
    ^Mh                        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          Z5dS )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    `/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/linalg/tests/test_matfuncs.py%_get_al_mohy_higham_2012_experiment_1r)      sO     	"""   	 &+		, 	, 	,A
 H    c                   &    e Zd Zd Zd Zd Zd ZdS )	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          ||           d S )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   s    000000...111---	/ 0 0
 QQQOOO000OOONNN	P Q Q
 !HH!!B'''''r*   c                 ^    t          g dg dg dg dg          }t          |d           d S )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@   sA    ;;;yyy999=>>aer*   c                 d    t          g dg dg dg dg df          }t          |d           d S )Nr.   r/   r2   r3   r4   FrD   rF   rG   s     r(   test_defective2zTestSignM.test_defective2E   s^    &&&'''((('''$$$& ' ' 	aer*   c           
      p    t          g dg dg dg dg dg dg dg          }t          |d	           d S )
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   sp    1111110000000001110002 3 3 	aer*   N)__name__
__module____qualname__r?   rH   rJ   rX    r*   r(   r,   r,   0   sP        ( ( (  
      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                            d          ej                            deeej        eej        g          d                         Zej        j        ej                            deeej        eej        g          d                         ZdS )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           d S )NrL   rN   rR   rT   rU   rV   rW      g@y                FrD   )r   r   r   )r;   r<   ms      r(   r?   zTestLogM.test_nils]   s    1111110000000001110002 3 3 a[[_R"QUr*   c                     t                      }t          |d          \  }}t          |          }t          ||dd           d S )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   sM     233AE***F||ad??????r*   c                     t                      }t          |t          j        d          \  }}t	          |          }t          t          j        ||dd                      d S )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   sa     23326666
DJ''BKadGGGGHHHHHr*   c                    t           j                            d           t          dd          D ]}t           j                            ||          }t          j        ddd          D ]}||z  }t           j                            |          }d| d| }t          |d	
          \  }}|	                    |          }	t          |	|           t          |d	
          \  }
}t          |
          }t          |||           d S )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 	GAA..JRA.. G G& I%%a((-q--!-- !&ae 4 4 4%,[[%9%9" 2A666  $AE222$(LL! 11gFFFFFG	G 	Gr*   c                    t           j                            d           t          dd          D ]}t           j                            ||          dt           j                            ||          z  z   }t          j        ddd          D ]:}||z  }t          |d	          \  }}t          |          }t          ||           ;d S 
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! 	1 	1AA..biooa6K6K1KKJRA.. 1 1&#AE222#F||a0000	1	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                            |          }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            *d S )
NFDGrB   r         c              3   :   K   | ]}|j         p
|j        d k     V  dS r   Nimagreal.0ws     r(   	<genexpr>zFTestLogM.test_logm_type_preservation_and_conversion.<locals>.<genexpr>   /      <<QAF0afqj<<<<<<r*   r#   FrD   )scipyr}   r~   r	   anyr%   r   r&   r   r$   charcomplex)r;   complex_dtype_charsmatrix_as_listr   r'   rg   rh   s          r(   *test_logm_type_preservation_and_conversionz3TestLogM.test_logm_type_preservation_and_conversion   sy    .Q!Q Q!Q Q!Q Q!Q 	" 	> 	>N $$^44A<<!<<<<<<=== u555A...LFDFL%-@@AAA w777A...LFDFL%)<<=== .6666A...LFDFL%)<<====/	> 	>r*   c                    g dg dg dg}t           t          fD ]}t          j        ||          }t          j                            |          }t          dt          j        |j	                  
                                k                t          |d          \  }}t          t          j        |j        t          j                             t          t!          |          |           d S )N)rB   rB   r   )r   rB   rB   )rB   r   rB   r#   {Gz?FrD   )r&   r   r%   r   r   r}   r~   r	   absoluter   sumr   
issubdtyper$   inexactr   r   )r;   r   dtXr   Yrh   s          r(   test_complex_spectrum_real_logmz(TestLogM.test_complex_spectrum_real_logm   s     YY			999-. 	( 	(B"%%%A$$Q''AD2;qv..2244455515)))GAtBM!'2:66777DGGQ''''	( 	(r*   c                    ddgddggddgddggfD ]n}t           t          fD ]]}t          j        ||          }t	          |d          \  }}t          t          j        |j        t          j                             ^od S )NrB   r   r#   FrD   )	r&   r   r%   r   r   r	   r   r$   complexfloating)r;   r   r   r'   rg   rh   s         r(   test_real_mixed_sign_spectrumz&TestLogM.test_real_mixed_sign_spectrum   s     Q!R!Q!Q " 	I 	IA Wn I IHQb)))#AE222flB4FGGHHHHI	I 	Ir*   c                 $   t          j        ddgddgg          }t          j        ddgddgg          }||j        ||j        fD ]J}t          j        }t          |t          |d          \  }}t          |          }t          ||d           Kd S )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    Hq!fr2h'((JAA'((ACAC 	. 	.A0K"#3T15IIIGAtQAAqu-----		. 	.r*   c                     t          j        dgg          }t          j        }t	          |t
          |d          \  }}t          |          }t          ||d           d S )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   s_    HvhZ  ,F/quEEE4GG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           d S )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   sV   Vb!Ws^rufSj!_-Q////Q////!Wq#hhslAbeG$q#be)C-&89Q////Q////!Wq#hhslACIcM 23Q////Q//////r*   c                     d}t          j        ||f          t          j        |          z   }d|j        _        t          |           d S )N   F)r%   onesr   flags	writeabler   r;   r   r<   s      r(   test_readonlyzTestLogM.test_readonly   s>    GQFOObk!nn,!Qr*   z6ValueError: attempt to get argmax of an empty sequencereasonr   c                     t          j        d|          }t          |          }t          j        d|          }t          |          }|j        dk    sJ |j        |j        k    sJ d S Nr   r   r#   r   )r%   emptyr   eyeshaper$   )r;   r   r<   log_aa0log_a0s         r(   
test_emptyzTestLogM.test_empty   sp     HV2&&&QVAR   b{f$$$${fl******r*   r$   c                    t          j        t          d          5  t          j        t                    5  t	          t          j        d|                     d d d            n# 1 swxY w Y   d d d            d S # 1 swxY w Y   d S )Nzlogm result may be inaccurate)matchr   r   r#   )pytestwarnsRuntimeWarningr   r   r%   zeros)r;   r$   s     r(   test_no_ZeroDivisionErrorz"TestLogM.test_no_ZeroDivisionError   s    l>1PQQQ 	0 	0l566	0 	0&...///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0s4   A>$A&A>&A*	*A>-A*	.A>>BB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 I IG G G*1 1 1> > ><
( 
( 
(	I 	I 	I [. . . [* * *0 0 0   [VWW[TC
GR\#RSS+ + TS XW+ [[WsE2:w&UVV0 0 WV 0 0 0r*   r^   c                   4   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                            d          d             Zd Zd Zd Zd Zd Zd Zej                            deeej        e ej!        g          d             Z"dS )	TestSqrtMc                 D   t           j                            d          }t          dd          D ]o}|                    ||          }t          j        ddd          D ]@}||z  }t          |d          \  }}|                    |          }t          ||           Apd S )	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    i##D))q! 	7 	7A1aJRA.. 7 7& %ae 4 4 4%,[[%9%9" 2A6666	7	7 	7r*   c                 x   t           j                            d          }t          dd          D ]}|                    ||          d|                    ||          z  z   }t          j        ddd          D ]@}||z  }t          |d	          \  }}|                    |          }t          ||           Ad S r   r   r   s	            r(   r   z(TestSqrtM.test_round_trip_random_complex  s    i##D))q! 	7 	7A1a2		!Q+??JRA.. 7 7& %ae 4 4 4%,[[%9%9" 2A6666	7	7 	7r*   c                    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	          ||          |           d S )	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   !WW;;;a!9a!999   KKKr!AJqAJII     GAJ!#b**Q///AEQ///2!#c#,,q111AEQ///2!#c#,,q111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ddgddggfD ](}t           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            *d S )
Nr   rB   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS 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  s    .Q!Q Q!Q Q!Q Q!Q Q!Q " 	? 	?N $$^44A<<!<<<<<<=== u555A!!%000MGTGM&.AABBB w777A!!%000MGTGM&*==>>> .6666A!!%000MGTGM&*==>>>>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                            |          }t          t	          d |D                                  t          j        |t          	          }t          |d
          \  }}t          |j	        j
        |v            t          j        |t          	          }t          |d
          \  }}t          |j	        j
        |v            d S )Nr   rB   r   r   r   rB   r   r   r   rB   rB   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r(   r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>\  /      88,!&1*888888r*   r#   FrD   )r   r}   r~   r	   r   r%   r   r   r   r$   r   r&   r   s          r(   9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumzCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumS  s"   -Q!R!Q!Q IIIyyy13 	? 	?N $$^44AC88a88888999 w777A!!%000MGTGM&*==>>> u555A!!%000MGTGM&*==>>>>#	? 	?r*   c                    t           j                            d           t          dd          D ]}t           j                            ||          dt           j                            ||          z  z   }t          |d|          \  }}t          |t           j        	                    |d                     t          dd          D ]'}t          |d|          \  }}t          ||           (d S )	Nrr   rB      r   Fr   r   
   )
r%   rx   ry   rz   randr{   r   r   r}   matrix_power)r;   r   r'   A_sqrtm_defaultrh   r   A_sqrtm_news          r(   test_blocksizeszTestSqrtM.test_blocksizesh  s    
	tq! 	> 	>A	q!$$r")//!Q*?*?'??A$)!%1$E$E$E!OTAry55oqIIJJJ"1b\\ > >	$)!%9$M$M$M!T====>		> 	>r*   c                     t                      }t          |d          \  }}|                    |          }t          ||d           t          t	          j        |          t	          j        |                     d S )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  sq    133ae,,,{{7++ad3333--rwqzz:::::r*   c                     t           t          fD ]k}t          j        g dg dg dg dg|          }t	          |d          \  }}t          t          j        |                                                     ld S )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{  s    u* 	- 	-B	 &(	) ) )A
 "!%000MGTBHW%%))++,,,,	- 	-r*   c                 x   t           t          fD ]}t          j        g dg dg dg|          }t          j        g dg dg dg|          }t	          ||                    |                     t          |d          \  }}t          t          j        |          	                                           d S )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!%%((+++ "!%000MGTBHW%%))++,,,,	- 	-r*   c                     t           j                            d           t           j                            dd          }t	          |d          }t          |                    |          |           d S )Nrr   r   TrD   )r%   rx   ry   r  r   r   r   )r;   r'   r   s      r(   	test_dispzTestSqrtM.test_disp  s]    
	tINN1a  !$a!$$$$$r*   c                     ddgddgg}ddgddgg}t          t          j        ||          |d	           t          t          |          |d	           d S )
N               @ru   r                       ?      ?r         ?      rc   r   )r   r%   r   r   r;   r   Rs      r(   r   z0TestSqrtM.test_opposite_sign_complex_eigenvalues  sf    !Wq#hAYD	"q!ae4444a!%000000r*   c                 ~   t          j        g dg dg dg dg          }t          j        t          d          ddt          d          gg dg dt          d          ddt          d          gg          }t          t          j        ||          |d           t          t          |          |d           d S )N)rB   r   r   rB   r  r   r   rc   r   )r%   r   r   r   r   r   r  s      r(   test_gh4866zTestSqrtM.test_gh4866  s    Hlll"ll"ll"ll$ % % HtCyy!QS		2"ll"llCyy!QS		24 5 5 	q!ae4444a!%000000r*   c                    t          j        g d          }t          j        t          d          ddg          }t          t          j        ||          |d           t          t          |          |d           d S )N)r   rB   r   r   rB   r   rc   r   )r%   diagr   r   r   r   r  s      r(   test_gh5336zTestSqrtM.test_gh5336  sp    GIIIGT!WWaO$$q!ae4444a!%000000r*   c                     t          j        d          }t          j        d          }t          t          j        ||          |d           t          t	          |          |d           d S )Nr   rc   r   )r%   r   r   r   r   r  s      r(   test_gh7839zTestSqrtM.test_gh7839  s`    HVHVq!ae4444a!%000000r*   zfailing on macOS after gh-20212r   c                     t          j        d          }|                    d           t          j        |d           t          j        t          |                    sJ d S )N)   r(  gGz?rB   )r%   r   fillfill_diagonal	isrealobjr   r;   r   s     r(   test_gh17918zTestSqrtM.test_gh17918  sU    HX	t
A|E!HH%%%%%%%r*   c                 &   t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ d S Nr  r  r#   )	r%   r   uint8r   r$   float64uint16uint32uint64r,  s     r(   -test_data_size_preservation_uint_in_float_outz7TestSqrtM.test_data_size_preservation_uint_in_float_out  s    HXRX...Qxx~++++HXRY///Qxx~++++HXRY///Qxx~++++HXRY///Qxx~++++++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          j        dt           j                  }t          |          j        t           j        k    sJ d S r/  )	r%   r   int8r   r$   r2  int16int32int64r,  s     r(   ,test_data_size_preservation_int_in_float_outz6TestSqrtM.test_data_size_preservation_int_in_float_out  s    HXRW---Qxx~++++HXRX...Qxx~++++HXRX...Qxx~++++HXRX...Qxx~++++++r*   c                 V   t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ d S )Nr   ru   r   r#   )	r%   r   r8  r   r$   
complex128r9  r:  r;  r,  s     r(   +test_data_size_preservation_int_in_comp_outz5TestSqrtM.test_data_size_preservation_int_in_comp_out  s    Hq!fq"g&bg666Qxx~....Hq!fq"g&bh777Qxx~....Hq!fq"g&bh777Qxx~....Hq!fq"g&bh777Qxx~......r*   c                 T   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          rDt          j        dt           j                  }t          |          j        t           j        k    sJ d S d S )Nr0  r#   float128)	r%   r   float16r   r$   r   r2  hasattrrB  r,  s     r(   .test_data_size_preservation_float_in_float_outz8TestSqrtM.test_data_size_preservation_float_in_float_out  s    HXRZ000Qxx~++++HXRZ000Qxx~++++HXRZ000Qxx~++++2z"" 	0555A88>RZ////	0 	0//r*   c                    t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          j        ddgddggt           j                  }t          |          j        t           j        k    sJ t          t           d          r_t          t           d          rLt          j        ddgddggt           j
                  }t          |          j        t           j        k    sJ d S d S d S )Nr   ru   r   r>  r#   rB  
complex256)r%   r   rC  r   r$   r   r   r2  r?  rD  rB  r,  s     r(   -test_data_size_preservation_float_in_comp_outz7TestSqrtM.test_data_size_preservation_float_in_comp_out  s7   Hq!fq"g&bj999Qxx~----Hq!fq"g&bj999Qxx~----Hq!fq"g&bj999Qxx~....2z"" 	3wr<'@'@ 	31a&1b'*"+>>>A88>R]2222	3 	3 	3 	322r*   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          rJt          j        ddgddggt           j                  }t          |          j        t           j        k    sJ d S d S )Nr  ru   r   r  r#   rG  )r%   r   r   r   r$   r?  rD  rG  r,  s     r(   ,test_data_size_preservation_comp_in_comp_outz6TestSqrtM.test_data_size_preservation_comp_in_comp_out  s    Hr1g3x(===Qxx~----Hr1g3x(>>>Qxx~....2|$$ 	32q'As8,BMBBBA88>R]2222	3 	322r*   r   c                     t          j        d|          }t          |          }t          j        d|          }t          |          }|j        dk    sJ |j        |j        k    sJ d S r   )r%   r   r   r   r   r$   )r;   r   r<   sr   s0s         r(   r   zTestSqrtM.test_empty   sn    HV2&&&!HHVAR   2YYw&    w"(""""""r*   N)#rY   rZ   r[   r   r   r   r   r  r	  r  r  r  r  r   r!  r$  r&  r   r   r   r-  r6  r<  r@  rE  rH  rJ  r   r   r&   r%   r   r   r   r   r\   r*   r(   r   r   
  s       7 7 77 7 72 2 2*? ? ?>? ? ?*	> 	> 	>; ; ;	- 	- 	-- - -"% % %1 1 1
1 
1 
11 1 11 1 1 [?@@& & A@&, , ,, , ,/ / /	0 	0 	0	3 	3 	33 3 3 [TC
GR\#RSS# # T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                            d	
          d             Zd ZdS )TestFractionalMatrixPowerc                    t           j                            d           t          dd          D ]}t          dd          D ]}t           j                            ||          dt           j                            ||          z  z   }t          j        ddd          D ]J}||z  }t          |d|z            }t           j                            ||          }t          ||           Kd S )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! 	5 	5A1a[[ 5 5Y__Q22R")//!Q:O:O5OO
[Q22 5 5E"U*A4Q!<<F#%9#9#9&!#D#DL#L!4444	55	5 	5r*   c                    t           j                            d           t          dd          D ]}t          dd          D ]}t           j                            ||          }t          j        ddd          D ]J}||z  }t          |d|z            }t           j                            ||          }t          ||           Kd S )Nrr   rB   r   rt   ru   rv   rQ  rR  s           r(   r   z6TestFractionalMatrixPower.test_round_trip_random_float  s    
 		tq! 	5 	5A1a[[ 5 5Y__Q22
[Q22 5 5E"U*A4Q!<<F#%9#9#9&!#D#DL#L!4444	55	5 	5r*   c                    t           j                            d           dD ]}t          d          D ]}t           j                            ||          dt           j                            ||          z  z   }t          |d          }t           j                            |d          }t          ||           t          |d          }t           j                            |d          }t          ||           t          |d	          }t           j                            |d
          }t          ||           	d S )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2YY & &IOOAq))BA1F1F,FF5a==!y55k1EE<000+At44I**;<<1%%%+As33I**;;;1%%%%&	& 	&r*   c                 L   t           j                            d          }d}t          |          D ]}|                    dd          }|                                }t          j        |                    dd                    }|                    ||g          }ddg|                    d	                   r|d
|                    ||g          z  z   }||z  }t          ||          }t          |d          \  }	}
t          |	|z            }t          ||           d S )Nl   fm1    rB   r   rt   sizeTFr   r   rD   )r%   rx   default_rngrz   integersexpchoicer   r   r   r   )r;   r   nsamplesrX  r   rS  matrix_scaler'   A_powerrg   rh   A_power_expm_logms               r(   test_random_matrices_and_powersz9TestFractionalMatrixPower.test_random_matrices_and_powers8  s'    i##$455x 	8 	8AQ""A

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

A
''Ae}SZZ]]+ 5SZZaVZ4444L A
 .a33G...LFD $VaZ 0 0G%67777%	8 	8r*   c                    t                      }t          |t          j        d          \  }}t	          |d          \  }}t          j        |d          }t          |d          }t          ||d           t          ||           t          ||           dD ]m}t          ||          }t          |d|z            }t          ||d           t          t          j	        |d          t          j	        |d                     nd S )	NFrD   r   gdy=r  )r   g?rB   r   )
r)   r   r%   r   r   r   _remainder_matrix_powerr   r   r  )	r;   r'   A_funm_sqrtrh   r   A_rem_powerre  rS  ri   s	            r(   r  z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1Q  s   133 !BG%888Tae,,,'?3GG)!S11W59999)))---  	E 	EA-a33G27AaC@@LL!$7777BGL!44bgammDDDD		E 	Er*   c                 r   t           j                            d           t           j                            d          dt           j                            d          z  z   D ]T}t	          d          D ]B}t          j        ||          }|t          j        |           z  dz
  }t          ||           CUd S )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$$rBIOOB,?,?'?? 	8 	8A1XX 8 8.Fq!LL
"'1"++-1

J77778	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                            |          }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            ֐#d S )	Nr   rB   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r(   r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>{  r   r*   333333rW  gffffff
@r#   )r   r}   r~   r	   r   r%   r   r&   r   r$   r   r   r;   r   r   r   rS  r'   re  s          r(   %test_type_preservation_and_conversionz?TestFractionalMatrixPower.test_type_preservation_and_conversionm  s   
 .Q!Q Q!Q Q!Q Q!Q 	" 	C 	CN $$^44A<<!<<<<<<=== , C C H^59991!Q77*2EEFFF H^7;;;1!Q77*.AABBB XnE::::1!Q77*.AABBBBC	C 	Cr*   c                    d}ddgddggddgddggg dg dg dgfD ]}t           j                            |          }t          t	          d |D                                  d	D ]}t          j        |t          
          }t          ||          }t          |j	        j
        |v            t          j        |t          
          }t          ||          }t          |j	        j
        |v            d S )Nr   rB   r   r   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r(   r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>  r   r*   ru  r#   )r   r}   r~   r	   r   r%   r   r   r   r$   r   r&   rx  s          r(   3test_type_conversion_mixed_sign_or_complex_spectrumzMTestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum  s1   -Q!R!Q!Q IIIyyy13 	C 	CN $$^44AC88a88888999 , 
C 
C H^7;;;1!Q77*.AABBB H^59991!Q77*.AABBBB
C	C 	Cr*   zToo unstable across LAPACKs.r   c                    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 ]E}t	          ||          }t          t          j        |                                                     FdD ]5}t	          ||          }t	          |d|z            }t          ||           6d S )Nr   rB   r   r   rs   r  )r   rB   rB   )r   r   rB   r#   )gffffffrw  rv  g)rW  gzG?)	r&   r   r%   r   r   r	   r  r  r   )r;   r   newtyper'   rS  re  ri   s          r(   test_singularz'TestFractionalMatrixPower.test_singular  s"    Q!Q Q!Q Q!Q IIIzzz2	4 	5 	5N "7+ 5 5H^7;;;1 5 5A5a;;GBHW--11334444$ 5 5A5a;;G#:7AaC#H#HL#L!444455	5 	5r*   c                     ddgddgg}ddgddgg}t          t          j        ||          |d	           t          t          |d
          |d	           d S )Nr  ru   r   r  r  r   r  rc   r   r   )r   r%   r   r   r  s      r(   r   z@TestFractionalMatrixPower.test_opposite_sign_complex_eigenvalues  sk    !Wq#hAYD	"q!ae4444/377GGGGGGr*   N)rY   rZ   r[   r   r   rZ  rg  r  rr  ry  r|  r   r   r   r  r   r\   r*   r(   rO  rO    s        	5 	5 	55 5 5& & &$8 8 82E E E(8 8 8!C !C !CFC C C2 [<==5 5 >=5&H H H H Hr*   rO  c            
          e Zd Zd Zd Zej                            dee	e
eeeeg          ej                            deeej        eej        g          ej                            dddg          d                                     Zd	 Zd
 Zd Zej        j        ej                            d          d                         ZdS )TestExpMc                 v    t          ddgddgg          }t          t          |          ddgddgg           d S )NrA   r   rB   )r   r   r   rG   s     r(   	test_zerozTestExpM.test_zero  sC    Bq61Q%.!!!$q''Aa5!A-88888r*   c                     t          d          }t          |t          j        t          j        gg                     d S )NrB   )r   r   r%   r   r   )r;   elts     r(   test_single_eltzTestExpM.test_single_elt  s3    1ggRXvh//00000r*   funcr   r   r   )rB   rB   c                     t          j        ||          }t          j        d|          } ||          } ||          }|j        |k    sJ |j        |j        k    sJ d S )Nr#   r0  )r%   r   r   r$   )r;   r  r   r   r'   A0resultresult0s           r(   test_small_empty_matrix_inputz&TestExpM.test_small_empty_matrix_input  st     HU"%%%Xhb)))a$r((|u$$$$|w},,,,,,r*   c                    t           j        }t          ddgddgg          }|dz  dz   d|z  z  }|dz  dz
  |z  }t          t	          |          t          ||g|dz  |gg                     t	          |                    t           j                            j        j        dk    sJ t	          |                    t           j	                            j        j        dk    sJ d S )NrB   ru   r   r   f)
r%   r   r   r   r   astyper   r$   r   r   )r;   r   r<   aabbs        r(   test_2x2_inputzTestExpM.test_2x2_input  s    DAq6Aq6"##dQh1dQh\QR2a4*'=!>!>???AHHR\**++16#====AHHRZ(())/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	          |          |           d S )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   DH1v1v&1v2w'1v1v&1v1v&1vBx(	* 25	6 6 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                 l    d}t          j        ||f          }d|j        _        t	          |           d S )Nr`   F)r%   r   r   r   r   r   s      r(   r   zTestExpM.test_readonly  s1    GQFOO!Qr*   r   c                    t          j        dt                    }t           j                            d          }|                    ddd          }|                    ddd          }|                    d          |||f<   t          j        dt                    }|                                |d<   t          |          \  }}|dk    sJ t          |          }t           j
                            t          |          |           t          d	          D ]1}t          |          }	t           j
                            ||	           2d S )
N)  r  r#   d   r   i  i  )r   r  r  rv   r   )r%   r   r&   rx   r_  r`  r   copyr   r   testingr   r   rz   )
r;   r'   r   rX  jAmra   rL  	first_resnext_ress
             r(   test_gh18086zTestExpM.test_gh18086   s#    HZu---i##C((LLC%%LLC%%**S//!Q$Xm51111"2&&1AvvvvGG	

,,T)__a@@@q 	F 	FAAwwHJ00HEEEE	F 	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 9 91 1 1 [VdD$eUE%RSS[T3rz7BL"QRR[Wvv&677- - 87 SR TS-< < <( ( (.   [[1F F  F F Fr*   r  c                       e Zd Zd Zd Zd Zd Zej        j	        ej        
                    d          d                         ZdS )	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                            |          }t          j                            |          d ddd f         }i ddiddifD ]3}t          ||fi |\  }}t          ||           t          ||           4d S )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  sL   HLLLLLLLL	
    HFF    HFF    ))!,, <,,Q//ABB7HU+h~-FG 	@ 	@F.:1a.J.J6.J.J+M+M=99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                            |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        	                    |          }t          j        	                    |          d ddd f         }t          ||          \  }}t          ||           t          ||           d S )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   XLLLLLLLL	
   
 XFF   
 XFF   
 "L--j!<<555ss3_QRR5HII& 	@ 	@FBL.;B?EL.;B?E55=1M!$55E
"A
"A
"A!L--a00M$|0033BQBF;.:1a.@.@+M+M=999,.>????	@ 	@r*   c           	         t           j                            d          }t           j        j        t           j        j        t           j        j        t           j        j        f}d}t          |          D ]d}||                    d                   }|                                }|	                    dd          } |||f          } |||f          }	t          j                            |d          }
||
z  }||z  }||	z  }t          j        t          j        ||g          t          j        t          j        |          |g          g          }t          j                            |          }t          j                            |          d ||d f         }t#          ||          \  }}t%          ||d	           t%          ||d
	           fd S )Nl   ]"1 r  ru   r      r]  rB   gHj>r   gHz>)r%   rx   r_  uniformnormalstandard_cauchyexponentialrz   rb  r`  r   r}   r   vstackhstack
zeros_liker   r   r   )r;   r   rfuncsntestsrX  rfuncr  r   r  r  r  r   r'   r   r   r  r  r  r  s                      r(   	test_fuzzzTestExpmFrechet.test_fuzzP  s   i##$455 	!	 	)	%	'
 v 	K 	KA3::a==)EOO--MQ##AQqE***JQqE***J % 1 1*a @ @!$55E
"A
"A		1a&!!	2=++Q/002 3 3A "L--a00M$|0033BQBF;.:1a.@.@+M+M=tDDDD,.>TJJJJJ#	K 	Kr*   c                 ^   t          j        ddgddggt                    }t          j        ddgdd	ggt                    }t          j                            |d
           t          ||d          \  }}t          ||d          \  }}t          ||           t          ||           d S )Ng]؉??gvP?g^?guÝ?r#   gS,?g| @gJt?g~3?rB   r  r  r  )r%   r   r&   r   r}   r   r   r   )r;   r'   r   sps_expmsps_frechetblockEnlarge_expmblockEnlarge_frechets          r(   test_problematic_matrixz'TestExpmFrechet.test_problematic_matrixl  s    HZ(Z(       HZ(Z(       	!Q ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r*   zthis test is deliberately slowr   c                 &   d}t           j                            ||f          }t           j                            ||f          }t          ||d          \  }}t          ||d          \  }}t	          ||           t	          ||           d S )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     I!!1v!..I!!1v!.. ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r*   N)rY   rZ   r[   r  r  r  r  r   r   slowskipr  r\   r*   r(   r  r    s        @ @ @.@ @ @BK K K8; ; ;$ [[=>>
; 
; ?> 
; 
; 
;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epsrS  p_normperturbationX_primescaled_relative_errors
             r(   _help_expm_cond_searchr    sh    

1agA!WWF7fvo.L1|#$$G 1--#>!!!r*   c                     | t           j                            |          t           j                            |           z  z  S r  )r   r}   r   )r'   r   s     r(   _normalized_liker    s2    !!!$$u|'8'8';';;<<r*   c                 x     | |          } | ||z             }t          ||z
            t          |          z  S r  )r   )r  r'   r  r   r  s        r(   _relative_errorr    s@    	!AaL !!G!tAww&&r*   c                   J    e Zd Zd Zd Zd Zej        j        d             Z	dS )TestExpmConditionNumberc                     t           j                            d           t          dd          D ]A}t           j                            ||          }t          |          }t          d|           Bd S )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  sj    
	tq! 	( 	(A	1%%AaLLEa''''	( 	(r*   c                     t          j        g dg dg dg dg          }t          |          }t          d|           d S )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  s_    HIII<<<///###	   !$&&&&&r*   c                 z   t           j                            d           t          j        ddd          D ]B}t          j        |gg          }t          t          |          t          |                     Ct          j        ddd          D ]B}t          j        |gg          }t          t          |          t          |                     Ct          d          D ]W}t           j        
                    d	d	          }t          t          |          t          j        |          d
                    Xd S )N90  r  r   r  )numr>  r   r  rB   r   )r%   rx   ry   linspacer   r   r   absr|   rz   r{   r   )r;   xr'   rX  s       r(   test_univariatez'TestExpmConditionNumber.test_univariate  s   
	uR+++ 	2 	2A1#AIaLL#a&&1111R+++ 	2 	2A1#AIaLL#a&&1111r 	@ 	@A	1%%AIaLL"+a..*>????	@ 	@r*   c           	         t           j                            d          }d}d}t          |          D ]}|                    dd          }|                    ||          }t          j                            |          }t          |          }t          j                            |          }	t          |          }
t          j        t          ||||	|          }t          j        ||z            }t          ||d          }|j        } ||          }|t#          t          j        ||j                  |          z  }t)          t          ||          }t+          || |z             t          d          D ]r}|t#           |j        |j         |          z  }t+          t          |          t          |                     t)          t          ||          }t-          ||           st-          |dd|z  z   |z  |
z             d S )	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  rc  rX  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   i##E**x 	H 	HAAq!!A		!QA\&&q))FQA\&&q))FaLLE !"8vq&#/ /AGAaCLLE1eJ777C5D1T77D+BJtQW,E,EqIIIF+D!V<<MMD53;777 1XX @ @/		170CQGGGVd6ll;;; /a @ @!-????
 ma!C%i3->-FGGGG?	H 	Hr*   N)
rY   rZ   r[   r  r  r  r   r   r  r
  r\   r*   r(   r  r    sj        ( ( (' ' '
@ 
@ 
@ [#H #H #H #H #Hr*   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestKhatriRaoc           
      ^   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           d S )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 0 	1eaW&'W&("X&("X%/ 0 0 	1 	1 	1
 rxA''1a&)9)9::17F+++++r*   c                     t          j        t                    5  t          g dg dg          }t          ddgddgg          }t	          ||           d d d            d S # 1 swxY w Y   d S )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    ]:&& 	 	yyy yy" # #A1v1v    Aq!	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s   ;A""A&)A&c                 j   t          j        t                    5  t          g d          }t          g d          }t	          ||           d d d            n# 1 swxY w Y   t          j        t                    5  t          g d          }t          g dg dg          }t	          ||           d d d            n# 1 swxY w Y   t          j        t                    5  t          g dg dg          }t          g d          }t	          ||           d d d            d S # 1 swxY w Y   d S )Nr  r  )r`   r  rv   r  r  s      r(   test_to_assure_2d_arrayz%TestKhatriRao.test_to_assure_2d_array  s    ]:&& 	 	iii  Aiii  Aq!		 	 	 	 	 	 	 	 	 	 	 	 	 	 	 ]:&& 	 	iii  A				  A q!	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 ]:&& 	 					  A iii  Aq!	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s5   3AA A=7C  CC$7D((D,/D,c                    t          ddgddgg          t          ddgddgg          t                    }t          j        fd	t	          j        d                   D                       j        }t          ||           d S )
NrB   r   r   ru   r   rs   r`   r  c                 b    g | ]+}t          j        d d |f         d d |f                   ,S r  )r%   kron)r   ro  r<   r  s     r(   
<listcomp>z@TestKhatriRao.test_equality_of_two_equations.<locals>.<listcomp>  sM     6 6 6 '!AAAqD'1QQQT733 6 6 6r*   )r   r   r%   r  rz   r   r   r   )r;   res1res2r<   r  s      @@r(   test_equality_of_two_equationsz,TestKhatriRao.test_equality_of_two_equations  s    Aq6Aq6"##Aq6Aq6"##!Qy 6 6 6 6 6#(#4#46 6 6 7 778 	 	4&&&&&r*   c                 n   t          j        d          }t          j        d          }t          ||          }t          |t          j        d                     t          j        d          }t          j        d          }t          ||          }t          |t          j        d                     d S )N)r   r   )r   r   )r   r   )r   r   )r  r   )r%   r   r   r   )r;   r<   r  ress       r(   r   zTestKhatriRao.test_empty  s    HVHVARXf--...HVHVARXg../////r*   N)rY   rZ   r[   r  r  r  r$  r   r\   r*   r(   r  r    s_        
, 
, 
,    2' ' '	0 	0 	0 	0 	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   rO  r  r  r  r  r  r  r  r\   r*   r(   <module>r/     s            , , , , , , , , , , , ,P P P P P P P P P P P P P P P P     A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A + * * * * * 6 6 6 6 6 6 E E E E E E ! ! ! ! # # # # # #  *' ' ' ' ' ' ' 'Vl0 l0 l0 l0 l0 l0 l0 l0^~# ~# ~# ~# ~# ~# ~# ~#BvH vH vH vH vH vH vH vHrOF OF OF OF OF OF OF OFdt; t; t; t; t; t; t; t;n" " "= = =' ' 'BH BH BH BH BH BH BH BHJB0 B0 B0 B0 B0 B0 B0 B0 B0 B0r*   