U
    Ì6{i(. ã                   @   sz
  d Z ddlZddlZddlZddlZddlZddl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 ddlmZ ddlmZmZmZmZ ddlmZ ddlmZmZmZmZmZ ddlm Z  dd	l!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z* d
d„ Z+e&Z,dñdd„Z&dd„ Z-dd„ Z.dd„ Z/ddddddhZ0G dd„ dƒZ1dd„ Z2e	j3 4d ¡ g Z5e5e2de1d!e
d"d#gd$d%gged&�e
d#d"ged&�ƒe1d'e
d"d#gd$d%gged&�e
d#d"ged&�ƒe1d(e
d"d#gd$d%gged&�e
d#d"d%gd$d%d)gged&�ƒe1d*e
d+d,gd-d.gged&�e
d/d+ged&�ƒe1d0e
d+d,gd-d.gged&�e
d/d+ged&�ƒe1d1e
d+d,gd-d.gged&�e
d/d+d2gd3d4d5gged&�ƒe1d6e	j6d7ed&�e	j6d8ed&�dhd9�e1d:e	j3 7d;d;¡e	j3 7d;¡ƒe1d<e	j3 7d=d=¡e	j3 7d=¡ƒe1d>d=d?gd@dAggd?d=gƒg
ƒ7 Z5e5e2de1dBe
d"d#d$gd$d%d)gged&�e
d#d"ged&�ƒe1dCe
d"d#gd$d%gdDd)gged&�e
d#d"d$ged&�ƒe1dEe
d"d#d$gd$d%d)gged&�e
d#d"ged&�ƒe1dFe
d"d#gd$d%gdDd)gged&�e
d#d"d$ged&�ƒe1dGe
dHdIdJgdKdLdMgged&�e
d/d+ged&�ƒe1dNe
dHdIgdJdOgdPdQgged&�e
d/d+dJged&�ƒe1dRe
dHdIdJgdKdLdMgged&�e
d/d+ged&�ƒe1dSe
dHdIgdJdOgdPdQgged&�e
d/d+dJged&�ƒe1dTe
dHdIdJgdKdLdMgged&�e
d/d+gdUdVgged&�ƒe1dWe
dHdIgdJdOgdPdQgged&�e
d/d+gdUdVgdUdVgged&�ƒe1dXe	j3 7d;dY¡e	j3 7d;¡ƒe1dZe	j3 7d=d[¡e	j3 7d=¡ƒe1d\e	j3 7d[d=¡e	j3 7d[¡ƒe1d]e	j3 7ddA¡e	j3 7d¡dhd9�e1d^e	j3 7dAd¡e	j3 7dA¡dhd9�gƒ7 Z5e5e2de1d_e
d"d#gd#d"gged&�dƒe1d`e
d"d#gd#d"gged&�dƒe1dae
d"d,gdbd=gged&�dƒe1dce
d"d,gdbd=gged&�dƒe1dde	j6d7ed&�ddhd9�e1ded=d?gd?d=ggdƒe1dfe
d"d#gd#d"ggƒdƒe1dge	j3 7d=d=¡dƒgƒ7 Z5dhdi„ Z8e5e8ƒ 7 Z5djdk„ Z9dldm„ Z:e5e:ƒ 7 Z5G dndo„ doƒZ;G dpdq„ dqe;ƒZ<G drds„ dse;ƒZ=G dtdu„ due;ƒZ>G dvdw„ dwe;ƒZ?G dxdy„ dye;ƒZ@G dzd{„ d{e;ƒZAd|d}„ ZBd~d„ ZCG d€d�„ d�e<e?ƒZDG d‚dƒ„ dƒeDƒZEG d„d…„ d…e<e?ƒZFG d†d‡„ d‡eFƒZGG dˆd‰„ d‰e<e?ƒZHG dŠd‹„ d‹eHƒZIG dŒd�„ d�e<e?ƒZJG dŽd�„ d�eJƒZKG d�d‘„ d‘ƒZLG d’d“„ d“e<e?ƒZMG d”d•„ d•eMeLƒZNG d–d—„ d—e>eAƒZOG d˜d™„ d™eOeLƒZPG dšd›„ d›e<e?ƒZQG dœd�„ d�eQƒZRG dždŸ„ dŸe<e=e?e@ƒZSG d d¡„ d¡eSƒZTG d¢d£„ d£e>eAƒZUG d¤d¥„ d¥eUƒZVG d¦d§„ d§e<e?ƒZWG d¨d©„ d©eWƒZXG dªd«„ d«e<e=ƒZYG d¬d­„ d­eYƒZZej[ \d®d¯d°„ d±D ƒ¡G d²d³„ d³ƒƒZ]G d´dµ„ dµe>eAƒZ^G d¶d·„ d·ƒZ_G d¸d¹„ d¹e>eAƒZ`G dºd»„ d»ƒZaG d¼d½„ d½ƒZbG d¾d¿„ d¿ebƒZcG dÀdÁ„ dÁebƒZdG dÂdÃ„ dÃedecƒZeG dÄdÅ„ dÅƒZfG dÆdÇ„ dÇebƒZgG dÈdÉ„ dÉebƒZhG dÊdË„ dËebƒZiG dÌdÍ„ dÍeeegƒZjG dÎdÏ„ dÏeeehƒZkG dÐdÑ„ dÑeeeiƒZlG dÒdÓ„ dÓƒZmdÔdÕ„ ZnG dÖd×„ d×ƒZoG dØdÙ„ dÙƒZpdÚdÛ„ ZqdÜdÝ„ ZrdÞdß„ Zsej[jtdàdá„ ƒZuG dâdã„ dãƒZvG dädå„ dåƒZwG dædç„ dçƒZxdèdé„ Zyej[jzdêdë�dìdí„ ƒZ{ej[j|e* dîdë�dïdð„ ƒZ}dS )òz# Test functions for linalg module

é    N)ÚarrayÚsingleÚdoubleÚcsingleÚcdoubleÚdotÚidentityÚmatmul)Úswapaxes)ÚmultiplyÚ
atleast_2dÚinfÚasarray)Úlinalg)Úmatrix_powerÚnormÚmatrix_rankÚ	multi_dotÚLinAlgError)Ú_multi_dot_matrix_chain_order)	Úassert_Úassert_equalÚassert_raisesÚassert_array_equalÚassert_almost_equalÚassert_allcloseÚsuppress_warningsÚassert_raises_regexÚHAS_LAPACK64c                 C   s"   t | ƒt|tjƒrt |ƒntjkS ©N)ÚtypeÚ
isinstanceÚnpÚndarray)ÚoutÚin_© r&   úB/tmp/pip-unpacked-wheel-dv5xso59/numpy/linalg/tests/test_linalg.pyÚconsistent_subclass   s    ÿr(   é   é   c                 K   s8   t | ƒjjttfkr|}n|}t| |fd|i|—Ž d S )NÚdecimal)r   Údtyper    r   r   Úold_assert_almost_equal)ÚaÚbÚsingle_decimalÚdouble_decimalÚkwr+   r&   r&   r'   r   $   s    r   c                 C   s   t t tttt tti|  S r   )r   r   r   r   ©r,   r&   r&   r'   Úget_real_dtype,   s       ÿÿr4   c                 C   s   t ttttttti|  S r   )r   r   r   r   r3   r&   r&   r'   Úget_complex_dtype1   s       ÿÿr5   c                 C   s   | t tfkrdS dS d S )Ngñhãˆµøä>g•dyáý¥=)r   r   r3   r&   r&   r'   Úget_rtol6   s    r6   ÚsquareÚ	nonsquareÚ	hermitianÚgeneralizedúsize-0Ústridedc                   @   s*   e Zd Zeƒ fdd„Zdd„ Zdd„ ZdS )Ú
LinalgCasec                 C   s.   t t|tƒƒ || _|| _|| _t|ƒ| _dS )z¢
        A bundle of arguments to be passed to a test case, with an identifying
        name, the operands a and b, and a set of tags to filter the tests
        N)r   r!   ÚstrÚnamer.   r/   Ú	frozensetÚtags)Úselfr?   r.   r/   rA   r&   r&   r'   Ú__init__F   s
    zLinalgCase.__init__c                 C   s   || j | j| jd� dS )zN
        Run the function `do` on this test case, expanding arguments
        ©rA   N)r.   r/   rA   )rB   Údor&   r&   r'   ÚcheckQ   s    zLinalgCase.checkc                 C   s   d| j › d�S )Nz<LinalgCase: ú>)r?   ©rB   r&   r&   r'   Ú__repr__W   s    zLinalgCase.__repr__N)Ú__name__Ú
__module__Ú__qualname__ÚsetrC   rF   rI   r&   r&   r&   r'   r=   E   s   r=   c                 C   s,   | t kstdƒ‚|D ]}|j| hB |_q|S )z^
    Add the given tag (a string) to each of the cases (a list of LinalgCase
    objects)
    zInvalid tag)Úall_tagsÚAssertionErrorrA   )ÚtagZcasesÚcaser&   r&   r'   Ú	apply_tag[   s    rR   éÒ  r   ç      ð?ç       @ç      @ç      @r3   r   Zdouble_2ç      @r   y      ð?       @y       @      @y      @      @y      @      @y       @      ð?r   Z	cdouble_2y      ð?      @y      ð?       Ày      ð?      Ày      ð?      ÀZ0x0©r   r   ©r   rD   Z8x8é   Z1x1é   Znonarrayé   é   é   Zsingle_nsq_1Zsingle_nsq_2g      @Zdouble_nsq_1Zdouble_nsq_2Zcsingle_nsq_1y      ð?      ð?y       @       @y      @      Ày      @      Ày      @      "@y      @       @Zcsingle_nsq_2y      @      "Ày      @      Ày      @       @Zcdouble_nsq_1Zcdouble_nsq_2Zcdouble_nsq_1_2y      ð?      ð¿y       @       ÀZcdouble_nsq_2_2Z8x11é   Z1x5é   Z5x1Z0x4Z4x0ZhsingleZhdoubleZhcsingley       @      ÀZhcdoubleZhemptyZ	hnonarrayZmatrix_b_onlyZhmatrix_1x1c                  C   s  g } t D �]}t|jtjƒsqt |jd|j d|j g¡}|jd krLd }nt |jd|j d|j g¡}t|jd |||j	dhB d�}|  
|¡ t |jgd d ¡ d|jj ¡}|jd krÆd }n$t |jgd d ¡ d|jj ¡}t|jd	 |||j	dhB d�}|  
|¡ q| S )
Nr]   r^   é   r)   Z_tile3r:   rD   ©r^   r]   Z_tile213)ÚCASESr!   r.   r"   r#   r   r/   r=   r?   rA   ÚappendÚreshapeÚshape)Ú	new_casesrQ   r.   r/   Únew_caser&   r&   r'   Ú_make_generalized_casesë   s*    


ÿ
$
$
ÿrj   c                 c   sè  t | tjƒs| dfV  dS dg| j }d|d< | jdkr@d|d< | jdkrRd	|d
< tjt|ƒŽ D �]€}dd„ t| j|ƒD ƒ}tdd„ |D ƒƒ}tj	|| j
d�}| tj¡ d¡ || }| |d< | | j¡}tt || k¡ƒ |dd dd„ |D ƒ¡ fV  | jdk�rF| jd dk�rFt| jƒ}d|d< tjjj| |d�}|dfV  | jdk�r�| jd dk�r�t| jƒ}d|d< tjjj| |d�}|dfV  | jdkr`| jdd… dkr`t| jƒ}d|d< d|d< tjjj| |d�}|dfV  q`dS )z<
    Generate cartesian product of strides for all axes
    ZnopN©r\   )r\   r^   éüÿÿÿéÿÿÿÿr\   éþÿÿÿr]   )r\   rl   éýÿÿÿc                 S   s   g | ]\}}t || ƒ‘qS r&   )Úabs)Ú.0r.   r/   r&   r&   r'   Ú
<listcomp>  s     z%_stride_comb_iter.<locals>.<listcomp>c                 S   s   g | ]}t d d |ƒ‘qS r   )Úslice)rq   Úrepeatr&   r&   r'   rr     s     r3   l   ï>[= .Zstride_Ú_c                 S   s   g | ]}d | ‘qS )z%+dr&   )rq   Újr&   r&   r'   rr   (  s     r   )ÚstridesZstride_xxx_0Zstride_xxx_0_x©r\   r\   Zstride_xxx_0_0)r!   r"   r#   ÚndimÚ	itertoolsÚproductÚtupleÚziprg   Úemptyr,   ÚviewZuint32ÚfillÚ	__class__r   ÚallÚjoinÚlistrw   ÚlibZstride_tricksZ
as_strided)ÚxZ
stride_setZrepeatsÚ	new_shapeZslicesÚxiÚsr&   r&   r'   Ú_stride_comb_iter  sF    







rŠ   c               	   C   sn   g } t D ]`}t|jƒD ]P\}}t|jƒD ]<\}}t|jd | d | |||jdhB d�}|  |¡ q(qq| S )Nru   r<   rD   )rd   rŠ   r.   r/   r=   r?   rA   re   )rh   rQ   r.   Za_labelr/   Zb_labelri   r&   r&   r'   Ú_make_strided_cases=  s    
ÿr‹   c                   @   s"   e Zd ZeZeƒ eƒ fdd„ZdS )ÚLinalgTestCasec                 C   s‚   | j D ]v}|j|@ |krq|j|@ r&qz| | j¡ W q tk
rz } z&d|›d�}|t ¡ 7 }t|ƒ|‚W 5 d}~X Y qX qdS )zx
        Run func on each of the cases with all of the tags in require, and none
        of the tags in exclude
        zIn test case: z

N)Ú
TEST_CASESrA   rF   rE   Ú	ExceptionÚ	tracebackÚ
format_excrO   )rB   ÚrequireÚexcluderQ   ÚeÚmsgr&   r&   r'   Úcheck_casesQ  s    

zLinalgTestCase.check_casesN)rJ   rK   rL   rd   r�   rM   r•   r&   r&   r&   r'   rŒ   N  s   rŒ   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚLinalgSquareTestCasec                 C   s   | j dhddhd� d S )Nr7   r:   r;   ©r‘   r’   ©r•   rH   r&   r&   r'   Útest_sq_casesg  s    ÿz"LinalgSquareTestCase.test_sq_casesc                 C   s   | j ddhdhd� d S )Nr7   r;   r:   r—   r˜   rH   r&   r&   r'   Útest_empty_sq_casesk  s    
ÿz(LinalgSquareTestCase.test_empty_sq_casesN)rJ   rK   rL   r™   rš   r&   r&   r&   r'   r–   e  s   r–   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚLinalgNonsquareTestCasec                 C   s   | j dhddhd� d S )Nr8   r:   r;   r—   r˜   rH   r&   r&   r'   Útest_nonsq_casesr  s    ÿz(LinalgNonsquareTestCase.test_nonsq_casesc                 C   s   | j ddhdhd� d S )Nr8   r;   r:   r—   r˜   rH   r&   r&   r'   Útest_empty_nonsq_casesv  s    
ÿz.LinalgNonsquareTestCase.test_empty_nonsq_casesN)rJ   rK   rL   rœ   r�   r&   r&   r&   r'   r›   p  s   r›   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚHermitianTestCasec                 C   s   | j dhddhd� d S )Nr9   r:   r;   r—   r˜   rH   r&   r&   r'   Útest_herm_cases}  s    ÿz!HermitianTestCase.test_herm_casesc                 C   s   | j ddhdhd� d S )Nr9   r;   r:   r—   r˜   rH   r&   r&   r'   Útest_empty_herm_cases�  s    
ÿz'HermitianTestCase.test_empty_herm_casesN)rJ   rK   rL   rŸ   r    r&   r&   r&   r'   rž   {  s   rž   c                   @   s,   e Zd Zejjdd„ ƒZejjdd„ ƒZdS )ÚLinalgGeneralizedSquareTestCasec                 C   s   | j ddhdhd� d S )Nr:   r7   r;   r—   r˜   rH   r&   r&   r'   Útest_generalized_sq_casesˆ  s    
ÿz9LinalgGeneralizedSquareTestCase.test_generalized_sq_casesc                 C   s   | j dddhd� d S )Nr:   r7   r;   ©r‘   r˜   rH   r&   r&   r'   Útest_generalized_empty_sq_cases�  s    z?LinalgGeneralizedSquareTestCase.test_generalized_empty_sq_casesN)rJ   rK   rL   ÚpytestÚmarkÚslowr¢   r¤   r&   r&   r&   r'   r¡   †  s   
r¡   c                   @   s,   e Zd Zejjdd„ ƒZejjdd„ ƒZdS )Ú"LinalgGeneralizedNonsquareTestCasec                 C   s   | j ddhdhd� d S )Nr:   r8   r;   r—   r˜   rH   r&   r&   r'   Útest_generalized_nonsq_cases”  s    
ÿz?LinalgGeneralizedNonsquareTestCase.test_generalized_nonsq_casesc                 C   s   | j dddhd� d S )Nr:   r8   r;   r£   r˜   rH   r&   r&   r'   Ú"test_generalized_empty_nonsq_cases™  s    zELinalgGeneralizedNonsquareTestCase.test_generalized_empty_nonsq_casesN)rJ   rK   rL   r¥   r¦   r§   r©   rª   r&   r&   r&   r'   r¨   ’  s   
r¨   c                   @   s,   e Zd Zejjdd„ ƒZejjdd„ ƒZdS )ÚHermitianGeneralizedTestCasec                 C   s   | j ddhdhd� d S )Nr:   r9   r;   r—   r˜   rH   r&   r&   r'   Útest_generalized_herm_cases   s    
ÿz8HermitianGeneralizedTestCase.test_generalized_herm_casesc                 C   s   | j dddhdhd� d S )Nr:   r9   r;   Únoner—   r˜   rH   r&   r&   r'   Ú!test_generalized_empty_herm_cases¥  s    ÿz>HermitianGeneralizedTestCase.test_generalized_empty_herm_casesN)rJ   rK   rL   r¥   r¦   r§   r¬   r®   r&   r&   r&   r'   r«   ž  s   
r«   c                 C   sÂ   t | ƒ} | jdkr´| j|jkr<| jd d… |jdd …  }n(| j|jd kr\| jd d… }ntdƒ‚tj|t | |¡d�}tjt	t
| jd d… ƒŽ D ]}t| | || ƒ||< q”|S t| |ƒS d S )Nr^   rm   r\   zNot implemented...r3   rn   )r   ry   rg   Ú
ValueErrorr"   r~   Zcommon_typerz   r{   ÚmapÚranger   )r.   r/   r‡   ÚrÚcr&   r&   r'   Údot_generalized«  s    
r´   c                 C   sL   t | ƒ} | jdkr:tj| j| jd�}t| jd ƒ|d< |S t| jd ƒS d S )Nr^   r3   rn   .r   )r   ry   r"   r~   rg   r,   r   )r.   r²   r&   r&   r'   Úidentity_like_generalized¾  s    
rµ   c                   @   s   e Zd Zdd„ ZdS )Ú
SolveCasesc                 C   s.   t  ||¡}t|t||ƒƒ tt||ƒƒ d S r   )r   Úsolver   r´   r   r(   )rB   r.   r/   rA   r†   r&   r&   r'   rE   Ê  s    zSolveCases.doN©rJ   rK   rL   rE   r&   r&   r&   r'   r¶   È  s   r¶   c                   @   s:   e Zd Zej deeee	g¡dd„ ƒZ
dd„ Zdd„ ZdS )	Ú	TestSolver,   c                 C   s2   t jddgddgg|d�}tt ||¡j|ƒ d S ©Nr\   ç      à?r3   )r"   r   r   r   r·   r,   ©rB   r,   r†   r&   r&   r'   Ú
test_typesÑ  s    zTestSolve.test_typesc              	   C   s.  G dd„ dt jƒ}t  d¡ ddd¡}t  d¡ ddd¡ |¡}t ||¡d d …dd…d d …f }t |d d …dd…dd…f |d d …dd…d d …f ¡}t||ƒ tt	||ƒƒ t
tjtj|d d …dd…dd…f |ƒ t
ttj||d d …dd…d d …f ƒ t  d¡ ddd¡}t
ttj||ƒ t
ttj|dd… |dd… ƒ t  d¡ dd¡ |¡}t ||¡d d …dd…f }t |d d …dd…dd…f |d d …dd…f ¡}t||ƒ tt	||ƒƒ t  d¡ dd¡}t
ttj||ƒ t
ttj|dd… |dd… ƒ t
ttj|d d …dd…dd…f |ƒ d S )	Nc                   @   s   e Zd ZdS )z,TestSolve.test_0_size.<locals>.ArraySubclassN©rJ   rK   rL   r&   r&   r&   r'   ÚArraySubclass×  s   r¿   r[   r]   r)   r\   r^   r   )r"   r#   Úarangerf   r   r   r·   r   r   r!   r   r   r¯   ©rB   r¿   r.   r/   ÚexpectedÚresultr&   r&   r'   Útest_0_sizeÖ  s*    "8
(& 2
 zTestSolve.test_0_sizec                 C   s  G dd„ dt jƒ}t  d¡ ddd¡}t  d¡ ddd¡ |¡}t ||¡d d …d d …dd…f }t ||d d …d d …dd…f ¡}t||ƒ tt	||ƒƒ t ||¡d d …dd…dd…f }t |d d …dd…dd…f |d d …dd…dd…f ¡}t||ƒ tt	||ƒƒ d S )	Nc                   @   s   e Zd ZdS )z.TestSolve.test_0_size_k.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿   ù  s   r¿   r_   r\   r]   r)   r^   r   )
r"   r#   rÀ   rf   r   r   r·   r   r   r!   rÁ   r&   r&   r'   Útest_0_size_k÷  s    ""
"8
zTestSolve.test_0_size_kN)rJ   rK   rL   r¥   r¦   Úparametrizer   r   r   r   r½   rÄ   rÅ   r&   r&   r&   r'   r¹   Ð  s   
!r¹   c                   @   s   e Zd Zdd„ ZdS )ÚInvCasesc                 C   s0   t  |¡}tt||ƒt|ƒƒ tt||ƒƒ d S r   )r   Úinvr   r´   rµ   r   r(   )rB   r.   r/   rA   Za_invr&   r&   r'   rE     s
    

ÿzInvCases.doNr¸   r&   r&   r&   r'   rÇ   
  s   rÇ   c                   @   s2   e Zd Zej deeee	g¡dd„ ƒZ
dd„ ZdS )ÚTestInvr,   c                 C   s0   t jddgddgg|d�}tt |¡j|ƒ d S rº   )r"   r   r   r   rÈ   r,   r¼   r&   r&   r'   r½     s    zTestInv.test_typesc                 C   s²   G dd„ dt jƒ}t jdt jd� |¡}t |¡}t|jj	t j
kƒ t|j|jƒ tt||ƒƒ t jdt jd� |¡}t |¡}t|jj	t jkƒ t|j|jƒ tt||ƒƒ d S )Nc                   @   s   e Zd ZdS )z*TestInv.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿     s   r¿   ©r   r\   r\   r3   rY   )r"   r#   ÚzerosÚint_r   r   rÈ   r   r,   r    Úfloat64r   rg   r!   Ú	complex64©rB   r¿   r.   Úresr&   r&   r'   rÄ     s    

zTestInv.test_0_sizeN©rJ   rK   rL   r¥   r¦   rÆ   r   r   r   r   r½   rÄ   r&   r&   r&   r'   rÉ     s   
rÉ   c                   @   s   e Zd Zdd„ ZdS )ÚEigvalsCasesc                 C   s&   t  |¡}t  |¡\}}t||ƒ d S r   )r   ÚeigvalsÚeigr   )rB   r.   r/   rA   ÚevÚevaluesÚevectorsr&   r&   r'   rE   ,  s    
zEigvalsCases.doNr¸   r&   r&   r&   r'   rÒ   *  s   rÒ   c                   @   s2   e Zd Zej deeee	g¡dd„ ƒZ
dd„ ZdS )ÚTestEigvalsr,   c                 C   s`   t jddgddgg|d�}tt |¡j|ƒ t jddgddgg|d�}tt |¡jt|ƒƒ d S ©Nr\   r»   r3   rm   )r"   r   r   r   rÓ   r,   r5   r¼   r&   r&   r'   r½   3  s    zTestEigvals.test_typesc                 C   s²   G dd„ dt jƒ}t jdt jd� |¡}t |¡}t|jj	t j
kƒ td|jƒ tt|t jƒƒ t jdt jd� |¡}t |¡}t|jj	t jkƒ td|jƒ tt|t jƒƒ d S )Nc                   @   s   e Zd ZdS )z.TestEigvals.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿   <  s   r¿   rÊ   r3   ©r   r\   rY   rZ   )r"   r#   rË   rÌ   r   r   rÓ   r   r,   r    rÍ   r   rg   r!   rÎ   rÏ   r&   r&   r'   rÄ   :  s    

zTestEigvals.test_0_sizeNrÑ   r&   r&   r&   r'   rØ   2  s   
rØ   c                   @   s   e Zd Zdd„ ZdS )ÚEigCasesc                 C   sX   t  |¡\}}tt||ƒt |¡t |¡dd d d …f  t|jƒd� tt	||ƒƒ d S )N.©Úrtol)
r   rÔ   r   r´   r"   r   r6   r,   r   r(   )rB   r.   r/   rA   rÖ   r×   r&   r&   r'   rE   O  s    
 þzEigCases.doNr¸   r&   r&   r&   r'   rÛ   M  s   rÛ   c                   @   s2   e Zd Zej deeee	g¡dd„ ƒZ
dd„ ZdS )ÚTestEigr,   c                 C   s�   t jddgddgg|d�}t j |¡\}}t|j|ƒ t|j|ƒ t jddgddgg|d�}t j |¡\}}t|jt|ƒƒ t|jt|ƒƒ d S rÙ   )r"   r   r   rÔ   r   r,   r5   ©rB   r,   r†   ÚwÚvr&   r&   r'   r½   X  s    zTestEig.test_typesc                 C   sú   G dd„ dt jƒ}t jdt jd� |¡}t |¡\}}t|jj	t j
kƒ t|jj	t j
kƒ t|j|jƒ td|jƒ tt|t jƒƒ t jdt jd� |¡}t |¡\}}t|jj	t jkƒ t|jj	t jkƒ t|j|jƒ td|jƒ tt|t jƒƒ d S )Nc                   @   s   e Zd ZdS )z*TestEig.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿   f  s   r¿   rÊ   r3   rÚ   rY   rZ   )r"   r#   rË   rÌ   r   r   rÔ   r   r,   r    rÍ   r   rg   r!   rÎ   ©rB   r¿   r.   rÐ   Zres_vr&   r&   r'   rÄ   d  s    zTestEig.test_0_sizeNrÑ   r&   r&   r&   r'   rÞ   W  s   
rÞ   c                   @   s.   e Zd ZdZej deee	e
g¡dd„ ƒZdS )ÚSVDBaseTestsFr,   c                 C   sx   t jddgddgg|d�}t |¡\}}}t|j|ƒ t|jt|ƒƒ t|j|ƒ tj|d| jd�}t|jt|ƒƒ d S )Nr\   r»   r3   F©Ú
compute_uvr9   )r"   r   r   Úsvdr   r,   r4   r9   )rB   r,   r†   Úur‰   Úvhr&   r&   r'   r½   ~  s    zSVDBaseTests.test_typesN)rJ   rK   rL   r9   r¥   r¦   rÆ   r   r   r   r   r½   r&   r&   r&   r'   rã   {  s   rã   c                   @   s   e Zd Zdd„ ZdS )ÚSVDCasesc              	   C   sp   t  |d¡\}}}t|tt |¡t |¡dd d d …f  t |¡ƒt|jƒd� tt	||ƒƒ tt	||ƒƒ d S )NF.rÜ   )
r   ræ   r   r´   r"   r   r6   r,   r   r(   )rB   r.   r/   rA   rç   r‰   Úvtr&   r&   r'   rE   ‹  s    &ÿþzSVDCases.doNr¸   r&   r&   r&   r'   ré   ‰  s   ré   c                   @   s   e Zd Zdd„ ZdS )ÚTestSVDc                 C   s˜   t  d¡}tj|d| jd�\}}}t|jdƒ t|jdƒ t|t  d¡ƒ t  d¡}tj|d| jd�\}}}t|jdƒ t|jdƒ t|t  d¡ƒ dS )	z6 Empty input should put an identity matrix in u or vh )r_   r   Trä   ©r_   r_   rY   r_   )r   r_   N)r"   r~   r   ræ   r9   r   rg   Úeye)rB   r†   rç   r‰   rè   r&   r&   r'   Útest_empty_identity•  s    

zTestSVD.test_empty_identityN)rJ   rK   rL   rî   r&   r&   r&   r'   rë   ”  s   rë   c                   @   s   e Zd Zdd„ ZdS )ÚSVDHermitianCasesc              	   C   sò   t j|ddd�\}}}t|tt |¡t |¡dd d d …f  t |¡ƒt|jƒd� dd„ }tt 	|||ƒ¡t 
t |jd ¡|j¡ƒ tt 	|||ƒ¡t 
t |jd ¡|j¡ƒ tt |¡dd d d…f |ƒ tt||ƒƒ tt||ƒƒ d S )	NFT©r9   .rÜ   c                 S   s<   t t| jƒƒ}|d |d  |d< |d< t tj| |d�¡S )Nrn   rm   ©Úaxes)r„   r±   ry   r"   ÚconjÚ	transpose)Úmatrò   r&   r&   r'   r9   «  s    z'SVDHermitianCases.do.<locals>.hermitianrm   )r   ræ   r   r´   r"   r   r6   r,   r   r	   Úbroadcast_torí   rg   r   Úsortr   r(   )rB   r.   r/   rA   rç   r‰   rê   r9   r&   r&   r'   rE   ¦  s    &ÿþ,,zSVDHermitianCases.doNr¸   r&   r&   r&   r'   rï   ¤  s   rï   c                   @   s   e Zd ZdZdS )ÚTestSVDHermitianTN)rJ   rK   rL   r9   r&   r&   r&   r'   rø   ·  s   rø   c                   @   s   e Zd Zdd„ ZdS )Ú	CondCasesc                 C   sê  t |ƒ}d|kr"tttj|ƒ d S tj|dd�}tt |¡|d |d  ddd� tt |d	¡|d |d  ddd� tt |d
¡|d |d  ddd� tj |¡}tt |d¡t	|ƒ 
d
¡ d¡t	|ƒ 
d
¡ d¡ ddd� tt |d¡t	|ƒ 
d
¡ d¡t	|ƒ 
d
¡ d¡ ddd� tt |tj¡t	|ƒ 
d¡ d¡t	|ƒ 
d¡ d¡ ddd� tt |tj ¡t	|ƒ 
d¡ d¡t	|ƒ 
d¡ d¡ ddd� tt |d¡t t	|ƒd	  
d¡ 
d¡t	|ƒd	  
d¡ 
d¡ ¡ddd� d S )Nr;   F)rå   ).r   ).rm   ra   r`   ©r0   r1   r]   rn   r\   rm   Úfro)r   r   r   r   Úcondræ   r   r"   rÈ   rp   ÚsumÚmaxÚminr   Úsqrt)rB   r.   r/   rA   r³   r‰   Zcinvr&   r&   r'   rE   ¾  sp      þ
  þ
  þ
& ý
& ý& ý& ý
ÿ üzCondCases.doNr¸   r&   r&   r&   r'   rù   »  s   rù   c                   @   s>   e Zd Zdd„ Zdd„ Zejjdddd�d	d
„ ƒZdd„ Z	dS )ÚTestCondc                 C   s†   t dddgdddgdddggƒ}tt |t¡dƒ tt |t ¡dƒ tt |d¡dƒ tt |d¡d	ƒ tt |d
¡t d¡ƒ d S )NrT   r   r\   g       ÀrV   r_   gUUUUUUå?rm   r»   rû   gUUUUU6@)r   r   r   rü   r   r"   r   ©rB   ÚAr&   r&   r'   Útest_basic_nonsvdê  s     zTestCond.test_basic_nonsvdc                 C   sx   t  d¡t  d¡g}d dddg}ddg}t ||¡D ]\}}tt ||¡dkƒ q4t ||¡D ]\}}t ||¡ q^d S )N©r]   r]   r\   r]   rû   rm   rn   ç  4&õkC)r"   rË   Úonesrz   r{   r   r   rü   )rB   ZAsÚp_posZp_negr  Úpr&   r&   r'   Útest_singularó  s    zTestCond.test_singularTFz/Platform/LAPACK-dependent failure, see gh-18914)ÚrunÚreasonc                 C   sö   d dddddg}d dddg}t  d¡}t j|d< |D ].}t ||¡}tt|t jƒƒ tt  |¡ƒ q4t  d¡}t j|d	< |D ]t}t ||¡}tt  |d ¡ƒ ||krÈt|d
 dkƒ t|d dkƒ q|tt  |d
 ¡ ƒ tt  |d ¡ ƒ q|d S )Nr\   rm   r]   rn   rû   r  rÚ   )r^   r]   r]   )r\   r   r\   r   r  )	r"   r  Únanr   rü   r   r!   Zfloat_Úisnan)rB   Úpsr  r  r	  r³   r&   r&   r'   Útest_nan  s$    



zTestCond.test_nanc                 C   sŒ   t j d¡ t j dddd¡}d|d< d|d< dD ]T}t ||¡}t|d t jƒ t|d t jƒ tt  	|d ¡ƒ tt  	|d ¡ƒ q2d S )	NrS   r]   r   rY   rx   )Nr\   r]   rû   rm   rn   rÚ   ©r\   r   )
r"   ÚrandomÚseedÚrandr   rü   r   r   r   Úisfinite)rB   r  r	  r³   r&   r&   r'   Útest_stacked_singular  s    zTestCond.test_stacked_singularN)
rJ   rK   rL   r  r
  r¥   r¦   Úxfailr  r  r&   r&   r&   r'   r  é  s   	
ÿ
r  c                   @   s   e Zd Zdd„ ZdS )Ú	PinvCasesc                 C   s<   t  |¡}t}t||||ƒ|ƒ|ddd� tt||ƒƒ d S )Nra   r`   rú   ©r   Úpinvr´   r   r   r(   ©rB   r.   r/   rA   Za_ginvr   r&   r&   r'   rE   1  s    
zPinvCases.doNr¸   r&   r&   r&   r'   r  ,  s   r  c                   @   s   e Zd ZdS )ÚTestPinvNr¾   r&   r&   r&   r'   r  9  s   r  c                   @   s   e Zd Zdd„ ZdS )ÚPinvHermitianCasesc                 C   s@   t j|dd�}t}t||||ƒ|ƒ|ddd� tt||ƒƒ d S )NTrð   ra   r`   rú   r  r  r&   r&   r'   rE   ?  s    zPinvHermitianCases.doNr¸   r&   r&   r&   r'   r  =  s   r  c                   @   s   e Zd ZdS )ÚTestPinvHermitianNr¾   r&   r&   r&   r'   r  G  s   r  c                   @   s   e Zd Zdd„ ZdS )ÚDetCasesc           
      C   sÌ   t  |¡}t  |¡\}}t|ƒjjttfkr<t|ƒ t¡}nt|ƒ t	¡}t  
|¡}t|tj|dd�ƒ t|t |¡ tj|dd�ƒ t |¡}t |¡}|dk}	tt ||	 ¡dƒ t||	  t ƒ d S )Nrm   ©Úaxisr   r\   )r   ÚdetÚslogdetr   r,   r    r   r   Úastyper   rÓ   r   r   Úreducer"   ÚexpZ
atleast_1drp   r   r   )
rB   r.   r/   rA   Údr‰   ZldÚadrÕ   Úmr&   r&   r'   rE   M  s    



zDetCases.doNr¸   r&   r&   r&   r'   r  K  s   r  c                   @   s:   e Zd Zdd„ Zej deee	e
g¡dd„ ƒZdd„ ZdS )	ÚTestDetc                 C   s   t t dgg¡dƒ t tt dgg¡ƒtƒ t t dgg¡dƒ t tt dgg¡ƒtƒ t t dgg¡dt fƒ t tt dgg¡d ƒtƒ t tt dgg¡d ƒtƒ t t dgg¡dt fƒ t tt dgg¡d ƒtƒ t tt dgg¡d ƒtƒ d S )Nç        y                r   r\   )r   r   r"  r    r   r   r#  r   rH   r&   r&   r'   Ú	test_zero`  s    zTestDet.test_zeror,   c                 C   s^   t jddgddgg|d�}tt j |¡j|ƒ t j |¡\}}t|jt|ƒƒ t|j|ƒ d S rº   )r"   r   r   r   r"  r,   r#  r4   )rB   r,   r†   Úphr‰   r&   r&   r'   r½   m  s
    zTestDet.test_typesc                 C   sð   t jdt jd�}t |¡}t|dƒ t|jjt jkƒ t 	|¡}t|dƒ t|d jjt jkƒ t|d jjt j
kƒ t jdt jd�}t |¡}t|dƒ t|jjt jkƒ t 	|¡}t|dƒ t|d jjt jkƒ t|d jjt jkƒ d S )NrY   r3   rT   r  r   r\   )r"   rË   rÎ   r   r"  r   r   r,   r    r#  Úfloat32rÍ   )rB   r.   rÐ   r&   r&   r'   rÄ   u  s     







zTestDet.test_0_sizeN)rJ   rK   rL   r,  r¥   r¦   rÆ   r   r   r   r   r½   rÄ   r&   r&   r&   r'   r*  _  s   
r*  c                   @   s   e Zd Zdd„ ZdS )Ú
LstsqCasesc                 C   sL  t  |¡}|j\}}t |d¡\}}}	tj||dd�\}
}}}|dkrVt|
dk ¡ ƒ ||krzt|t	||
ƒƒ t
||ƒ n
t
||ƒ t|| |¡ƒ ||krú||krút  tt  	||
¡| ƒ¡d jdd�}t  |¡}t  |¡jdkrød|_t
|j|jƒ nt  g ¡ t|
ƒ¡}t||ƒ tt  |jt j¡ƒ tt|
|ƒƒ tt||ƒƒ d S )	NFrm   ©Zrcondr   r]   r   r\   rk   )r"   r   rg   r   ræ   Úlstsqr   r‚   r   r   r   Z__array_wrap__rp   rý   ry   r   r   r    Ú
issubdtyper,   Úfloatingr(   )rB   r.   r/   rA   Úarrr)  Únrç   r‰   rê   r†   Ú	residualsÚrankÚsvZexpect_residsr&   r&   r'   rE   ‹  s2    


ÿÿ

zLstsqCases.doNr¸   r&   r&   r&   r'   r/  ‰  s   r/  c                
   @   sF   e Zd Zdd„ Zej dddgdddd	d
ddg¡dd„ ƒZdd„ ZdS )Ú	TestLstsqc           	      C   sô   t  ddddddgddddddgddddddgddddddgg¡j}t  ddddddg¡}tƒ �Š}| td¡}t ||¡\}}}}t|d	kƒ tj||d
d�\}}}}t|d	kƒ tj||d d�\}}}}t|dkƒ tt	|ƒdkƒ W 5 Q R X d S )Nr+  rT   rU   rW   rV   r\   r   z`rcond` parameter will changer_   rm   r0  r^   )
r"   r   ÚTr   ÚrecordÚFutureWarningr   r1  r   Úlen)	rB   r.   r/   Úsuprà   r†   r6  r7  r‰   r&   r&   r'   Útest_future_rcond¨  s    ýzTestLstsq.test_future_rcondr)  r5  Ún_rhs)r_   r]   r]   )r   r_   r\   )r   r_   r]   )r_   r   r\   )r_   r   r]   )r_   r]   r   )r   r   r   c                 C   sÜ   t  || ¡ ||¡}t  ||f¡}tj||d d�\}}}}	|dkrTt|dk ¡ ƒ t|j	||fƒ t|j	||krx|fndƒ ||kr´|dkr´|t  
||¡ }
t||
|
 jdd�ƒ t|t||ƒƒ t|	j	t||ƒfƒ d S )Nr0  r   rZ   rn   r   )r"   rÀ   rf   r  r   r1  r   r‚   r   rg   r   r   rý   rÿ   )rB   r)  r5  r@  r.   r/   r†   r6  r7  r‰   r²   r&   r&   r'   Útest_empty_a_bº  s    
zTestLstsq.test_empty_a_bc              	   C   sj   t  ddddg¡}t  ddddd	g¡}t  |t  t|ƒ¡g¡j}ttd
ƒ� tj	||d d� W 5 Q R X d S )Nr   r\   r]   r^   rm   gš™™™™™É?gÍÌÌÌÌÌì?gÍÌÌÌÌÌ @gffffff
@zIncompatible dimensionsr0  )
r"   r   Zvstackr  r=  r:  r   r   r   r1  )rB   r†   Úyr  r&   r&   r'   Útest_incompatible_dimsÒ  s
    z TestLstsq.test_incompatible_dimsN)	rJ   rK   rL   r?  r¥   r¦   rÆ   rA  rC  r&   r&   r&   r'   r9  §  s   ù	
r9  Údtc                 C   s   g | ]}t  |¡‘qS r&   )r"   r,   )rq   r³   r&   r&   r'   rr   Û  s     rr   z?bBhHiIqQefdgFDGOc                   @   sØ   e Zd Ze d¡Zeddddg Zeddddg Zeddddg ZeeeegZ	e
ddgddggƒZe egggd ¡Zee d¡e d¡e d¡g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 )ÚTestMatrixPowerr_   r^   r   r\   r]   r“   ÚgÚGc                 C   s˜   | j  |¡}tt|dd d d d ƒ| jƒ tt|dd d d d ƒ| j ƒ tt|dd d d d ƒ| jƒ tt|dd d d d ƒ| jƒ d S )Nr]   éd   i   é    r   r\   r^   )Úrshft_1r$  r   r   Úrshft_0Úrshft_2Úrshft_3)rB   rD  Zrshftr&   r&   r'   Útest_large_powerè  s"     ÿ ÿ ÿ ÿz TestMatrixPower.test_large_powerc                 C   s>   dd„ }| j D ]*}|| |¡ƒ |tkr|| j |¡ƒ qd S )Nc                 S   s*   t | dƒ}t|t| ƒƒ t|j| jƒ d S )Nr   )r   r   rµ   r,   )ÚMÚmzr&   r&   r'   Útzô  s    
z.TestMatrixPower.test_power_is_zero.<locals>.tz©Ú	rshft_allr$  ÚobjectÚstacked©rB   rD  rQ  rõ   r&   r&   r'   Útest_power_is_zeroó  s
    
z"TestMatrixPower.test_power_is_zeroc                 C   s>   dd„ }| j D ]*}|| |¡ƒ |tkr|| j |¡ƒ qd S )Nc                 S   s&   t | dƒ}t|| ƒ t|j| jƒ d S )Nr\   )r   r   r,   )rõ   rP  r&   r&   r'   rQ  ÿ  s    

z-TestMatrixPower.test_power_is_one.<locals>.tzrR  rV  r&   r&   r'   Útest_power_is_oneþ  s
    
z!TestMatrixPower.test_power_is_onec                 C   s>   dd„ }| j D ]*}|| |¡ƒ |tkr|| j |¡ƒ qd S )Nc                 S   s>   t | dƒ}| jtkrtnt}t||| | ƒƒ t|j| jƒ d S )Nr]   )r   r,   rT  r	   r   r   )rõ   rP  Úmmulr&   r&   r'   rQ  
  s    
z-TestMatrixPower.test_power_is_two.<locals>.tzrR  rV  r&   r&   r'   Útest_power_is_two	  s
    
z!TestMatrixPower.test_power_is_twoc                 C   s0   dd„ }| j D ]}|| jkr|| |¡ƒ qd S )Nc                 S   s4   t | dƒ}| jtkrtnt}t||| ƒt| ƒƒ d S ©Nrm   )r   r,   rT  r	   r   r   rµ   )rõ   ZinvmatrY  r&   r&   r'   rQ    s    
 ÿz3TestMatrixPower.test_power_is_minus_one.<locals>.tz)rS  Údtnoinvr$  rV  r&   r&   r'   Útest_power_is_minus_one  s    

z'TestMatrixPower.test_power_is_minus_onec                 C   s.   | j  |¡}ttt|dƒ ttt|dgƒ d S )Ng      ø?r\   )rK  r$  r   Ú	TypeErrorr   ©rB   rD  rõ   r&   r&   r'   Útest_exceptions_bad_power   s    z)TestMatrixPower.test_exceptions_bad_powerc                 C   sP   t ttt dg|¡dƒ t ttt dgdgg|¡dƒ t ttt d|¡dƒ d S )Nr\   r]   )r_   r^   r]   )r   r   r   r"   r   r  )rB   rD  r&   r&   r'   Útest_exceptions_non_square%  s    z*TestMatrixPower.test_exceptions_non_squarec                 C   s,   || j krd S | j |¡}ttt|dƒ d S r[  )r\  Únoninvr$  r   r   r   r_  r&   r&   r'   Útest_exceptions_not_invertible*  s    
z.TestMatrixPower.test_exceptions_not_invertibleN)rJ   rK   rL   r"   rí   rK  rJ  rL  rM  rS  r   rb  ÚblockrU  rT  r,   r\  rN  rW  rX  rZ  r]  r`  ra  rc  r&   r&   r&   r'   rE  Û  s    
rE  c                   @   s   e Zd Zdd„ ZdS )ÚTestEigvalshCasesc                 C   s^   t  |d¡}t  |¡\}}|jdd� t||t|jƒd� t  |d¡}t||t|jƒd� d S )NÚLrm   r   rÜ   ÚU)r   ÚeigvalshrÔ   r÷   r   r6   r,   )rB   r.   r/   rA   rÕ   rÖ   r×   Úev2r&   r&   r'   rE   3  s    zTestEigvalshCases.doNr¸   r&   r&   r&   r'   re  1  s   re  c                   @   sB   e Zd Zej deeee	g¡dd„ ƒZ
dd„ Zdd„ Zdd	„ Zd
S )ÚTestEigvalshr,   c                 C   s:   t jddgddgg|d�}t j |¡}t|jt|ƒƒ d S rº   )r"   r   r   rh  r   r,   r4   )rB   r,   r†   rà   r&   r&   r'   r½   @  s    zTestEigvalsh.test_typesc                 C   sX   t jddgddggt jd�}ttt jj|dd� ttt jj|dƒ ttt jj|dƒ d S ©Nr\   r»   r3   Zlrong©ZUPLOÚlowerÚupper)r"   r   r.  r   r¯   r   rh  ©rB   r†   r&   r&   r'   Útest_invalidF  s    zTestEigvalsh.test_invalidc                 C   sì   t jddgddggt jd�}t jddgddggt jd�}t jddgt jd�}tt jƒ}t j |¡}t|||d� t jj|dd�}t|||d� t jj|dd�}t|||d� t jj|d	d�}t|||d� t jj|d
d�}t|||d� d S ©Nr   r\   r3   rm   rÜ   rf  rl  Úlrg  rç   )r"   r   r   r6   r   rh  r   )rB   ÚKloÚKupÚtgtrÝ   rà   r&   r&   r'   Ú	test_UPLOL  s    
zTestEigvalsh.test_UPLOc                 C   s²   G dd„ dt jƒ}t jdt jd� |¡}t |¡}t|jj	t j
kƒ td|jƒ tt|t jƒƒ t jdt jd� |¡}t |¡}t|jj	t jkƒ td|jƒ tt|t jƒƒ d S )Nc                   @   s   e Zd ZdS )z/TestEigvalsh.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿   d  s   r¿   rÊ   r3   rÚ   rY   rZ   )r"   r#   rË   rÌ   r   r   rh  r   r,   r    rÍ   r   rg   r!   rÎ   r.  rÏ   r&   r&   r'   rÄ   b  s    

zTestEigvalsh.test_0_sizeN©rJ   rK   rL   r¥   r¦   rÆ   r   r   r   r   r½   rp  rv  rÄ   r&   r&   r&   r'   rj  ?  s
   
rj  c                   @   s   e Zd Zdd„ ZdS )ÚTestEighCasesc           
      C   sÆ   t  |¡\}}t  |¡\}}|jdd� t||ƒ tt||ƒt |¡dd d d …f t |¡ t	|j
ƒd� t  |d¡\}}	t||ƒ tt||	ƒt |¡dd d d …f t |	¡ t	|j
ƒt|ƒd� d S )Nrm   r   .rÜ   rg  )rÝ   Úerr_msg)r   ÚeighrÔ   r÷   r   r   r´   r"   r   r6   r,   Úrepr)
rB   r.   r/   rA   rÕ   ZevcrÖ   r×   ri  Zevc2r&   r&   r'   rE   w  s    

 þ

  þzTestEighCases.doNr¸   r&   r&   r&   r'   rx  u  s   rx  c                   @   sB   e Zd Zej deeee	g¡dd„ ƒZ
dd„ Zdd„ Zdd	„ Zd
S )ÚTestEighr,   c                 C   sJ   t jddgddgg|d�}t j |¡\}}t|jt|ƒƒ t|j|ƒ d S rº   )r"   r   r   rz  r   r,   r4   rß   r&   r&   r'   r½   Œ  s    zTestEigh.test_typesc                 C   sX   t jddgddggt jd�}ttt jj|dd� ttt jj|dƒ ttt jj|dƒ d S rk  )r"   r   r.  r   r¯   r   rz  ro  r&   r&   r'   rp  “  s    zTestEigh.test_invalidc                 C   s   t jddgddggt jd�}t jddgddggt jd�}t jddgt jd�}tt jƒ}t j |¡\}}t|||d� t jj|dd�\}}t|||d� t jj|dd�\}}t|||d� t jj|d	d�\}}t|||d� t jj|d
d�\}}t|||d� d S rq  )r"   r   r   r6   r   rz  r   )rB   rs  rt  ru  rÝ   rà   rá   r&   r&   r'   rv  ™  s    
zTestEigh.test_UPLOc                 C   sú   G dd„ dt jƒ}t jdt jd� |¡}t |¡\}}t|jj	t j
kƒ t|jj	t j
kƒ t|j|jƒ td|jƒ tt|t jƒƒ t jdt jd� |¡}t |¡\}}t|jj	t jkƒ t|jj	t jkƒ t|j|jƒ td|jƒ tt|t jƒƒ d S )Nc                   @   s   e Zd ZdS )z+TestEigh.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿   ±  s   r¿   rÊ   r3   rÚ   rY   rZ   )r"   r#   rË   rÌ   r   r   rz  r   r,   r    rÍ   r   rg   r!   rÎ   r.  râ   r&   r&   r'   rÄ   ¯  s    zTestEigh.test_0_sizeNrw  r&   r&   r&   r'   r|  ‹  s
   
r|  c                   @   s    e Zd ZdZdZedd„ ƒZdS )Ú_TestNormBaseNc                 C   s:   t | jjtjƒr"t|j| jjƒ ntt |jjtjƒƒ d S r   )	Ú
issubclassr,   r    r"   Zinexactr   Úrealr   r3  )r†   rÐ   r&   r&   r'   Úcheck_dtypeÊ  s    z_TestNormBase.check_dtype)rJ   rK   rL   rD  ÚdecÚstaticmethodr€  r&   r&   r&   r'   r}  Æ  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 )Ú_TestNormGeneralc                 C   sF   t tg ƒdƒ t ttg | jd�ƒdƒ t tttg | jd�ƒƒdƒ d S )Nr+  r3   )r   r   r   rD  r   rH   r&   r&   r'   Ú
test_emptyÕ  s    z_TestNormGeneral.test_emptyc           	   
   C   sr  t  dddg¡}t jd }t jd }|| }|D �]:}| |¡}t|t j ƒ}|  ||¡ t|dƒ tƒ �2}| 	t
d¡ t|dƒ}|  ||¡ t|dƒ W 5 Q R X t|dƒ}|  ||¡ t|dƒ t|dƒ}|  ||¡ t|d	ƒ t|dƒ}|  ||¡ t||j d	¡|j d
¡ ƒ t|dƒ}|  ||¡ t||j d	¡|j d¡ ƒ t|t jƒ}|  ||¡ t|dƒ q0d S )Nr\   r   Ú
AllIntegerZAllFloatr+  údivide by zero encounteredrm   r]   rU   r»   r_   g      Ð?rT   )r"   r   Ú	typecodesr$  r   r   r€  r   r   ÚfilterÚRuntimeWarningr,   r    ©	rB   r.   Zexact_typesZinexact_typesZ	all_typesZ	each_typeÚatZanr>  r&   r&   r'   Útest_vector_return_typeÚ  s:    











z(_TestNormGeneral.test_vector_return_typec                    s‚   ddddg}ddddg}ddddg}‡ fd	d
„}|||fD ]}||ƒ q:t |ˆ jd�t |ˆ jd�t |ˆ jd�fD ]}||ƒ qpd S )Nr\   r]   r^   r_   rm   rn   ro   rl   c                    sÔ   t jjt| ƒdˆ jd� t jjt| tƒdˆ jd� t jjt| t ƒdˆ jd� t jjt| dƒdˆ jd� t jjt| dƒdˆ jd� t jjt| d	ƒdˆ jd� t jjt| d
ƒdˆ jd� t jjt| dƒdˆ jd� d S )Ng�¥6Ò­è@©r+   rW   rT   r\   ç      $@rm   g¸…ëQ¸Þ?r]   rn   gÊsÔcÙÑê?r   r_   )r"   Útestingr   r   r�  r   )rá   rH   r&   r'   Ú_test  s0    ÿÿÿÿÿÿÿÿz+_TestNormGeneral.test_vector.<locals>._testr3   )r   rD  )rB   r.   r/   r³   r�  rá   r&   rH   r'   Útest_vector  s    
ÿz_TestNormGeneral.test_vectorc           	   	      s¼  t dddgdddgg| jd�‰ d dd	dddtjtj fD ]h‰‡ ‡fd
d„tˆ jd ƒD ƒ}ttˆ ˆd	d�|ƒ ‡ ‡fdd„tˆ jd	 ƒD ƒ}ttˆ ˆdd�|ƒ q8tjdd| jd� 	ddd¡‰ˆj
}d ddddtjtj dfD ]Ø‰t t| |ƒd¡D ]¾}|\}}|d	k �r||7 }|d	k �r&||7 }||k�rDtttˆˆ|d� qötˆˆ|d�}|||  ‰||k �rŠ‡‡‡fdd„tˆjˆ ƒD ƒ}n ‡‡‡fdd„tˆjˆ ƒD ƒ}t||ƒ qöqÞd S )Nr\   r]   r^   r_   ra   r)   r3   rm   r   c                    s$   g | ]}t ˆ d d …|f ˆd�‘qS ©N©Úord©r   ©rq   Úk©r  Úorderr&   r'   rr   '  s     z._TestNormGeneral.test_axis.<locals>.<listcomp>©r”  r!  c                    s$   g | ]}t ˆ |d d …f ˆd�‘qS r’  r•  r–  r˜  r&   r'   rr   )  s     é   rn   rû   c                    s*   g | ]"}t ˆ d d … j|ˆd�ˆd�‘qS ©Nr   r“  )r   Útaker–  ©ÚBÚk_indexr™  r&   r'   rr   ?  s   ÿc                    s,   g | ]$}t ˆ d d … j|ˆd�jˆd�‘qS rœ  )r   r�  r:  r–  rž  r&   r'   rr   B  s   ÿ)r   rD  r"   ÚInfr±   rg   r   r   rÀ   rf   ry   rz   Úcombinationsr   r¯   )	rB   Z	expected0Z	expected1Zndr!  Zrow_axisZcol_axisr5  rÂ   r&   )r  rŸ  r   r™  r'   Ú	test_axis!  s6    



ÿÿz_TestNormGeneral.test_axisc           	   
   C   sæ  t jdd| jd� ddd¡}d}d}t|d d d	�}t|d d d
d�}tt  |¡|| d d ¡d� d}t|j	|k| |j	|d d ¡ƒ d dddddt j
t j
 fD ]†}t|jƒD ]v}t|||d	�}t|||d
d�}tt  |¡|| ||¡d� t|j	ƒ}d||< t|ƒ}t|j	|k| |j	|||¡ƒ q¨qšd ddddt j
t j
 ddf	D ]¢}t t|jƒd¡D ]ˆ}t|||d	�}t|||d
d�}tt  |¡|| ||¡d� t|j	ƒ}d||d < d||d < t|ƒ}t|j	|k| |j	|||¡ƒ �qT�q>d S )Nr\   r›  r3   r]   r^   r_   zorder {0}, axis = {1}z;Shape mismatch found {0}, expected {1}, order={2}, axis={3}rš  T)r”  r!  Zkeepdims)ry  )r\   r\   r\   rm   r   rn   rû   Únuc)r"   rÀ   rD  rf   r   r   ÚsqueezeÚformatr   rg   r¡  r±   ry   r„   r|   rz   Úpermutations)	rB   r  Zallclose_errZ	shape_errrÂ   ÚfoundZexpected_shaper™  r—  r&   r&   r'   Útest_keepdimsF  sN    
ÿ
ÿ
ÿ

ÿ 
ÿ

ÿz_TestNormGeneral.test_keepdimsN)rJ   rK   rL   r„  rŒ  r‘  r£  r©  r&   r&   r&   r'   rƒ  Ó  s
   )%rƒ  c                   @   s:   e Zd ZejZdd„ Zdd„ Zdd„ Zdd„ Zd	d
„ Z	dS )Ú_TestNorm2Dc                 C   s    t t| jg g| jd�ƒdƒ d S )Nr3   r+  )r   r   r   rD  rH   r&   r&   r'   Útest_matrix_emptyv  s    z_TestNorm2D.test_matrix_emptyc           	   
   C   sv  |   dddgdddgg¡}tjd }d}|| }|D �]:}| |¡}t|tj ƒ}|  ||¡ t|dƒ tƒ �2}| 	t
d¡ t|dƒ}|  ||¡ t|dƒ W 5 Q R X t|dƒ}|  ||¡ t|dƒ t|d	ƒ}|  ||¡ t|d
ƒ t|dƒ}|  ||¡ t|dƒ t|tjƒ}|  ||¡ t|dƒ t|dƒ}|  ||¡ t|dƒ t|dƒ}|  ||¡ tjj|ddd� q4d S )Nr\   r   r…  ZfdFDrU   r†  rm   rT   r]   gªLXèz¶û?rn   rû   r¤  gU&,t=Û@r)   r�  )r   r"   r‡  r$  r   r   r€  r   r   rˆ  r‰  r�  rŠ  r&   r&   r'   Útest_matrix_return_typey  s@    














z#_TestNorm2D.test_matrix_return_typec                 C   sÚ   | j ddgddgg| jd�}tt|ƒdƒ tt|dƒdƒ tt|dƒd	ƒ tt|tƒd
ƒ tt|t ƒdƒ tt|dƒd	ƒ tt|dƒdƒ tt|dƒdƒ tt|dƒdƒ ttt|dƒ ttt|dƒ ttt|dƒ d S )Nr\   r^   ra   rb   r3   g…¹ŽT"@rû   r¤  rŽ  g      (@rW   rm   rX   r]   g„öW³?"@rn   gÑ—€Ê„ì?Znofroro   r   )r   rD  r   r   r   r   r¯   r  r&   r&   r'   Útest_matrix_2x2¬  s    z_TestNorm2D.test_matrix_2x2c                 C   sÀ   d| j dddgdddgdddgg| jd� }tt|ƒd	ƒ tt|d
ƒd	ƒ tt|dƒdƒ tt|tƒdƒ tt|t ƒdƒ tt|dƒdƒ tt|dƒdƒ tt|dƒdƒ tt|dƒdƒ d S )Ngš™™™™™¹?r\   r]   r^   r)   r   ra   r3   grj=Q0î?rû   r¤  gþB+pcõ?gš™™™™™ñ?g333333ã?rT   rm   gš™™™™™Ù?gû&Þê.dì?rn   gÜ¸Õ ˆçÈ?)r   rD  r   r   r   r  r&   r&   r'   Útest_matrix_3x3¼  s    &ÿz_TestNorm2D.test_matrix_3x3c                 C   s
  | j dddgdddgg| jd�}tjdd| jd� ddd¡}ttt|d	d
ƒ ttt|dd
ƒ tttddgd	d ƒ tttddgdd ƒ tttddgdd ƒ dD ]4}ttt||d ƒ ttt||dƒ ttt||dƒ qœttjt|d dƒ ttjt|d dƒ ttt|d dƒ d S )Nr\   r]   r^   r_   ra   r)   r3   r›  rû   r   r¤  Útest©r   r^   rÚ   )r\   r]   ©r]   r^   )r   r\   r]   )	r   rD  r"   rÀ   rf   r   r¯   r   Z	AxisError)rB   r  rŸ  r™  r&   r&   r'   Útest_bad_argsÍ  s     z_TestNorm2D.test_bad_argsN)
rJ   rK   rL   r"   r   r«  r¬  r­  r®  r²  r&   r&   r&   r'   rª  q  s   3rª  c                   @   s   e Zd ZdS )Ú	_TestNormNr¾   r&   r&   r&   r'   r³  é  s   r³  c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )ÚTestNorm_NonSystematicc                 C   s*   t jdt jd�}tt|dd�ddd� d S )Né
   r3   r^   r“  gÍÌÌÌÌL)@r]   r�  )r"   rÀ   Z
longdoubler-   r   ro  r&   r&   r'   Útest_longdouble_normï  s    z+TestNorm_NonSystematic.test_longdouble_normc                 C   s,   t jdgt jd�}tt|dd�ddd� d S )Ni   €r3   r^   r“  l        ra   r�  )r"   r   Zint32r-   r   ro  r&   r&   r'   Útest_intminõ  s    z"TestNorm_NonSystematic.test_intminc                 C   sŽ   t jdt jd�}d|d< d|d< d}tt jj|dd	�|d
d� | t j¡}tt jj|dd	�|dd� | t j¡}tt jj|dd	�|dd� d S )N©r]   r3   y      @      @r   y      À      @r\   g¨ËþÿV;'@r^   r“  rµ  r�  é	   ra   )	r"   r~   Zclongdoubler-   r   r   r$  Ú
complex128rÎ   )rB   r'  rÐ   r&   r&   r'   Útest_complex_high_ordû  s    z,TestNorm_NonSystematic.test_complex_high_ordN)rJ   rK   rL   r¶  r·  r»  r&   r&   r&   r'   r´  í  s   r´  c                   @   s   e Zd ZejZdZdS )Ú_TestNormDoubleBaser*   N)rJ   rK   rL   r"   r   rD  r�  r&   r&   r&   r'   r¼  	  s   r¼  c                   @   s   e Zd ZejZdZdS )Ú_TestNormSingleBaser)   N)rJ   rK   rL   r"   r.  rD  r�  r&   r&   r&   r'   r½    s   r½  c                   @   s   e Zd ZejZdZdS )Ú_TestNormInt64Baser*   N)rJ   rK   rL   r"   Zint64rD  r�  r&   r&   r&   r'   r¾    s   r¾  c                   @   s   e Zd ZdS )ÚTestNormDoubleNr¾   r&   r&   r&   r'   r¿    s   r¿  c                   @   s   e Zd ZdS )ÚTestNormSingleNr¾   r&   r&   r&   r'   rÀ    s   rÀ  c                   @   s   e Zd ZdS )ÚTestNormInt64Nr¾   r&   r&   r&   r'   rÁ     s   rÁ  c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestMatrixRankc                 C   sÊ   t dtt d¡ƒƒ t d¡}d|d< t t|ƒdƒ t tt d¡ƒdƒ t tddddgƒdƒ t tt d¡ƒdƒ t tdgƒdƒ t |t d¡t d¡g¡}t t|ƒt dddg¡ƒ t tdƒdƒ d S )	Nr_   r+  ©rm   rm   r^   rì   r   r\   )r_   )r   r   r"   rí   rË   r   )rB   ÚIÚmsr&   r&   r'   Útest_matrix_rank&  s    
zTestMatrixRank.test_matrix_rankc                 C   s    t dtt d¡dd�ƒ t dtt d¡dd�ƒ t dtt d¡dd�ƒ t d¡}d|d< t d	t|dd�ƒ d
|d< t dt|ddd�ƒ t d	t|ddd�ƒ d S )Nr_   Trð   r\   rì   r   r+  rÃ  r^   g:Œ0âŽyE>g¾Ü|"•BE>)r9   Ztolgµ;ä¡ˆ°E>)r   r   r"   rí   r  rË   )rB   rÄ  r&   r&   r'   Útest_symmetric_rank:  s    
z"TestMatrixRank.test_symmetric_rankN)rJ   rK   rL   rÆ  rÇ  r&   r&   r&   r'   rÂ  $  s   rÂ  c                  C   sž   t j d¡} tdƒD ]„}| jdd�}|d d …df |d d …df  |d d …df< tt|ƒdƒ |d d …d	f |d d …d
f  |d d …df< tt|ƒdƒ qd S )NiŠ3rH  )é(   rµ  ©Úsizer\   r]   r   r¹  r_   ra   r^   r[   )r"   r  ZRandomStater±   Únormalr   r   )ÚrngÚiÚXr&   r&   r'   Útest_reduced_rankH  s    ,,rÏ  c                	   @   s¤   e Zd ZejZdd„ Zej ddgdddg¡dd	„ ƒZ	d
d„ Z
dd„ Zdd„ Zej ddddddg¡ej ddddg¡ej dejejejejg¡dd„ ƒƒƒZdS )ÚTestQRc                 C   s®  t |ƒ}|j}|j\}}t||ƒ}tj|dd�\}}t|j|kƒ t|j|kƒ tt||ƒƒ tt||ƒƒ t|j||fkƒ t|j||fkƒ tt	||ƒ|ƒ tt	|j
 ¡ |ƒt |¡ƒ tt |¡|ƒ tj|dd�\}	}
t|	j|kƒ t|
j|kƒ tt|	|ƒƒ tt|
|ƒƒ t|	j||fkƒ t|
j||fkƒ tt	|	|
ƒ|ƒ tt	|	j
 ¡ |	ƒt |¡ƒ tt |
¡|
ƒ tj|dd�}t|j|kƒ tt||ƒƒ t||
ƒ d S )NÚcomplete©ÚmodeÚreducedr²   )r    r,   rg   rÿ   r   Úqrr   r!   r   r   r:  ró   r"   rí   Útriu)rB   r.   Úa_typeÚa_dtyper)  r5  r—  Úqr²   Úq1Úr1Úr2r&   r&   r'   Úcheck_qrY  s8    

zTestQR.check_qrr)  r5  )r^   r   r°  rY   c                 C   st   t ||ƒ}t ||f¡}|  |¡ tjj|dd�\}}t|jtjƒ t|jtjƒ t|j	||fƒ t|j	|fƒ d S )NÚrawrÒ  )
rÿ   r"   r~   rÝ  r   rÕ  r   r,   r   rg   )rB   r)  r5  r—  r.   ÚhÚtaur&   r&   r'   Útest_qr_empty€  s    

zTestQR.test_qr_emptyc                 C   sÄ   | j ddgddgddggtjd�}tj|dd	�\}}t|jtjkƒ t|jtjkƒ t|jd
kƒ t|jdkƒ tj|jdd	�\}}t|jtjkƒ t|jtjkƒ t|jdkƒ t|jdkƒ d S )Nr\   r]   r^   r_   ra   r)   r3   rÞ  rÒ  r±  r¸  rc   )	r   r"   r   r   rÕ  r   r,   rg   r:  )rB   r.   rß  rà  r&   r&   r'   Útest_mode_raw‘  s    "zTestQR.test_mode_rawc                 C   sÂ   |   ddgddgg¡}|   ddgddgddgg¡}dD ]8}| |¡}| |¡}|  |¡ |  |¡ |  |j¡ q6dD ]H}dd| |¡  }dd| |¡  }|  |¡ |  |¡ |  |j¡ qtd S )	Nr\   r]   r^   r_   ra   r)   Úfdù              ð?)r   r$  rÝ  r:  )rB   r.   r/   rD  Úm1Úm2r&   r&   r'   Útest_mode_all_but_economic§  s    





z!TestQR.test_mode_all_but_economicc                 C   sf  t |ƒ}|j}|jdd … \}}t||ƒ}tj|dd�\}}t|j|kƒ t|j|kƒ tt||ƒƒ tt||ƒƒ t|jdd … ||fkƒ t|jdd … ||fkƒ tt	||ƒ|ƒ t
 |jd ¡}	t
 |	|jd d… |jd fd  ¡}
tt	t|ddƒ ¡ |ƒ|
ƒ tt
 |dd d …d d …f ¡|ƒ tj|dd�\}}t|j|kƒ t|j|kƒ tt||ƒƒ tt||ƒƒ t|jdd … ||fkƒ t|jdd … ||fkƒ tt	||ƒ|ƒ t
 |jd ¡}	t
 |	|jd d… |jd fd  ¡}
tt	t|ddƒ ¡ |ƒ|
ƒ tt
 |dd d …d d …f ¡|ƒ tj|dd�}t|j|kƒ tt||ƒƒ t||ƒ d S )	Nrn   rÑ  rÒ  rm   r]   .rÔ  r²   )r    r,   rg   rÿ   r   rÕ  r   r!   r   r	   r"   r   rö   r
   ró   rÖ  )rB   r.   r×  rØ  r)  r5  r—  rÙ  r²   ZI_matZstack_I_matrÚ  rÛ  rÜ  r&   r&   r'   Úcheck_qr_stacked¸  sL    
ÿ"ÿÿ"zTestQR.check_qr_stackedrÊ  )r^   r_   )r_   r^   rì   Ú
outer_sizer  r¸  )r]   r^   r_   rD  c                 C   sP   t jj|| d� |¡}t jj|| d� |¡}|  |¡ |  |d|  ¡ d S )NrÉ  rä  )r"   r  rË  r$  rè  )rB   ré  rÊ  rD  r  rŸ  r&   r&   r'   Útest_stacked_inputså  s    

zTestQR.test_stacked_inputsN)rJ   rK   rL   r"   r   rÝ  r¥   r¦   rÆ   rá  râ  rç  rè  r   r   r   r   rê  r&   r&   r&   r'   rÐ  U  s<   'ý
-   þ  ÿ  þrÐ  c                   @   sR   e Zd Zej ddddddg¡ej dejejej	ej
f¡dd	„ ƒƒZd
d„ ZdS )ÚTestCholeskyrg   rx   r  ©r^   r^   )é2   rí  )r^   rµ  rµ  r,   c              
   C   sÜ   t j d¡ t jj|Ž }t  |t j¡r:|dt jj|Ž   }ttt|ƒƒƒ}d|dd …< t  	| 
|¡ ¡ |¡}t j||d�}t j |¡}t  	|| 
|¡ ¡ ¡}t|||› d|› d|› d|› �d|jd	  t  |¡j d
� d S )Nr\   rä  )rm   rn   rn   r3   ú Ú
iô  r   )ry  Zatol)r"   r  r  Úrandnr2  Zcomplexfloatingr„   r±   r=  r	   rô   ró   r   r   Úcholeskyr   rg   ZfinfoZeps)rB   rg   r,   r.   Útr³   r/   r&   r&   r'   Útest_basic_propertyø  s    þz TestCholesky.test_basic_propertyc                 C   s¶   G dd„ dt jƒ}t jdt jd� |¡}t |¡}t|j|jƒ t	|j
jt jkƒ t	t|t jƒƒ t jdt jd� |¡}t |¡}t|j|jƒ t	|j
jt jkƒ t	t|t jƒƒ d S )Nc                   @   s   e Zd ZdS )z/TestCholesky.test_0_size.<locals>.ArraySubclassNr¾   r&   r&   r&   r'   r¿     s   r¿   rÊ   r3   )r\   r   r   )r"   r#   rË   rÌ   r   r   rñ  r   rg   r   r,   r    rÍ   r!   rÎ   rÏ   r&   r&   r'   rÄ     s    

zTestCholesky.test_0_sizeN)rJ   rK   rL   r¥   r¦   rÆ   r"   r.  rÍ   rÎ   rº  ró  rÄ   r&   r&   r&   r'   rë  õ  s    ÿ ÿrë  c                  C   s˜   t jdkrd} nd} tjtjfD ]r}tjd|d�}| | ¡}| d¡ ¡ }t|j	jdƒ t
jt
jt
jfD ](}||ƒ}t|||ƒƒ t|||ƒƒ qhq d S )NÚlittleú<rG   r_   r3   ÚSú=)ÚsysÚ	byteorderr"   r.  rÍ   rí   ZnewbyteorderZbyteswapr   r,   r   rÈ   r"  r  r   )ZnativeZdttr4  Zn_arrZsw_arrZroutinerÐ   r&   r&   r'   Útest_byteorder_check#  s    

rú  c                  C   sp   t  ddgddgg¡} t  ddgddgg¡}t  ddddg¡dd d… }| |d< ||d< tt jjt jj|ƒ d S )Nr\   r]   r^   r_   .rY   )r"   r   rË   r   r   r   rÈ   )Z
invertibleZnon_invertibler†   r&   r&   r'   Ú test_generalized_raise_multiloop8  s    rû  c                  C   sR  d} zt  ¡ }W n" ttfk
r2   t d¡ Y nX |dk�r(t  d¡ t  d¡ dd l}| |j	d¡ zt
jj ¡  W n2 tk
rŒ   Y n  tk
rª   t  t j¡ Y nX z0t
 dgg¡}t
jj ddd|d||dd¡	 W n< tk
�r } zdt|ƒk�rt  | ¡ W 5 d }~X Y nX t  t j¡ n&t  ¡ \}}t  |¡| k�rNt d¡ d S )	Néÿ   zNot POSIX or fork failed.r   r\   rY   rT   zDORGQR parameter number 5zNumpy xerbla not linked in.)ÚosÚforkÚOSErrorÚAttributeErrorr¥   ÚskipÚcloseÚresourceZ	setrlimitZRLIMIT_COREr"   r   Úlapack_liteZxerblar¯   rŽ   Ú_exitÚ	EX_CONFIGr   Zdorgqrr>   ÚwaitÚWEXITSTATUS)Z	XERBLA_OKÚpidr  r.   r“   Ústatusr&   r&   r'   Útest_xerbla_overrideF  sH    


      ýr  c                  C   sd   ddg} t  d¡}| D ]H}|jdd|d�}t tjd|g¡ |jdd|d�}t tjd|g¡ qd S )	NzPyQt5.QtWidgetsZIPythonzÕ
    import sys
    {before}
    try:
        import {bad_lib}
    except ImportError:
        sys.exit(0)
    {after}
    x = np.ones(2, dtype=np.float32)
    sys.exit(0 if np.allclose(x.dot(x), 2.0) else 1)
    zimport numpy as npÚ )ÚbeforeÚafterÚbad_libz-c)r  r  r  )ÚtextwrapÚdedentr¦  Ú
subprocessÚ
check_callrø  Ú
executable)Zbad_libsÚtemplater  Úcoder&   r&   r'   Útest_sdot_bug_8577w  s    

ÿÿ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 )ÚTestMultiDotc              	   C   sl   t j d¡}t j d¡}t j d¡}tt|||gƒ| |¡ |¡ƒ tt|||gƒt  |t  ||¡¡ƒ d S ©N©r)   r]   ©r]   r)   ©r"   r  r   r   r   )rB   r  rŸ  ÚCr&   r&   r'   Ú(test_basic_function_with_three_argumentsœ  s
     z5TestMultiDot.test_basic_function_with_three_argumentsc                 C   sN   t j d¡}t j d¡}tt||gƒ| |¡ƒ tt||gƒt  ||¡ƒ d S r  r  )rB   r  rŸ  r&   r&   r'   Ú&test_basic_function_with_two_arguments¦  s    z3TestMultiDot.test_basic_function_with_two_argumentsc                 C   s\   t j d¡}t j d¡}t j d¡}t j d¡}tt||||gƒ| |¡ |¡ |¡ƒ d S )Nr  r  ©r]   r\   r  )rB   r  rŸ  r  ÚDr&   r&   r'   Ú9test_basic_function_with_dynamic_programming_optimization®  s
    zFTestMultiDot.test_basic_function_with_dynamic_programming_optimizationc                 C   sL   t j d¡}t j d¡}t j d¡}t j d¡}tt||||gƒjdƒ d S )Nr]   r  r  r  r¸  ©r"   r  r   r   rg   )rB   ÚA1drŸ  r  r!  r&   r&   r'   Útest_vector_as_first_argument·  s
    z*TestMultiDot.test_vector_as_first_argumentc                 C   sL   t j d¡}t j d¡}t j d¡}t j d¡}tt||||gƒjdƒ d S )Nr  r  r]   )r)   r#  )rB   r  rŸ  r  ÚD1dr&   r&   r'   Útest_vector_as_last_argumentÁ  s
    z)TestMultiDot.test_vector_as_last_argumentc                 C   sL   t j d¡}t j d¡}t j d¡}t j d¡}tt||||gƒjdƒ d S )Nr]   r  r  r&   r#  )rB   r$  rŸ  r  r&  r&   r&   r'   Ú&test_vector_as_first_and_last_argumentË  s
    z3TestMultiDot.test_vector_as_first_and_last_argumentc              	   C   s€   t j d¡}t j d¡}t j d¡}t  d¡}t|||g|d�}||ksLt‚t|| |¡ |¡ƒ t|t  |t  ||¡¡ƒ d S )Nr  r  ©r$   ©r"   r  rË   r   rO   r   r   )rB   r  rŸ  r  r$   Úretr&   r&   r'   Útest_three_arguments_and_outÕ  s    
z)TestMultiDot.test_three_arguments_and_outc                 C   sd   t j d¡}t j d¡}t  d¡}t||g|d�}||ks>t‚t|| |¡ƒ t|t  ||¡ƒ d S )Nr  r  )r)   r)   r)  r*  )rB   r  rŸ  r$   r+  r&   r&   r'   Útest_two_arguments_and_outâ  s    
z'TestMultiDot.test_two_arguments_and_outc                 C   sz   t j d¡}t j d¡}t j d¡}t j d¡}t  d¡}t||||g|d�}||ksZt‚t|| |¡ |¡ |¡ƒ d S )Nr  r  r   )r)   r\   r)  r*  )rB   r  rŸ  r  r!  r$   r+  r&   r&   r'   Ú-test_dynamic_programming_optimization_and_outì  s    
z:TestMultiDot.test_dynamic_programming_optimization_and_outc                 C   sh  t j d¡t j d¡t j d¡t j d¡t j d¡t j d¡g}t  ddd	d
ddgddddddgddddddgddddddgddddddgddddddgg¡}t jddddddgddddddgddddddgddddddgddddddgddddddggtd�}|d8 }t|dd�\}}tt  |d d …dd …f ¡t  |d d …dd …f ¡ƒ tt  |¡t  |¡ƒ d S )!N)é   é#   )r0  é   )r1  ra   )ra   rµ  )rµ  é   )r2  r›  r+  g     ÃÎ@g     Ã¾@g    €OÂ@g    €1Ç@g    €ŠÍ@g     ‚¤@g     ±@g     Õ»@g     ‚Ä@g     p‡@g     ˆ£@g     ÿ´@g     @�@g     X«@g     ˆ³@r   r\   r^   r]   r_   ra   r3   T)Zreturn_costsrm   )r"   r  r   Úintr   r   rÖ  )rB   ZarraysZ
m_expectedZ
s_expectedr‰   r)  r&   r&   r'   Útest_dynamic_programming_logicø  s:    





ûûûûÿz+TestMultiDot.test_dynamic_programming_logicc                 C   s&   t ttg ƒ t tttj d¡gƒ d S )Nrì  )r   r¯   r   r"   r  rH   r&   r&   r'   Útest_too_few_input_arrays  s    z&TestMultiDot.test_too_few_input_arraysN)rJ   rK   rL   r  r  r"  r%  r'  r(  r,  r-  r.  r4  r5  r&   r&   r&   r'   r  š  s   
	



r  c                   @   sv   e Zd Zej de d¡dfe d¡dfg¡dd„ ƒZej dd	d
g¡dd„ ƒZ	ej dddg¡dd„ ƒZ
dd„ ZdS )ÚTestTensorinvzarr, ind©r_   r)   r[   r]   r]   ©r^   r^   r]   r\   c              	   C   s&   t tƒ� tj||d� W 5 Q R X d S )N©Úind)r   r   r   Ú	tensorinv)rB   r4  r:  r&   r&   r'   Útest_non_square_handling  s    
z&TestTensorinv.test_non_square_handlingz
shape, ind)©r_   r)   r[   r^   r]   )©é   r[   r^   r\   c                 C   sN   t  d¡}||_tj||d�}|j|d … |jd |…  }|j}t||ƒ d S )Nr?  ©r.   r:  )r"   rí   rg   r   r;  r   )rB   rg   r:  r.   ÚainvrÂ   Úactualr&   r&   r'   Útest_tensorinv_shape%  s    
z"TestTensorinv.test_tensorinv_shaper:  r   rn   c              	   C   s6   t  d¡}d|_ttƒ� tj||d� W 5 Q R X d S )Nr?  r=  r@  )r"   rí   rg   r   r¯   r   r;  )rB   r:  r.   r&   r&   r'   Útest_tensorinv_ind_limit2  s    

z&TestTensorinv.test_tensorinv_ind_limitc                 C   sJ   t  d¡}d|_tj|dd�}t  d¡}tt  ||d¡t j ||¡ƒ d S )Nr?  r>  r\   r9  )	r"   rí   rg   r   r;  r  r   Ú	tensordotÚtensorsolve)rB   r.   rA  r/   r&   r&   r'   Útest_tensorinv_result;  s
    

z#TestTensorinv.test_tensorinv_resultN)rJ   rK   rL   r¥   r¦   rÆ   r"   r  r<  rC  rD  rG  r&   r&   r&   r'   r6    s    þ
ý
 ÿ
r6  c                   @   sV   e Zd Zej de d¡dfe d¡dfg¡dd„ ƒZej dd	d
dg¡dd„ ƒZ	dS )ÚTestTensorsolveza, axesr7  Nr8  )r   r]   c              	   C   s<   t tƒ�* t |jd d… ¡}tj|||d� W 5 Q R X d S ©Nr]   rñ   )r   r   r"   r  rg   r   rF  )rB   r.   rò   r/   r&   r&   r'   r<  F  s    
z(TestTensorsolve.test_non_square_handlingrg   )r]   r^   r)   )r^   r_   r_   r^   )r   r^   r^   r   c                 C   sN   t jj|Ž }t  |jd d… ¡}t j ||¡}tt j||t	|jƒd�|ƒ d S rI  )
r"   r  rð  r  rg   r   rF  r   rE  r=  )rB   rg   r.   r/   r†   r&   r&   r'   Útest_tensorsolve_resultO  s    z'TestTensorsolve.test_tensorsolve_result)
rJ   rK   rL   r¥   r¦   rÆ   r"   r  r<  rJ  r&   r&   r&   r'   rH  D  s   þ
ÿrH  c               	   C   s>   t jddgddggdd�} ttdƒ� t | ¡ W 5 Q R X d S )Nr\   rn   r]   ra   Zfloat16r3   zunsupported in linalg)r"   r   r   r^  r   rñ  )r4  r&   r&   r'   Útest_unsupported_commontypeY  s    rK  z,Bad memory reports lead to OOM in ci testing)r  c                  C   sR   d} t jd| gt jd�}t jddgt jd�}d|d< t  ||¡}t|d dƒ d S )Nì        r\   r3   )r   rm   )r"   rË   r.  r  r   r   )r5  r.   r/   r³   r&   r&   r'   Útest_blas64_dotd  s    rM  z*Numpy not compiled with 64-bit BLAS/LAPACKc            
   	   C   sº   t j} t jjj}d}d}|}t jddg| d�}t jdg| d�}t jdg| d�}|||||||ddƒ}t|d dƒ t|d |ƒ t|d |ƒ t| ¡ ƒ}	t	d	|	  k o®d
k n  ƒ d S )Nl       r\   r3   rm   r   Úinfor)  r5  rL  l        )
r"   rÍ   r   r  ZdgeqrfrË   r   r3  Úitemr   )
r,   Zlapack_routiner)  r5  Zldar.   Zworkrà  ÚresultsZlworkr&   r&   r'   Ú!test_blas64_geqrf_lwork_smoketestn  s    
rQ  )r)   r*   )~Ú__doc__rý  rø  rz   r�   r  r  r¥   Znumpyr"   r   r   r   r   r   r   r   r	   Z
numpy.corer
   r   r   r   r   r   Znumpy.linalgr   r   r   r   r   Znumpy.linalg.linalgr   Znumpy.testingr   r   r   r   r   r   r   r   r   r(   r-   r4   r5   r6   rN   r=   rR   r  r  rd   r~   r  rj   rŠ   r‹   rŒ   r–   r›   rž   r¡   r¨   r«   r´   rµ   r¶   r¹   rÇ   rÉ   rÒ   rØ   rÛ   rÞ   rã   ré   rë   rï   rø   rù   r  r  r  r  r  r  r*  r/  r9  r¦   rÆ   rE  re  rj  rx  r|  r}  rƒ  rª  r³  r´  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÏ  rÐ  rë  rú  rû  r  r§   r  r  r6  rH  rK  r  rM  r  rQ  r&   r&   r&   r'   Ú<module>   s   (,

    þþþþþþþý
þ
þþã#þþþþ ÿý ÿý ÿý ÿý ÿý ÿý
þ
þ
þ
ý
ýÎ9þþþþýþþþé 
0

:	
$.Cý
*4U6; x$ !.1
" )
	
ÿ