(phGjSSKJr SSKJrJrJrJrJrJr SSK J r SSK J r SSK Jr SSKJr SS KJr \(aSS KJrJrJrJrJrJr SS KJr SS KrSS Kr"S S\5r"SS\5r"SS\5r "SS\5r!SS.S=Sjjr"SS.S>Sjjr#S?Sjr$SS.S@Sjjr%SASjr&S?Sjr'S?S jr(SBS!jr)SS"S#.SCS$jjr*SDS%jr+S S&.SES'jjr,S?S(jr-SBS)jr.S S&.SES*jjr/S+S,.SFS-jjr0SGS.jr1S/r2SBS0jr3S1S2.SHS3jjr4SIS4jr5SS5.SJS6jjr6SS S7.SKS8jjr7SS.S>S9jjr8S SSS:.SLS;jjr9/S`. See its docstring for more information. z2Only floating-point dtypes are allowed in cholesky) dtyper TypeErrornplinalgcholesky_arrayr _newmTr r r )xr7Lr4s r&r=r=-sx ww&&LMM 188$A JJqM   77y*- -QA ::a=r%axiscUR[;dUR[;a [S5eURUR:wa [ S5eUR S:Xa [ S5eURUS:wa [ S5e[ R"[R"URURUS95$)zn Array API compatible wrapper for :py:func:`np.cross `. See its docstring for more information. z(Only numeric dtypes are allowed in crossz"x1 and x2 must have the same shaperz/cross() requires arrays of dimension at least 1zcross() dimension must equal 3rD) r9rr:shape ValueErrorndimr r?r;crossr>)x1x2rEs r&rKrK@s  xx&"((/*IBCC xx288=>> ww!|JKK xx~9:: ::bhhryy"))$? @@r%cUR[;a [S5e[R"[ R RUR55$)zx Array API compatible wrapper for :py:func:`np.linalg.det `. See its docstring for more information. z-Only floating-point dtypes are allowed in det) r9rr:r r?r;r<detr>rAs r&rOrORs= ww&&GHH ::biimmAHH- ..r%)offsetc l[R"[R"URUSSS95$)zt Array API compatible wrapper for :py:func:`np.diagonal `. See its docstring for more information. rC)rQaxis1axis2)r r?r;diagonalr>)rArQs r&rVrV_s& ::bkk!((62N OOr%cUR[;a [S5e[[ [ R [RRUR556$)zz Array API compatible wrapper for :py:func:`np.linalg.eigh `. 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See its docstring for more information. z(Only numeric dtypes are allowed in tracerSrC)rQrTrUr9) r9rr:rrr r r r?r;rvtracer>)rArQr9s r&rrzsv  wwo%BCC } 77g E WW !E ::bjj!((6SU]b!cd eer%cvUR[;dUR[;a [S5e[URUR5nSX0R- -[ UR 5-nSX1R- -[ UR 5-nXBXR:wa [S5e[R"URUR5upg[R"XbS5n[R"XrS5nUSSSS24US-n[R"US5$)Nz)Only numeric dtypes are allowed in vecdot)rz6x1 and x2 must have the same size along the given axisrC.).N).rr)r9rr:rrrJtuplerHrIr;broadcast_arraysr>moveaxisr r?) rLrMrErJx1_shapex2_shapex1_x2_ress r&vecdotrs xx&"((/*ICDD rww DTGG^$uRXX6HTGG^$uRXX6H~'QRR""299bii8HC ++c $C ++c $C c4l c)n ,C ::c)n %%r%rfc ^ UR[;a [S5eURnUcUR 5nSnO[ U[ 5(a[XR5m [ U 4Sj[UR555nX-n[R"XG5R[R"UVs/sHoRUPM sn[S9/UVs/sHoRUPM snQ75nSnOUn[ R""[R$R'XEUS95n U(ae[)UR5n [Uc[UR5OUUR5nUHnSX'M [U [ U 55n U $s snfs snf)rez.Only floating-point dtypes are allowed in normrc36># UHoT;dM Uv M g7f)Nr).0inormalized_axiss r& vector_norm..sJ 1/1IQQ s  )r9)rErcr)r9rr:r>ravelrurrrJranger; transposer prodrHintr r?r<rglist) rArErbrcr_axisrestnewshaperrrHrs @r& vector_normrs^ ww&&HII A | GGI D% /tVV<Jaff JJ; LL % - - WW$/$Qggaj$/s ; YSW>XSWawwqzSW>X Y [ **RYY^^As^; Xs F8 2F= )r=rKrOrVrYr[r]r_rhrjrzr}rrrrrrqrrrrr)rAr r7boolreturnr )rLr rMr rErrr )rAr rr )rAr rQrrr )rAr rr)rLr rMr rr )rAr rbrrcz2Optional[Union[int, float, Literal['fro', 'nuc']]]rr )rAr rkrrr )rAr rlzOptional[Union[float, Array]]rr )rAr rzLiteral['reduced', 'complete']rr()rAr rr-)rAr rrrr2)rAr rzUnion[Array, Tuple[Array, ...]])rLr rMr rz/Union[int, Tuple[Sequence[int], Sequence[int]]]rr )rAr rQrr9zOptional[Dtype]rr ) rAr rEz%Optional[Union[int, Tuple[int, ...]]]rbrrczOptional[Union[int, float]]rr ); __future__r_dtypesrrrrr r _manipulation_functionsr _elementwise_functionsr _array_objectr core.numericrtypingr_typingrrrrrrr numpy.linalgnumpyr;rr(r-r2r=rKrOrVrYr[r]r_rhrjrzr}rrrrrrrqrrrrr__all__rr%r&rsD"-( / II z J ,1&35A$ /,-P B 4 / 7(27rw [ ;GK:05 6$@D<"?H I H008 4/3 ]"AcdE)*Df*46&,OSejPQ+Z Fr%