o
    g(                     @   sH  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d	 Z!G d
d dZ"G dd dZ#G dd dZ$G dd dZ%G dd dZ&G dd dZ'dd Z(dd Z)dd Z*G dd dZ+G d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                  C   s*   t jg dg dg dg dgtd} | 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)A r   ^/home/ubuntu/cloudmapper/venv/lib/python3.10/site-packages/scipy/linalg/tests/test_matfuncs.py%_get_al_mohy_higham_2012_experiment_1   s   r    c                   @   ,   e Zd Zdd Zdd Zdd Zdd Zd	S )
	TestSignMc                 C   sb   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      $g      @g      4r%   r&   g333333#g333333#@g     9g.r&   g#@g333333g      2@g3333332@       @)g'@'Rqgy.@ge@5@r+   )g@ȽUЛ'?g9\g+%r,   )gRQQ?gGzgffffffr-   )gר#w?î?gk#egC,Nr.   )g@42
gF(@gcs@@r/   )r   r   r   )selfacrrr   r   r   	test_nils0   s   zTestSignM.test_nilsc                 C   s0   t g dg dg dg dg}t|dd d S )N)           r   r   )r6   r   r6   r   r   r   r   r6   )r   r   r6   r   Fdispr   r   r0   r1   r   r   r   test_defective1>   s    zTestSignM.test_defective1c                 C   s6   t g dg dg dg dg df}t|dd d S )Nr#   r$   r'   r(   r)   Fr8   r:   r;   r   r   r   test_defective2C   s   zTestSignM.test_defective2c              	   C   sB   t g dg dg dg dg dg dg dg}t|dd	 d S )
Nr&         9@r5   r5   r5   r5   r5   r5               $@      @rC   rC   r5   r5   r5   r*         .@rC   rC   r5   r5   r5   r5   r5   rE   rC   r5   r5   r5   r5   r5   rC   rB   r5   r5   r5   r5   r5   r5   r&   r?   r5   r5   r5   r5   r5   r5   rA   Fr8   r:   r;   r   r   r   test_defective3M   s   zTestSignM.test_defective3N)__name__
__module____qualname__r4   r<   r=   rJ   r   r   r   r   r"   .   s
    
r"   c                   @   sd   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd ZdS )TestLogMc              	   C   sV   t g dg dg dg dg dg dg dg}tdd	 d
 | }t|dd d S )Nr>   r@   rD   rF   rG   rH   rI      g@y                Fr8   )r   r   r   )r0   r1   mr   r   r   r4   [   s   zTestLogM.test_nilsc                 C   s2   t  }t|dd\}}t|}t||ddd d S )NFr8   g-C6
?+=rtolatol)r    r   r   r   )r0   r   A_logminfoA_round_tripr   r   r   *test_al_mohy_higham_2012_experiment_1_logmg   s   z3TestLogM.test_al_mohy_higham_2012_experiment_1_logmc                 C   s>   t  }t|tjdd\}}t|}ttj||ddd  d S )NFr8   h㈵>rQ   rR   )r    r   r   logr   r   allclose)r0   r   
A_funm_logrV   rW   r   r   r   .test_al_mohy_higham_2012_experiment_1_funm_logo   s   z7TestLogM.test_al_mohy_higham_2012_experiment_1_funm_logc                 C   s   t jd tddD ]H}t j||}t dddD ]7}|| }t j|}d||}t	|dd	\}}|
|}	t|	| t|dd	\}
}t|
}t|||d
 qqd S )N  r6         	   zM:{0} eivals:{1}Fr8   )err_msg)r   randomseedrangerandnlogspacelinalgeigvalsformatr   r   r   r   r   )r0   n
M_unscaledscaleMWrc   M_sqrtmrV   M_sqrtm_round_tripM_logmM_logm_round_tripr   r   r   test_round_trip_random_floatw   s   

z%TestLogM.test_round_trip_random_floatc                 C   s~   t jd tddD ]1}t j||dt j||  }t dddD ]}|| }t|dd	\}}t|}t|| q$qd S 
Nr^   r6   r_                 ?r`   ra   rb   Fr8   )	r   rd   re   rf   rg   rh   r   r   r   )r0   rl   rm   rn   ro   rs   rV   M_round_tripr   r   r   test_round_trip_random_complex   s    z'TestLogM.test_round_trip_random_complexc                 C   s   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 ]Z}t j|}ttdd |D   tj|td}t|d	d
\}}t|j	j
|v tj|td}t|d	d
\}}t|j	j
|v  tj|td }t|d	d
\}}t|j	j
|v  q d S )NFDGr6   r         c                 s        | ]}|j p|jd k V  qdS r   Nimagreal.0wr   r   r   	<genexpr>       zFTestLogM.test_logm_type_preservation_and_conversion.<locals>.<genexpr>r   Fr8   )scipyri   rj   r   anyr   r   r   r   r   charcomplex)r0   complex_dtype_charsmatrix_as_listrp   r   rU   rV   r   r   r   *test_logm_type_preservation_and_conversion   s$   z3TestLogM.test_logm_type_preservation_and_conversionc                 C   s   g dg dg dg}t tfD ]4}tj||d}tj|}tdt|j	
 k  t|dd\}}tt|jtj tt|| qd S )N)r6   r6   r~   )r~   r6   r6   )r6   r~   r6   r   {Gz?Fr8   )r   r   r   r   r   ri   rj   r   absoluter   sumr   
issubdtyper   inexactr   r   )r0   ro   dtXr   YrV   r   r   r   test_complex_spectrum_real_logm   s   z(TestLogM.test_complex_spectrum_real_logmc                 C   sj   ddgddggddgddggfD ]"}t tfD ]}tj||d}t|dd\}}tt|jtj qqd S )Nr6   r   r   Fr8   )	r   r   r   r   r   r   r   r   complexfloating)r0   ro   r   r   rU   rV   r   r   r   test_real_mixed_sign_spectrum   s   z&TestLogM.test_real_mixed_sign_spectrumc                 C   sv   t ddgddgg}t ddgddgg}||j||jfD ]}tj}t|t|dd\}}t|}t	||dd qd S )Nr   rw   r6   Fr8   rQ   rT   )
r   r   asarrayTr   LogmExactlySingularWarningr   r   r   r   )r0   r   Bro   expected_warningLrV   Er   r   r   test_exactly_singular   s   zTestLogM.test_exactly_singularc                 C   sB   t dgg}tj}t|t|dd\}}t|}t||dd d S )Ng0.++Fr8   rQ   r   )r   r   r   LogmNearlySingularWarningr   r   r   r   )r0   ro   r   r   rV   r   r   r   r   test_nearly_singular   s
   zTestLogM.test_nearly_singularc                 C   s  ddgddgg}dt jd gt j d dgg}tt||dd tt||dd ddgdd	gg}dt j d d
t j gdd	t j d gg}tt||dd tt||dd ddgdd	gg}dt j d dgdd	t j d gg}tt||dd tt||dd d S )Nr   r6   r         ?rQ   r   rw   ra   y             r~   )r   pir   r   r   )r0   r   r   r   r   r   &test_opposite_sign_complex_eigenvalues   s   *$z/TestLogM.test_opposite_sign_complex_eigenvaluesN)rK   rL   rM   r4   rX   r]   ru   ry   r   r   r   r   r   r   r   r   r   r   rN   Y   s    
	rN   c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)S )*	TestSqrtMc                 C   sn   t jd tddD ])}t j||}t dddD ]}|| }t|dd\}}||}t|| qqd S )	Nr^   r6   r_   r`   ra   rb   Fr8   	r   rd   re   rf   rg   rh   r   r   r   r0   rl   rm   rn   ro   rq   rV   rr   r   r   r   ru      s   
z&TestSqrtM.test_round_trip_random_floatc                 C   s   t jd tddD ]2}t j||dt j||  }t dddD ]}|| }t|dd	\}}||}t|| q$qd S rv   r   r   r   r   r   ry      s    
z(TestSqrtM.test_round_trip_random_complexc                 C   s   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d }tt||| t|dddd }tt||| d S )	Ng      ?)      ?r   r   r6   r   r7   )r6   r   r   r   Fr9   	blocksizer~   )r   r   shaper   r   r   )r0   eser1   sarl   esar   r   r   test_bad   s$   




zTestSqrtM.test_badc                 C   s  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 |D   tj|td}t|d	d
\}}t|j	j
|v tj|td}t|d	d
\}}t|j	j
|v  tj|td }t|d	d
\}}t|j	j
|v  q'd S )Nrz   r6   r   r~   r   c                 s   r   r   r   r   r   r   r   r   #  r   zHTestSqrtM.test_sqrtm_type_preservation_and_conversion.<locals>.<genexpr>r   Fr8   )r   ri   rj   r   r   r   r   r   r   r   r   r   r0   r   r   rp   r   A_sqrtmrV   r   r   r   +test_sqrtm_type_preservation_and_conversion  s&   z5TestSqrtM.test_sqrtm_type_preservation_and_conversionc                 C   s   d}ddgddggddgddggg dg dg dgfD ]A}t j|}ttdd	 |D  tj|td
}t|dd\}}t|j	j
|v  tj|td
}t|dd\}}t|j	j
|v  qd S )Nrz   r6   r   r   r   r6   r   r   r   r6   r6   r   r   c                 s   r   r   r   r   r   r   r   r   =  r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>r   Fr8   )r   ri   rj   r   r   r   r   r   r   r   r   r   r   r   r   r   9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum4  s   zCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumc                 C   s   t jd tddD ];}t j||dt j||  }t|d|d\}}t|t j	|d tddD ]}t|d|d\}}t|| q5qd S )	Nr^   r6      rw   Fr   r~   
   )
r   rd   re   rf   randrg   r   r   ri   matrix_power)r0   rl   r   A_sqrtm_defaultrV   r   A_sqrtm_newr   r   r   test_blocksizesI  s    zTestSqrtM.test_blocksizesc                 C   sH   t  }t|dd\}}||}t||dd tt|t| d S )NFr8   rY   rS   )r    r   r   r   r   tril)r0   r   r   rV   rW   r   r   r   %test_al_mohy_higham_2012_experiment_1T  s
   
z/TestSqrtM.test_al_mohy_higham_2012_experiment_1c                 C   sZ   t tfD ]&}tjg dg dg dg dg|d}t|dd\}}tt|  qd S )N)r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r   Fr8   )intr   r   r   r   r   isnanall)r0   r   r   r   rV   r   r   r   test_strict_upper_triangular\  s   z&TestSqrtM.test_strict_upper_triangularc                 C   s   t tfD ];}tjg dg dg dg|d}tjg dg dg dg|d}t||| t|dd\}}tt|	  qd S )Nr   r   r   r   r   r   Fr8   )
r   r   r   r   r
   r   r   r   r   r   )r0   r   r   r   B_sqrtmrV   r   r   r   test_weird_matrixg  s&   zTestSqrtM.test_weird_matrixc                 C   s:   t jd t jdd}t|dd}t||| d S )Nr^   r   Tr8   )r   rd   re   r   r   r   r   )r0   r   r   r   r   r   	test_dispx  s   zTestSqrtM.test_dispc                 C   sL   ddgddgg}ddgddgg}t t|||dd	 t t||dd	 d S )
N               @ra   r                       ?      ?r~         ?      rQ   r   )r   r   r   r   r0   ro   Rr   r   r   r     s   z0TestSqrtM.test_opposite_sign_complex_eigenvaluesc              
   C   s   t g dg dg dg dg}t tdddtdgg dg dtdddtdgg}tt |||dd tt||dd d S )N)r6   r   r   r6   r   r   r   rQ   r   )r   r   r   r   r   r   r   r   r   r   test_gh4866  s   
zTestSqrtM.test_gh4866c                 C   sN   t g d}t tdddg}tt |||dd tt||dd d S )N)r~   r6   r   r~   r6   r   rQ   r   )r   diagr   r   r   r   r   r   r   r   test_gh5336  s   zTestSqrtM.test_gh5336c                 C   s@   t d}t d}tt |||dd tt||dd d S )N)r~   r~   rQ   r   )r   zerosr   r   r   r   r   r   r   test_gh7839  s   

zTestSqrtM.test_gh7839c                 C      t jdt jd}t|jt jksJ t jdt jd}t|jt jks$J t jdt jd}t|jt jks6J t jdt j	d}t|jt j
ksHJ d S Nr   r   r   )r   r   uint8r   r   float16uint16uint32float32uint64float64r0   ro   r   r   r   -test_data_size_preservation_uint_in_float_out     z7TestSqrtM.test_data_size_preservation_uint_in_float_outc                 C   r   r   )r   r   int8r   r   r   int16int32r   int64r   r   r   r   r   ,test_data_size_preservation_int_in_float_out  r   z6TestSqrtM.test_data_size_preservation_int_in_float_outc                 C   s   t jddgddggt jd}t|jt jksJ t jddgddggt jd}t|jt jks0J t jddgddggt jd}t|jt jksHJ t jddgddggt jd}t|jt j	ks`J d S )Nr~   ra   r   r   )
r   r   r   r   r   	complex64r   r   r   
complex128r   r   r   r   +test_data_size_preservation_int_in_comp_out  s   z5TestSqrtM.test_data_size_preservation_int_in_comp_outc                 C   s   t jdt jd}t|jt jksJ t jdt jd}t|jt jks$J t jdt jd}t|jt jks6J tt drMt jdt jd}t|jt jksOJ d S d S )Nr   r   float128)	r   r   r   r   r   r   r   hasattrr   r   r   r   r   .test_data_size_preservation_float_in_float_out  s   
z8TestSqrtM.test_data_size_preservation_float_in_float_outc                 C   s   t jddgddggt jd}t|jt jksJ t jddgddggt jd}t|jt jks0J t jddgddggt jd}t|jt jksHJ t	t drjt	t drlt jddgddggt j
d}t|jt jksnJ d S d S d S )Nr~   ra   r   r   r   r   
complex256)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   -test_data_size_preservation_float_in_comp_out  s   z7TestSqrtM.test_data_size_preservation_float_in_comp_outc                 C   s   t jddgddggt jd}t|jt jksJ tt drMt jddgddggt jd}t|jt jks5J t jddgddggt jd}t|jt jksOJ d S d S )Nr   ra   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   ,test_data_size_preservation_comp_in_comp_out  s   
z6TestSqrtM.test_data_size_preservation_comp_in_comp_outN)rK   rL   rM   ru   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r      s*    

r   c                   @   sj   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
ejjdddd Zdd ZdS )TestFractionalMatrixPowerc                 C   s   t jd tddD ];}tddD ]3}t j||dt j||  }t dddD ]}|| }t|d| }t j||}t	|| q+qqd S )Nr^   r6      rw   r`   ra   rb   
r   rd   re   rf   rg   rh   r   ri   r   r   r0   prl   rm   rn   ro   M_rootrx   r   r   r   ry     s    z8TestFractionalMatrixPower.test_round_trip_random_complexc                 C   s   t jd tddD ]2}tddD ]*}t j||}t dddD ]}|| }t|d| }t j||}t	|| q"qqd S )Nr^   r6   r   r`   ra   rb   r   r   r   r   r   ru     s   z6TestFractionalMatrixPower.test_round_trip_random_floatc                 C   s   t jd dD ]L}tdD ]E}t j||dt j||  }t|d}t j|d}t|| t|d}t j|d}t|| t|d	}t j|d
}t|| qqd S )Nr^   )r~   r   r   r   rw   皙?r   gigffffff@   )	r   rd   re   rf   rg   r   ri   r   r   )r0   rl   iro   M_one_fifthrx   r   r   r   r   r   (test_larger_abs_fractional_matrix_powers  s    




zBTestFractionalMatrixPower.test_larger_abs_fractional_matrix_powersc                 C   s   t jd d}t|D ]I}tdd}t j }t tdd}t j||}tdr9|dt j||  }|| }t||}t	|dd	\}}	t
|| }
t||
 qd S )
Nr^      r6   r   r`   )TFrw   Fr8   )r   rd   re   rf   	randrangerg   expchoicer   r   r   r   )r0   nsamplesr   rl   r   matrix_scaler   A_powerrU   rV   A_power_expm_logmr   r   r   test_random_matrices_and_powers  s   


z9TestFractionalMatrixPower.test_random_matrices_and_powersc           	      C   s   t  }t|tjdd\}}t|dd\}}t|d}t|d}t|| t	|| t	|| dD ]"}t||}t|d| }t	||dd t	t
|dt
|d q1d S )NFr8   r   )r   g?r6   r   r   )r    r   r   r   r   r   _remainder_matrix_powerr   r
   r   r   )	r0   r   A_funm_sqrtrV   r   A_rem_powerr	  r   rW   r   r   r   r   &  s   




z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1c                 C   sj   t jd t jddt jd  D ]}tdD ]}t||}|t |  d }t|| qqd S )Nr^   r   rw   r   r6   )	r   rd   re   rg   rf   r   _briggs_helper_functionexp2r   )r0   r1   k
x_observed
x_expectedr   r   r   test_briggs_helper_function:  s    z5TestFractionalMatrixPower.test_briggs_helper_functionc                 C   s   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 ]V}t j|}ttdd |D   dD ]?}tj|td	}t||}t|j	j
|v tj|td	}t||}t|j	j
|v  tj|td	 }t||}t|j	j
|v  q6q d S )
Nrz   r6   r   r~   r   c                 s   r   r   r   r   r   r   r   r   P  r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>333333r   gffffff
@r   )r   ri   rj   r   r   r   r   r   r   r   r   r   r0   r   r   rp   r   r   r	  r   r   r   %test_type_preservation_and_conversionB  s(   


z?TestFractionalMatrixPower.test_type_preservation_and_conversionc                 C   s   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
D ]*}tj|td}t||}t|j	j
|v  tj|td}t||}t|j	j
|v  q1qd S )Nrz   r6   r   r   r   r   r   c                 s   r   r   r   r   r   r   r   r   n  r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>r  r   )r   ri   rj   r   r   r   r   r   r   r   r   r   r  r   r   r   3test_type_conversion_mixed_sign_or_complex_spectrume  s    

zMTestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrumzToo unstable across LAPACKs.reasonc                 C   s   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 ]9}t tfD ]2}tj||d	}d
D ]}t||}tt|  q2dD ]}t||}t|d| }t|| qEq'q!d S )Nr   r6   r~   r   r_   r   )r   r6   r6   )r   r   r6   r   )gffffffr  r  g)r   gzG?)	r   r   r   r   r   r   r   r   r   )r0   r   newtyper   r   r	  rW   r   r   r   test_singular~  s"   

z'TestFractionalMatrixPower.test_singularc                 C   sN   ddgddgg}ddgddgg}t t|||dd	 t t|d
|dd	 d S )Nr   ra   r   r   r   r~   r   rQ   r   r   )r   r   r   r   r   r   r   r   r     s   z@TestFractionalMatrixPower.test_opposite_sign_complex_eigenvaluesN)rK   rL   rM   ry   ru   r  r  r   r  r  r  pytestmarkxfailr  r   r   r   r   r   r     s    #
r   c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestExpMc                 C   s2   t ddgddgg}tt|ddgddgg d S )Nr5   r   r6   )r   r   r   r;   r   r   r   	test_zero  s   zTestExpM.test_zeroc                 C   s"   t d}t|ttjgg d S )Nr6   )r   r   r   r   r   )r0   eltr   r   r   test_single_elt  s   zTestExpM.test_single_eltc                 C   s$   t d}t|}|jdksJ d S )Nr   r   r   )r   r   r   size)r0   r   resultr   r   r   test_empty_matrix_input  s   
z TestExpM.test_empty_matrix_inputc                 C   s   t j}tddgddgg}|d d d|  }|d d | }tt|t||g|d |gg t|t jjjdks>J t|t j	jjdksLJ d S )Nr6   ra   r~   r{   f)
r   r   r   r   r   astyper   r   r   r   )r0   r   r1   aabbr   r   r   test_2x2_input  s   " zTestExpM.test_2x2_inputc                 C   sx  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d	}t |d d d
|  |d d | g|d d d | |d d d
|  ggdd|d
   d|d
  d  d|d
  d dd|d
    g|d
 d dd|d
    dd|d
   |d
 d  ggdd|  |d d  dd|  d|d  d  gdd
|  |d d
  dd|  d|d  d  ggdd|d
   d|d  d  dd|d
   d|d  d  gdd|d
   d|d  d  dd|d
   d|d  d  ggdd
|  d| d
  dd
|  d| d
  gdd
|  d| d
  dd
|  d| d
  ggg}tt|| d S )Nr6   ra   r   r   r   r`   r{   )orderr~   rO   r   r_   )r   r   r   r   r   )r0   r   r1   a_resr   r   r   test_nx2x2_input  s6   "&>622>>..zTestExpM.test_nx2x2_inputN)rK   rL   rM   r#  r%  r)  r.  r3  r   r   r   r   r"    s    	r"  c                   @   sJ   e Zd Zdd Zdd Zdd Zdd Zejj	ejj
d	d
dd ZdS )TestExpmFrechetc           	      C   s   t jg dg dg dg dgtd}t jddgdd	ggtd}t jd
dgddggtd}tj|}tj|d ddd f }i ddiddifD ]}t||fi |\}}t|| t|| qJd S )Nr6   r~   r   ra   r   r_   rO   r   r   r   r6   r~   r   r   r   r_   r   r6   r~   r   r_   r   ra   rO   r   methodSPSblockEnlarge)r   r   r   r   ri   r   r   r   )	r0   ro   r   r   expected_expmexpected_frechetkwargsobserved_expmobserved_frechetr   r   r   test_expm_frechet  s6   
z!TestExpmFrechet.test_expm_frechetc                 C   s.  t jg dg dg dg dgtd}t jddgdd	ggtd}t jd
dgddggtd}tj|d}g d}t|d d |dd  }|D ]M\}}tjjj| }	tjjj| }
d|	|
  }|| }|| }|| }|| }tj	|}tj	|d ddd f }t
||\}}t|| t|| qGd S )Nr5  r6  r7  r8  r   r6   r~   r   r_   r   ra   rO   r   )r6   r   r   rO   rb            r   r   )r   r   r   r   ri   r   zip_expm_frechetell_table_61r   r   r   )r0   
M_original
A_original
E_originalA_original_norm_1selected_m_listm_neighbor_pairsmambell_aell_btarget_norm_1rn   ro   r   r   r<  r=  r?  r@  r   r   r   test_small_norm_expm_frechet  sJ   
z,TestExpmFrechet.test_small_norm_expm_frechetc              	   C   s  t jjt jjt jjt jjf}d}t|D ]p}t|}td}t	dd}|||fd}|||fd}t
j|d}	||	 }
|
| }|
| }t t ||gt t ||gg}t
j|}t
j|d ||d f }t||\}}t||dd t||d	d qd S )
Nd   r   r~      r'  r6   gHj>r   gHz>)r   rd   uniformnormalstandard_cauchyexponentialrf   r  expovariater  r   ri   r   vstackhstack
zeros_liker   r   r   )r0   rfuncsntestsr   rfuncrR  rl   rI  rJ  rK  rn   r   r   ro   r<  r=  r?  r@  r   r   r   	test_fuzz  s4   

zTestExpmFrechet.test_fuzzc                 C   s~   t jddgddggtd}t jddgdd	ggtd}tj|d
 t||dd\}}t||dd\}}t|| t|| d S )Ng]؉??gvP?g^?guÝ?r   gS,?g| @gJt?g~3?r6   r:  r9  r;  )r   r   r   r   ri   r   r   r   )r0   r   r   sps_expmsps_frechetblockEnlarge_expmblockEnlarge_frechetr   r   r   test_problematic_matrix  s*   


z'TestExpmFrechet.test_problematic_matrixzthis test is deliberately slowr  c                 C   sd   d}t jj||fd}t jj||fd}t||dd\}}t||dd\}}t|| t|| d S )Ni  rV  r:  rc  r;  )r   rd   rZ  r   r   )r0   rl   r   r   rd  re  rf  rg  r   r   r   test_medium_matrix0  s   


z"TestExpmFrechet.test_medium_matrixN)rK   rL   rM   rA  rS  rb  rh  r  r   slowskipri  r   r   r   r   r4    s    !r4  c           
      C   sL   t || j}t|}|| ||  }t| | }t|| ||  }	|	 S N)r   reshaper   r   r   )
r   A_normr   X_normepsr   p_normperturbationX_primescaled_relative_errorr   r   r   _help_expm_cond_search?  s   ru  c                 C   s   | t j|t j|   S rl  )r   ri   r   )r   r   r   r   r   _normalized_likeH  s   rv  c                 C   s(   | |}| || }t || t | S rl  )r   )r*  r   rr  r   rs  r   r   r   _relative_errorL  s   rw  c                   @   s4   e Zd Zdd Zdd Zdd Zejjdd Z	d	S )
TestExpmConditionNumberc                 C   s@   t jd tddD ]}t j||}t|}td| qd S )Nr^   r6   ra   r   )r   rd   re   rf   rg   r   r	   )r0   rl   r   kappar   r   r   test_expm_cond_smokeS  s   z,TestExpmConditionNumber.test_expm_cond_smokec                 C   s8   t 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	   )r0   r   ry  r   r   r   test_expm_bad_condition_numberZ  s   z6TestExpmConditionNumber.test_expm_bad_condition_numberc                 C   s   t jd t jddddD ]}t |gg}tt|t| qt jddddD ]}t |gg}tt|t| q)t	dD ]}t j
d	d	}tt|t |d
  q@d S )N90  r1  r   rB  )numr   r~   r   r6   r&  )r   rd   re   linspacer   r   r   absrh   rf   rg   r   )r0   xr   r   r   r   r   test_univariated  s   z'TestExpmConditionNumber.test_univariatec              	   C   sD  t jd d}d}t|D ]}t jdd}t j||}tj|}t	|}tj|}t
|}	tt|||||}
t || }t|
|dd}|j}|
|}|tt ||j| }tt	||}t|| |  tdD ]"}|tt jj|j | }tt|t| tt	||}t|| qot|dd|  | |	  qd S )	Nr|  rY   r   r~   r   zL-BFGS-Brc  r6   )r   rd   re   rf   randintrg   r   ri   r   r   r   	functoolspartialru  onesr   r  rv  rm  r   rw  r   r	   )r0   rp  r  r   rl   r   rn  r   ro  ry  r*  guessoutxoptyoptp_bestp_best_relerrjp_randp_rand_relerrr   r   r   test_expm_cond_fuzzp  s6   
z+TestExpmConditionNumber.test_expm_cond_fuzzN)
rK   rL   rM   rz  r{  r  r  r   rj  r  r   r   r   r   rx  R  s    
rx  c                   @   r!   )
TestKhatriRaoc                 C   s~   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ddgtddg}t|jd d S )Nr6   r~   r   ra   r   r_   rO   r      rU  rD            )ra   r~   )r   r   r
   r   emptyr   r0   r1   br   r   r   
test_basic  s   zTestKhatriRao.test_basicc                 C   sb   t t" tg dg dg}tddgddgg}t|| W d    d S 1 s*w   Y  d S )Nr6   r~   r   ra   r   r_   r6   r~   r   ra   r  raises
ValueErrorr   r   r  r   r   r   test_number_of_columns_equality  s   "z-TestKhatriRao.test_number_of_columns_equalityc                 C   s   t t tg d}tg d}t|| W d    n1 s!w   Y  t t tg d}tg dg dg}t|| W d    n1 sKw   Y  t t tg dg dg}tg d}t|| W d    d S 1 svw   Y  d S )Nr  r  )rO   r   rb   r  r  r   r   r   test_to_assure_2d_array  s*   	"z%TestKhatriRao.test_to_assure_2d_arrayc                    sf   t ddgddgg t ddgddggt }t fd	d
tjd D j}t|| d S )Nr6   r~   r   ra   r   r_   rO   r   c                    s0   g | ]}t  d d |f d d |f qS rl  )r   kron)r   r  r1   r  r   r   
<listcomp>  s    (z@TestKhatriRao.test_equality_of_two_equations.<locals>.<listcomp>)r   r   r   r\  rf   r   r   r
   )r0   res1res2r   r  r   test_equality_of_two_equations  s   
z,TestKhatriRao.test_equality_of_two_equationsN)rK   rL   rM   r  r  r  r  r   r   r   r   r    s
    r  )-__doc__rd   r  numpyr   r   r   r   r   numpy.testingr   r   r   r	   r
   r   r  scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   scipy.linalg._expm_frechetscipy.optimizer   r    r"   rN   r   r   r"  r4  ru  rv  rw  rx  r  r   r   r   r   <module>   s6    0+  v :0v	E