+
    /i              	          R t ^ RIt^ RIHt ^ RIHtHtHt ^ RI	H
t
Ht ^ RIt^ RIHt R tR tR tR	 tR
 tR t]P*                  P-                  RR7      R 4       t]P*                  P1                  R]]]P6                  ]]P:                  .4      ]P*                  P1                  R]]]P6                  ]]P:                  .4      R 4       4       tR# )z1Test functions for linalg._solve_toeplitz module
N)levinson)solvetoeplitzsolve_toeplitz)assert_equalassert_allclose)raisesc                     \         P                  P                  R 4      p R EF-  pV P                  V4      pV P	                  4       R8  d    VRV P                  V4      ,          ,           pV P                  V4      pV P	                  4       R8  d    VRV P                  V4      ,          ,           pV P                  V4      pV P	                  4       R8  d    VRV P                  V4      ,          ,           p\        W#3V4      p\        \        W#R7      V4      p\        WV4       \        W$R7      p\        \        V4      V4      p\        WV4       EK0  	  R# )  g      ?              ?rbN)         
   )	nprandomRandomStaterandnrandr   r   r   r   )r   ncr   yactualdesireds          d/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/linalg/tests/test_solve_toeplitz.pytest_solve_equivalencer      s   YY""4(FLLO;;=3Ba((ALLO;;=3Ba((ALLO;;=3Ba((A  q)(!,(  'Q'('     c            	         \         P                  P                  R 4      p V P                  ^4      pV P                  ^4      pR F~  pR Fu  pV P                  ! V!  V,           p\	        W3VR7      p\        \        WR7      V4      p\        VP                  V4       \        VP                  V4       \        Wg4       Kw  	  K  	  R# )r
   r   r   N)    r   ))   )r#   r   )
r   r   r   r   r   r   r   r   shaper   )r   r   r   offsetyshaper   r   r   s           r   test_multiple_rhsr'   %   s    YY""4(FQAQA$Ff%.A#QEQ/FHQ,a0Gv./F, % r    c                  z    . ROp . ROp. ROp\        W3V4      p\        \        WR7      V4      p\        W44       R# )r   r   N)r   r   r#      )r   r   	      )   r   r#   r   )r   r   r   r   )r   r   r   r   r   s        r   test_native_list_argumentsr-   3   s8    AAAQE1%FHQ$a(GF$r    c                     \         P                  P                  R 4      p ^pV P                  V4      pV P                  V4      pV P                  V4      p^ V^ &   \	        \         P
                  P                  \        W#3VR7       R# )r
   r   Nr   r   r   r   assert_raiseslinalgLinAlgErrorr   )r   r   r   r   r   s        r   test_zero_diag_errorr3   <   sh    YY""4(F	AQAQAQAAaD"))''!%r    c                      \         P                  P                  R 4      p . ROpV P                  ^4      p\	        \         P
                  P                  \        WR7       R# )r
   r   N)r   r   r   r/   )r   r   r   s      r   test_wikipedia_counterexampler5   H   s@     YY""4(FAQA"))''@r    c            	         \         P                  P                  R 4      p V P                  ^
4      pV P                  ^
4      R,           p^.p^.p\	        ^^
4       Fc  pVP                  \        VRV^,
           V^V R7      R,          4       VP                  \        VRV^,
           V^V R7      R,          4       Ke  	  \         P                  ! VR^ R1,          VRR 34      p\         P                  ! VR^ R1,          P                  4       VRR 34      p\        WaR,          R7      w  r\        WrR,          R7      w  r\        W9RR 4       \        WJRR 4       R# )r
   r   Nr   :r   NN)r   r   r   r   rangeappendr   concatenateconjr   r   )r   y_dy_zreflection_coeffs_dreflection_coeffs_zi
y_d_concat
y_z_concat_ref_dref_zs              r   test_reflection_coeffsrG   Q   s<    YY""4(F
,,r
C
,,r
R
C##1b\"">#f!+Qq#J2#NO"">#f!+Qq#J2#NO  R"Ws3Bx 89JR"W!2!2!4c#2h ?@J
"g.HA
"g.HA's4's4r    z!Instability of Levinson iteration)reasonc                  
   \         P                  P                  R 4      p ^dpR\         P                  ! V4      ^,          ,          pV P	                  V4      p\        W#R7      p\        \        V4      V4      p\        WE4       R# )r
   g?r   N)	r   r   r   aranger   r   r   r   r   )r   r   r   r   	solution1	solution2s         r   test_unstablerM   g   sb     YY""4(FA		!a AQAq&Ihqk1%II)r    dt_cdt_bc           	         \         P                  ! . V R 7      p\         P                  ! . VR 7      p\        W#4      pVP                  R8X  g   Q hVP                  \        \         P                  ! ^^.V R 7      \         P
                  ! ^VR 7      4      P                  8X  g   Q h\         P                  ! RVR 7      p\        W#4      pVP                  R8X  g   Q hVP                  VP                  8X  g   Q hR# ))dtypeN)r"   )r"   r"   )r   arrayr   r$   rQ   onesempty)rN   rO   r   r   xx1s   &&    r   
test_emptyrW   {   s     	4 A
4 AqA77d??77nRXXq!fD%A&(ggat&<>>CeD D D 	t$A		B88v88qwwr    )__doc__numpyr   scipy.linalg._solve_toeplitzr   scipy.linalgr   r   r   numpy.testingr   r   pytestr   r0   r   r'   r-   r3   r5   rG   markxfailrM   parametrizeintfloatfloat32complex	complex64rW    r    r   <module>rg      s     1 8 8 7  *)2-%	%A5, =>* ?*& #ubjj'2<<!PQ#ubjj'2<<!PQ R Rr    