+
    /i                        ^ RI t ^ RIt^ RIHt ^ RIHtHtHt ^ RI	H
t
Ht ]P                  ! ^^ .^ ^..4      t]P                  ! . RO.4      t^ ..R^..^ ...^ ..R^..^ ...^	..R^..^	...^	..R^..^	...]R]P                  ! ^4      ].]R]P                  ! ^4      ].]R]]! ]^ ,          4      ,          ]P                   P#                  ]4      ]! ]^ ,          4      ,          ..t^^.^^... RO.^.^.^... RO. RO.^^.^^.^^..^^.^R... RO.^.^.R... RO. RO.^^.RR.^^... RO. RO. RO.]P&                  ! R4      ]P&                  ! R4      ]P&                  ! R4      .tR tR	 tR
 tR t] P2                  P5                  R]]]P:                  ]]P>                  .4      ] P2                  P5                  R. RO4      ] P2                  P5                  RRR.4      R 4       4       4       t R# )     N)norm)assert_assert_allcloseassert_equal)polareighrightleft              @c                 V    \        WR 7      w  rE\        WBRR7       \        WSRR7       R# )sideV瞯<atolN)r   r   )ar   
expected_u
expected_pups   &&&&  b/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/linalg/tests/test_decomp_polar.pycheck_precomputed_polarr   '   s$     DAA.A.    c                    \         P                  ! \         P                  ! \        4      P                  4      p\         P
                  ! V 4      pVP                  w  r4\        V R R7      w  rV\        VP                  W434       \        VP                  WD34       \        VP                  V4      WR7       W48  dK   \        VP                  4       P                  P                  V4      \         P                  ! V4      RR7       MI\        VP                  VP                  4       P                  4      \         P                  ! V4      RR7       \        VP                  4       P                  V4       \        VRR7      pV\        V4      R8  ,          p\!        V^ 8  P#                  4       4       \        V RR7      w  rV\        VP                  W434       \        VP                  W334       \        VP                  V4      WR7       W48  dK   \        VP                  4       P                  P                  V4      \         P                  ! V4      RR7       MI\        VP                  VP                  4       P                  4      \         P                  ! V4      RR7       \        VP                  4       P                  V4       \        VRR7      pV\        V4      R8  ,          p\!        V^ 8  P#                  4       4       R# )	r	   r   r   r   T)eigvals_onlyg+=r
   N)npsqrtfinfofloatepsasarrayshaper   r   r   dotconjTeyer   absr   all)	r   product_atolaamnr   r   evalsnonzero_evalss	   &        r   verify_polarr/   /   s    77288E?../L	AB88DA!DA1&!1&!AEE!Ha3v

q)266!95Aaffhjj)266!95AAFFHJJ"&E#e*u,-M]a$$&' DA1&!1&!AEE!Ha3v

q)266!95Aaffhjj)266!95AAFFHJJ"&E#e*u,-M]a$$&'r   c                  >    \          F  w  rr#\        WW#4       K  	  R # N)precomputed_casesr   )r   r   r   r   s       r   test_precomputed_casesr3   V   s    +<'@ ,=r   c                  6    \          F  p \        V 4       K  	  R # r1   )verify_casesr/   )r   s    r   test_verify_casesr6   [   s    Q r   dtr"   r   c                    \         P                  ! WR 7      pVw  rEVR8X  d   WD3MWU3p\        W2R7      w  rx\        \         P                  ! ^V R 7      4      w  r\	        VP
                  V	P
                  4       \	        VP
                  V
P
                  4       VP                  V8X  g   Q hVP                  V8X  g   Q h\         P                  ! V^ 8H  4      '       g   Q hR# ))dtyper
   r   N)r   emptyr   r&   r   r9   r"   r(   )r7   r"   r   r   r+   r,   p_shaper   r   u_np_ns   &&&        r   
test_emptyr>   _   s     	!ADAqfQFGDARVVAR()HC#))$#))$77e77g66!q&>>>r   )      r@   )r?   r@      )rA      r   y      @      @)r?   r@   r   )r?   r@   y      @       @)rA   y      @      y             y      @       y      @      ?)i'  
   r?   )r@   r   )r   r?   r@   r   r   r   r@   r@   r   )rE   rF   rG   )!pytestnumpyr   numpy.linalgr   numpy.testingr   r   r   scipy.linalgr   r   arraydiag2a13r&   r%   r#   r2   r:   r5   r   r/   r3   r6   markparametrizeintr   float32complex	complex64r>    r   r   <module>rW      sK      B B $ 	1a&1a&!"hh	{ 	cUGqcUaSE"cUFaSEQC5!cUGqcUaSE"cUFaSEQC5!
GRVVAY&
FBFF1Iu%'3tCF|#SUUYYs^DQL%@A  VaVKS1#sO	VaVaVVaYLS1#t>"VdF^aV$[),HHVHHVHHV$/$(NA
 UBJJNO#;<&'!23 4 = Pr   