
    !YHh                        d Z ddlZddlZddlmZmZmZmZ ddlm	Z	m
Z
mZmZmZmZ ddlZddlZddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z! ddlm"Z" ddl#m$Z$ ddl%m&Z& ddl'Zdd	l(m)Z) d
 Z* G d d      Z+ G d d      Z, G d d      Z- G d d      Z. G d d      Z/ G d d      Z0d Z1d Z2d Z3 G d d      Z4 G d d      Z5y)z, Test functions for linalg.matfuncs module

    N)arrayidentitydotsqrt)assert_array_almost_equalassert_allcloseassert_assert_array_lessassert_array_equalassert_warns)funmsignmlogmsqrtmfractional_matrix_powerexpmexpm_frechet	expm_condnorm
khatri_raocosmsinmtanmcoshmsinhmtanhm)_matfuncs_inv_ssq)pick_pade_structure)LogmExactlySingularWarning)minimizec                  T    t        j                  g dg dg dg dgt              } | S )aW  
    Return the test matrix from Experiment (1) of [1]_.

    References
    ----------
    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2012)
           "Improved Inverse Scaling and Squaring Algorithms
           for the Matrix Logarithm."
           SIAM Journal on Scientific Computing, 34 (4). C152-C169.
           ISSN 1095-7197

    )g3d?     L@r"   r"   )r   gRal!A?r"   r"   )r   r   gQI?r"   )r   r   r   g^?dtype)npr   float)As    Y/var/www/html/planif/env/lib/python3.12/site-packages/scipy/linalg/tests/test_matfuncs.py%_get_al_mohy_higham_2012_experiment_1r)      s/     	" 	 &+		,A
 H    c                   $    e Zd Zd Zd Zd Zd Zy)	TestSignMc                     t        g dg dg dg dg dg      }t        g dg dg dg d	g d
g      }t        |      }t        ||       y )Ng333333=@g3333338g     `Q@gfffffH@g      @gffffff"g@      2g0       g      $g      @g      4r0   r1   g333333#g333333#@g     9g.r1   g#@g333333g      2@g3333332@       @)g'@'Rqgy.@ge@5@r6   )g@ȽUЛ'?g9\g+%r7   )gRQQ?gGzgffffffr8   )gר#w?î?gk#egC,Nr9   )g@42
gF(@gcs@@r:   )r   r   r   )selfacrrs       r(   	test_nilszTestSignM.test_nils2   sW    00.1-	/ 0
 QO0ON	P Q
 !H!!B'r*   c                 L    t        g dg dg dg dg      }t        |d       y )N)           r   r   )rB   r   rB   r   r   r   r   rB   )r   r   rB   r   Fdispr   r   r;   r<   s     r(   test_defective1zTestSignM.test_defective1@   s    ;y9=>aer*   c                 R    t        g dg dg dg dg df      }t        |d       y )Nr.   r/   r2   r3   r4   FrD   rF   rG   s     r(   test_defective2zTestSignM.test_defective2E   s,    &'('$& ' 	aer*   c           
      ^    t        g dg dg dg dg dg dg dg      }t        |d	       y )
Nr1         9@rA   rA   rA   rA   rA   rA               $@      @rQ   rQ   rA   rA   rA   r5         .@rQ   rQ   rA   rA   rA   rA   rA   rS   rQ   rA   rA   rA   rA   rA   rQ   rP   rA   rA   rA   rA   rA   rA   r1   rM   rA   rA   rA   rA   rA   rA   rO   FrD   rF   rG   s     r(   test_defective3zTestSignM.test_defective3O   s2    11000102 3 	aer*   N)__name__
__module____qualname__r?   rH   rJ   rX    r*   r(   r,   r,   0   s    (
r*   r,   c            	          e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	        Zej                  j                  d
        Zd Zd Zej                  j%                  d      ej                  j'                  deeej.                  eej2                  g      d               Zej                  j                  ej                  j'                  deeej.                  eej2                  g      d               Zy)TestLogMc           
          t        g dg dg dg dg dg dg dg      }t        d      d	z  d
z   |z
  }t        |d       y )NrL   rN   rR   rT   rU   rV   rW      g@y                FrD   )r   r   r   )r;   r<   ms      r(   r?   zTestLogM.test_nils]   sI    11000102 3 a[_R"QUr*   c                 l    t               }t        |d      \  }}t        |      }t        ||dd       y )NFrD   g-C6
?+=rtolatol)r)   r   r   r   )r;   r'   A_logminfoA_round_trips        r(   *test_al_mohy_higham_2012_experiment_1_logmz3TestLogM.test_al_mohy_higham_2012_experiment_1_logmi   s3     23AE*F|ad?r*   c                     t               }t        |t        j                  d      \  }}t	        |      }t        t        j                  ||dd              y )NFrD   h㈵>rc   rd   )r)   r   r%   logr   r	   allclose)r;   r'   
A_funm_logrh   ri   s        r(   .test_al_mohy_higham_2012_experiment_1_funm_logz7TestLogM.test_al_mohy_higham_2012_experiment_1_funm_logq   sG     232666
DJ'BKKadGGHr*   c                    t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      }t        j
                  ddd      D ]  }||z  }t         j                  j                  |      }d| d| }t        |d	
      \  }}|j                  |      }	t        |	|       t        |d	
      \  }
}t        |
      }t        |||         y )N  rB         	   zM:z eivals:FrD   )err_msg)r%   randomseedrangerandnlogspacelinalgeigvalsr   r   r   r   r   )r;   n
M_unscaledscaleMWrw   M_sqrtmrh   M_sqrtm_round_tripM_logmM_logm_round_trips               r(   test_round_trip_random_floatz%TestLogM.test_round_trip_random_floaty   s    
		tq! 	GAA.JRA. G& II%%a(qc!- !&ae 4%,[[%9" 2A6  $AE2$(L! 11gFG	Gr*   c                 |   t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        j
                  ddd      D ].  }||z  }t        |d	      \  }}t        |      }t        ||       0  y 
Nrr   rB   rs                 ?rt   ru   rv   FrD   )	r%   rx   ry   rz   r{   r|   r   r   r   )r;   r   r   r   r   r   rh   M_round_trips           r(   test_round_trip_random_complexz'TestLogM.test_round_trip_random_complex   s    
		tq! 	1AA.biiooa6K1KKJRA. 1&#AE2#F|a0	1	1r*   c                    d}ddgddggddgddggddgddggddgddggfD ]#  }t         j                  j                  |      }t        t	        d |D                      t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v       t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v        t        j                  |t               }t        |d	      \  }}t        |j                  j                  |v        & y )
NFDGrB   r         c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   Nimagreal.0ws     r(   	<genexpr>zFTestLogM.test_logm_type_preservation_and_conversion.<locals>.<genexpr>   $     <QAFF0affqj0<   ')r#   FrD   )scipyr}   r~   r	   anyr%   r   r&   r   r$   charcomplex)r;   complex_dtype_charsmatrix_as_listr   r'   rg   rh   s          r(   *test_logm_type_preservation_and_conversionz3TestLogM.test_logm_type_preservation_and_conversion   s8    .Q!Q Q!Q Q!Q Q!Q 	" 	>N $$^4A<!<<<= u5A.LFDFLL%%-@@A w7A.LFDFLL%%)<<= .66A.LFDFLL%%)<<=/	>r*   c                    g dg dg dg}t         t        fD ]  }t        j                  ||      }t        j
                  j                  |      }t        dt        j                  |j                        j                         k         t        |d      \  }}t        t        j                  |j                  t        j                               t        t!        |      |        y )N)rB   rB   r   )r   rB   rB   )rB   r   rB   r#   {Gz?FrD   )r&   r   r%   r   r   r}   r~   r	   absoluter   sumr   
issubdtyper$   inexactr   r   )r;   r   dtXr   Yrh   s          r(   test_complex_spectrum_real_logmz(TestLogM.test_complex_spectrum_real_logm   s     	9-. 	(B"%A$$Q'AD2;;qvv.2244515)GAtBMM!''2::67DGQ'	(r*   c                    ddgddggddgddggfD ]q  }t         t        fD ]`  }t        j                  ||      }t	        |d      \  }}t        t        j                  |j                  t        j                               b s y )NrB   r   r#   FrD   )	r&   r   r%   r   r   r	   r   r$   complexfloating)r;   r   r   r'   rg   rh   s         r(   test_real_mixed_sign_spectrumz&TestLogM.test_real_mixed_sign_spectrum   s     Q!R!Q!Q " 	IA Wn IHHQb)#AE2fllB4F4FGHI	Ir*   c                 ,   t        j                  ddgddgg      }t        j                  ddgddgg      }||j                  ||j                  fD ]A  }t        j
                  }t        |t        |d      \  }}t        |      }t        ||d       C y )Nr   r   rB   FrD   rc   rf   )
r%   r   asarrayTr   r   r   r   r   r   )r;   r'   Br   expected_warningLrh   Es           r(   test_exactly_singularzTestLogM.test_exactly_singular   s    HHq!fr2h'(JJAA'(ACCACC 	.A0KK"#3T15IGAtQAAqu-		.r*   c                     t        j                  dgg      }t        j                  }t	        |t
        |d      \  }}t        |      }t        ||d       y )Ng0.++FrD   rc   r   )r%   r   r   LogmNearlySingularWarningr   r   r   r   )r;   r   r   r   rh   r   s         r(   test_nearly_singularzTestLogM.test_nearly_singular   sJ    HHvhZ ,FF/quE4G15)r*   c                    ddgddgg}dt         j                  dz  gt         j                   dz  dgg}t        t        |      |d       t        t	        |      |d       ddgdd	gg}dt         j                  z  dz  d
t         j                  z  gdd	t         j                  z  dz  gg}t        t        |      |d       t        t	        |      |d       ddgdd	gg}dt         j                  z  dz  dgdd	t         j                  z  dz  gg}t        t        |      |d       t        t	        |      |d       y )Nr   rB   r         ?rc   r   r   ru   y             r   )r%   pir   r   r   )r;   r   r   s      r(   &test_opposite_sign_complex_eigenvaluesz/TestLogM.test_opposite_sign_complex_eigenvalues   s   Vb!Ws^ruufSj!_-Q/Q/!Wq#hhslAbeeG$q#bee)C-&89Q/Q/!Wq#hhslACIcM 23Q/Q/r*   c                     d}t        j                  ||f      t        j                  |      z   }d|j                  _        t        |       y )N   F)r%   onesr   flags	writeabler   r;   r   r<   s      r(   test_readonlyzTestLogM.test_readonly   s8    GGQFObkk!n,!Qr*   z6ValueError: attempt to get argmax of an empty sequencereasonr   c                     t        j                  d|      }t        |      }t        j                  d|      }t        |      }|j                  dk(  sJ |j
                  |j
                  k(  sJ y Nr   r   r#   r   )r%   emptyr   eyeshaper$   )r;   r   r<   log_aa0log_a0s         r(   
test_emptyzTestLogM.test_empty   s^     HHV2&QVVAR b{{f$$${{fll***r*   r$   c                     t        j                  t        d      5  t        j                  t              5  t	        t        j                  d|             d d d        d d d        y # 1 sw Y   xY w# 1 sw Y   y xY w)Nzlogm result may be inaccurate)matchr   r   r#   )pytestwarnsRuntimeWarningr   r   r%   zeros)r;   r$   s     r(   test_no_ZeroDivisionErrorz"TestLogM.test_no_ZeroDivisionError   s]     ll>1PQ 	0ll56	0&./	0 	0 	0 	0 	0 	0s"   A4!A(A4(A1	-A44A=N)rY   rZ   r[   r?   rj   rp   r   r   r   r   r   r   markthread_unsafer   r   r   r   xfailparametrizeintr&   r%   float32r   	complex64r   r   r\   r*   r(   r^   r^   [   s   	@IG*1><
(	I [[. . [[* *0 [[VW[[TC

GR\\#RS+ T X+ [[[[WsE2::w&UV0 W 0r*   r^   c                   >   e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zej$                  j'                  d      d        Zd Zd Zd Zd Zd Zd Zej$                  j7                  deeej>                  e ejB                  g      d        Z"y)	TestSqrtMc                 $   t         j                  j                  d      }t        dd      D ]b  }|j	                  ||      }t        j
                  ddd      D ]4  }||z  }t        |d      \  }}|j                  |      }t        ||       6 d y )	Nrr   rB   rs   rt   ru   rv   FrD   	r%   rx   RandomStaterz   r{   r|   r   r   r   	r;   rngr   r   r   r   r   rh   r   s	            r(   r   z&TestSqrtM.test_round_trip_random_float  s    ii##D)q! 	7A1aJRA. 7& %ae 4%,[[%9" 2A6	7	7r*   c                 P   t         j                  j                  d      }t        dd      D ]x  }|j	                  ||      d|j	                  ||      z  z   }t        j
                  ddd      D ]4  }||z  }t        |d	      \  }}|j                  |      }t        ||       6 z y r   r   r   s	            r(   r   z(TestSqrtM.test_round_trip_random_complex  s    ii##D)q! 	7A1a2		!Q+??JRA. 7& %ae 4%,[[%9" 2A6	7	7r*   c                 p   d}t        |      }t        g dd|ddgdd|dgg dg      }t        g dd|ddgdd|dgg dg      }|j                  d   }t        t	        ||      |       t        |d|      d   }t        t	        ||      |       t        |dd      d   }t        t	        ||      |       y )	Ng      ?)g      ?r   r   rB   r   rC   )rB   r   r   r   FrE   	blocksizer   )r   r   r   r   r   r   )r;   eser<   sar   esas          r(   test_badzTestSqrtM.test_bad  s    !W;a!9a!9  Kr!AJqAJ   GGAJ!#b*Q/AEQ/2!#c#,q1AEQ/2!#c#,q1r*   c                    d}ddgddggddgddggddgddggddgddggddgddggfD ]#  }t         j                  j                  |      }t        t	        d |D                      t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v       t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v        t        j                  |t               }t        |d	      \  }}t        |j                  j                  |v        & y )
Nr   rB   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r(   r   zHTestSqrtM.test_sqrtm_type_preservation_and_conversion.<locals>.<genexpr>B  r   r   r#   FrD   )r   r}   r~   r	   r   r%   r   r&   r   r$   r   r   r;   r   r   r   r'   A_sqrtmrh   s          r(   +test_sqrtm_type_preservation_and_conversionz5TestSqrtM.test_sqrtm_type_preservation_and_conversion4  sH    .Q!Q Q!Q Q!Q Q!Q Q!Q " 	?N $$^4A<!<<<= u5A!!%0MGTGMM&&.AAB w7A!!%0MGTGMM&&*==> .66A!!%0MGTGMM&&*==>1	?r*   c                    d}ddgddggddgddggg dg dg dgfD ]  }t         j                  j                  |      }t        t	        d |D                     t        j                  |t        	      }t        |d
      \  }}t        |j                  j                  |v        t        j                  |t        	      }t        |d
      \  }}t        |j                  j                  |v         y )Nr   rB   r   r   r   rB   r   r   r   rB   rB   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r(   r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>\  $     8,!&&1*,8r   r#   FrD   )r   r}   r~   r	   r   r%   r   r   r   r$   r   r&   r   s          r(   9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumzCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumS  s    -Q!R!Q!Q Iy13 	?N $$^4AC8a889 w7A!!%0MGTGMM&&*==> u5A!!%0MGTGMM&&*==>#	?r*   c                    t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      dt         j                  j                  ||      z  z   }t        |d|      \  }}t        |t         j                  j                  |d             t        dd      D ]  }t        |d|      \  }}t        ||       !  y )	Nrr   rB      r   Fr   r   
   )
r%   rx   ry   rz   randr{   r   r   r}   matrix_power)r;   r   r'   A_sqrtm_defaultrh   r   A_sqrtm_news          r(   test_blocksizeszTestSqrtM.test_blocksizesh  s    
		tq! 	>A		q!$r"))//!Q*?'??A$)!%1$E!OTAryy55oqIJ"1b\ >	$)!%9$M!T=>		>r*   c                     t               }t        |d      \  }}|j                  |      }t        ||d       t        t	        j
                  |      t	        j
                  |             y )NFrD   rl   re   )r)   r   r   r   r%   tril)r;   r'   r   rh   ri   s        r(   %test_al_mohy_higham_2012_experiment_1z/TestSqrtM.test_al_mohy_higham_2012_experiment_1s  sO    13ae,{{7+ad3-rwwqz:r*   c                     t         t        fD ]a  }t        j                  g dg dg dg dg|      }t	        |d      \  }}t        t        j                  |      j                                c y )N)r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r#   FrD   )r   r&   r%   r   r   r	   isnanall)r;   r   r'   r   rh   s        r(   test_strict_upper_triangularz&TestSqrtM.test_strict_upper_triangular{  se    u* 	-B	 &(	)A
 "!%0MGTBHHW%))+,	-r*   c                 T   t         t        fD ]  }t        j                  g dg dg dg|      }t        j                  g dg dg dg|      }t	        ||j                  |             t        |d      \  }}t        t        j                  |      j                                 y )Nr   r   r   r   r   r#   FrD   )
r   r&   r%   r   r   r   r   r	   r  r  )r;   r   r'   r   B_sqrtmrh   s         r(   test_weird_matrixzTestSqrtM.test_weird_matrix  s    u* 	-B #%&A  #%&A q!%%(+ "!%0MGTBHHW%))+,	-r*   c                     t         j                  j                  d       t         j                  j                  dd      }t	        |d      }t        |j                  |      |       y )Nrr   r   TrD   )r%   rx   ry   r  r   r   r   )r;   r'   r   s      r(   	test_dispzTestSqrtM.test_disp  sD    
		tIINN1a !$a!$r*   c                     ddgddgg}ddgddgg}t        t        j                  ||      |d	       t        t        |      |d	       y )
N               @ru   r                       ?      ?r         ?      rc   r   )r   r%   r   r   r;   r   Rs      r(   r   z0TestSqrtM.test_opposite_sign_complex_eigenvalues  sL    !Wq#hAYD	"q!ae4a!%0r*   c                 J   t        j                  g dg dg dg dg      }t        j                  t        d      ddt        d      gg dg dt        d      ddt        d      gg      }t        t        j                  ||      |d       t        t        |      |d       y )N)rB   r   r   rB   r  r   r   rc   r   )r%   r   r   r   r   r   r  s      r(   test_gh4866zTestSqrtM.test_gh4866  s    HHl"""$ % HHtCy!QS	2""Cy!QS	24 5 	q!ae4a!%0r*   c                     t        j                  g d      }t        j                  t        d      ddg      }t        t        j                  ||      |d       t        t        |      |d       y )N)r   rB   r   r   rB   r   rc   r   )r%   diagr   r   r   r   r  s      r(   test_gh5336zTestSqrtM.test_gh5336  sN    GGIGGT!WaO$q!ae4a!%0r*   c                     t        j                  d      }t        j                  d      }t        t        j                  ||      |d       t        t	        |      |d       y )Nr   rc   r   )r%   r   r   r   r   r  s      r(   test_gh7839zTestSqrtM.test_gh7839  sD    HHVHHVq!ae4a!%0r*   zfailing on macOS after gh-20212r   c                     t        j                  d      }|j                  d       t        j                  |d       t        j                  t        |            sJ y )N)   r)  gGz?rB   )r%   r   fillfill_diagonal	isrealobjr   r;   r   s     r(   test_gh17918zTestSqrtM.test_gh17918  sA    HHX	t
A||E!H%%%r*   c                 l   t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ y Nr  r  r#   )	r%   r   uint8r   r$   float64uint16uint32uint64r-  s     r(   -test_data_size_preservation_uint_in_float_outz7TestSqrtM.test_data_size_preservation_uint_in_float_out  s    HHXRXX.Qx~~+++HHXRYY/Qx~~+++HHXRYY/Qx~~+++HHXRYY/Qx~~+++r*   c                 l   t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ y r0  )	r%   r   int8r   r$   r3  int16int32int64r-  s     r(   ,test_data_size_preservation_int_in_float_outz6TestSqrtM.test_data_size_preservation_int_in_float_out  s    HHXRWW-Qx~~+++HHXRXX.Qx~~+++HHXRXX.Qx~~+++HHXRXX.Qx~~+++r*   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ y )Nr   ru   r   r#   )	r%   r   r9  r   r$   
complex128r:  r;  r<  r-  s     r(   +test_data_size_preservation_int_in_comp_outz5TestSqrtM.test_data_size_preservation_int_in_comp_out  s    HHq!fq"g&bgg6Qx~~...HHq!fq"g&bhh7Qx~~...HHq!fq"g&bhh7Qx~~...HHq!fq"g&bhh7Qx~~...r*   c                    t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j
                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ t        t         d      rNt        j                  dt         j                        }t        |      j                  t         j                  k(  sJ y y )Nr1  r#   float128)	r%   r   float16r   r$   r   r3  hasattrrC  r-  s     r(   .test_data_size_preservation_float_in_float_outz8TestSqrtM.test_data_size_preservation_float_in_float_out  s    HHXRZZ0Qx~~+++HHXRZZ0Qx~~+++HHXRZZ0Qx~~+++2z"5A8>>RZZ/// #r*   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ t        t         d      ret        t         d      rTt        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ y y y )Nr   ru   r   r?  r#   rC  
complex256)r%   r   rD  r   r$   r   r   r3  r@  rE  rC  r-  s     r(   -test_data_size_preservation_float_in_comp_outz7TestSqrtM.test_data_size_preservation_float_in_comp_out  s
   HHq!fq"g&bjj9Qx~~---HHq!fq"g&bjj9Qx~~---HHq!fq"g&bjj9Qx~~...2z"wr<'@1a&1b'*"++>A8>>R]]222 (A"r*   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ t        j                  ddgddggt         j
                        }t        |      j                  t         j
                  k(  sJ t        t         d      rTt        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ y y )Nr  ru   r   r  r#   rH  )r%   r   r   r   r$   r@  rE  rH  r-  s     r(   ,test_data_size_preservation_comp_in_comp_outz6TestSqrtM.test_data_size_preservation_comp_in_comp_out  s    HHr1g3x(=Qx~~---HHr1g3x(>Qx~~...2|$2q'As8,BMMBA8>>R]]222 %r*   r   c                     t        j                  d|      }t        |      }t        j                  d|      }t        |      }|j                  dk(  sJ |j
                  |j
                  k(  sJ y r   )r%   r   r   r   r   r$   )r;   r   r<   sr   s0s         r(   r   zTestSqrtM.test_empty   s\    HHV2&!HVVAR 2Yww&   ww"(("""r*   N)#rY   rZ   r[   r   r   r   r   r  r
  r  r  r  r  r   r"  r%  r'  r   r   r   r.  r7  r=  rA  rF  rI  rK  r   r   r&   r%   r   r   r   r   r\   r*   r(   r   r   
  s    772*?>?*	>;	--"%1
111 [[?@& A&,,/	0	33 [[TC

GR\\#RS# T#r*   r   c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	
      d        Zd Zy)TestFractionalMatrixPowerc                    t         j                  j                  d       t        dd      D ]  }t        dd      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        j
                  ddd      D ]B  }||z  }t        |d|z        }t         j                  j                  ||      }t        ||       D   y )Nrr   rB   r   r   rt   ru   rv   
r%   rx   ry   rz   r{   r|   r   r}   r  r   r;   pr   r   r   r   M_rootr   s           r(   r   z8TestFractionalMatrixPower.test_round_trip_random_complex  s    
		tq! 	5A1a[ 5YY__Q2R"))//!Q:O5OO
[[Q2 5E"U*A4Q!<F#%99#9#9&!#DL#L!4	55	5r*   c                 ~   t         j                  j                  d       t        dd      D ]  }t        dd      D ]~  }t         j                  j	                  ||      }t        j
                  ddd      D ]B  }||z  }t        |d|z        }t         j                  j                  ||      }t        ||       D   y )Nrr   rB   r   rt   ru   rv   rR  rS  s           r(   r   z6TestFractionalMatrixPower.test_round_trip_random_float  s    
 			tq! 	5A1a[ 5YY__Q2
[[Q2 5E"U*A4Q!<F#%99#9#9&!#DL#L!4	55	5r*   c                 J   t         j                  j                  d       dD ]  }t        d      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        |d      }t         j                  j                  |d      }t        ||       t        |d      }t         j                  j                  |d      }t        ||       t        |d	      }t         j                  j                  |d
      }t        ||         y )Nrr   )r   r   r   r  r   皙?r   gigffffff@r)  )	r%   rx   ry   rz   r{   r   r}   r  r   )r;   r   ir   M_one_fifthr   r   r   s           r(   (test_larger_abs_fractional_matrix_powerszBTestFractionalMatrixPower.test_larger_abs_fractional_matrix_powers&  s    
		t 	&A2Y &IIOOAq)BA1F,FF5a=!yy55k1E<0+At4II**;<1%+As3II**;;1%&	&r*   c                    t         j                  j                  d      }d}t        |      D ]  }|j	                  dd      }|j                         }t        j
                  |j	                  dd            }|j                  ||g      }ddg|j                  d	         r|d
|j                  ||g      z  z   }||z  }t        ||      }t        |d      \  }	}
t        |	|z        }t        ||        y )Nl   fm1    rB   r   rt   sizeTFr   r   rD   )r%   rx   default_rngrz   integersexpchoicer   r   r   r   )r;   r   nsamplesrY  r   rT  matrix_scaler'   A_powerrg   rh   A_power_expm_logms               r(   test_random_matrices_and_powersz9TestFractionalMatrixPower.test_random_matrices_and_powers8  s     ii##$45x 	8AQ"A

A 66#,,r1"56L

A
'Ae}SZZ]+SZZaVZ444L A
 .a3G.LFD $VaZ 0G%67%	8r*   c                    t               }t        |t        j                  d      \  }}t	        |d      \  }}t        j                  |d      }t        |d      }t        ||d       t        ||       t        ||       dD ]_  }t        ||      }t        |d|z        }t        ||d       t        t        j                  |d      t        j                  |d             a y )	NFrD   r   gdy=r  )r   g?rB   r   )
r)   r   r%   r   r   r   _remainder_matrix_powerr   r   r  )	r;   r'   A_funm_sqrtrh   r   A_rem_powerrf  rT  ri   s	            r(   r  z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1Q  s    13 !BGG%8Tae,'??3G)!S1W59)-  	EA-a3G27AaC@LL!$7BGGL!4bggamD		Er*   c                 l   t         j                  j                  d       t         j                  j                  d      dt         j                  j                  d      z  z   D ]P  }t	        d      D ]@  }t        j                  ||      }|t        j                  |       z  dz
  }t        ||       B R y )Nrr   r  r   r   rB   )	r%   rx   ry   r{   rz   r   _briggs_helper_functionexp2r   )r;   r<   k
x_observed
x_expecteds        r(   test_briggs_helper_functionz5TestFractionalMatrixPower.test_briggs_helper_functione  s    
		t$rBIIOOB,?'?? 	8A1X 8.FFq!L
"''1"+-1

J78	8r*   c                    d}ddgddggddgddggddgddggddgddggfD ]  }t         j                  j                  |      }t        t	        d |D                      dD ]  }t        j                  |t              }t        ||      }t        |j                  j                  |v       t        j                  |t              }t        ||      }t        |j                  j                  |v        t        j                  |t               }t        ||      }t        |j                  j                  |v         ! y )	Nr   rB   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r(   r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>{  r   r   333333rX  gffffff
@r#   )r   r}   r~   r	   r   r%   r   r&   r   r$   r   r   r;   r   r   r   rT  r'   rf  s          r(   %test_type_preservation_and_conversionz?TestFractionalMatrixPower.test_type_preservation_and_conversionm  sA   
 .Q!Q Q!Q Q!Q Q!Q 	" 	CN $$^4A<!<<<= , C HH^591!Q7**2EEF HH^7;1!Q7**.AAB XXnE::1!Q7**.AABC	Cr*   c                    d}ddgddggddgddggg dg dg dgfD ]  }t         j                  j                  |      }t        t	        d |D                     d	D ]  }t        j                  |t        
      }t        ||      }t        |j                  j                  |v        t        j                  |t        
      }t        ||      }t        |j                  j                  |v          y )Nr   rB   r   r   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r(   r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>  r  r   rv  r#   )r   r}   r~   r	   r   r%   r   r   r   r$   r   r&   ry  s          r(   3test_type_conversion_mixed_sign_or_complex_spectrumzMTestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum  s    -Q!R!Q!Q Iy13 	CN $$^4AC8a889 , 
C HH^7;1!Q7**.AAB HH^591!Q7**.AAB
C	Cr*   zToo unstable across LAPACKs.r   c                 z   ddgddggddgddggddgddggg dg dg dgfD ]  }t         t        fD ]  }t        j                  ||	      }d
D ]:  }t	        ||      }t        t        j                  |      j                                < dD ])  }t	        ||      }t	        |d|z        }t        ||       +   y )Nr   rB   r   r   rs   r  )r   rB   rB   )r   r   rB   r#   )gffffffrx  rw  g)rX  gzG?)	r&   r   r%   r   r   r	   r  r  r   )r;   r   newtyper'   rT  rf  ri   s          r(   test_singularz'TestFractionalMatrixPower.test_singular  s     Q!Q Q!Q Q!Q Iz2	4 	5N "7+ 5HH^7;1 5A5a;GBHHW-11345 % 5A5a;G#:7AaC#HL#L!455	5r*   c                     ddgddgg}ddgddgg}t        t        j                  ||      |d	       t        t        |d
      |d	       y )Nr  ru   r   r  r  r   r  rc   r   r   )r   r%   r   r   r  s      r(   r   z@TestFractionalMatrixPower.test_opposite_sign_complex_eigenvalues  sP    !Wq#hAYD	"q!ae4/37Gr*   N)rY   rZ   r[   r   r   r[  rh  r  rs  rz  r}  r   r   r   r  r   r\   r*   r(   rP  rP    s[    	55&$82E(8!CFC2 [[<=5 >5&Hr*   rP  c            
          e Zd Zd Zd Zej                  j                  dee	e
eeeeg      ej                  j                  deeej$                  eej(                  g      ej                  j                  dddg      d                      Zd	 Zd
 Zd Zej                  j2                  ej                  j5                  d      d               Zy)TestExpMc                 \    t        ddgddgg      }t        t        |      ddgddgg       y )NrA   r   rB   )r   r   r   rG   s     r(   	test_zerozTestExpM.test_zero  s2    Bq61Q%.!!$q'Aa5!A-8r*   c                 x    t        d      }t        |t        j                  t        j                  gg             y )NrB   )r   r   r%   r   r   )r;   elts     r(   test_single_eltzTestExpM.test_single_elt  s&    1gRXXvh/0r*   funcr   r   r   )rB   rB   c                     t        j                  ||      }t        j                  d|      } ||      } ||      }|j                  |k(  sJ |j                  |j                  k(  sJ y )Nr#   r1  )r%   r   r   r$   )r;   r  r   r   r'   A0resultresult0s           r(   test_small_empty_matrix_inputz&TestExpM.test_small_empty_matrix_input  s^     HHU"%XXhb)ar(||u$$$||w}},,,r*   c                    t         j                  }t        ddgddgg      }|dz  dz   d|z  z  }|dz  dz
  |z  }t        t	        |      t        ||g|dz  |gg             t	        |j                  t         j                              j                  j                  dk(  sJ t	        |j                  t         j                              j                  j                  dk(  sJ y )NrB   ru   r   r   f)
r%   r   r   r   r   astyper   r$   r   r   )r;   r   r<   aabbs        r(   test_2x2_inputzTestExpM.test_2x2_input  s    DDAq6Aq6"#dQh1dQh\QR2a4*'=!>?AHHR\\*+1166#===AHHRZZ()//44;;;r*   c                    t         j                  }t        j                  ddgddggddgddggddgddggddgddggddgddgggd	      }t        j                  |dz  dz   d
|z  z  |dz  dz
  |z  g|dz  dz
  dz  |z  |dz  dz   d
|z  z  ggdd|d
z  z  z  d|d
z  z  dz  z   d|d
z  z  dz  dd|d
z  z  z  z
  g|d
z  dz  dd|d
z  z  z  z
  dd|d
z  z  z  |d
z  dz  z   ggdd|z  z  |dz  dz  z   dd|z  z  d|dz  z  dz  z   gdd
|z  z  |dz  d
z  z   dd|z  z  d|dz  z  dz  z   ggdd|d
z  z  z  d|dz  z  dz  z   dd|d
z  z  z  d|dz  z  dz  z   gdd|d
z  z  z  d|dz  z  dz  z   dd|d
z  z  z  d|dz  z  dz  z   ggdd
|z  z  d|z  d
z  z   dd
|z  z  d|z  d
z  z   gdd
|z  z  d|z  d
z  z
  dd
|z  z  d|z  d
z  z
  ggg      }t        t	        |      |       y )NrB   ru   r   r   r   rt   r   )orderr   r`   r  rs   )r%   r   r   r   r   )r;   r   r<   a_ress       r(   test_nx2x2_inputzTestExpM.test_nx2x2_input  s   DDHH1v1v&1v2w'1v1v&1v1v&1vBx(	* 25	6 T!VacNQT!VQJ7T!VQJqL1a46AaC.9;qAvJ!Q$z1AadFA:a1a4j3HIqDF1a1f:-q!AqD&z!Q$q&/@ACqsGAqDFNB!Ha1faZ,?@!HQT!VOQ!Wa1faZ-?@BqAvJ!Q$z12qAv;!Q$z3IJ!Q$K1a4
2AqAvJ!Q$z4IJL!Hac1W,b!A#h!Qw.>?qsGQqS!GOQ!Wac1W_=?  	Q'r*   c                 n    d}t        j                  ||f      }d|j                  _        t	        |       y )Nr`   F)r%   r   r   r   r   r   s      r(   r   zTestExpM.test_readonly  s+    GGQFO!Qr*   r   c                 T   t        j                  dt              }t         j                  j	                  d      }|j                  ddd      }|j                  ddd      }|j                  d      |||f<   t        j                  dt              }|j                         |d<   t        |      \  }}|dk(  sJ t        |      }t         j                  j                  t        |      |       t        d	      D ]-  }t        |      }	t         j                  j                  ||	       / y )
N)  r  r#   d   r   i  i  )r   r  r  rv   r   )r%   r   r&   rx   r`  ra  r   copyr   r   testingr   r   rz   )
r;   r'   r   rY  jAmra   rM  	first_resnext_ress
             r(   test_gh18086zTestExpM.test_gh18086   s     HHZu-ii##C(LLC%LLC%**S/!Q$XXm511"2&1AvvG	


,,T)_a@q 	FAAwHJJ00HE	Fr*   N)rY   rZ   r[   r  r  r   r   r   r   r   r   r   r   r   r   r   r&   r%   r   r   r   r  r  r  r   r   	fail_slowr  r\   r*   r(   r  r    s    91 [[VdD$eUE%RS[[T3rzz7BLL"QR[[Wvv&67- 8 S T-<(. [[[[1F  Fr*   r  c                       e Zd Zd Zd Zd Zd Zej                  j                  ej                  j                  d      d               Zy)	TestExpmFrechetc                    t        j                  g dg dg dg dgt              }t        j                  ddgdd	ggt              }t        j                  d
dgddggt              }t        j                  j                  |      }t        j                  j                  |      d ddd f   }i ddiddifD ]*  }t        ||fi |\  }}t        ||       t        ||       , y )NrB   r   r   ru   r   rs   r`   r  r   r   rB   r   r   r   r   rs   r#   rB   r   r   rs   r   ru   r`   r  methodSPSblockEnlarge)r%   r   r&   r   r}   r   r   r   )	r;   r   r'   r   expected_expmexpected_frechetkwargsobserved_expmobserved_frechets	            r(   test_expm_frechetz!TestExpmFrechet.test_expm_frechet  s    HH	
  HHFF  HHFF  ))!, <<,,Q/AB7HU+h~-FG 	@F.:1a.J6.J+M+M=9,.>?	@r*   c                    t        j                  g dg dg dg dgt              }t        j                  ddgdd	ggt              }t        j                  d
dgddggt              }t        j                  j                  |d      }g d}t        |d d |dd        }|D ]  \  }}t        j                  j                  j                  |   }	t        j                  j                  j                  |   }
d|	|
z   z  }||z  }||z  }||z  }||z  }t        j                  j                  |      }t        j                  j                  |      d ddd f   }t        ||      \  }}t        ||       t        ||        y )Nr  r  r  r  r#   rB   r   r   rs   r   ru   r`   r  )rB   r   r   r`   rv            r   r   )r%   r   r&   r   r}   r   zip_expm_frechetell_table_61r   r   r   )r;   
M_original
A_original
E_originalA_original_norm_1selected_m_listm_neighbor_pairsmambell_aell_btarget_norm_1r   r   r'   r   r  r  r  r  s                       r(   test_small_norm_expm_frechetz,TestExpmFrechet.test_small_norm_expm_frechet/  s   XX	
 
 XXFF 
 XXFF 
 "LL--j!<5s3_QR5HI& 	@FBLL..;;B?ELL..;;B?E55=1M!$55E
"A
"A
"A!LL--a0M$||003BQBF;.:1a.@+M+M=9,.>?	@r*   c           	         t         j                  j                  d      }t         j                  j                  t         j                  j                  t         j                  j
                  t         j                  j                  f}d}t        |      D ]D  }||j                  d         }|j                         }|j                  dd      } |||f      } |||f      }	t        j                  j                  |d      }
||
z  }||z  }||	z  }t        j                  t        j                  ||g      t        j                  t        j                  |      |g      g      }t        j                  j!                  |      }t        j                  j!                  |      d ||d f   }t#        ||      \  }}t%        ||d	       t%        ||d
	       G y )Nl   ]"1 r  ru   r      r^  rB   gHj>r   gHz>)r%   rx   r`  uniformnormalstandard_cauchyexponentialrz   rc  ra  r   r}   r   vstackhstack
zeros_liker   r   r   )r;   r   rfuncsntestsrY  rfuncr  r   r  r  r  r   r'   r   r   r  r  r  r  s                      r(   	test_fuzzzTestExpmFrechet.test_fuzzP  s   ii##$45 		!!		  		))		%%	'
 v 	KA3::a=)EOO-MQ#AQqE*JQqE*J % 1 1*a @!$55E
"A
"A				1a&!		2==+Q/02 3A "LL--a0M$||003BQBF;.:1a.@+M+M=tD,.>TJ#	Kr*   c                 <   t        j                  ddgddggt              }t        j                  ddgdd	ggt              }t        j                  j                  |d
       t        ||d      \  }}t        ||d      \  }}t        ||       t        ||       y )Ng]؉??gvP?g^?guÝ?r#   gS,?g| @gJt?g~3?rB   r  r  r  )r%   r   r&   r   r}   r   r   r   )r;   r'   r   sps_expmsps_frechetblockEnlarge_expmblockEnlarge_frechets          r(   test_problematic_matrixz'TestExpmFrechet.test_problematic_matrixl  s    HHZ(Z(   HHZ(Z(   	!Q ,1U!$+2>1^3-//"34%9:r*   zthis test is deliberately slowr   c                    d}t         j                  j                  ||f      }t         j                  j                  ||f      }t        ||d      \  }}t        ||d      \  }}t	        ||       t	        ||       y )Ni  r^  r  r  r  )r%   rx   r  r   r   )r;   r   r'   r   r  r  r  r  s           r(   test_medium_matrixz"TestExpmFrechet.test_medium_matrix~  s     II!!1v!.II!!1v!. ,1U!$+2>1^3-//"34%9:r*   N)rY   rZ   r[   r  r  r  r  r   r   slowskipr  r\   r*   r(   r  r    sS    @.@BK8;$ [[[[=>
; ? 
;r*   r  c                     t        j                  || j                        }t        |      }||z  ||z  z  }t	        | |z         }t        ||z
        ||z  z  }	|	 S N)r%   reshaper   r   r   )
r'   A_normr   X_normepsrT  p_normperturbationX_primescaled_relative_errors
             r(   _help_expm_cond_searchr    sa    


1aggA!WF7fvo.L1|#$G 1-#>!!!r*   c                     | t         j                  j                  |      t         j                  j                  |       z  z  S r  )r   r}   r   )r'   r   s     r(   _normalized_liker    s0    !!!$u||'8'8';;<<r*   c                 \     | |      } | ||z         }t        ||z
        t        |      z  S r  )r   )r  r'   r  r   r  s        r(   _relative_errorr    s2    	!AL !G!tAw&&r*   c                   V    e Zd Zd Zd Zd Zej                  j                  d        Z	y)TestExpmConditionNumberc                     t         j                  j                  d       t        dd      D ]9  }t         j                  j	                  ||      }t        |      }t        d|       ; y )Nrr   rB   ru   r   )r%   rx   ry   rz   r{   r   r
   )r;   r   r'   kappas       r(   test_expm_cond_smokez,TestExpmConditionNumber.test_expm_cond_smoke  sN    
		tq! 	(A		1%AaLEa'	(r*   c                 t    t        j                  g dg dg dg dg      }t        |      }t        d|       y )N)g(gٙBgx@g  =g ZdB)r   gzNV7g@g  2p)r   r   gᙥT g?W[E@)r   r   r   gT!g yhG)r%   r   r   r
   )r;   r'   r  s      r(   test_expm_bad_condition_numberz6TestExpmConditionNumber.test_expm_bad_condition_number  s6    HHI</#	  !$&r*   c                 @   t         j                  j                  d       t        j                  ddd      D ]7  }t        j                  |gg      }t        t        |      t        |             9 t        j                  ddd      D ]7  }t        j                  |gg      }t        t        |      t        |             9 t        d      D ]M  }t         j                  j                  d	d	      }t        t        |      t        j                  |      d
          O y )N90  r  r   r  )numr?  r   r  rB   r   )r%   rx   ry   linspacer   r   r   absr|   rz   r{   r   )r;   xr'   rY  s       r(   test_univariatez'TestExpmConditionNumber.test_univariate  s    
		uR+ 	2A1#AIaL#a&1	2 R+ 	2A1#AIaL#a&1	2 r 	@A		1%AIaL"++a.*>?	@r*   c           	         t         j                  j                  d      }d}d}t        |      D ]  }|j	                  dd      }|j                  ||      }t        j                  j                  |      }t        |      }t        j                  j                  |      }	t        |      }
t        j                  t        ||||	|      }t        j                  ||z        }t        ||d      }|j                   } ||      }|t#        t        j$                  ||j&                        |      z  }t)        t        ||      }t+        || |z         t        d      D ]c  }|t#         |j
                  |j&                   |      z  }t+        t        |      t        |             t)        t        ||      }t-        ||       e t-        |dd|z  z   |z  |
z          y )	Nr  rl   r  r   r   zL-BFGS-Br  rB   )r%   rx   r   rz   randintr{   r   r}   r   r   r   	functoolspartialr  r   r    r  r  r  r   r  r   r
   )r;   r   r  rd  rY  r   r'   r  r   r  r  r  guessoutxoptyoptp_bestp_best_relerrr  p_randp_rand_relerrs                        r(   test_expm_cond_fuzzz+TestExpmConditionNumber.test_expm_cond_fuzz  s   ii##E*x 	HAAq!A		!QA\\&&q)FQA\\&&q)FaLE !!"8vq&#/AGGAaCLE1eJ7C55DT7D+BJJtQWW,EqIIF+D!V<MMD53;7 1X @/			1770CQGGVd6l; /a @!-?	@ ma!C%i3->-FG?	Hr*   N)
rY   rZ   r[   r  r  r  r   r   r  r  r\   r*   r(   r  r    s2    ('
@ [[#H #Hr*   r  c                   *    e Zd Zd Zd Zd Zd Zd Zy)TestKhatriRaoc           
      2   t        t        ddgddgg      t        ddgddgg            }t        |t        dd	gdd
gddgddgg             t        t        j                  ddg      t        j                  ddg            }t        |j
                  d       y )NrB   r   r   ru   r   rs   r`   r     r  r            )ru   r   )r   r   r   r%   r   r   r;   r<   bs      r(   
test_basiczTestKhatriRao.test_basic  s    uq!fq!f-.q!fq!f-.0 	1eaW&'W&("X&("X%/ 0 	1
 rxxA'1a&)9:177F+r*   c                     t        j                  t              5  t        g dg dg      }t        ddgddgg      }t	        ||       d d d        y # 1 sw Y   y xY w)NrB   r   r   ru   r   rs   rB   r   r   ru   r   raises
ValueErrorr   r   r  s      r(   test_number_of_columns_equalityz-TestKhatriRao.test_number_of_columns_equality  s]    ]]:& 	y " #A1v1v  Aq!	 	 	s   /AAc                    t        j                  t              5  t        g d      }t        g d      }t	        ||       d d d        t        j                  t              5  t        g d      }t        g dg dg      }t	        ||       d d d        t        j                  t              5  t        g dg dg      }t        g d      }t	        ||       d d d        y # 1 sw Y   xY w# 1 sw Y   bxY w# 1 sw Y   y xY w)Nr  r  )r`   r  rv   r  r  s      r(   test_to_assure_2d_arrayz%TestKhatriRao.test_to_assure_2d_array  s    ]]:& 	i Ai Aq!		 ]]:& 	i A A q!	 ]]:& 	 A i Aq!	 		 		 		 	s#   'C""+C..+C:"C+.C7:Dc                 L   t        ddgddgg      }t        ddgddgg      }t        ||      }t        j                  t	        |j
                  d         D cg c]&  }t        j                  |d d |f   |d d |f         ( c}      j                  }t        ||       y c c}w )	NrB   r   r   ru   r   rs   r`   r  )	r   r   r%   r  rz   r   kronr   r   )r;   r<   r  res1rp  res2s         r(   test_equality_of_two_equationsz,TestKhatriRao.test_equality_of_two_equations  s    Aq6Aq6"#Aq6Aq6"#!Qyy#(#46 ''!AqD'1QT73 6 778q 	 	4&6s   +B!c                 X   t        j                  d      }t        j                  d      }t        ||      }t        |t        j                  d             t        j                  d      }t        j                  d      }t        ||      }t        |t        j                  d             y )N)r   r   )r   r   )r   r   )r   r   )r  r   )r%   r   r   r   )r;   r<   r  ress       r(   r   zTestKhatriRao.test_empty  sx    HHVHHVARXXf-.HHVHHVARXXg./r*   N)rY   rZ   r[   r  r  r  r#  r   r\   r*   r(   r  r    s    
,2'	0r*   r  )6__doc__r  numpyr%   r   r   r   r   numpy.testingr   r   r	   r
   r   r   r   scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   scipy.linalg._matfuncsr   scipy.linalg._matfuncs_inv_ssqr   scipy.linalg._expm_frechetscipy.optimizer    r)   r,   r^   r   rP  r  r  r  r  r  r  r  r\   r*   r(   <module>r.     s      , ,P P  A A A A A + 6 E ! #*' 'Vl0 l0^~# ~#BvH vHrOF OFdt; t;n"='BH BHJB0 B0r*   