++a.C--$C%6tyykBD D 488Styy%@ dG $ $):!9  rc([U5(aURU5$URn[ [U5SS5[ [U5SSSSS25-nURU5nURn[ [U5SS5[ [U5SSSSS25-nURU5RU5nU[La[$US:XdUS:Xa[UR5nOI[ [UR5SS5[ [UR5SSSSS25-nURU5$![a& [R "U5nURnGNaf=f)Nrwrr ) r! _mul_scalarrkAttributeErrorr5rirZr_r_matmul_dispatchNotImplemented)rnrSo_ndimpermtrs_ndimrets r:_rmatmul_dispatch_coo_base._rmatmul_dispatchsa   ##E* * $vs+,uU6]235G"5M/NND&BYYFvs+,uU6]235G"5M/NND..&77;Cn$%%{fkSXXU388_Sb12U5?23;OPTRTPT;U5VV==& &!" $ 5) $s E!!,FFc[U5(aURU5$[U5(dg[U5(dW[R "U5nUR S:Xa$UR[R:Xa[$UR UR S:a&UR S:a[R"X5$URSnSnUR[RLGa&URU4:XaUR!U5$URUS4:Xa@UR!UR#55nUR$"/URSSQSP76$UR S:Xa#USUSURSS3n['U5eURS U:XaKURSS nURSS nXx:wa[R("Xx5 UR+U5$['US USURS S 35e[U5(aUR-U5$[U5(GasUR S:Hn UR S:Hn U (aUR%UR.5nU (a UR%URSS45nX1RS :wa!['US USURS S 35eUR S :dUR S :a:URSS nURSS nXx:wa[R("Xx5 UR1U5nU (a@UR%[3URSS 5[3URSS5-5nU (aUR%URSS5nU$g![a UnGN@f=f![&a ['S 5ef=f![&a ['S 5ef=f)Nrrrz)matmul: dimension mismatch with signaturer z (n,k=z),(k=z,)->(n,)rwz&Batch dimensions are not broadcastablez (n,..,k=z,..,m)->(n,..,m)r)r!multiplyrr"r5 asanyarrayrkr3object_rgrfrerrfrndarrayrarrrdbroadcast_shapes_matmul_multivectorrdr_matmul_sparserZ) rnrSother_ar err_prefixr|msg batch_shape_A batch_shape_B self_is_1d other_is_1ds r:rf_coo_base._matmul_dispatchs   ==' '75>>mmE*G||q W]]bjj%@&%   99q=UZZ!^++D8 8 JJrN@ ??bjj ({{qd"**511{{q!f$,,U[[];~~:tzz#2:::zzQ# F1#U5;;q>2B(K o%{{2!# $ 3B % CR 0  1S++MI//66 !l)A3eEKKO3DDTU   ##E* * E??aJ**/K||D$5$56 u{{1~q&9:KKO# !l)A3eEKKO3DDTU yy1} Q $ 3B % CR 0  1S++MI((/Ffll3B.?(@(-fll23.?(@)AB Sb(9:MM O"  2&S()QRRSP&S()QRRSs* O O4O6 OOO36P c 6[URRURR5nURS:dURS:GaURS:XanUR SUR S5R U5nUR [UR SS5[UR SS5-5$[R"UR SSUR SS5nX@R SS-nXAR SS-nURU5n[R"X5nX@R SS-UR SS-n[R"XrS9n[UR[UR 5UR S[R "U5[R "U5[R""UR$5UR&UR)S5U5 U$URS:Xa7UR SUR S4nUR*nUR,n OEURS:Xa5UR S4nUR$Sn[R."U5n [R"WUS9n[1URUR SW WUR&UR)S5U5 UR3[5U5S 9$) Nrr rrwrr2rr)type)rr3rQrkrrfrurZr5rt _broadcast_to broadcast_torrrr@r6rr`rarrzr}ryrviewr) rnrS result_dtyper|broadcast_shape self_shape other_shaper`rzr}s r:ru_coo_base._matmul_multivectors\"4::??EKK4D4DE 99>UZZ1_yyA~aA7KKER~~eEKK,<&=ekkRTRUFV@W&WXX 11$**Sb/5;;sPRCSTO(::bc?:J)KK,<>RSAQQLXXl?F #djj/5;;r? " 5rxx 7M "t{{ ; $ 5;;s+;V EM 99> JJqM5;;q>:L((C((C YY!^!KKN,L++a.C--$C,l;5;;r?CEKK$4f >{{U {,,rc|[U5(d[U5(dy[U5(di[R"U5nUR S:Xa6UR [R:Xa[S[U5S35eUR UR S:aA[R"U5(dUR S:a[R"X5$[R"U5(aX-$[U5(aURU5$UR S:wa [S5eUR S:XaZUR S:XaJURSURS:wa&[#SURS URS 35eX-$UR S :XaZUR S :XaJURSURS:wa&[#SURS URS 35eX-$UR%U5$![a UnGNf=f) ahReturn 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 rPz" are not aligned for inner productrz are not aligned for matmul)rr"r!r5rqrkr3rrrcrrfreisscalarrdot _dense_dotrgrd _sparse_dot)rnrSo_arrays r:r _coo_base.dot+sj75>>\%5H5HmmE*G||q W]]bjj%@"DT%[MQR STT   99q=bkk%00EJJqL;;t+ + ;;u  <  5>>??5) ) \\U ">? ? YY!^ azz!} A. 74::,eEKK=!E"FGG<  YY!^ azz!} A. 74::,eEKK=!>"?@@< ##E* *3"  s H++ H;:H;c URS:HnURS:HnU(aURUR5nU(a URURSS45nURSURS:wa&[ SURSURS35e[ UR URURS- /5n[ UR URURS- /5nURSSnURSSURSS-n[R"U5URS4nURS[R"U54n X@R S4n UR SU4n [URU 4U5n [URU 4U 5n X-R5nXg-nXg4n/n[UR U5H,unnUR[R"UU55 M. [URU4U5nU(aURUSS5nU(aURUSS5nU$) Nr rrrwrrP are not aligned for n-D dotr)rkrrrfrd_ravel_non_reduced_axesr`rrrrarhrextendr5r)rnrSr|r}self_raveled_coordsother_raveled_coordsself_nonreduced_shapeother_nonreduced_shaperavel_coords_shape_selfravel_coords_shape_otherself_2d_coordsother_2d_coordsself_2dother_2drcombined_shapeshapes prod_coordscsprod_arrs r:r_coo_base._sparse_dotsTYY!^ jjAo  << 1 12D MM5;;q>1"56E ::b>U[[_ , 74::,eEKK=!?"@AA 6dkk6:jj499Q;-Q6u||7<{{UZZPQ\N T!% 3B!&Sb!1EKK4D!D$(99-B#CTZZPR^"T$)KKOTYY?U5V#W -{{2? <<+-ABTYY79PQejj/:1"56E ::b>U[[_ , 74::,eEKK=!?"@AA JJsOdc%++&6&:; ;djjo M #djj/A"56Dzz#2Sb)99EKK>,/ '' QR(89H '' Sb(9:HrcH^^[T5(dy[T5(di[R"T5nURS:Xa6UR [R :Xa[S[T5S35eTR [TRTRU5upE[UU4Sj[XE555(a [S5e[T5(aTRTXE5$TR!TXE5$![a UmNf=f)a4 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: 'rc3f># UH&upTRUTRU:gv M( g7frNr)r7axbxrSrns r:r;&_coo_base.tensordot..Cs/9762zz"~R07s.1z*sizes of the corresponding axes must match)r"rr5rqrkr3rrrcrrfre _process_axesrerrd_dense_tensordot_sparse_tensordot)rnrSr other_array axes_self axes_others`` r: tensordot_coo_base.tensordotsru~~huoo--.K1$):):bjj)H"Ed5k]RS TUU $ !.diiT J  9 79 9 9IJ J 5>>(( F F))%G G" $# $s D D! D!c^^^^[TR5n[TR5n[TRTRT5n[R "TVs/sHnTRUPM snTVs/sHnTRUPM sn5n[TRTRT5n [R "TV s/sHn TRU PM sn TV s/sHn TRU PM sn 5n [ UU4Sj[U555n [ UU4Sj[U555n [R"U 5[R"TVs/sHnTRUPM sn54n[R"TVs/sHnTRUPM sn5[R"U 54nXh4nX4n[TRU4U5n[TRU4U5nUU-R5nX-n/n[URX45H5unnU(dMUR[R"UU55 M7 U/:Xa[!UR5$[URU4US9$s snfs snfs sn fs sn fs snfs snf)Nc3R># UHnUT;dM TRUv M g7frNr)r7rrrns r:r;._coo_base._sparse_tensordot..]s*&6?O!#9!4'5djjn?O ''c3R># UHnUT;dM TRUv M g7frNr)r7rrrSs r:r;r_s*'8AR2"$J"6(7u{{2ARrr)r@rfrr`r5ravel_multi_indexrZr_rrrrarhrrrsum)rnrSrr ndim_self ndim_otherself_non_red_coordsrself_reduced_coordsother_non_red_coordsaother_reduced_coordsrrrrrrrrrrr`rrs```` r:r_coo_base._sparse_tensordotMsv O % 6dkk4::6?A 22'0 1yT[[_y 1Y3WYrDJJrNY3WY6u||U[[7A C!33&0 1jU\\!_j 1J3WJqEKKNJ3W !&&6uY?O&6!6!&'8zAR'8"8$(99-B#C $ I*NIb4::b>I*N O#Q$(II.T2u{{2.T$U$(II.D$E$G .C/FTYY79PQejj/: !$))V,NCCQ 23W 23W+O.Ts$$J9J> K7K >K 3KcV[UR5n[UR5n[U5Vs/sH ofU;dM UPM nnUVs/sHoRUPM n nUVs/sHoRUPM n n[U5Vs/sH nXc;dM UPM n nUVs/sHoRUPM n nU Vs/sHoRUPM n nXr-nU SSU-U SS-nURU5n[R"X5n/U Q[ R "U 5P7n/U SSQ[ R "U 5PU SSQ7nURU5RURU55$s snfs snfs snfs snfs snfs snfr) r@rfr_rr5rrrr)rnrSrrrrrnon_reduced_axes_selfrreduced_shape_selfnon_reduced_shape_selfnon_reduced_axes_otherreduced_shape_othernon_reduced_shape_other permute_self permute_other reshape_self reshape_others r:r_coo_base._dense_tensordots O % .3I.> V.>IBU.> V5>?YjjmY?9N!O9NA**Q-9N!O/4Z/@";/@%'%9#%/@";7ABz!{{1~zB;Q"R;Qa;;q>;Q"R,8 "3B '* 47Mbc7R R ~~l+ U2O/O;M1NO 71#267 BU8V7057 ||L)--emmM.JKK)!W?!O";B"Rs/ F F F/F F#F/F! F&cURS:a&URS:a[R"X5$URnURn[R "USSUSS5n[ U5USS-n[ U5USS-nURU5nURU5n[U5n [U5n X-R5n [U /UQURSPURSP7S9$)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. Returns: prod (COO): The resulting n-D sparse array after multiplication. rNrwrr) rkrrvrfr5rtrZr _block_diagrh_extract_block_diag) rnrSrrrself_new_shapeother_new_shapeself_broadcastedother_broadcastedself_block_diagother_block_diagprod_block_diags r:rv_coo_base._matmul_sparses  99q=UZZ!^))$6 6ZZ kk --j"o{3B?OP/*RS/A0;rs3CC--n=!//@&&67&'89+=DDF# EOETZZ^EU[[_E  rc hURU:XaU(aUR5$U$URn[U5[U5:a [S5eS[U5[U5- -[ U5-n[ S[ XA555(a[SUS35eURU5n[UR[U5S9nURnURnUSSnSn USUS:waVUSn X-n [R"Xz5n[R"[R"S XS 9UR 5n U 4n[#S [U5S-*S5Hn XLX:waXn X-n [U5n [R"Xz5n[ [R"XS-SU 55n[R"[R"S XS 9U 5n U 4U-nM[R"XlU 5n U 4U-nM [%Xx4U5$) NzDNew shape must have at least as many dimensions as the current shaperc3F# UHupUS:g=(a X:gv M g7frEr)r7ons r:r;*_coo_base._broadcast_to..s"E/DtqQ!16!/Ds!zcurrent shape z- cannot be broadcast to new shape {new_shape}r-rr rr2rw)rfrLr@rdrZrerrrr`rHrar5tilerepeatr0rr_r)rn new_shaperL old_shaperfr9r`rr cum_repeat repeat_countnew_dimrrs r:r_coo_base._broadcast_tos :: ""&499; 0D 0JJ  y>C N *56 6IY785;KK Es5/DE E E~i[9BBC C||E"#DKKIG 99BC[  9 " %$R=L  &Jwwx6Hii !\ KTXXVG!JrSZ\?B/Ax9<'(| * (m778:"277:cd+;\#JK ))BIIa$OQTU%Z*4 ''&)Z8%Z*4 !0$(/;;r)r\r`rarb)NNFrN)NF)returnN)NN)F)r)T)r)2__name__ __module__ __qualname____firstlineno___formatr_r[rXpropertyr}setterrzrr__doc__rrrmrrrrrrrhrr r,rr5r:rr&rLrTrXr\rarmrfrurrrrrrrvr__static_attributes__rrr:r$r$sGa IGTGR ZZGG  ZZ44!OFoo--GO;(oo--GO W$1199MN2?$ ))11I$L^^++FN%2oo--GOB D16 MM))EMD,MM))EM MM))EM($,,44H$*NR )&>30  D'4\~!-HV+r7r>nHb1DhL6( V52r *x&- '/+ dE*-.e <# UHoT:=(d UT*:v M g7frNr)r7rndim_as r:r; _process_axes..=!=fV|+rVG|+f!c3F># UHoT:=(d UT*:v M g7frNr)r7rndim_bs r:r;r>rrz/axes indices are out of bounds for input arraysz3axes must be an integer or a tuple/list of integersr) rYrrrdlistr_rZr@rerc)rrraxes_aaxes_brs`` r:rr1s3$ !8tc&&11MN NeFTM623eDk" D5$- ( ( t9>DE E v;#f+ %KL L =f= = = =f= = =NO O >MNN>D EfdaxdVmT1fF E>D EfdaxdVmT1fF E >F Es E-E c0^[U5n[U5Vs/sH oDU;dM UPM nnU(d[R"TS5$UVs/sHoAUPM nn[ U4SjU55n[R "Xv5$s snfs snf)Nrc3.># UH nTUv M g7frNr)r7rBr`s r:r;*_ravel_non_reduced_axes..TsG6Fsvc{6Fs)r@r_r5ryrZr)r`rfrrkrnon_reduced_axesnon_reduced_shapenon_reduced_coordss` r:rrHs u:D%*4[C[rdN[C }}VAY''.>>-=rr-=>G6FGG    2 FFD?s BBBc[U5S:XaUS$[U5S:XaUup4UupVUS:XaCU[SUS- 5-[SUS- 5-n[US9n[R"XEUS9U-$US:XaCU[SUS- 5-[SUS- 5-n[US9n[R"X6US9U-$[ S5e[R "XUS 9$) z;Like np.ravel_multi_index, but avoids some overflow issues.r rrrr-r2Fz'order' must be 'C' or 'F'r)r@rHrr5rprdr) r`rfrnrowsncolsr}rzr.r9s r:rrZs 6{aay 6{a  C<c!UQY//#a2CCF'v6I;;u;cA A c\c!UQY//#a2CCF'v6I;;u;cA A9: :  U ;;rc"[U[5$)aIs `x` of coo_matrix type? 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 )rYr)rs r:rros. a $$rc\rSrSrSrSrg)ria 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]]) rN)rrrrrrrrr:rrskrrc\rSrSrSrSrSrg)ria 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]]) cSU;a%URS5URS54US'URRU5 g)Nr`r}rz)pop__dict__update)rnstates r: __setstate__coo_matrix.__setstate__js> 5  %yy/51ABE(O U#rrN)rrrrrrrrrr:rrsn`$rr)r)2r __docformat____all__rwarningsrnumpyr5 _lib._utilr_matrixr _sparsetoolsr r r rrrr_baserrrr_datarr_sputilsrrrrrrrrr r!r"rFr$rrrrrrrrrrr:r%s8% 7 '000GF.QQQQb< mb