+
    &j                    R   ^ RI Ht ^ RIt^ RIt^ RIHt ^ RIt^RIHtH	t	 ^RI
HtHtHt ]'       d   ^ RIHt  ! R R]4      tR	 tR
 tR t]]R R l4       4       t]]RR/R R ll4       4       t]]R R l4       4       t]]R5R R ll4       4       t]]R R l4       4       t]]R6R R ll4       4       t]]R5R R ll4       4       t]]R7R R ll4       4       t]]R R l4       4       t]]R R  l4       4       t]]R5R! R" ll4       4       t]]R8R# R$ ll4       4       t ]]R9R% R& ll4       4       t!]]R' R( l4       4       t"]]R:R) R* ll4       4       t#]]R;R+ R, ll4       4       t$]]R- R. l4       4       t%]]R<R/ R0 ll4       4       t&]]R1 R2 l4       4       t']]R<R3 R4 ll4       4       t(R# )=    )annotationsN)TYPE_CHECKING)_dtypes_impl_util)	ArrayLikeKeepDims
normalizer)Sequencec                      ] tR t^tRtR# )LinAlgError N)__name__
__module____qualname____firstlineno____static_attributes__r       k/Users/jameslopez/projects/CWCArchive/cwc-podcast/.venv/lib/python3.14/site-packages/torch/_numpy/linalg.pyr   r      s    r   r   c                    V P                   P                  '       gK   V P                   P                  '       g/   V P                  \        P
                  ! 4       P                  4      p V # N)dtypeis_floating_point
is_complextor   default_dtypesfloat_dtypeas   &r   _atleast_float_1r      sC    GG%%%);););DD,,.::;Hr   c                   \         P                  ! W4      pVP                  '       g2   VP                  '       g    \         P                  ! 4       P
                  p\        P                  ! W4      p \        P                  ! W4      pW3# r   )r   result_type_implr   r   r   r   r   cast_if_needed)r   bdtyps   && r   _atleast_float_2r%      sa    ((.D"""dooo**,88Q%AQ%A4Kr   c                F   a  \         P                  ! S 4      V 3R  l4       pV# )c                    <  S! V / VB #   \         P                  P                   d   p\        TP                  !  hR p?ii ; ir   )torch_C_LinAlgErrorr   args)r+   kwdsefuncs   *, r   wrappedlinalg_errors.<locals>.wrapped(   sA    	'&&&xx$$ 	'qvv&&	's    A=A)	functoolswraps)r.   r/   s   f r   linalg_errorsr3   '   s%    __T' ' Nr   c                   V ^8  d   QhRR/#    r   r   r   )formats   "r   __annotate__r8   7   s     + +I +r   c                V    \        V 4      p \        P                  P                  W4      # r   )r   r(   linalgmatrix_power)r   ns   &&r   r;   r;   5   s#     	A<<$$Q**r   outc                   V ^8  d   QhRR/# )r6   inputszSequence[ArrayLike]r   )r7   s   "r   r8   r8   >   s     * *) *r   c               @    \         P                  P                  V 4      # r   )r(   r:   	multi_dot)r?   r=   s   &$r   rA   rA   <   s     <<!!&))r   c                    V ^8  d   QhRRRR/# r6   r   r   r#   r   )r7   s   "r   r8   r8   G   s     $ $Y $9 $r   c                Z    \        W4      w  r\        P                  P                  W4      # r   )r%   r(   r:   solve)r   r#   s   &&r   rE   rE   E   s%     A!DA<<a##r   c                    V ^8  d   QhRRRR/# rC   r   )r7   s   "r   r8   r8   N   s     @ @Y @9 @r   c                    \        W4      w  rV P                  '       g   VP                  '       d   R MRp\        P                  P	                  WW#R7      # )gelsgelsd)rconddriver)r%   is_cudar(   r:   lstsq)r   r#   rJ   rK   s   &&& r   rM   rM   L   sC     A!DA yyyAIIIV7F<<a%??r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8   X   s      9 r   c                Z    \        V 4      p \        P                  P                  V 4      pV# r   )r   r(   r:   invr   results   & r   rP   rP   V   s'     	A\\a FMr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8   `   s     A AI Ar   c                Z    \        V 4      p \        P                  P                  WVR 7      # ))rtol	hermitian)r   r(   r:   pinv)r   rJ   rV   s   &&&r   rW   rW   ^   s(     	A<<Qi@@r   c                    V ^8  d   QhRRRR/# rC   r   )r7   s   "r   r8   r8   g   s     5 59 5 5r   c                ^    \        W4      w  r\        P                  P                  WVR 7      # ))dims)r%   r(   r:   tensorsolve)r   r#   axess   &&&r   r[   r[   e   s*     A!DA<<##At#44r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8   n   s     . . .r   c                X    \        V 4      p \        P                  P                  WR 7      # ))ind)r   r(   r:   	tensorinv)r   r_   s   &&r   r`   r`   l   s&     	A<<!!!!--r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8   x   s      9 r   c                V    \        V 4      p \        P                  P                  V 4      # r   )r   r(   r:   detr   s   &r   rc   rc   v   s#     	A<<Ar   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s     # #y #r   c                V    \        V 4      p \        P                  P                  V 4      # r   )r   r(   r:   slogdetr   s   &r   rf   rf   }   s#     	A<<""r   c                   V ^8  d   QhRR/# )r6   xr   r   )r7   s   "r   r8   r8      s     B BI Br   c                R   \        V 4      p V P                  4       ^ 8X  d4   \        P                  ! V P                  RR 4      ^ 8X  d   \        R4      h\        P                  P                  WR7      p\        P                  ! \        P                  ! V4      \        R4      V4      # )r   Nz#cond is not defined on empty arrays)pinf)r   numelmathprodshaper   r(   r:   condwhereisnanfloat)rh   rj   rR   s   && r   rq   rq      s|     	A 	wwyA~$))AGGBCL1Q6?@@\\q&F
 ;;u{{6*E%L&AAr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s     R R9 Rr   c                V   \        V 4      p V P                  ^8  d   \        V ^ 8g  P                  4       4      # VfK   ^ p\	        V P
                  RR 4      \        P                  ! V P                  4      P                  ,          pMT^ rC\        P                  P                  WWBR7      # )r6   N)atolrU   rV   rl   )r   ndimintanymaxrp   r(   finfor   epsr:   matrix_rank)r   tolrV   rw   rU   s   &&&  r   r~   r~      s     	AvvzAF<<>""
{17723< 5;;qww#7#;#;;!d<<##At#QQr   c                    V ^8  d   QhRRRR/# )r6   rh   r   keepdimsr   r   )r7   s   "r   r8   r8      s     3 3I 3h 3r   c                Z    \        V 4      p \        P                  P                  WVR 7      # ))orddim)r   r(   r:   norm)rh   r   axisr   s   &&&&r   r   r      s(     	A<<QT22r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s     $ $	 $r   c                V    \        V 4      p \        P                  P                  V 4      # r   )r   r(   r:   choleskyr   s   &r   r   r      s#     	A<<  ##r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s      ) r   c                    \        V 4      p \        P                  P                  WR 7      pVR8X  d   VP                  pV# ))moder)r   r(   r:   qrR)r   r   rR   s   && r   r   r      s7     	A\\__Q_*Fs{Mr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s      9 r   c                    \        V 4      p V'       g    \        P                  P                  V 4      # \        P                  P	                  WR 7      pV# ))full_matrices)r   r(   r:   svdvalssvd)r   r   
compute_uvrV   rR   s   &&&& r   r   r      sD     	A||##A&& \\a=FMr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s      9 r   c                .   \        V 4      p \        P                  P                  V 4      w  rV P	                  4       '       gR   VP	                  4       '       d<   VP
                  ^ 8H  P                  4       '       d   VP                  pVP                  pW3# r   )r   r(   r:   eigr   imagallreal)r   wvts   &  r   r   r      sh     	ALLQEA<<>>allnn!&&A+1B1B1D1DFFWW5Lr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s     + +I +r   c                X    \        V 4      p \        P                  P                  WR 7      # )UPLO)r   r(   r:   eighr   r   s   &&r   r   r      s&     	A<<Q**r   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s      y r   c                   \        V 4      p \        P                  P                  V 4      pV P	                  4       '       gF   VP	                  4       '       d0   VP
                  ^ 8H  P                  4       '       d   VP                  pV# r   )r   r(   r:   eigvalsr   r   r   r   rQ   s   & r   r   r      s`     	A\\!!!$F<<>>f//11v{{a7G6L6L6N6NMr   c                   V ^8  d   QhRR/# r5   r   )r7   s   "r   r8   r8      s     / /	 /r   c                X    \        V 4      p \        P                  P                  WR 7      # r   )r   r(   r:   eigvalshr   s   &&r   r   r      s&     	A<<   ..r   r   )gV瞯<F)r6   )NF)NNF)reduced)TTF)L))
__future__r   r1   rn   typingr   r(    r   r   _normalizationsr   r   r	   collections.abcr
   	Exceptionr   r   r%   r3   r;   rA   rE   rM   rP   rW   r[   r`   rc   rf   rq   r~   r   r   r   r   r   r   r   r   r   r   r   <module>r      s   #      ! < < (	) 	 +  +
 *$ *  * $  $
 @  @    A  A
 5  5
 .  .   
 #  #
 B  B  R  R 3  3 $  $
          +  +
    /  /r   