
    Yhi                     *   d Z ddlZddlZddlZddlmZmZmZ ddlm	Z	m
Z
mZmZmZmZm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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          Z0 G d d          Z1d Z2d Z3d Z4 G d d          Z5 G d d          Z6ej7        8                    deeeg          d              Z9d! Z:dS )"z, Test functions for linalg.matfuncs module

    N)arrayidentitysqrt)assert_array_almost_equalassert_allcloseassert_assert_array_lessassert_array_equalassert_warnssuppress_warnings)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)LinAlgWarning)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    r/var/www/tools.fuzzalab.pt/emblema-extractor/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      4r1   r2   g333333#g333333#@g     9g.r2   g#@g333333g      2@g3333332@       @)g'@'Rqgy.@ge@5@r7   )g@ȽUЛ'?g9\g+%r8   )gRQQ?gGzgffffffr9   )gר#w?î?gk#egC,Nr:   )g@42
gF(@gcs@@r;   )r   r   r   )selfacrrs       r)   	test_nilszTestSignM.test_nils4   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                 Z    t          g dg dg dg dg          }t          |           d S )N)           r   r   )rC   r   rC   r   r   r   r   rC   )r   r   rC   r   r   r   r<   r=   s     r)   test_defective1zTestSignM.test_defective1B   s7    ;;;yyy999=>>ar+   c                 `    t          g dg dg dg dg df          }t          |           d S )Nr/   r0   r3   r4   r5   rE   rF   s     r)   test_defective2zTestSignM.test_defective2G   sT    &&&'''((('''$$$& ' ' 	ar+   c           
      l    t          g dg dg dg dg dg dg dg          }t          |           d S )Nr2         9@rB   rB   rB   rB   rB   rB               $@      @rP   rP   rB   rB   rB   r6         .@rP   rP   rB   rB   rB   rB   rB   rR   rP   rB   rB   rB   rB   rB   rP   rO   rB   rB   rB   rB   rB   rB   r2   rL   rB   rB   rB   rB   rB   rB   rN   rE   rF   s     r)   test_defective3zTestSignM.test_defective3Q   sf    1111110000000001110002 3 3 	ar+   N)__name__
__module____qualname__r@   rG   rI   rW    r+   r)   r-   r-   2   sP        ( ( (  
      r+   r-   c            	       V   e Zd Zd Zej                            d          d             Zej                            d          d             Zd Z	d Z
d Zd Zd	 Zd
 Zej        j        d             Zej        j        d             Zd Zd Zej                            d          ej                            deeej        eej        g          d                         Zej        j        ej                            deeej        eej        g          d                         ZdS )TestLogMc                 N    t           j                            d          | _        d S )Nl   >gO*31 )r&   randomdefault_rngrng)r<   s    r)   setup_methodzTestLogM.setup_method^   s    9(()9::r+   z$ignore:.*inaccurate.*:RuntimeWarningc           
          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 S )NrK   rM   rQ   rS   rT   rU   rV      g@y                )r   r   r   )r<   r=   ms      r)   r@   zTestLogM.test_nilsa   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"Qr+   c                     t                      }t          |          }t          |          }t          ||dd           d S )Ng-C6
?+=rtolatol)r*   r   r   r   )r<   r(   A_logmA_round_trips       r)   *test_al_mohy_higham_2012_experiment_1_logmz3TestLogM.test_al_mohy_higham_2012_experiment_1_logmn   sB     233aF||ad??????r+   c                     t                      }t          |t          j                  }t	          |          }t          t          j        ||dd                      d S )Nh㈵>rg   rh   )r*   r   r&   logr   r   allclose)r<   r(   
A_funm_logrl   s       r)   .test_al_mohy_higham_2012_experiment_1_funm_logz7TestLogM.test_al_mohy_higham_2012_experiment_1_funm_logw   sU     233!RV__
J''BKadGGGGHHHHHr+   c                    t          dd          D ]}| j                            ||f          }t          j        ddd          D ]}||z  }t          j                            |          }d| d| }t          |          }||z  }t          ||           t                      5 }	|	
                    t          	           t          |          }
t          |
          }t          |||
           d d d            n# 1 swxY w Y   Čd S )NrC      size   	   zM:z eivals:category)err_msg)rangera   uniformr&   logspacelinalgeigvalsr   r   r   filterRuntimeWarningr   r   )r<   n
M_unscaledscaleMWr}   M_sqrtmM_sqrtm_round_tripsupM_logmM_logm_round_trips               r)   test_round_trip_random_floatz%TestLogM.test_round_trip_random_float   sy   q! 	K 	KA))1v)66JRA.. K K& I%%a((-q--!--  ((%,w%6" 2A666 '(( KCJJJ777!!WWF(,V%#$5q'JJJJK K K K K K K K K K K K K K KK	K 	Ks   &AC>>DDc                 <   t          dd          D ]}| j                            ||f          d| j                            ||f          z  z   }t          j        ddd          D ]5}||z  }t          |          }t          |          }t          ||           6d S )NrC   ru                 ?rx   ry   rz   )r~   ra   standard_normalr&   r   r   r   r   )r<   r   r   r   r   r   M_round_trips          r)   test_round_trip_random_complexz'TestLogM.test_round_trip_random_complex   s    q! 	1 	1A(22Aq6::TX55q!f===>JRA.. 1 1&a#F||a0000	1	1 	1r+   c                 |   d}ddgddggddgddggddgddggddgddggfD ]}t           j                            |          }t          t	          d |D                                   t          j        |t                    }t          |          }t          |j	        j
        |v           t          j        |t                    }t          |          }t          |j	        j
        |v            t          j        |t                     }t          |          }t          |j	        j
        |v            d S )NFDGrC   r         c              3   :   K   | ]}|j         p
|j        d k     V  dS r   Nimagreal.0ws     r)   	<genexpr>zFTestLogM.test_logm_type_preservation_and_conversion.<locals>.<genexpr>   /      <<QAF0afqj<<<<<<r+   r$   )scipyr   r   r   anyr&   r   r'   r   r%   charcomplex)r<   complex_dtype_charsmatrix_as_listr   r(   rk   s         r)   *test_logm_type_preservation_and_conversionz3TestLogM.test_logm_type_preservation_and_conversion   sX    .Q!Q Q!Q Q!Q Q!Q 	" 	> 	>N $$^44A<<!<<<<<<=== u555A!WWFFL%-@@AAA w777A!WWFFL%)<<=== .6666A!WWF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          |          }t          t          j        |j        t          j                             t          t!          |          |           d S )N)rC   rC   r   )r   rC   rC   )rC   r   rC   r$   {Gz?)r'   r   r&   r   r   r   r   r   absoluter   sumr   
issubdtyper%   inexactr   r   )r<   r   dtXr   Ys         r)   test_complex_spectrum_real_logmz(TestLogM.test_complex_spectrum_real_logm   s     YY			999-. 	( 	(B"%%%A$$Q''AD2;qv..22444555QABM!'2:66777DGGQ''''	( 	(r+   c                     ddgddggddgddggfD ]l}t           t          fD ][}t          j        ||          }t	          |          \  }}t          t          j        |j        t          j                             \md S )NrC   r   r$   )	r'   r   r&   r   r   r   r   r%   complexfloating)r<   r   r   r(   rk   infos         r)   test_real_mixed_sign_spectrumz&TestLogM.test_real_mixed_sign_spectrum   s     Q!R!Q!Q " 	I 	IA Wn I IHQb)))#Aww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 ]E}t          j        }t          |t          |          }t          |          }t          ||d           Fd S )Nr   r   rC   rg   rj   )
r&   r   asarrayTr   r   r   r   r   r   )r<   r(   Br   expected_warningLEs          r)   test_exactly_singularzTestLogM.test_exactly_singular   s    Hq!fr2h'((JAA'((ACAC 	. 	.A0K-tQ77AQAAqu-----		. 	.r+   c                     t          j        dgg          }t          j        }t	          |t
          |          }t          |          }t          ||d           d S )Ng0.++rg   r   )r&   r   r   LogmNearlySingularWarningr   r   r   r   )r<   r   r   r   r   s        r)   test_nearly_singularzTestLogM.test_nearly_singular   sV    HvhZ  ,F)433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   rC   r         ?rg   r   r   ry                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$   )pytestwarnsr   r   r   r&   zeros)r<   r%   s     r)   test_no_ZeroDivisionErrorz"TestLogM.test_no_ZeroDivisionError  s    l>1PQQQ 	0 	0l566	0 	0&...///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0s4   A>$A&A>&A*	*A>-A*	.A>>BBN)rX   rY   rZ   rb   r   markfilterwarningsr@   rm   rs   r   r   r   r   r   thread_unsafer   r   r   r   xfailparametrizeintr'   r&   float32r   	complex64r   r   r[   r+   r)   r]   r]   ]   s       ; ; ; [ FGG	 	 HG	 [ FGG@ @ HG@I I IK K K.	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                       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d Zd Zd Zd Zd Zej                            deeej        eej        g          d             Zd Z d Z!d Z"dS )	TestSqrtMc                 <   t           j                            d          }t          dd          D ]k}|                    ||f          }t          j        ddd          D ];}||z  }t          |          }|                    |          }t          ||           <ld S )Nl   &\31 rC   ru   rx   ry   rz   	r&   r_   r`   r~   r   r   r   dotr   r<   ra   r   r   r   r   r   r   s           r)   r   z&TestSqrtM.test_round_trip_random_float  s    i##$455q! 	7 	7A,,aV44JRA.. 7 7&((%,[[%9%9" 2A6666	7	7 	7r+   c                 r   t           j                            d          }t          dd          D ]}|                    ||f          d|                    ||f          z  z   }t          j        ddd          D ];}||z  }t          |          }|                    |          }t          ||           <d S )Nl   &\31 rC   ru   r   rx   ry   rz   r   r   s           r)   r   z(TestSqrtM.test_round_trip_random_complex  s    i##$455q! 	7 	7A--q!f55s22Aq6:::;JRA.. 7 7&((%,[[%9%9" 2A6666	7	7 	7r+   c                    d}t          |          }t          g dd|ddgdd|dgg dg          }t          g dd|ddgdd|dgg dg          }t          ||z  |           t          |          }t          ||z  |           d S )Ng      ?)      ?r   r   rC   r   rD   )rC   r   r   r   )r   r   r   r   )r<   eser=   saesas         r)   test_badzTestSqrtM.test_bad*  s    !WW;;;a!9a!999   KKKr!AJqAJII     	""r'1---Ahh!#)Q/////r+   c                    d}ddgddggddgddggddgddggddgddggddgddggfD ]Z}t           j                            |          }t          t	          d |D                                   t                      5 }|                    t                     t          j	        |t                    }t          |          }t          |j        j        |v           t          j	        |t                    }t          |          }t          |j        j        |v            t          j	        |t                     }t          |          }t          |j        j        |v            d d d            n# 1 swxY w Y   \d S )	Nr   rC   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r)   r   zHTestSqrtM.test_sqrtm_type_preservation_and_conversion.<locals>.<genexpr>I  r   r+   r{   r$   )r   r   r   r   r   r   r   r    r&   r   r'   r   r%   r   r   )r<   r   r   r   r   r(   A_sqrtms          r)   +test_sqrtm_type_preservation_and_conversionz5TestSqrtM.test_sqrtm_type_preservation_and_conversion;  s    .Q!Q Q!Q Q!Q Q!Q Q!Q " 	C 	CN $$^44A<<!<<<<<<=== #$$ C

M
222 H^5999((*2EEFFF H^7;;;((*.AABBB XnE::::((*.AABBB!C C C C C C C C C C C C C C C	C 	Cs   ?C,E77E;	>E;	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          |          }t          |j	        j
        |v            t          j        |t          	          }t          |          }t          |j	        j
        |v            d S )
Nr   rC   r   r   r   rC   r   )r   r   r   rC   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>g  /      88,!&1*888888r+   r$   )r   r   r   r   r   r&   r   r   r   r%   r   r'   )r<   r   r   r   r(   r   s         r)   9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumzCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum^  s   -Q!R!Q!Q JJJ			24 	? 	?N $$^44AC88a88888999 w777AAhhGGM&*==>>> u555AAhhGGM&*==>>>>#	? 	?r+   c                     t                      }t          |          }||z  }t          ||d           t          t          j        |          t          j        |                     d S )Nro   ri   )r*   r   r   r&   tril)r<   r(   r   rl   s       r)   %test_al_mohy_higham_2012_experiment_1z/TestSqrtM.test_al_mohy_higham_2012_experiment_1s  s_    133(((ad3333--rwqzz:::::r+   c                    t           t          fD ]}t          j        g dg dg dg dg|          }t	                      5 }|                    t                     t          |          }t          t          j	        |          t          j
        d                     t          j        |                                          sJ t          j        |                                          sJ 	 d d d            n# 1 swxY w Y   d S )N)r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r$   r{   )ry   ry   )r   r'   r&   r   r   r   r    r   r   r	  r   isnanr   isinf)r<   r   r(   r   r   s        r)   test_strict_upper_triangularz&TestSqrtM.test_strict_upper_triangular{  sH    u* 	/ 	/B	 &(	) ) )A
 #$$ /

M
222(( 0 0"(62B2BCCCx((,,.....x((,,....../ / / / / / / / / / / / / / /	/ 	/s   B/C==D	D	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               @ry   r                       ?      ?r         ?      rg   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          ||z  |d           t	                      5 }|                    t                     t          t          |          |d           d d d            d S # 1 swxY w Y   d S )N)rC   r   r   rC   r  r   r   rg   r   r{   )r&   r   r   r   r   r   r    r   r<   r   r  r   s       r)   test_gh4866zTestSqrtM.test_gh4866  s?   Hlll"ll"ll"ll$ % % HtCyy!QS		2"ll"llCyy!QS		24 5 5 	Aqu----   	5CJJJ...E!HHae4444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5s   ;C$$C(+C(c                 f   t          j        g d          }t          j        t          d          ddg          }t          ||z  |d           t	                      5 }|                    t                     t          t          |          |d           d d d            d S # 1 swxY w Y   d S )N)r   rC   r   r   rC   r   rg   r   r{   )r&   diagr   r   r   r   r    r   r  s       r)   test_gh5336zTestSqrtM.test_gh5336  s    GIIIGT!WWaO$$Aqu----   	5CJJJ...E!HHae4444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5s   ;B&&B*-B*c                    t          j        d          }t          j        d          }t                      5 }|                    t                     t          t          |          |d           d d d            d S # 1 swxY w Y   d S )Nr   r{   rg   r   )r&   r   r   r   r    r   r   r  s       r)   test_gh7839zTestSqrtM.test_gh7839  s    HVHV   	5CJJJ...E!HHae4444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5s   ;A??BBc                     t          j        d          }|                    d           t          j        |d           t          j        t          |                    sJ d S )N)   r   gGz?rC   )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        g dg dg dg          }t          |          }t          ||z  |d           t          |                    t           j                            }t          ||z  |d           d S )N)r   rB   rB   )r   rC   r   )r   r   r   rg   r   gư>)r&   r   r   r   astyper   )r<   r   sqs      r)   test_gh23278zTestSqrtM.test_gh23278  s    HlllKKK<==1XXR////188BL))**R......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   uint8r   r%   float64uint16uint32uint64r$  s     r)   -test_data_size_preservation_uint_in_float_outz7TestSqrtM.test_data_size_preservation_uint_in_float_out  s    F2RX&&&Qxx~++++F2RY'''Qxx~++++F2RY'''Qxx~++++F2RY'''Qxx~++++++r+   c                 &   t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ t          j        dt           j                  }t          |          j        t           j        k    sJ d S r+  )	r&   r   int8r   r%   r.  int16int32int64r$  s     r)   ,test_data_size_preservation_int_in_float_outz6TestSqrtM.test_data_size_preservation_int_in_float_out  s    F2RW%%%Qxx~++++F2RX&&&Qxx~++++F2RX&&&Qxx~++++F2RX&&&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   ry   r   r$   )	r&   r   r4  r   r%   
complex128r5  r6  r7  r$  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 )Nr,  r$   float128)	r&   r   float16r   r%   r   r.  hasattrr>  r$  s     r)   .test_data_size_preservation_float_in_float_outz8TestSqrtM.test_data_size_preservation_float_in_float_out  s    F2RZ(((Qxx~++++F2RZ(((Qxx~++++F2RZ(((Qxx~++++2z"" 	0r---A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   ry   r   r:  r$   r>  
complex256)r&   r   r?  r   r%   r   r   r.  r;  r@  r>  r$  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  ry   r   r  r$   rC  )r&   r   r   r   r%   r;  r@  rC  r$  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+   c           
      p   t           j                            d          }d}|                    dd|z  d|z  f          }t          j        |d          t          j        d|z            z   t          j        |          }}||z  }|d d d d dd d df         }t          j        |          d d dd ddd df         }t          t          |d d d d dd d df                   t          |                     t          t          |d d dd ddd df                   t          |                     d S )	Nl   &\31    r   r   rv   r   )krC   )
r&   r_   r`   r   r	  r   triuasfortranarrayr   r   )r<   ra   r   r(   r   UA_noncontig_cA_noncontig_fs           r)   test_cf_noncontig_nd_inputsz%TestSqrtM.test_cf_noncontig_nd_inputs  s?    i##$455KKa1ac]K++wqB"&1++-rwqzz1E!!!SSqS##A#+)!,,QQQ1add];a33Q3!n--u]/C/CDDDa14a4A.//}1E1EFFFFFr+   c                 z    t          j        g dt                    }t          t	          |          |           d S )N)ry   r   r   r   )r   r%   )r&   r   r'   r
   r   )r<   r(   s     r)   test_empty_sizeszTestSqrtM.test_empty_sizes+  s6    H<<<u555588Q'''''r+   c                    t           j                            d          }|                    d          }|d d d d dd d df         }|d d d d dd d df                                         }t          t          |          t          |                     |d d d d d d df         }|d d d d d d df                                         }t          t          |          t          |                     |d d d d dd d f         }|d d d d dd d f                                         }t          t          |          t          |                     d S )Nl   &\31 )r   r   r   rv   r   )r&   r_   r`   r   copyr   r   )	r<   ra   r(   A_negneg_origA_negneg_copyA_posneg_origA_posneg_copyA_negpos_origA_negpos_copys	            r)   test_negative_strideszTestSqrtM.test_negative_strides/  si   i##$455KKYK''!!!TTrT44R4-(!!!TTrT44R4-(--//m,,eM.B.BCCC!!!QQQ"*!!!QQQ"***,,m,,eM.B.BCCC!!!TTrT111*!!!TTrT111***,,m,,eM.B.BCCCCCr+   N)#rX   rY   rZ   r   r   r   r   r  r
  r  r   r  r  r  r%  r)  r2  r8  r<  rA  rD  rF  r   r   r   r   r'   r&   r   r   r   r   rR  rT  r]  r[   r+   r)   r   r     s       7 7 7	7 	7 	70 0 0"!C !C !CF? ? ?*; ; ;/ / /*&1 1 15 5 55 5 55 5 5& & &/ / /, , ,, , ,/ / /	0 	0 	0	3 	3 	33 3 3 [TC
GR\#RSS# # TS#G G G( ( (D D D D D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 )N  rC   r   r   rx   ry   rz   
r&   r_   seedr~   randnr   r   r   matrix_powerr   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 )Nra  rC   r   rx   ry   rz   rb  rf  s           r)   r   z6TestFractionalMatrixPower.test_round_trip_random_floatK  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 )Nra  )r   r   r   r,  r   皙?r   gigffffff@r   )	r&   r_   rc  r~   rd  r   r   re  r   )r<   r   ir   M_one_fifthr   r   r   s           r)   (test_larger_abs_fractional_matrix_powerszBTestFractionalMatrixPower.test_larger_abs_fractional_matrix_powersZ  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                 B   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          |          }	t          |	|z            }
t          ||
           d S )Nl   fm1    rC   r   rx   rv   TFr   r   )r&   r_   r`   r~   integersexpchoicer   r   r   r   )r<   ra   nsamplesrl  r   rg  matrix_scaler(   A_powerrk   A_power_expm_logms              r)   test_random_matrices_and_powersz9TestFractionalMatrixPower.test_random_matrices_and_powersl  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!WWF $VaZ 0 0G%67777%	8 	8r+   c                    t                      }t          |t          j                  }t	          |          }t          j        |d          }t          |d          }t          ||d           t          ||           t          ||           dD ]m}t          ||          }t          |d|z            }t          ||d           t          t          j	        |d          t          j	        |d                     nd S )Nr   gdy=r  )r   g?rC   r   )
r*   r   r&   r   r   r   _remainder_matrix_powerr   r   r	  )r<   r(   A_funm_sqrtr   A_rem_powerrv  rg  rl   s           r)   r
  z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1  s    133 1bg&&(('?3GG)!S11W59999)))---  	E 	EA-a33G27AaC@@LL!$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 )Nra  r,  r   r   rC   )	r&   r_   rc  rd  r~   r   _briggs_helper_functionexp2r   )r<   r=   rL  
x_observed
x_expecteds        r)   test_briggs_helper_functionz5TestFractionalMatrixPower.test_briggs_helper_function  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   rC   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rk  gffffff
@r$   )r   r   r   r   r   r&   r   r'   r   r%   r   r   r<   r   r   r   rg  r(   rv  s          r)   %test_type_preservation_and_conversionz?TestFractionalMatrixPower.test_type_preservation_and_conversion  s   
 .Q!Q Q!Q Q!Q Q!Q 	" 	C 	CN $$^44A<<!<<<<<<=== , C C H^59991!Q77*2EEFFF H^7;;;1!Q77*.AABBB XnE::::1!Q77*.AABBBBC	C 	Cr+   c                    d}ddgddggddgddggg dg dg dgfD ]}t           j                            |          }t          t	          d |D                                  d	D ]}t          j        |t          
          }t          ||          }t          |j	        j
        |v            t          j        |t          
          }t          ||          }t          |j	        j
        |v            d S )Nr   rC   r   r   r  )r   r   rC   r  c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r)   r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>  r  r+   r  r$   )r   r   r   r   r   r&   r   r   r   r%   r   r'   r  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   rC   r   r   ru   )r   r   r   )r   rC   rC   )r   r   rC   r$   )gffffffr  r  g)rk  gzG?)	r'   r   r&   r   r   r   r  allr   )r<   r   newtyper(   rg  rv  rl   s          r)   test_singularz'TestFractionalMatrixPower.test_singular  s"    Q!Q Q!Q Q!Q IIIzzz2	4 	5 	5N "7+ 5 5H^7;;;1 5 5A5a;;GBHW--11334444$ 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  ry   r   r  r  r   r  rg   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)rX   rY   rZ   r   r   rn  rx  r
  r  r  r  r   r   r   r  r   r[   r+   r)   r_  r_  ?  s        	5 	5 	55 5 5& & &$8 8 82E E E(8 8 8!C !C !CFC C C2 [<==5 5 >=5&H H H H Hr+   r_  c            
          e Zd Zd Zd Zej                            dee	e
eeeeg          ej                            deeej        eej        g          ej                            dddg          d                                     Zd	 Zd
 Zd Zej        j        ej                            d          d                         ZdS )TestExpMc                 v    t          ddgddgg          }t          t          |          ddgddgg           d S )NrB   r   rC   )r   r   r   rF   s     r)   	test_zerozTestExpM.test_zero  sC    Bq61Q%.!!!$q''Aa5!A-88888r+   c                     t          d          }t          |t          j        t          j        gg                     d S )NrC   )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   )rC   rC   c                     t          j        ||          }t          j        d|          } ||          } ||          }|j        |k    sJ |j        |j        k    sJ d S )Nr$   )r,  r,  )r&   r   r   r%   )r<   r  r   r   r(   A0resultresult0s           r)   test_small_empty_matrix_inputz&TestExpM.test_small_empty_matrix_input  st     HU"%%%Xhb)))a$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 )NrC   ry   r   r   f)
r&   r   r   r   r   r'  r   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 )NrC   ry   r   r   r   rx   r   )orderr   rd      ru   )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 )Nrd   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$   d   r   i  i  )r   r  r  rz   r   )r&   r   r'   r_   r`   rq  r   rV  r   r   testingr   r   r~   )
r<   r(   ra   rl  jAmre   rH  	first_resnext_ress
             r)   test_gh18086zTestExpM.test_gh180864  s#    HZu---i##C((LLC%%LLC%%**S//!Q$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)rX   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   	fail_slowr  r[   r+   r)   r  r    s-       9 9 91 1 1 [VdD$eUE%RSS[T3rz7BL"QRR[Wvv&677- - 87 SR TS-< < <( ( (.   [[1F F  F F Fr+   r  c                       e Zd Zd Zd Zd Zd Zej        j	        ej        
                    d          d                         ZdS )	TestExpmFrechetc                    t          j        g dg dg dg dgt                    }t          j        ddgdd	ggt                    }t          j        d
dgddggt                    }t          j                            |          }t          j                            |          d ddd f         }i ddiddifD ]3}t          ||fi |\  }}t          ||           t          ||           4d S )NrC   r   r   ry   r   ru   rd   r  r   r   rC   r   r   r   r   ru   r$   rC   r   r   ru   r   ry   rd   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_frechetL  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$   rC   r   r   ru   r   ry   rd   r  )rC   r   r   rd   rz      rK     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_frechetc  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  ry   r      rv   rC   gHj>r   gHz>)r&   r_   r`   r   normalstandard_cauchyexponentialr~   rs  rq  r   r   r   vstackhstack
zeros_liker   r   r   )r<   ra   rfuncsntestsrl  rfuncr  r   r  r  r  r   r(   r   r   r  r  r  r  s                      r)   	test_fuzzzTestExpmFrechet.test_fuzz  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?rC   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_matrix  s    HZ(Z(       HZ(Z(       	!Q ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r+   zthis test is deliberately slowr   c                 &   d}t           j                            ||f          }t           j                            ||f          }t          ||d          \  }}t          ||d          \  }}t	          ||           t	          ||           d S )Ni  rv   r  r  r  )r&   r_   r  r   r   )r<   r   r(   r   r  r  r  r  s           r)   test_medium_matrixz"TestExpmFrechet.test_medium_matrix  s     I!!1v!..I!!1v!.. ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r+   N)rX   rY   rZ   r  r  r  r  r   r   slowskipr  r[   r+   r)   r  r  J  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epsrg  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 )Nra  rC   ry   r   )r&   r_   rc  r~   rd  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,  rC   r   )r&   r_   rc  linspacer   r   r   absr   r~   rd  r   )r<   xr(   rl  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  ro   r,  r   r   zL-BFGS-Br  rC   )r&   r_   RandomStater~   randintrd  r   r   r   r   r   	functoolspartialr  r   r!   r
  r  r  r   r  r   r	   )r<   ra   r  rt  rl  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)
rX   rY   rZ   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 )NrC   r   r   ry   r   ru   rd   r     r  r            )ry   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rC   r   r   ry   r   ru   rC   r   r   ry   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&  )rd   r  rz   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$7D((D,/D,c                    t          ddgddgg          t          ddgddgg          t                    }t          j        fd	t	          j        d                   D                       j        }t          ||           d S )
NrC   r   r   ry   r   ru   rd   r  c                 b    g | ]+}t          j        d d |f         d d |f                   ,S r  )r&   kron)r   rL  r=   r"  s     r)   
<listcomp>z@TestKhatriRao.test_equality_of_two_equations.<locals>.<listcomp>M  sM     6 6 6 '!AAAqD'1QQQT733 6 6 6r+   )r   r   r&   r  r~   r   r   r
   )r<   res1res2r=   r"  s      @@r)   test_equality_of_two_equationsz,TestKhatriRao.test_equality_of_two_equationsH  s    Aq6Aq6"##Aq6Aq6"##!Qy 6 6 6 6 6#(#4#46 6 6 7 778 	 	4&&&&&r+   c                 n   t          j        d          }t          j        d          }t          ||          }t          |t          j        d                     t          j        d          }t          j        d          }t          ||          }t          |t          j        d                     d S )N)r   r   )r   r   )r   r   )r   r   )r  r   )r&   r   r   r   )r<   r=   r"  ress       r)   r   zTestKhatriRao.test_emptyR  s    HVHVARXf--...HVHVARXg../////r+   N)rX   rY   rZ   r#  r*  r,  r3  r   r[   r+   r)   r  r    s_        
, 
, 
,    2' ' '	0 	0 	0 	0 	0r+   r  r  c                     t          j                    5   | t          j        d          d           d d d            d S # 1 swxY w Y   d S )Nr   F)disp)r   deprecated_callr&   r   )r  s    r)   test_disp_depr9  ]  s     
		!	! $ $RVAYYU####$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $s    AAAc                      t          j                    5  t          t          j        d          d           d d d            d S # 1 swxY w Y   d S )Nr   r,  )	blocksize)r   r8  r   r&   r   r[   r+   r)   test_blocksize_depr<  c  s    			!	! ' 'bfQii2&&&&' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 's   $AA	A	);__doc__r  r   numpyr&   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_frechetr    scipy.optimizer!   r*   r-   r]   r   r_  r  r  r  r  r  r  r  r   r   r9  r<  r[   r+   r)   <module>rE     s)             ' ' ' ' ' ' ' ' ' '. . . . . . . . . . . . . . . . . .    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s0 s0 s0 s0 s0 s0 s0 s0liD iD iD iD iD iD iD iDX	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0H u-/ /$ $/ /$' ' ' ' 'r+   