a
    Re%                     @   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   T/var/www/sunrise/env/lib/python3.9/site-packages/scipy/linalg/tests/test_matfuncs.py%_get_al_mohy_higham_2012_experiment_1   s    r    c                   @   s,   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aZ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   )r4   r   r4   r   r   r   r   r4   )r   r   r4   r   Fdispr   r   r/   r0   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(   Fr6   r8   r9   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@r3   r3   r3   r3   r3   r3               $@      @rA   rA   r3   r3   r3   r)         .@rA   rA   r3   r3   r3   r3   r3   rC   rA   r3   r3   r3   r3   r3   rA   r@   r3   r3   r3   r3   r3   r3   r%   r=   r3   r3   r3   r3   r3   r3   r?   Fr6   r8   r9   r   r   r   test_defective3M   s    zTestSignM.test_defective3N)__name__
__module____qualname__r2   r:   r;   rH   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>   rB   rD   rE   rF   rG      g@y                Fr6   )r   r   r   )r/   r0   mr   r   r   r2   [   s    zTestLogM.test_nilsc                 C   s2   t  }t|dd\}}t|}t||ddd d S )NFr6   g-C6
?+=rtolatol)r    r   r   r   )r/   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 )NFr6   h㈵>rO   rP   )r    r   r   logr   r   Zallclose)r/   r   Z
A_funm_logrT   rU   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 ]}t j||}t dddD ]r}|| }t j|}d| d| }t|d	d
\}}|	|}	t
|	| t|d	d
\}
}t|
}t
|||d q6qd S )N  r4         	   zM:z eivals:Fr6   )err_msg)r   randomseedrangerandnlogspacelinalgeigvalsr   r   r   r   r   )r/   n
M_unscaledscaleMWr_   M_sqrtmrT   M_sqrtm_round_tripM_logmZ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 ]b}t j||dt j||  }t dddD ].}|| }t|dd	\}}t|}t|| qHqd S 
NrZ   r4   r[                 ?r\   r]   r^   Fr6   )	r   r`   ra   rb   rc   rd   r   r   r   )r/   rg   rh   ri   rj   rn   rT   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 ]}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Gr4   r         c                 s   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   Fr6   )scipyre   rf   r   anyr   r   r   r   r   charcomplex)r/   complex_dtype_charsmatrix_as_listrk   r   rS   rT   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 ]h}tj||d}tj|}tdt|j	
 k  t|dd\}}tt|jtj tt|| qd S )N)r4   r4   rx   )rx   r4   r4   )r4   rx   r4   r   {Gz?Fr6   )r   r   r   r   r   re   rf   r   absoluter|   sumr   
issubdtyper   Zinexactr   r   )r/   rj   dtXr   YrT   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 ]D}t tfD ]6}tj||d}t|dd\}}tt|jtj q,q d S )Nr4   r   r   Fr6   )	r   r   r   r   r   r   r   r   Zcomplexfloating)r/   rj   r   r   rS   rT   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 ]4}tj}t|t|dd\}}t|}t	||dd q<d S )Nr   rq   r4   Fr6   rO   rR   )
r   r   ZasarrayTr   ZLogmExactlySingularWarningr   r   r   r   )r/   r   Brj   expected_warningLrT   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.++Fr6   rO   r   )r   r   r   ZLogmNearlySingularWarningr   r   r   r   )r/   rj   r   r   rT   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   r4   r         ?rO   r   rq   r]   y             rx   )r   pir   r   r   )r/   r   r   r   r   r   &test_opposite_sign_complex_eigenvalues   s    *$z/TestLogM.test_opposite_sign_complex_eigenvaluesN)rI   rJ   rK   r2   rV   rY   ro   rs   r   r   r   r   r   r   r   r   r   r   rL   Y   s   
	rL   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$ Zd%d& Zd'd( Zd)S )*	TestSqrtMc                 C   sn   t jd tddD ]R}t j||}t dddD ]0}|| }t|dd\}}||}t|| q6qd S )	NrZ   r4   r[   r\   r]   r^   Fr6   	r   r`   ra   rb   rc   rd   r   r   r   r/   rg   rh   ri   rj   rl   rT   rm   r   r   r   ro      s    
z&TestSqrtM.test_round_trip_random_floatc                 C   s   t jd tddD ]d}t j||dt j||  }t dddD ]0}|| }t|dd	\}}||}t|| qHqd S rp   r   r   r   r   r   rs      s     
z(TestSqrtM.test_round_trip_random_complexc                 C   s   d}t |}tg dd|ddgdd|dgg dg}tg dd|ddgdd|dgg dg}|jd }tt||| t|d|dd }tt||| t|dddd }tt||| d S )	Ng      ?)      ?r   r   r4   r   r5   )r4   r   r   r   Fr7   	blocksizerx   )r   r   shaper   r   r   )r/   eser0   sarg   Zesar   r   r   test_bad   s$    




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 ]}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  qNd S )Nrt   r4   r   rx   ry   c                 s   s   | ]}|j p|jd k V  qdS rz   r{   r~   r   r   r   r   #  r   zHTestSqrtM.test_sqrtm_type_preservation_and_conversion.<locals>.<genexpr>r   Fr6   )r   re   rf   r   r   r   r   r   r   r   r   r   r/   r   r   rk   r   A_sqrtmrT   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 ]}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  q8d S )Nrt   r4   r   r   r   r4   r   r   r   r4   r4   r   r   c                 s   s   | ]}|j p|jd k V  qdS rz   r{   r~   r   r   r   r   =  r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>r   Fr6   )r   re   rf   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 ]v}t j||dt j||  }t|d|d\}}t|t j	|d tddD ] }t|d|d\}}t|| qjqd S )	NrZ   r4      rq   Fr   rx   
   )
r   r`   ra   rb   randrc   r   r   re   matrix_power)r/   rg   r   ZA_sqrtm_defaultrT   r   Z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 )NFr6   rW   rQ   )r    r   r   r   r   tril)r/   r   r   rT   rU   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 ]L}tjg dg dg dg dg|d}t|dd\}}tt|  qd S )N)r   ry   r   r   )r   r   ry   r   )r   r   r   ry   r   r   r   r   r   Fr6   )intr   r   r   r   r   isnanall)r/   r   r   r   rT   r   r   r   test_strict_upper_triangular\  s    z&TestSqrtM.test_strict_upper_triangularc                 C   s   t tfD ]v}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   Fr6   )
r   r   r   r   r
   r   r   r   r   r   )r/   r   r   r   ZB_sqrtmrT   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 )NrZ   ry   Tr6   )r   r`   ra   r   r   r   r   )r/   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               @r]   r                       ?      ?rx         ?      rO   r   )r   r   r   r   r/   rj   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)r4   r   r   r4   r   r   r   rO   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)rx   r4   r   rx   r4   r   rO   r   )r   Z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)rx   rx   rO   r   )r   zerosr   r   r   r   r   r   r   test_gh7839  s    

zTestSqrtM.test_gh7839c                 C   s   t jdt jd}t|jt jks$J t jdt jd}t|jt jksHJ t jdt jd}t|jt jkslJ t jdt j	d}t|jt j
ksJ d S Nr   r   r   )r   r   Zuint8r   r   float16Zuint16Zuint32float32Zuint64float64r/   rj   r   r   r   -test_data_size_preservation_uint_in_float_out  s    z7TestSqrtM.test_data_size_preservation_uint_in_float_outc                 C   s   t jdt jd}t|jt jks$J t jdt jd}t|jt jksHJ t jdt jd}t|jt jkslJ t jdt j	d}t|jt j
ksJ d S r   )r   r   int8r   r   r   int16int32r   int64r   r   r   r   r   ,test_data_size_preservation_int_in_float_out  s    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s0J 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sJ t jddgddggt jd}t|jt j	ksJ d S )Nrx   r]   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$J t jdt jd}t|jt jksHJ t jdt jd}t|jt jkslJ tt drt jdt jd}t|jt jksJ d S )Nr   r   float128)	r   r   r   r   r   r   r   hasattrr   r   r   r   r   .test_data_size_preservation_float_in_float_out  s    
z8TestSqrtM.test_data_size_preservation_float_in_float_outc                 C   s   t jddgddggt jd}t|jt jks0J t jddgddggt jd}t|jt jks`J t jddgddggt jd}t|jt jksJ t	t drt	t drt jddgddggt j
d}t|jt jksJ d S )Nrx   r]   r   r   r   r   
complex256)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   -test_data_size_preservation_float_in_comp_out  s    z7TestSqrtM.test_data_size_preservation_float_in_comp_outc                 C   s   t jddgddggt jd}t|jt jks0J tt drt jddgddggt jd}t|jt jksjJ t jddgddggt jd}t|jt jksJ d S )Nr   r]   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   ,test_data_size_preservation_comp_in_comp_out  s    
z6TestSqrtM.test_data_size_preservation_comp_in_comp_outN)rI   rJ   rK   ro   rs   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r      s(   

r   c                   @   sj   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
ejjdddd Zdd ZdS )TestFractionalMatrixPowerc                 C   s   t jd tddD ]v}tddD ]f}t j||dt j||  }t dddD ]2}|| }t|d| }t j||}t	|| qVq$qd S )NrZ   r4      rq   r\   r]   r^   
r   r`   ra   rb   rc   rd   r   re   r   r   r/   prg   rh   ri   rj   ZM_rootrr   r   r   r   rs     s     z8TestFractionalMatrixPower.test_round_trip_random_complexc                 C   s   t jd tddD ]d}tddD ]T}t j||}t dddD ]2}|| }t|d| }t j||}t	|| qDq$qd S )NrZ   r4   r   r\   r]   r^   r   r   r   r   r   ro     s    z6TestFractionalMatrixPower.test_round_trip_random_floatc                 C   s   t jd dD ]}tdD ]}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 )NrZ   )rx   ry   r   r   rq   皙?r   gigffffff@   )	r   r`   ra   rb   rc   r   re   r   r   )r/   rg   irj   ZM_one_fifthrr   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 ]}tdd}t j }t tdd}t j||}tdrr|dt j||  }|| }t||}t	|dd	\}}	t
|| }
t||
 qd S )
NrZ      r4   r   r\   )TFrq   Fr6   )r   r`   ra   rb   	randrangerc   expchoicer   r   r   r   )r/   nsamplesr   rg   r   Zmatrix_scaler   A_powerrS   rT   Z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||dd t|| t|| dD ]D}t||}t|d| }t||dd tt	|dt	|d qfd S )	NFr6   r   g|=r   )r   g?r4   r   )
r    r   r   r   r   r   Z_remainder_matrix_powerr   r   r   )	r/   r   ZA_funm_sqrtrT   r   ZA_rem_powerr   r   rU   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|| q4q(d S )NrZ   r   rq   r   r4   )	r   r`   ra   rc   rb   r   Z_briggs_helper_functionZexp2r   )r/   r0   kZ
x_observedZ
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 ]}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  qlq@d S )
Nrt   r4   r   rx   ry   c                 s   s   | ]}|j p|jd k V  qdS rz   r{   r~   r   r   r   r   P  r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>333333r   gffffff
@r   )r   re   rf   r   r   r   r   r   r   r   r   r   r/   r   r   rk   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}tj|td}t||}t|j	j
|v  tj|td}t||}t|j	j
|v  qbq8d S )Nrt   r4   r   r   r   r   r   c                 s   s   | ]}|j p|jd k V  qdS rz   r{   r~   r   r   r   r   n  r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>r   r   )r   re   rf   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 ]r}t tfD ]d}tj||d	}d
D ] }t||}tt|  qddD ]&}t||}t|d| }t|| qqNqBd S )Nr   r4   rx   ry   r[   r   )r   r4   r4   )r   r   r4   r   )gffffffr   r   g)r   gzG?)	r   r   r   r   r   r   r   r   r   )r/   r   Znewtyper   r   r   rU   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   r]   r   r   r   rx   r   rO   r   r   )r   r   r   r   r   r   r   r   r     s    z@TestFractionalMatrixPower.test_opposite_sign_complex_eigenvaluesN)rI   rJ   rK   rs   ro   r   r   r   r   r   r   pytestmarkZ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 )Nr3   r   r4   )r   r   r   r9   r   r   r   	test_zero  s    zTestExpM.test_zeroc                 C   s"   t d}t|ttjgg d S )Nr4   )r   r   r   r   r   )r/   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)r/   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sJ d S )Nr4   r]   rx   ru   f)
r   r   r   r   r   Zastyper   r   r   r   )r/   r   r0   ZaaZ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 )Nr4   r]   ry   r   r   r\   ru   )orderrx   rM   r   r[   )r   r   r   r   r   )r/   r   r0   Za_resr   r   r   test_nx2x2_input  s6    "&>622>>..zTestExpM.test_nx2x2_inputN)rI   rJ   rK   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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|| qd S )Nr4   rx   ry   r]   r   r[   rM   r   r   r   r4   rx   r   r   r   r[   r   r4   rx   r   r[   ry   r]   rM   r   methodSPSblockEnlarge)r   r   r   r   re   r   r   r   )	r/   rj   r   r   expected_expmexpected_frechetkwargsobserved_expmobserved_frechetr   r   r   test_expm_frechet  s4    
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 ]\}}tjjj| }	tjjj| }
d|	|
  }|| }|| }|| }|| }tj	|}tj	|d ddd f }t
||\}}t|| t|| qd S )Nr  r  r  r  r   r4   rx   r   r[   ry   r]   rM   r   )r4   ry   r   rM   r^            r   r   )r   r   r   r   re   r   zipZ_expm_frechetZell_table_61r   r   r   )r/   Z
M_original
A_original
E_originalA_original_norm_1Zselected_m_listZm_neighbor_pairsmambZell_aZell_btarget_norm_1ri   rj   r   r   r  r  r  r  r   r   r   test_small_norm_expm_frechet  sH    
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 ]}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   rx      r  r4   gHj>r   gHz>)r   r`   uniformnormalZstandard_cauchyexponentialrb   r   expovariater   r   re   r   vstackZhstackZ
zeros_liker   r   r   )r/   ZrfuncsZntestsr   Zrfuncr#  rg   r  r  r   ri   r   r   rj   r  r  r  r  r   r   r   	test_fuzz  s2    

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?r4   r  r  r  )r   r   r   r   re   r   r   r   )r/   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  r'  r  r.  r  )r   r`   r*  r   r   )r/   rg   r   r   r/  r0  r1  r2  r   r   r   test_medium_matrix0  s    


z"TestExpmFrechet.test_medium_matrixN)rI   rJ   rK   r  r$  r-  r3  r   r   slowskipr4  r   r   r   r   r    s   !r  c           
      C   sL   t || j}t|}|| ||  }t| | }t|| ||  }	|	 S N)r   reshaper   r   r   )
r   A_normr   X_normepsr   Zp_normperturbationX_primeZscaled_relative_errorr   r   r   _help_expm_cond_search?  s    r>  c                 C   s   | t j|t j|   S r7  )r   re   r   )r   r   r   r   r   _normalized_likeH  s    r?  c                 C   s(   | |}| || }t || t | S r7  )r   )r  r   r<  r   r=  r   r   r   _relative_errorL  s    r@  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 ]$}t j||}t|}td| qd S )NrZ   r4   r]   r   )r   r`   ra   rb   rc   r   r	   )r/   rg   r   kappar   r   r   test_expm_cond_smokeS  s
    z,TestExpmConditionNumber.test_expm_cond_smokec                 C   s8   t g dg dg dg dg}t|}td| d S )N)g(gٙBgx@g  =g ZdB)r   gzNV7g@g  2p)r   r   gᙥT g?W[E@)r   r   r   gT!g yhG)r   r   r   r	   )r/   r   rB  r   r   r   test_expm_bad_condition_numberZ  s    z6TestExpmConditionNumber.test_expm_bad_condition_numberc                 C   s   t jd t jddddD ]$}t |gg}tt|t| qt jddddD ]$}t |gg}tt|t| qRt	dD ]*}t j
d	d	}tt|t |d
  qd S )N90  r
  r   r  )numr   rx   r   r4   r  )r   r`   ra   Zlinspacer   r   r   absrd   rb   rc   r   )r/   xr   r   r   r   r   test_univariated  s    z'TestExpmConditionNumber.test_univariatec              	   C   sF  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 ]D}|tt jj|j | }tt|t| tt	||}t|| qt|dd|  | |	  qd S )	NrE  rW   r   rx   r   zL-BFGS-Br.  r4   )r   r`   ra   rb   randintrc   r   re   r   r   r   	functoolspartialr>  Zonesr   rH  r?  r8  r   r@  r   r	   )r/   r;  r   r   rg   r   r9  r   r:  rB  r  guessoutZxoptZyoptZp_bestZp_best_relerrjZp_randZp_rand_relerrr   r   r   test_expm_cond_fuzzp  s4    
z+TestExpmConditionNumber.test_expm_cond_fuzzN)
rI   rJ   rK   rC  rD  rI  r   r   r5  rP  r   r   r   r   rA  R  s
   
rA  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
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 )Nr4   rx   ry   r]   r   r[   rM   r      r&  r            )r]   rx   )r   r   r
   r   emptyr   r/   r0   br   r   r   
test_basic  s    zTestKhatriRao.test_basicc                 C   s`   t tB tg dg dg}tddgddgg}t|| W d    n1 sR0    Y  d S )Nr4   rx   ry   r]   r   r[   r4   rx   ry   r]   r   Zraises
ValueErrorr   r   rW  r   r   r   test_number_of_columns_equality  s    z-TestKhatriRao.test_number_of_columns_equalityc                 C   s   t t2 tg d}tg d}t|| W d    n1 sB0    Y  t t: tg d}tg dg dg}t|| W d    n1 s0    Y  t t: tg dg dg}tg d}t|| W d    n1 s0    Y  d S )NrZ  r[  )rM   r   r^   r\  rW  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 )Nr4   rx   ry   r]   r   r[   rM   r   c                    s0   g | ](}t  d d |f d d |f qS r7  )r   Zkron)r   r   r0   rX  r   r   
<listcomp>  s   z@TestKhatriRao.test_equality_of_two_equations.<locals>.<listcomp>)r   r   r   r,  rb   r   r   r
   )r/   Zres1Zres2r   r`  r   test_equality_of_two_equations  s    

z,TestKhatriRao.test_equality_of_two_equationsN)rI   rJ   rK   rY  r^  r_  rb  r   r   r   r   rQ    s   rQ  )-__doc__r`   rK  numpyr   r   r   r   r   Znumpy.testingr   r   r   r	   r
   r   r   Zscipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   Zscipy.linalg._expm_frechetZscipy.optimizer   r    r!   rL   r   r   r   r  r>  r?  r@  rA  rQ  r   r   r   r   <module>   s4    0+  v :0v	E