
     h(                        d Z ddl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 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          Z'd Z(d Z)d Z* G d d          Z+ G d d          Z,d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)_matfuncs_inv_ssq)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/Sam_Eipo/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      4r(   r)   g333333#g333333#@g     9g.r)   g#@g333333g      2@g3333332@       @)g'@'Rqgy.@ge@5@r.   )g@ȽUЛ'?g9\g+%r/   )gRQQ?gGzgffffffr0   )gר#w?î?gk#egC,Nr1   )g@42
gF(@gcs@@r2   )r   r   r   )selfacrrs       r    	test_nilszTestSignM.test_nils0   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   )r:   r   r:   r   r   r   r   r:   )r   r   r:   r   Fdispr   r   r3   r4   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'   r*   r+   r,   Fr<   r>   r?   s     r    test_defective2zTestSignM.test_defective2C   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r)         9@r9   r9   r9   r9   r9   r9               $@      @rI   rI   r9   r9   r9   r-         .@rI   rI   r9   r9   r9   r9   r9   rK   rI   r9   r9   r9   r9   r9   rI   rH   r9   r9   r9   r9   r9   r9   r)   rE   r9   r9   r9   r9   r9   r9   rG   Fr<   r>   r?   s     r    test_defective3zTestSignM.test_defective3M   sp    1111110000000001110002 3 3 	aer"   N)__name__
__module____qualname__r7   r@   rB   rP    r"   r    r$   r$   .   sP        ( ( (  
      r"   r$   c                   P    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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 )NrD   rF   rJ   rL   rM   rN   rO      g@y                Fr<   )r   r   r   )r3   r4   ms      r    r7   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 )NFr<   g-C6
?+=rtolatol)r!   r   r   r   )r3   r   A_logminfoA_round_trips        r    *test_al_mohy_higham_2012_experiment_1_logmz3TestLogM.test_al_mohy_higham_2012_experiment_1_logmg   sM     233AE***F||ad??????r"   c                     t                      }t          |t          j        d          \  }}t	          |          }t          t          j        ||dd                      d S )NFr<   h㈵>r[   r\   )r!   r   r   logr   r	   allclose)r3   r   
A_funm_logr`   ra   s        r    .test_al_mohy_higham_2012_experiment_1_funm_logz7TestLogM.test_al_mohy_higham_2012_experiment_1_funm_logo   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                    ||          }t          |d	          \  }}|
                    |          }	t          |	|           t          |d	          \  }
}t          |
          }t          |||
           d S )N  r:         	   zM:{0} eivals:{1}Fr<   )err_msg)r   randomseedrangerandnlogspacelinalgeigvalsformatr   r   r   r   r   )r3   n
M_unscaledscaleMWro   M_sqrtmr`   M_sqrtm_round_tripM_logmM_logm_round_trips               r    test_round_trip_random_floatz%TestLogM.test_round_trip_random_floatw   s#   
	tq! 	G 	GAA..JRA.. G G& I%%a((,33Aq99 !&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 
Nrj   r:   rk                 ?rl   rm   rn   Fr<   )	r   rp   rq   rr   rs   rt   r   r   r   )r3   rx   ry   rz   r{   r   r`   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Gr:   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   Fr<   )scipyru   rv   r	   anyr   r   r   r   r   charcomplex)r3   complex_dtype_charsmatrix_as_listr|   r   r_   r`   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)r:   r:   r   )r   r:   r:   )r:   r   r:   r   {Gz?Fr<   )r   r   r   r   r   ru   rv   r	   absoluter   sumr   
issubdtyper   inexactr   r   )r3   r{   dtXr   Yr`   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 )Nr:   r   r   Fr<   )	r   r   r   r   r   r	   r   r   complexfloating)r3   r{   r   r   r_   r`   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   r:   Fr<   r[   r^   )
r   r   asarrayTr   LogmExactlySingularWarningr   r   r   r   )r3   r   Br{   expected_warningLr`   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.++Fr<   r[   r   )r   r   r   LogmNearlySingularWarningr   r   r   r   )r3   r{   r   r   r`   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   r:   r         ?r[   r   r   rm   y             r   )r   pir   r   r   )r3   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"   N)rQ   rR   rS   r7   rb   rh   r   r   r   r   r   r   r   r   rT   r"   r    rV   rV   Y   s        	 	 	@ @ @I I IG G G*1 1 1> > ><
( 
( 
(	I 	I 	I. . .* * *0 0 0 0 0r"   rV   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d ZdS )	TestSqrtMc                 X   t           j                            d           t          dd          D ]y}t           j                            ||          }t          j        ddd          D ]@}||z  }t          |d          \  }}|                    |          }t          ||           Azd S )	Nrj   r:   rk   rl   rm   rn   Fr<   	r   rp   rq   rr   rs   rt   r   r   r   r3   rx   ry   rz   r{   r}   r`   r~   s           r    r   z&TestSqrtM.test_round_trip_random_float   s    
	tq! 	7 	7AA..JRA.. 7 7& %ae 4 4 4%,[[%9%9" 2A6666	7	7 	7r"   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          ||           Ad S r   r   r   s           r    r   z(TestSqrtM.test_round_trip_random_complex   s    
	tq! 	7 	7AA..biooa6K6K1KKJ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      ?)      ?r   r   r:   r   r;   )r:   r   r   r   Fr=   	blocksizer   )r   r   shaper   r   r   )r3   eser4   sarx   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   r:   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>#  r   r"   r   Fr<   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r3   r   r   r|   r   A_sqrtmr`   s          r    +test_sqrtm_type_preservation_and_conversionz5TestSqrtM.test_sqrtm_type_preservation_and_conversion  s    .Q!Q Q!Q Q!Q Q!Q Q!Q " 	? 	?N $$^44A<<!<<<<<<=== u555A!!%000MGTGM&.AABBB w777A!!%000MGTGM&*==>>> .6666A!!%000MGTGM&*==>>>>1	? 	?r"   c                    d}ddgddggddgddggg dg dg dgfD ]}t           j                            |          }t          t	          d |D                                  t          j        |t          	          }t          |d
          \  }}t          |j	        j
        |v            t          j        |t          	          }t          |d
          \  }}t          |j	        j
        |v            d S )Nr   r:   r   r   r   r:   r   r   r   r:   r:   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r    r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>=  /      88,!&1*888888r"   r   Fr<   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r   s          r    9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumzCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum4  s"   -Q!R!Q!Q IIIyyy13 	? 	?N $$^44AC88a88888999 w777A!!%000MGTGM&*==>>> u555A!!%000MGTGM&*==>>>>#	? 	?r"   c                    t           j                            d           t          dd          D ]}t           j                            ||          dt           j                            ||          z  z   }t          |d|          \  }}t          |t           j        	                    |d                     t          dd          D ]'}t          |d|          \  }}t          ||           (d S )	Nrj   r:      r   Fr   r   
   )
r   rp   rq   rr   randrs   r   r   ru   matrix_power)r3   rx   r   A_sqrtm_defaultr`   r   A_sqrtm_news          r    test_blocksizeszTestSqrtM.test_blocksizesI  s    
	tq! 	> 	>A	q!$$r")//!Q*?*?'??A$)!%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 )NFr<   rd   r]   )r!   r   r   r   r   tril)r3   r   r   r`   ra   s        r    %test_al_mohy_higham_2012_experiment_1z/TestSqrtM.test_al_mohy_higham_2012_experiment_1T  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   Fr<   )intr   r   r   r   r	   isnanall)r3   r   r   r   r`   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   Fr<   )
r   r   r   r   r   r   r   r	   r   r   )r3   r   r   r   B_sqrtmr`   s         r    test_weird_matrixzTestSqrtM.test_weird_matrixg  s    u* 	- 	-B						 #%& & &A 						 #%& & &A q!%%((+++ "!%000MGTBHW%%))++,,,,	- 	-r"   c                     t           j                            d           t           j                            dd          }t	          |d          }t          |                    |          |           d S )Nrj   r   Tr<   )r   rp   rq   r   r   r   r   )r3   r   r   s      r    	test_dispzTestSqrtM.test_dispx  s]    
	tINN1a  !$a!$$$$$r"   c                     ddgddgg}ddgddgg}t          t          j        ||          |d	           t          t          |          |d	           d S )
N               @rm   r                       ?      ?r         ?      r[   r   )r   r   r   r   r3   r{   Rs      r    r   z0TestSqrtM.test_opposite_sign_complex_eigenvalues  sf    !Wq#hAYD	"q!ae4444a!%000000r"   c                 ~   t          j        g dg dg dg dg          }t          j        t          d          ddt          d          gg dg dt          d          ddt          d          gg          }t          t          j        ||          |d           t          t          |          |d           d S )N)r:   r   r   r:   r   r   r   r[   r   )r   r   r   r   r   r   r   s      r    test_gh4866zTestSqrtM.test_gh4866  s    Hlll"ll"ll"ll$ % % HtCyy!QS		2"ll"llCyy!QS		24 5 5 	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   r:   r   r   r:   r   r[   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 )N)r   r   r[   r   )r   zerosr   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"   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   float16uint16uint32float32uint64float64r3   r{   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   r  int16int32r  int64r
  r  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   rm   r   r   )
r   r   r  r   r   	complex64r  r  r  
complex128r  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   r  r   r   r  r
  hasattrr  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"" 	1555A88>R[0000	1 	100r"   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   rm   r   r  r   r  
complex256)r   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          t           d          rt          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 d S )Nr   rm   r   r   r   r  )r   r   r  r   r   r  r  r  r  s     r    ,test_data_size_preservation_comp_in_comp_outz6TestSqrtM.test_data_size_preservation_comp_in_comp_out  s    Hr1g3x(===Qxx~....2|$$ 	32q'As8,BMBBBA88>R]22222q'As8,BMBBBA88>R]2222		3 	3 32r"   N)rQ   rR   rS   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r   rT   r"   r    r   r      s@       7 7 77 7 72 2 2*? ? ?>? ? ?*	> 	> 	>; ; ;	- 	- 	-- - -"% % %1 1 1
1 
1 
11 1 11 1 1	, 	, 	,	, 	, 	,
/ 
/ 
/	1 	1 	1
3 
3 
33 3 3 3 3r"   r   c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                            d	
          d             Zd ZdS )TestFractionalMatrixPowerc                    t           j                            d           t          dd          D ]}t          dd          D ]}t           j                            ||          dt           j                            ||          z  z   }t          j        ddd          D ]J}||z  }t          |d|z            }t           j                            ||          }t          ||           Kd S )Nrj   r:      r   rl   rm   rn   
r   rp   rq   rr   rs   rt   r   ru   r   r   r3   prx   ry   rz   r{   M_rootr   s           r    r   z8TestFractionalMatrixPower.test_round_trip_random_complex  s    
	tq! 	5 	5A1a[[ 5 5Y__Q22R")//!Q:O:O5OO
[Q22 5 5E"U*A4Q!<<F#%9#9#9&!#D#DL#L!4444	55	5 	5r"   c                    t           j                            d           t          dd          D ]}t          dd          D ]}t           j                            ||          }t          j        ddd          D ]J}||z  }t          |d|z            }t           j                            ||          }t          ||           Kd S )Nrj   r:   r$  rl   rm   rn   r%  r&  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 )Nrj   )r   r   r$  r   r   皙?r$  gigffffff@   )	r   rp   rq   rr   rs   r   ru   r   r   )r3   rx   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                 n   t           j                            d           d}t          |          D ]}t          j        dd          }t           j                                        }t          j        t          j        dd                    }t           j                            ||          }t          j        d          r&|dt           j                            ||          z  z   }||z  }t          ||          }t          |d	          \  }}	t          ||z            }
t          ||
           d S )
Nrj      r:   r$  rl   )TFr   Fr<   )r   rp   rq   rr   	randrangers   expchoicer   r   r   r   )r3   nsamplesr-  rx   r'  matrix_scaler   A_powerr_   r`   A_power_expm_logms              r    test_random_matrices_and_powersz9TestFractionalMatrixPower.test_random_matrices_and_powers  s    		tx 	8 	8A A&&A	!!A 6&"22q"9"9::L	1%%A}]++ 3RY__Q2222L A
 .a33G...LFD $VaZ 0 0G%67777%	8 	8r"   c                    t                      }t          |t          j        d          \  }}t	          |d          \  }}t          j        |d          }t          |d          }t          ||           t          ||           t          ||           dD ]m}t          ||          }t          |d|z            }t          ||d           t          t          j
        |d          t          j
        |d                     nd S )NFr<   r   )r   g?r:   r   r   )r!   r   r   r   r   r   _remainder_matrix_powerr   r   r   r   )	r3   r   A_funm_sqrtr`   r   A_rem_powerr7  r'  ra   s	            r    r   z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1&  s   133 !BG%888Tae,,,'?3GG)!S11;000)))---  	E 	EA-a33G27AaC@@LL!$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 )Nrj   r   r   r$  r:   )	r   rp   rq   rs   rr   r   _briggs_helper_functionexp2r   )r3   r4   k
x_observed
x_expecteds        r    test_briggs_helper_functionz5TestFractionalMatrixPower.test_briggs_helper_function:  s    
	t$$rBIOOB,?,?'?? 	8 	8A1XX 8 8.Fq!LL
"'1"++-1

J77778	8 	8r"   c                    d}ddgddggddgddggddgddggddgddggfD ]!}t           j                            |          }t          t	          d |D                                   dD ]}t          j        |t                    }t          ||          }t          |j	        j
        |v           t          j        |t                    }t          ||          }t          |j	        j
        |v            t          j        |t                     }t          ||          }t          |j	        j
        |v            ֐#d S )	Nr   r:   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r    r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>P  r   r"   333333r+  gffffff
@r   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r3   r   r   r|   r'  r   r7  s          r    %test_type_preservation_and_conversionz?TestFractionalMatrixPower.test_type_preservation_and_conversionB  s   
 .Q!Q Q!Q Q!Q Q!Q 	" 	C 	CN $$^44A<<!<<<<<<=== , C C H^59991!Q77*2EEFFF H^7;;;1!Q77*.AABBB XnE::::1!Q77*.AABBBBC	C 	Cr"   c                    d}ddgddggddgddggg dg dg dgfD ]}t           j                            |          }t          t	          d |D                                  d	D ]}t          j        |t          
          }t          ||          }t          |j	        j
        |v            t          j        |t          
          }t          ||          }t          |j	        j
        |v            d S )Nr   r:   r   r   r   r   r   c              3   :   K   | ]}|j         p
|j        d k     V  dS r   r   r   s     r    r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>n  r   r"   rG  r   )r   ru   rv   r	   r   r   r   r   r   r   r   r   rJ  s          r    3test_type_conversion_mixed_sign_or_complex_spectrumzMTestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrume  s1   -Q!R!Q!Q IIIyyy13 	C 	CN $$^44AC88a88888999 , 
C 
C H^7;;;1!Q77*.AABBB H^59991!Q77*.AABBBB
C	C 	Cr"   zToo unstable across LAPACKs.reasonc                    ddgddggddgddggddgddggg dg dg dgfD ]}t           t          fD ]}t          j        ||	          }d
D ]E}t	          ||          }t          t          j        |                                                     FdD ]5}t	          ||          }t	          |d|z            }t          ||           6d S )Nr   r:   r   r   rk   r   )r   r:   r:   )r   r   r:   r   )gffffffrI  rH  g)r+  gzG?)	r   r   r   r   r   r	   r   r   r   )r3   r   newtyper   r'  r7  ra   s          r    test_singularz'TestFractionalMatrixPower.test_singular~  s"    Q!Q Q!Q Q!Q IIIzzz2	4 	5 	5N "7+ 5 5H^7;;;1 5 5A5a;;GBHW--11334444$ 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   rm   r   r   r   r   r   r[   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)rQ   rR   rS   r   r   r/  r9  r   rD  rK  rN  pytestmarkxfailrS  r   rT   r"   r    r"  r"    s        	5 	5 	55 5 5& & &$8 8 82E E E(8 8 8!C !C !CFC C C2 [<==5 5 >=5&H H H H Hr"   r"  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestExpMc                 v    t          ddgddgg          }t          t          |          ddgddgg           d S )Nr9   r   r:   )r   r   r   r?   s     r    	test_zerozTestExpM.test_zero  sC    Bq61Q%.!!!$q''Aa5!A-88888r"   c                     t          d          }t          |t          j        t          j        gg                     d S )Nr:   )r   r   r   r   r   )r3   elts     r    test_single_eltzTestExpM.test_single_elt  s3    1ggRXvh//00000r"   c                 f    t          j        d          }t          |          }|j        dk    sJ d S )Nr   r   r   )r   r   r   size)r3   r   results      r    test_empty_matrix_inputz TestExpM.test_empty_matrix_input  s5    HVa{a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 )Nr:   rm   r   r   f)
r   r   r   r   r   astyper  r   r   r  )r3   r   r4   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 )Nr:   rm   r   r   r$  rl   r   )orderr   rX   r   rk   )r   r   r   r   r   )r3   r   r4   a_ress       r    test_nx2x2_inputzTestExpM.test_nx2x2_input  s   DH1v1v&1v2w'1v1v&1v1v&1vBx(	* 25	6 6 6 T!VacNQT!VQJ7T!VQJqL1a46AaC.9;qAvJ!Q$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$z4IJL!Hac1W,b!A#h!Qw.>?qsGQqS!GOQ!Wac1W_=?   	Q'''''r"   N)rQ   rR   rS   r[  r^  rc  ri  ro  rT   r"   r    rY  rY    s_        9 9 91 1 1     < < <( ( ( ( (r"   rY  c                       e Zd Zd Zd Zd Zd Zej        j	        ej        
                    d          d                         ZdS )	TestExpmFrechetc                    t          j        g dg dg dg dgt                    }t          j        ddgdd	ggt                    }t          j        d
dgddggt                    }t          j                            |          }t          j                            |          d ddd f         }i ddiddifD ]3}t          ||fi |\  }}t          ||           t          ||           4d S )Nr:   r   r   rm   r$  rk   rX   r   r   r   r:   r   r   r   r$  rk   r   r:   r   r$  rk   r   rm   rX   r   methodSPSblockEnlarge)r   r   r   r   ru   r   r   r   )	r3   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 )Nrs  rt  ru  rv  r   r:   r   r$  rk   r   rm   rX   r   )r:   r   r$  rX   rn            r   r   )r   r   r   r   ru   r   zip_expm_frechetell_table_61r   r   r   )r3   
M_original
A_original
E_originalA_original_norm_1selected_m_listm_neighbor_pairsmambell_aell_btarget_norm_1rz   r{   r   r   rz  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           	      h   t           j        j        t           j        j        t           j        j        t           j        j        f}d}t          |          D ]\}t          j        |          }t          j        d          }t          j	        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	           ^d S )
Nd   r   r      ra  r:   gHj>r   gHz>)r   rp   uniformnormalstandard_cauchyexponentialrr   r4  expovariater2  r   ru   r   vstackhstack
zeros_liker   r   r   )r3   rfuncsntestsr-  rfuncr  rx   r  r  r  rz   r   r   r{   rz  r{  r}  r~  s                     r    	test_fuzzzTestExpmFrechet.test_fuzz  s    	!	 	)	%	'
 v 	K 	KAM&))E".s33M B''AQqE***JQqE***J % 1 1*a @ @!$55E
"A
"A		1a&!!	2=++Q/002 3 3A "L--a00M$|0033BQBF;.:1a.@.@+M+M=tDDDD,.>TJJJJJ#	K 	Kr"   c                 ^   t          j        ddgddggt                    }t          j        ddgdd	ggt                    }t          j                            |d
           t          ||d          \  }}t          ||d          \  }}t          ||           t          ||           d S )Ng]؉??gvP?g^?guÝ?r   gS,?g| @gJt?g~3?r:   rx  rw  ry  )r   r   r   r   ru   r   r   r   )r3   r   r   sps_expmsps_frechetblockEnlarge_expmblockEnlarge_frechets          r    test_problematic_matrixz'TestExpmFrechet.test_problematic_matrix  s    HZ(Z(       HZ(Z(       	!Q ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r"   zthis test is deliberately slowrO  c                 &   d}t           j                            ||f          }t           j                            ||f          }t          ||d          \  }}t          ||d          \  }}t	          ||           t	          ||           d S )Ni  r  rx  r  ry  )r   rp   r  r   r   )r3   rx   r   r   r  r  r  r  s           r    test_medium_matrixz"TestExpmFrechet.test_medium_matrix0  s     I!!1v!..I!!1v!.. ,1U!$ !$ !$+2>1^3- 3- 3-//"3444%9:::::r"   N)rQ   rR   rS   r  r  r  r  rU  rV  slowskipr  rT   r"   r    rq  rq    s        @ @ @.@ @ @BK K K6; ; ;$ [[=>>
; 
; ?> 
; 
; 
;r"   rq  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epsr'  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   ru   r   )r   r   s     r    _normalized_liker  H  s2    !!!$$u|'8'8';';;<<r"   c                 x     | |          } | ||z             }t          ||z
            t          |          z  S r  )r   )re  r   r  r   r  s        r    _relative_errorr  L  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 )Nrj   r:   rm   r   )r   rp   rq   rr   rs   r   r
   )r3   rx   r   kappas       r    test_expm_cond_smokez,TestExpmConditionNumber.test_expm_cond_smokeS  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
   )r3   r   r  s      r    test_expm_bad_condition_numberz6TestExpmConditionNumber.test_expm_bad_condition_numberZ  s_    HIII<<<///###	   !$&&&&&r"   c                 z   t           j                            d           t          j        ddd          D ]B}t          j        |gg          }t          t          |          t          |                     Ct          j        ddd          D ]B}t          j        |gg          }t          t          |          t          |                     Ct          d          D ]W}t           j        
                    d	d	          }t          t          |          t          j        |          d
                    Xd S )N90  rm  r$  r  )numr  r   r   r:   r`  )r   rp   rq   linspacer   r   r   absrt   rr   rs   r   )r3   xr   r-  s       r    test_univariatez'TestExpmConditionNumber.test_univariated  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           	      V   t           j                            d           d}d}t          |          D ]}t           j                            dd          }t           j                            ||          }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 ]{}|t#          t          j        j        |j         |          z  }t+          t          |          t          |                     t)          t          ||          }t-          ||           |t-          |dd|z  z   |z  |	z             d S )	Nr  rd   r   r   r$  zL-BFGS-Br  r:   )r   rp   rq   rr   randintrs   r   ru   r   r   r   	functoolspartialr  onesr   r  r  r  r   r  r   r
   )r3   r  r5  r-  rx   r   r  r   r  r  re  guessoutxoptyoptp_bestp_best_relerrjp_randp_rand_relerrs                       r    test_expm_cond_fuzzz+TestExpmConditionNumber.test_expm_cond_fuzzp  s   
	ux 	H 	HA	!!!Q''A	1%%A\&&q))FQA\&&q))FaLLE !"8vq&#/ /AGAaCLLE1eJ777C5D1T77D+BJtQW,E,EqIIIF+D!V<<MMD53;777 1XX @ @/	0I1MMMVd6ll;;; /a @ @!-????
 ma!C%i3->-FGGGG?	H 	Hr"   N)
rQ   rR   rS   r  r  r  rU  rV  r  r  rT   r"   r    r  r  R  sj        ( ( (' ' '
@ 
@ 
@ [#H #H #H #H #Hr"   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestKhatriRaoc           
      ^   t          t          ddgddgg          t          ddgddgg                    }t          |t          dd	gdd
gddgddgg                     t          t          j        ddg          t          j        ddg                    }t          |j        d           d S )Nr:   r   r   rm   r$  rk   rX   r      r  r            )rm   r   )r   r   r   r   emptyr   r3   r4   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r:   r   r   rm   r$  rk   r:   r   r   rm   rU  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  )rX   r   rn   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$7D((D,/D,c                    t          ddgddgg          t          ddgddgg          t                    }t          j        fd	t	          j        d                   D                       j        }t          ||           d S )
Nr:   r   r   rm   r$  rk   rX   r   c                 b    g | ]+}t          j        d d |f         d d |f                   ,S r  )r   kron)r   rA  r4   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  rr   r   r   r   )r3   res1res2r4   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"   N)rQ   rR   rS   r  r  r  r  rT   r"   r    r  r    sP        
, 
, 
,    2' ' ' ' 'r"   r  )-__doc__rp   r  numpyr   r   r   r   r   numpy.testingr   r   r	   r
   r   r   rU  scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   scipy.linalg._expm_frechetscipy.optimizer   r!   r$   rV   r   r"  rY  rq  r  r  r  r  r  rT   r"   r    <module>r     sP             , , , , , , , , , , , ,P P P P P P P P P P P P P P P P     K K K K K K K K K K K K K K K K K K K K K K K K * * * * * * ! ! ! ! # # # # # #  *' ' ' ' ' ' ' 'VO0 O0 O0 O0 O0 O0 O0 O0dr3 r3 r3 r3 r3 r3 r3 r3jvH vH vH vH vH vH vH vHr-( -( -( -( -( -( -( -(`s; s; s; s; s; s; s; s;l" " "= = =' ' 'BH BH BH BH BH BH BH BHJ7' 7' 7' 7' 7' 7' 7' 7' 7' 7'r"   