,|hGddlmZddlmZmZmZmZmZmZddl m Z ddl m Z ddl mZddlmZdd lmZerdd lmZmZmZmZmZmZdd lmZdd lZdd lZGd deZGddeZGddeZ GddeZ!ddd=dZ"ddd>dZ#d?dZ$ddd@dZ%dAdZ&d?dZ'd?d Z(dBd!Z)dd"d#dCd$Z*dDd%Z+d d&dEd'Z,d?d(Z-dBd)Z.d d&dEd*Z/d+d,dFd-Z0dGd.Z1d/Z2dBd0Z3d1d2dHd3Z4dId4Z5dd5dJd6Z6dd d7dKd8Z7ddd>d9Z8d ddd:dLd;Z9gd<Z:y )M) annotations)_floating_dtypes_numeric_dtypesfloat32float64 complex64 complex128)reshape)conj)Array)normalize_axis_tuple) TYPE_CHECKING)LiteralOptionalSequenceTupleUnionDtype) NamedTupleNc"eZdZUded<ded<y) EighResultr eigenvalues eigenvectorsN__name__ __module__ __qualname____annotations__U/var/www/html/test/engine/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)uppercD|jtvr tdtjj |j }|rDtj|j}|jttfvr t|}|Stj|S)z Array API compatible wrapper for :py:func:`np.linalg.cholesky `. 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See its docstring for more information. z,Only floating-point dtypes are allowed in qrr~) r3rr4r%rRr r9r5r6qrr8)r;rs r#rrsJ ww&&FGG SRYY\\!((\%FG HHr"c|jtvr tdtt t j tjj|jS)z Array API compatible wrapper for :py:func:`np.linalg.slogdet `. See its docstring for more information. z1Only floating-point dtypes are allowed in slogdet) r3rr4r)rRr r9r5r6slogdetr8rJs r#rrsH ww&&KLL #ejj"))*;*;AHH*EF GGr"cddlm}m}m}m}m}m}m}ddlm } ||\}} ||||||\}} |||\} } |jdk(r | j}n | j}|| rdnd}tj|dddd 5|||| }ddd| j| d S#1swY"xYw) Nr) _makearray_assert_stacked_2d_assert_stacked_square _commonType isComplexTypeget_linalg_error_extobj_raise_linalgerror_singular) _umath_linalgrzDD->Dzdd->dcallignore)rinvalidoverdivideunder) signatureF)copy) linalg.linalgrrrrrrrr6rrDsolve1solver5errstateastype)abrrrrrrrr_wraptresult_tgufuncrrs r#_solver/s>>>' a=DAqq1mGAta#KAx vv{%%$$)+I 5v"88 E. 1a9 -. . // ..s  CCc|jtvs|jtvr tdtjt |j |j S)z Array API compatible wrapper for :py:func:`np.linalg.solve `. See its docstring for more information. z/Only floating-point dtypes are allowed in solve)r3rr4r r9rr8rZs r#rrKsG xx''288;K+KIJJ ::fRYY 2 33r"T full_matricesc |jtvr tdtt t j tjj|j|S)z Array API compatible wrapper for :py:func:`np.linalg.svd `. See its docstring for more information. z-Only floating-point dtypes are allowed in svdr) r3rr4r-rRr r9r5r6rkr8)r;rs r#rkrkXsJ ww&&GHH c%**biimmAHHMm&Z[ \\r"c|jtvr tdtjt j j|jdS)Nz1Only floating-point dtypes are allowed in svdvalsFrh) r3rr4r r9r5r6rkr8rJs r#svdvalsris?ww&&KLL ::biimmAHHm? @@r"axesc|jtvs|jtvr tdtjt j |j|j|S)Nz,Only numeric dtypes are allowed in tensordotr)r3rr4r r9r5 tensordotr8)rFrGrs r#rrqsK xx&"((/*IFGG ::bll299biidC DDr")rKr3c :|jtvr td|3|jtk(rt}n|jt k(rt }tjtjtj|j|dd|S)zz Array API compatible wrapper for :py:func:`np.trace `. See its docstring for more information. z(Only numeric dtypes are allowed in tracerMr=)rKrNrOr3) r3rr4rrr r r r9r5rptracer8)r;rKr3s r#rrzsv  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)r3rr4rlrDtuplerBrCr5broadcast_arraysr8moveaxisr r9) rFrGr?rDx1_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 )r3)r?r]r)r3rr4r8ravelrorrrDranger5 transposer prodrBintr r9r6ralist) r;r?r\r]r_axisrestnewshaperrrBrs @r# vector_normrsd ww&&HII A | GGI D% /tQVV<Jaff JJ$; LLH % - - WW$/Qaggaj/s ; YSW>Xaqwwqz>X Y [ **RYY^^AEs^; Xs F+ +F0 )r7rErIrPrSrUrWrYrbrdrtrwryr|rrrrkrrrrr)r;r r1boolreturnr )rFr rGr r?rrr )r;r rr )r;r rKrrr )r;r rr)rFr rGr rr )r;r r\rr]z2Optional[Union[int, float, Literal['fro', 'nuc']]]rr )r;r rerrr )r;r rfzOptional[Union[float, Array]]rr )r;r rzLiteral['reduced', 'complete']rr%)r;r rr))r;r rrrr-)r;r rzUnion[Array, Tuple[Array, ...]])rFr rGr rz/Union[int, Tuple[Sequence[int], Sequence[int]]]rr )r;r rKrr3zOptional[Dtype]rr ) r;r r?z%Optional[Union[int, Tuple[int, ...]]]r\rr]zOptional[Union[int, float]]rr ); __future__r_dtypesrrrrr r _manipulation_functionsr _elementwise_functionsr _array_objectr core.numericrtypingr_typingrrrrrrr numpy.linalgnumpyr5rr%r)r-r7rErIrPrSrUrWrYrbrdrtrwryr|rrrrrkrrrrr__all__r!r"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"