2i-GddlmZddlmZmZmZmZmZmZddl m Z ddl m Z ddl mZddlmZerdd lmZmZmZmZmZmZdd lmZdd lZdd lZGd d eZGddeZGddeZGddeZddddZ"ddd?dZ#d@dZ$d>dZ%d>dZ&dAd Z'dd!d"dBd#Z(dCd$Z)d d%dDd&Z*d>d'Z+dAd(Z,d d%dDd)Z-d*d+dEd,Z.dFd-Z/d.Z0dAd/Z1d0d1dGd2Z2dHd3Z3dd4dId5Z4dd d6dJd7Z5ddd=d8Z6d ddd9dKd:Z7gd;Z8y )L) annotations)_floating_dtypes_numeric_dtypesfloat32float64 complex64 complex128)reshape)Array)normalize_axis_tuple) TYPE_CHECKING)LiteralOptionalSequenceTupleUnionDtype) NamedTupleNc"eZdZUded<ded<y) EighResultr eigenvalues eigenvectorsN__name__ __module__ __qualname____annotations__M/var/www/html/acx/venv/lib/python3.12/site-packages/numpy/array_api/linalg.pyrrsr!rc"eZdZUded<ded<y)QRResultr QRNrr r!r"r$r$s  H Hr!r$c"eZdZUded<ded<y) SlogdetResultr sign logabsdetNrr r!r"r(r(!s Kr!r(c,eZdZUded<ded<ded<y) SVDResultr USVhNrr r!r"r,r,%s H H Ir!r,F)upperc|jtvr tdtjj |j }|rtj|jStj|S)z Array API compatible wrapper for :py:func:`np.linalg.cholesky `. 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See its docstring for more information. z(Only numeric dtypes are allowed in tracerLr<)rJrMrNr2) r2rr3rrr r r r8r4rotracer7)r:rJr2s r"rrusv  wwo%BCC } 77g E WW !E ::bjj!((6SU]b!cd eer!cr|jtvs|jtvr tdt|j|j}d||jz zt |j z}d||jz zt |j z}||||k7r tdtj|j|j\}}tj||d}tj||d}|ddddf|dz}tj|dS)Nz)Only numeric dtypes are allowed in vecdot)rz6x1 and x2 must have the same size along the given axisr<.).N).rr)r2rr3rkrCtuplerArBr4broadcast_arraysr7moveaxisr r8) rErFr>rCx1_shapex2_shapex1_x2_ress r"vecdotrs xx&"((/*ICDD rww DTBGG^$uRXX6HTBGG^$uRXX6H~$'QRR""299bii8HC ++c4 $C ++c4 $C c4l c)n ,C ::c)n %%r!r_c j |jtvr td|j}||j }d}nt |t rt||j t fdt|jD}||z}tj||jtj|Dcgc]}|j|c}tg|Dcgc]}|j|c}}d}n|}t!j"tj$j'|||} |rct)|j} t|t|jn||j}|D]}d| |< t| t | } | Scc}wcc}w)r^z.Only floating-point dtypes are allowed in normrc3,K|] }|vs| yw)Nr ).0inormalized_axiss r" zvector_norm..sJ1/1IQJs )r2)r>r\r)r2rr3r7ravelrnrrrCranger4 transposer prodrAintr r8r5r`list) r:r>r[r\r_axisrestnewshaperrrArs @r" vector_normrsd ww&&HII A | GGI D% /tQVV<Jaff JJ$; LLH % - - WW$/Qaggaj/s ; YSW>Xaqwwqz>X Y [ **RYY^^AEs^; Xs F+ +F0 )r6rDrHrOrRrTrVrXrarcrsrvrxr{rrrrjrrrrr)r:r r0boolreturnr )rEr rFr r>rrr )r:r rr )r:r rJrrr )r:r rr)rEr rFr rr )r:r r[rr\z2Optional[Union[int, float, Literal['fro', 'nuc']]]rr )r:r rdrrr )r:r rezOptional[Union[float, Array]]rr )r:r r~zLiteral['reduced', 'complete']rr$)r:r rr()r:r rrrr,)r:r rzUnion[Array, Tuple[Array, ...]])rEr rFr rz/Union[int, Tuple[Sequence[int], Sequence[int]]]rr )r:r rJrr2zOptional[Dtype]rr ) r:r r>z%Optional[Union[int, Tuple[int, ...]]]r[rr\zOptional[Union[int, float]]rr )9 __future__r_dtypesrrrrr r _manipulation_functionsr _array_objectr core.numericrtypingr_typingrrrrrrr numpy.linalgnumpyr4rr$r(r,r6rDrHrOrRrTrVrXrarcrsrvrxr{rrrrrjrrrrr__all__r r!r"rsA"- / II z J ,1  35A$ /,-P B 4 / 7(27rw [ ;GK:05 6$@D<"?H I H006 4/3 ]"AcdE)*Df*46&,OSejPQ+Z Fr!