U
    d(.                    @   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,dddZ&dd Z-dd Z.dd Z/ddddddhZ0G dd dZ1dd Z2e	j34d  g Z5e5e2de1d!e
d"d#gd$d%gged&e
d#d"ged&e1d'e
d"d#gd$d%gged&e
d#d"ged&e1d(e
d"d#gd$d%gged&e
d#d"d%gd$d%d)gged&e1d*e
d+d,gd-d.gged&e
d/d+ged&e1d0e
d+d,gd-d.gged&e
d/d+ged&e1d1e
d+d,gd-d.gged&e
d/d+d2gd3d4d5gged&e1d6e	j6d7ed&e	j6d8ed&dhd9e1d:e	j37d;d;e	j37d;e1d<e	j37d=d=e	j37d=e1d>d=d?gd@dAggd?d=gg
7 Z5e5e2de1dBe
d"d#d$gd$d%d)gged&e
d#d"ged&e1dCe
d"d#gd$d%gdDd)gged&e
d#d"d$ged&e1dEe
d"d#d$gd$d%d)gged&e
d#d"ged&e1dFe
d"d#gd$d%gdDd)gged&e
d#d"d$ged&e1dGe
dHdIdJgdKdLdMgged&e
d/d+ged&e1dNe
dHdIgdJdOgdPdQgged&e
d/d+dJged&e1dRe
dHdIdJgdKdLdMgged&e
d/d+ged&e1dSe
dHdIgdJdOgdPdQgged&e
d/d+dJged&e1dTe
dHdIdJgdKdLdMgged&e
d/d+gdUdVgged&e1dWe
dHdIgdJdOgdPdQgged&e
d/d+gdUdVgdUdVgged&e1dXe	j37d;dYe	j37d;e1dZe	j37d=d[e	j37d=e1d\e	j37d[d=e	j37d[e1d]e	j37ddAe	j37ddhd9e1d^e	j37dAde	j37dAdhd9g7 Z5e5e2de1d_e
d"d#gd#d"gged&de1d`e
d"d#gd#d"gged&de1dae
d"d,gdbd=gged&de1dce
d"d,gdbd=gged&de1dde	j6d7ed&ddhd9e1ded=d?gd?d=ggde1dfe
d"d#gd#d"ggde1dge	j37d=d=dg7 Z5dhdi Z8e5e8 7 Z5djdk Z9dldm Z:e5e: 7 Z5G dndo doZ;G dpdq dqe;Z<G drds dse;Z=G dtdu due;Z>G dvdw dwe;Z?G dxdy dye;Z@G dzd{ d{e;ZAd|d} ZBd~d ZCG dd de<e?ZDG dd deDZEG dd de<e?ZFG dd deFZGG dd de<e?ZHG dd deHZIG dd de<e?ZJG dd deJZKG dd dZLG dd de<e?ZMG dd deMeLZNG dd de>eAZOG dd deOeLZPG dd de<e?ZQG dd deQZRG dd de<e=e?e@ZSG dd deSZTG dd de>eAZUG dd deUZVG dd de<e?ZWG dd deWZXG dd de<e=ZYG dd deYZZej[\ddd dD G dd dZ]G dd de>eAZ^G dd dZ_G dd de>eAZ`G dd dZaG dd dZbG dd debZcG dd debZdG ddÄ dedecZeG ddń dŃZfG ddǄ debZgG ddɄ debZhG dd˄ debZiG dd̈́ deeegZjG ddτ deeehZkG ddф deeeiZlG ddӄ dӃZmddՄ ZnG ddׄ d׃ZoG ddل dكZpddۄ Zqdd݄ Zrdd߄ Zsej[jtdd ZuG dd dZvG dd dZwG dd dZxdd Zyej[jzdddd Z{ej[j|e* dddd Z}dS )z# Test functions for linalg module

    N)arraysingledoublecsinglecdoubledotidentitymatmul)swapaxes)multiply
atleast_2dinfasarray)linalg)matrix_powernormmatrix_rank	multi_dotLinAlgError)_multi_dot_matrix_chain_order)	assert_assert_equalassert_raisesassert_array_equalassert_almost_equalassert_allclosesuppress_warningsassert_raises_regexHAS_LAPACK64c                 C   s"   t | t|tjrt |ntjkS N)type
isinstancenpndarray)outZin_ r%   B/tmp/pip-unpacked-wheel-c1z6a0q8/numpy/linalg/tests/test_linalg.pyconsistent_subclass   s    r'         c                 K   s8   t | jjttfkr|}n|}t| |fd|i| d S )Ndecimal)r   dtyper    r   r   old_assert_almost_equal)absingle_decimaldouble_decimal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&   get_real_dtype,   s       r3   c                 C   s   t ttttttti|  S r   )r   r   r   r   r2   r%   r%   r&   get_complex_dtype1   s       r4   c                 C   s   | t tfkrdS dS d S )Ngh㈵>gdy=)r   r   r2   r%   r%   r&   get_rtol6   s    r5   square	nonsquare	hermitiangeneralizedsize-0stridedc                   @   s*   e Zd Ze fddZdd Zdd ZdS )
LinalgCasec                 C   s.   t t|t || _|| _|| _t|| _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!   strnamer-   r.   	frozensettags)selfr>   r-   r.   r@   r%   r%   r&   __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
        r@   N)r-   r.   r@   )rA   dor%   r%   r&   checkQ   s    zLinalgCase.checkc                 C   s   d| j  dS )Nz<LinalgCase: >)r>   rA   r%   r%   r&   __repr__W   s    zLinalgCase.__repr__N)__name__
__module____qualname__setrB   rE   rH   r%   r%   r%   r&   r<   E   s   r<   c                 C   s,   | t kstd|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)all_tagsAssertionErrorr@   )tagZcasescaser%   r%   r&   	apply_tag[   s    rQ     r         ?       @      @      @r2   r   Zdouble_2      @r   y      ?       @y       @      @y      @      @y      @      @y       @      ?r   Z	cdouble_2y      ?      @y      ?       y      ?      y      ?      Z0x0r   r   r   rC   Z8x8   Z1x1   Znonarray         Zsingle_nsq_1Zsingle_nsq_2g      @Zdouble_nsq_1Zdouble_nsq_2Zcsingle_nsq_1y      ?      ?y       @       @y      @      y      @      y      @      "@y      @       @Zcsingle_nsq_2y      @      "y      @      y      @       @Zcdouble_nsq_1Zcdouble_nsq_2Zcdouble_nsq_1_2y      ?      y       @       Zcdouble_nsq_2_2Z8x11   Z1x5   Z5x1Z0x4Z4x0ZhsingleZhdoubleZhcsingley       @      ZhcdoubleZhemptyZ	hnonarrayZmatrix_b_onlyZhmatrix_1x1c                  C   s  g } t D ]}t|jtj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rd }n$t|jgd d d|jj }t|jd	 |||j	dhB d}| 
| q| S )
Nr\   r]      r(   Z_tile3r9   rC   r]   r\   Z_tile213)CASESr!   r-   r"   r#   r   r.   r<   r>   r@   appendreshapeshape)	new_casesrP   r-   r.   new_caser%   r%   r&   _make_generalized_cases   s*    



$
$
ri   c                 c   s  t | tj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| D ]}dd t| j|D }tdd |D }tj	|| j
d}|tjd || }| |d< || j}tt|| k |dddd |D  fV  | jdkrF| jd dkrFt| j}d|d< tjjj| |d}|dfV  | jdkr| jd dkrt| j}d|d< tjjj| |d}|dfV  | jdkr`| jdd dkr`t| j}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]   r[   r\   )r[   rk   c                 S   s   g | ]\}}t || qS r%   )abs).0r-   r.   r%   r%   r&   
<listcomp>  s     z%_stride_comb_iter.<locals>.<listcomp>c                 S   s   g | ]}t d d |qS r   )slice)rp   repeatr%   r%   r&   rq     s     r2   l   >[= .Zstride__c                 S   s   g | ]}d | qS )z%+dr%   )rp   jr%   r%   r&   rq   (  s     r   )stridesZstride_xxx_0Zstride_xxx_0_xr[   r[   Zstride_xxx_0_0)r!   r"   r#   ndim	itertoolsproducttupleziprf   emptyr+   viewZuint32fill	__class__r   alljoinlistrv   libZstride_tricksZ
as_strided)xZ
stride_setZrepeats	new_shapeZslicesxisr%   r%   r&   _stride_comb_iter  sF    







r   c               	   C   sn   g } t D ]`}t|jD ]P\}}t|jD ]<\}}t|jd | d | |||jdhB d}| | q(qq| S )Nrt   r;   rC   )rc   r   r-   r.   r<   r>   r@   rd   )rg   rP   r-   Za_labelr.   Zb_labelrh   r%   r%   r&   _make_strided_cases=  s    
r   c                   @   s"   e Zd ZeZe e fddZdS )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||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)
TEST_CASESr@   rE   rD   	Exception	traceback
format_excrN   )rA   requireexcluderP   emsgr%   r%   r&   check_casesQ  s    

zLinalgTestCase.check_casesN)rI   rJ   rK   rc   r   rL   r   r%   r%   r%   r&   r   N  s   r   c                   @   s   e Zd Zdd Zdd ZdS )LinalgSquareTestCasec                 C   s   | j dhddhd d S )Nr6   r9   r:   r   r   r   rG   r%   r%   r&   test_sq_casesg  s    z"LinalgSquareTestCase.test_sq_casesc                 C   s   | j ddhdhd d S )Nr6   r:   r9   r   r   rG   r%   r%   r&   test_empty_sq_casesk  s    
z(LinalgSquareTestCase.test_empty_sq_casesN)rI   rJ   rK   r   r   r%   r%   r%   r&   r   e  s   r   c                   @   s   e Zd Zdd Zdd ZdS )LinalgNonsquareTestCasec                 C   s   | j dhddhd d S )Nr7   r9   r:   r   r   rG   r%   r%   r&   test_nonsq_casesr  s    z(LinalgNonsquareTestCase.test_nonsq_casesc                 C   s   | j ddhdhd d S )Nr7   r:   r9   r   r   rG   r%   r%   r&   test_empty_nonsq_casesv  s    
z.LinalgNonsquareTestCase.test_empty_nonsq_casesN)rI   rJ   rK   r   r   r%   r%   r%   r&   r   p  s   r   c                   @   s   e Zd Zdd Zdd ZdS )HermitianTestCasec                 C   s   | j dhddhd d S )Nr8   r9   r:   r   r   rG   r%   r%   r&   test_herm_cases}  s    z!HermitianTestCase.test_herm_casesc                 C   s   | j ddhdhd d S )Nr8   r:   r9   r   r   rG   r%   r%   r&   test_empty_herm_cases  s    
z'HermitianTestCase.test_empty_herm_casesN)rI   rJ   rK   r   r   r%   r%   r%   r&   r   {  s   r   c                   @   s,   e Zd Zejjdd Zejjdd ZdS )LinalgGeneralizedSquareTestCasec                 C   s   | j ddhdhd d S )Nr9   r6   r:   r   r   rG   r%   r%   r&   test_generalized_sq_cases  s    
z9LinalgGeneralizedSquareTestCase.test_generalized_sq_casesc                 C   s   | j dddhd d S )Nr9   r6   r:   r   r   rG   r%   r%   r&   test_generalized_empty_sq_cases  s    z?LinalgGeneralizedSquareTestCase.test_generalized_empty_sq_casesN)rI   rJ   rK   pytestmarkslowr   r   r%   r%   r%   r&   r     s   
r   c                   @   s,   e Zd Zejjdd Zejjdd ZdS )"LinalgGeneralizedNonsquareTestCasec                 C   s   | j ddhdhd d S )Nr9   r7   r:   r   r   rG   r%   r%   r&   test_generalized_nonsq_cases  s    
z?LinalgGeneralizedNonsquareTestCase.test_generalized_nonsq_casesc                 C   s   | j dddhd d S )Nr9   r7   r:   r   r   rG   r%   r%   r&   "test_generalized_empty_nonsq_cases  s    zELinalgGeneralizedNonsquareTestCase.test_generalized_empty_nonsq_casesN)rI   rJ   rK   r   r   r   r   r   r%   r%   r%   r&   r     s   
r   c                   @   s,   e Zd Zejjdd Zejjdd ZdS )HermitianGeneralizedTestCasec                 C   s   | j ddhdhd d S )Nr9   r8   r:   r   r   rG   r%   r%   r&   test_generalized_herm_cases  s    
z8HermitianGeneralizedTestCase.test_generalized_herm_casesc                 C   s   | j dddhdhd d S )Nr9   r8   r:   noner   r   rG   r%   r%   r&   !test_generalized_empty_herm_cases  s    z>HermitianGeneralizedTestCase.test_generalized_empty_herm_casesN)rI   rJ   rK   r   r   r   r   r   r%   r%   r%   r&   r     s   
r   c                 C   s   t | } | 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tj|t| |d}tjt	t
| jd d  D ]}t| | || ||< q|S t| |S d S )Nr]   rl   r[   zNot implemented...r2   rm   )r   rx   rf   
ValueErrorr"   r}   Zcommon_typery   rz   mapranger   )r-   r.   r   rcr%   r%   r&   dot_generalized  s    
r   c                 C   sL   t | } | jdkr:tj| j| jd}t| jd |d< |S t| jd S d S )Nr]   r2   rm   .r   )r   rx   r"   r}   rf   r+   r   )r-   r   r%   r%   r&   identity_like_generalized  s    
r   c                   @   s   e Zd Zdd ZdS )
SolveCasesc                 C   s.   t ||}t|t|| tt|| d S r   )r   solver   r   r   r'   )rA   r-   r.   r@   r   r%   r%   r&   rD     s    zSolveCases.doNrI   rJ   rK   rD   r%   r%   r%   r&   r     s   r   c                   @   s:   e Zd Zejdeeee	gdd Z
dd Zdd ZdS )		TestSolver+   c                 C   s2   t jddgddgg|d}tt||j| d S Nr[         ?r2   )r"   r   r   r   r   r+   rA   r+   r   r%   r%   r&   
test_types  s    zTestSolve.test_typesc              	   C   s.  G dd dt j}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|| tt	|| t
tjtj|d d ddddf | t
ttj||d d ddd d f  t dddd}t
ttj|| t
ttj|dd |dd  t ddd|}t||d d ddf }t|d d ddddf |d d ddf }t|| tt	|| t ddd}t
ttj|| t
ttj|dd |dd  t
ttj|d d ddddf | d S )	Nc                   @   s   e Zd ZdS )z,TestSolve.test_0_size.<locals>.ArraySubclassNrI   rJ   rK   r%   r%   r%   r&   ArraySubclass  s   r   rZ   r\   r(   r[   r]   r   )r"   r#   arangere   r~   r   r   r   r   r!   r   r   r   rA   r   r-   r.   expectedresultr%   r%   r&   test_0_size  s*    "8
(& 2
 zTestSolve.test_0_sizec                 C   s  G dd dt j}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|| tt	|| t||d d ddddf }t|d d ddddf |d d ddddf }t|| tt	|| d S )	Nc                   @   s   e Zd ZdS )z.TestSolve.test_0_size_k.<locals>.ArraySubclassNr   r%   r%   r%   r&   r     s   r   r^   r[   r\   r(   r]   r   )
r"   r#   r   re   r~   r   r   r   r   r!   r   r%   r%   r&   test_0_size_k  s    ""
"8
zTestSolve.test_0_size_kN)rI   rJ   rK   r   r   parametrizer   r   r   r   r   r   r   r%   r%   r%   r&   r     s   
!r   c                   @   s   e Zd Zdd ZdS )InvCasesc                 C   s0   t |}tt||t| tt|| d S r   )r   invr   r   r   r   r'   )rA   r-   r.   r@   Za_invr%   r%   r&   rD     s
    

zInvCases.doNr   r%   r%   r%   r&   r   
  s   r   c                   @   s2   e Zd Zejdeeee	gdd Z
dd ZdS )TestInvr+   c                 C   s0   t jddgddgg|d}tt|j| d S r   )r"   r   r   r   r   r+   r   r%   r%   r&   r     s    zTestInv.test_typesc                 C   s   G dd dt j}t jdt jd|}t|}t|jj	t j
k t|j|j tt|| t jdt jd|}t|}t|jj	t jk t|j|j tt|| d S )Nc                   @   s   e Zd ZdS )z*TestInv.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r     s   r   r   r[   r[   r2   rX   )r"   r#   zerosint_r~   r   r   r   r+   r    float64r   rf   r!   	complex64rA   r   r-   resr%   r%   r&   r     s    

zTestInv.test_0_sizeNrI   rJ   rK   r   r   r   r   r   r   r   r   r   r%   r%   r%   r&   r     s   
r   c                   @   s   e Zd Zdd ZdS )EigvalsCasesc                 C   s&   t |}t |\}}t|| d S r   )r   eigvalseigr   )rA   r-   r.   r@   evevaluesevectorsr%   r%   r&   rD   ,  s    
zEigvalsCases.doNr   r%   r%   r%   r&   r   *  s   r   c                   @   s2   e Zd Zejdeeee	gdd Z
dd ZdS )TestEigvalsr+   c                 C   s`   t jddgddgg|d}tt|j| t jddgddgg|d}tt|jt| d S Nr[   r   r2   rl   )r"   r   r   r   r   r+   r4   r   r%   r%   r&   r   3  s    zTestEigvals.test_typesc                 C   s   G dd dt j}t jdt jd|}t|}t|jj	t j
k td|j tt|t j t jdt jd|}t|}t|jj	t jk td|j tt|t j d S )Nc                   @   s   e Zd ZdS )z.TestEigvals.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r   <  s   r   r   r2   r   r[   rX   rY   )r"   r#   r   r   r~   r   r   r   r+   r    r   r   rf   r!   r   r   r%   r%   r&   r   :  s    

zTestEigvals.test_0_sizeNr   r%   r%   r%   r&   r   2  s   
r   c                   @   s   e Zd Zdd ZdS )EigCasesc                 C   sX   t |\}}tt||t|t|dd d d f  t|jd tt	|| d S )N.rtol)
r   r   r   r   r"   r   r5   r+   r   r'   )rA   r-   r.   r@   r   r   r%   r%   r&   rD   O  s    
 zEigCases.doNr   r%   r%   r%   r&   r   M  s   r   c                   @   s2   e Zd Zejdeeee	gdd Z
dd ZdS )TestEigr+   c                 C   s   t jddgddgg|d}t j|\}}t|j| t|j| t jddgddgg|d}t j|\}}t|jt| t|jt| d S r   )r"   r   r   r   r   r+   r4   rA   r+   r   wvr%   r%   r&   r   X  s    zTestEig.test_typesc                 C   s   G dd dt j}t jdt jd|}t|\}}t|jj	t j
k t|jj	t j
k t|j|j td|j tt|t j t jdt jd|}t|\}}t|jj	t jk t|jj	t jk t|j|j td|j tt|t j d S )Nc                   @   s   e Zd ZdS )z*TestEig.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r   f  s   r   r   r2   r   rX   rY   )r"   r#   r   r   r~   r   r   r   r+   r    r   r   rf   r!   r   rA   r   r-   r   Zres_vr%   r%   r&   r   d  s    zTestEig.test_0_sizeNr   r%   r%   r%   r&   r   W  s   
r   c                   @   s.   e Zd ZdZejdeee	e
gdd ZdS )SVDBaseTestsFr+   c                 C   sx   t jddgddgg|d}t|\}}}t|j| t|jt| t|j| tj|d| jd}t|jt| d S )Nr[   r   r2   F
compute_uvr8   )r"   r   r   svdr   r+   r3   r8   )rA   r+   r   ur   vhr%   r%   r&   r   ~  s    zSVDBaseTests.test_typesN)rI   rJ   rK   r8   r   r   r   r   r   r   r   r   r%   r%   r%   r&   r   {  s   r   c                   @   s   e Zd Zdd ZdS )SVDCasesc              	   C   sp   t |d\}}}t|tt|t|dd d d f  t|t|jd tt	|| tt	|| d S )NF.r   )
r   r   r   r   r"   r   r5   r+   r   r'   )rA   r-   r.   r@   r   r   vtr%   r%   r&   rD     s    &zSVDCases.doNr   r%   r%   r%   r&   r     s   r   c                   @   s   e Zd Zdd ZdS )TestSVDc                 C   s   t d}tj|d| jd\}}}t|jd t|jd t|t d t d}tj|d| jd\}}}t|jd t|jd t|t d dS )	z6 Empty input should put an identity matrix in u or vh )r^   r   Tr   r^   r^   rX   r^   )r   r^   N)r"   r}   r   r   r8   r   rf   eye)rA   r   r   r   r   r%   r%   r&   test_empty_identity  s    

zTestSVD.test_empty_identityN)rI   rJ   rK   r   r%   r%   r%   r&   r     s   r   c                   @   s   e Zd Zdd ZdS )SVDHermitianCasesc              	   C   s   t j|ddd\}}}t|tt|t|dd d d f  t|t|jd dd }tt	|||t
t|jd |j tt	|||t
t|jd |j tt|dd d df | tt|| tt|| d S )	NFTr8   .r   c                 S   s<   t t| j}|d |d  |d< |d< ttj| |dS )Nrm   rl   axes)r   r   rx   r"   conj	transpose)matr   r%   r%   r&   r8     s    z'SVDHermitianCases.do.<locals>.hermitianrl   )r   r   r   r   r"   r   r5   r+   r   r	   broadcast_tor   rf   r   sortr   r'   )rA   r-   r.   r@   r   r   r   r8   r%   r%   r&   rD     s    &,,zSVDHermitianCases.doNr   r%   r%   r%   r&   r     s   r   c                   @   s   e Zd ZdZdS )TestSVDHermitianTN)rI   rJ   rK   r8   r%   r%   r%   r&   r     s   r   c                   @   s   e Zd Zdd ZdS )	CondCasesc                 C   s  t |}d|kr"tttj| 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	|
d
dt	|
d
d ddd tt|dt	|
d
dt	|
d
d ddd tt|tjt	|
ddt	|
dd ddd tt|tj t	|
ddt	|
dd ddd tt|dtt	|d	 
d
dt	|d	 
d
d ddd d S )Nr:   F)r   ).r   ).rl   r`   r_   r/   r0   r\   rm   r[   rl   fro)r   r   r   r   condr   r   r"   r   ro   summaxminr   sqrt)rA   r-   r.   r@   r   r   Zcinvr%   r%   r&   rD     sp      
  
  
& 
& & & 
 zCondCases.doNr   r%   r%   r%   r&   r     s   r   c                   @   s>   e Zd Zdd Zdd Zejjddddd	d
 Zdd Z	dS )TestCondc                 C   s   t dddgdddgdddgg}tt|td tt|t d tt|dd tt|dd	 tt|d
td d S )NrS   r   r[   g       rU   r^   gUUUUUU?rl   r   r   gUUUUU6@)r   r   r   r   r   r"   r   rA   Ar%   r%   r&   test_basic_nonsvd  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 q4t||D ]\}}t|| q^d S )Nr\   r\   r[   r\   r   rl   rm     4&kC)r"   r   onesry   rz   r   r   r   )rA   ZAsp_posZp_negr  pr%   r%   r&   test_singular  s    zTestCond.test_singularTFz/Platform/LAPACK-dependent failure, see gh-18914)runreasonc                 C   s   d dddddg}d dddg}t d}t j|d< |D ].}t||}tt|t j tt | q4t d}t j|d	< |D ]t}t||}tt |d  ||krt|d
 dk t|d dk q|tt |d
   tt |d   q|d S )Nr[   rl   r\   rm   r   r  r   )r]   r\   r\   )r[   r   r[   r   r  )	r"   r  nanr   r   r   r!   Zfloat_isnan)rA   Zpsr  r  r  r   r%   r%   r&   test_nan  s$    



zTestCond.test_nanc                 C   s   t jd t jdddd}d|d< d|d< dD ]T}t||}t|d t j t|d t j tt 	|d  tt 	|d  q2d S )	NrR   r\   r   rX   rw   )Nr[   r\   r   rl   rm   r   r[   r   )
r"   randomseedrandr   r   r   r   r   isfinite)rA   r  r  r   r%   r%   r&   test_stacked_singular  s    zTestCond.test_stacked_singularN)
rI   rJ   rK   r  r	  r   r   xfailr  r  r%   r%   r%   r&   r     s   	

r   c                   @   s   e Zd Zdd ZdS )	PinvCasesc                 C   s<   t |}t}t||||||ddd tt|| d S )Nr`   r_   r   r   pinvr   r   r   r'   rA   r-   r.   r@   Za_ginvr   r%   r%   r&   rD   1  s    
zPinvCases.doNr   r%   r%   r%   r&   r  ,  s   r  c                   @   s   e Zd ZdS )TestPinvNr   r%   r%   r%   r&   r  9  s   r  c                   @   s   e Zd Zdd ZdS )PinvHermitianCasesc                 C   s@   t j|dd}t}t||||||ddd tt|| d S )NTr   r`   r_   r   r  r  r%   r%   r&   rD   ?  s    zPinvHermitianCases.doNr   r%   r%   r%   r&   r  =  s   r  c                   @   s   e Zd ZdS )TestPinvHermitianNr   r%   r%   r%   r&   r  G  s   r  c                   @   s   e Zd Zdd ZdS )DetCasesc           
      C   s   t |}t |\}}t|jjttfkr<t|t}nt|t	}t 
|}t|tj|dd t|t| tj|dd t|}t|}|dk}	tt||	 d t||	  t  d S )Nrl   axisr   r[   )r   detslogdetr   r+   r    r   r   astyper   r   r   r   reducer"   expZ
atleast_1dro   r   r   )
rA   r-   r.   r@   dr   Zldadr   mr%   r%   r&   rD   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 Zdd ZdS )	TestDetc                 C   s   t tdggd t ttdggt t tdggd t ttdggt t tdggdt f t ttdggd t t ttdggd t t tdggdt f t ttdggd t t ttdggd t d S )N        y                r   r[   )r   r   r   r    r   r   r!  r   rG   r%   r%   r&   	test_zero`  s    zTestDet.test_zeror+   c                 C   s^   t jddgddgg|d}tt j|j| t j|\}}t|jt| t|j| d S r   )r"   r   r   r   r   r+   r!  r3   )rA   r+   r   phr   r%   r%   r&   r   m  s
    zTestDet.test_typesc                 C   s   t jdt jd}t|}t|d t|jjt jk t	|}t|d t|d jjt jk t|d jjt j
k t jdt jd}t|}t|d t|jjt jk t	|}t|d t|d jjt jk t|d jjt jk d S )NrX   r2   rS   r  r   r[   )r"   r   r   r   r   r   r   r+   r    r!  float32r   )rA   r-   r   r%   r%   r&   r   u  s     







zTestDet.test_0_sizeN)rI   rJ   rK   r*  r   r   r   r   r   r   r   r   r   r%   r%   r%   r&   r(  _  s   
r(  c                   @   s   e Zd Zdd ZdS )
LstsqCasesc                 C   sL  t |}|j\}}t|d\}}}	tj||dd\}
}}}|dkrVt|
dk  ||krzt|t	||
 t
|| n
t
|| t||| ||kr||krt tt 	||
| d jdd}t |}t |jdkrd|_t
|j|j nt g t|
}t|| tt |jt j tt|
| tt|| d S )	NFrl   Zrcondr   r\   r  r[   rj   )r"   r   rf   r   r   lstsqr   r   r   r   r   Z__array_wrap__ro   r   rx   r   r~   r    
issubdtyper+   floatingr'   )rA   r-   r.   r@   arrr'  nr   r   r   r   	residualsranksvZexpect_residsr%   r%   r&   rD     s2    




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 Zdd ZdS )	TestLstsqc           	      C   s   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 }|td}t||\}}}}t|d	k tj||d
d\}}}}t|d	k tj||d d\}}}}t|dk tt	|dk W 5 Q R X d S )Nr)  rS   rT   rV   rU   r[   r   z`rcond` parameter will changer^   rl   r.  r]   )
r"   r   Tr   recordFutureWarningr   r/  r   len)	rA   r-   r.   supr   r   r4  r5  r   r%   r%   r&   test_future_rcond  s    zTestLstsq.test_future_rcondr'  r3  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   s   t || ||}t ||f}tj||d d\}}}}	|dkrTt|dk  t|j	||f t|j	||krx|fnd ||kr|dkr|t 
|| }
t||
|
 jdd t|t|| t|	j	t||f d S )Nr.  r   rY   rm   r  )r"   r   re   r  r   r/  r   r   r   rf   r   r   r   r   )rA   r'  r3  r>  r-   r.   r   r4  r5  r   r   r%   r%   r&   test_empty_a_b  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|gj}ttd
 tj	||d d W 5 Q R X d S )Nr   r[   r\   r]   rl   g?g?g @gffffff
@zIncompatible dimensionsr.  )
r"   r   Zvstackr  r;  r8  r   r   r   r/  )rA   r   yr  r%   r%   r&   test_incompatible_dims  s
    z TestLstsq.test_incompatible_dimsN)	rI   rJ   rK   r=  r   r   r   r?  rA  r%   r%   r%   r&   r7    s   	
r7  dtc                 C   s   g | ]}t |qS r%   )r"   r+   )rp   r   r%   r%   r&   rq     s     rq   z?bBhHiIqQefdgFDGOc                   @   s   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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 )TestMatrixPowerr^   r]   r   r[   r\   r   gGc                 C   s   | j |}tt|dd d d d | j tt|dd d d d | j  tt|dd d d d | j tt|dd d d d | j d S )Nr\   d   i       r   r[   r]   )rshft_1r"  r   r   rshft_0rshft_2rshft_3)rA   rB  Zrshftr%   r%   r&   test_large_power  s"        z TestMatrixPower.test_large_powerc                 C   s>   dd }| j D ]*}||| |tkr|| j| qd S )Nc                 S   s*   t | d}t|t|  t|j| j d S )Nr   )r   r   r   r+   )Mmzr%   r%   r&   tz  s    
z.TestMatrixPower.test_power_is_zero.<locals>.tz	rshft_allr"  objectstackedrA   rB  rO  r   r%   r%   r&   test_power_is_zero  s
    
z"TestMatrixPower.test_power_is_zeroc                 C   s>   dd }| j D ]*}||| |tkr|| j| qd S )Nc                 S   s&   t | d}t||  t|j| j d S )Nr[   )r   r   r+   )r   rN  r%   r%   r&   rO    s    

z-TestMatrixPower.test_power_is_one.<locals>.tzrP  rT  r%   r%   r&   test_power_is_one  s
    
z!TestMatrixPower.test_power_is_onec                 C   s>   dd }| j D ]*}||| |tkr|| j| qd S )Nc                 S   s>   t | d}| jtkrtnt}t||| |  t|j| j d S )Nr\   )r   r+   rR  r	   r   r   )r   rN  mmulr%   r%   r&   rO  
  s    
z-TestMatrixPower.test_power_is_two.<locals>.tzrP  rT  r%   r%   r&   test_power_is_two	  s
    
z!TestMatrixPower.test_power_is_twoc                 C   s0   dd }| j D ]}|| jkr||| qd S )Nc                 S   s4   t | d}| jtkrtnt}t||| t|  d S Nrl   )r   r+   rR  r	   r   r   r   )r   ZinvmatrW  r%   r%   r&   rO    s    
 z3TestMatrixPower.test_power_is_minus_one.<locals>.tz)rQ  dtnoinvr"  rT  r%   r%   r&   test_power_is_minus_one  s    

z'TestMatrixPower.test_power_is_minus_onec                 C   s.   | j |}ttt|d ttt|dg d S )Ng      ?r[   )rI  r"  r   	TypeErrorr   rA   rB  r   r%   r%   r&   test_exceptions_bad_power   s    z)TestMatrixPower.test_exceptions_bad_powerc                 C   sP   t tttdg|d t tttdgdgg|d t tttd|d d S )Nr[   r\   )r^   r]   r\   )r   r   r   r"   r   r  )rA   rB  r%   r%   r&   test_exceptions_non_square%  s    z*TestMatrixPower.test_exceptions_non_squarec                 C   s,   || j krd S | j|}ttt|d d S rY  )rZ  noninvr"  r   r   r   r]  r%   r%   r&   test_exceptions_not_invertible*  s    
z.TestMatrixPower.test_exceptions_not_invertibleN)rI   rJ   rK   r"   r   rI  rH  rJ  rK  rQ  r   r`  blockrS  rR  r+   rZ  rL  rU  rV  rX  r[  r^  r_  ra  r%   r%   r%   r&   rC    s    
rC  c                   @   s   e Zd Zdd ZdS )TestEigvalshCasesc                 C   s^   t |d}t |\}}|jdd t||t|jd t |d}t||t|jd d S )NLrl   r  r   U)r   eigvalshr   r   r   r5   r+   )rA   r-   r.   r@   r   r   r   ev2r%   r%   r&   rD   3  s    zTestEigvalshCases.doNr   r%   r%   r%   r&   rc  1  s   rc  c                   @   sB   e Zd Zejdeeee	gdd Z
dd Zdd Zdd	 Zd
S )TestEigvalshr+   c                 C   s:   t jddgddgg|d}t j|}t|jt| d S r   )r"   r   r   rf  r   r+   r3   )rA   r+   r   r   r%   r%   r&   r   @  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 ttt jj|d d S Nr[   r   r2   ZlrongZUPLOlowerupper)r"   r   r,  r   r   r   rf  rA   r   r%   r%   r&   test_invalidF  s    zTestEigvalsh.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}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[   r2   rl   r   rd  rj  lre  r   )r"   r   r   r5   r   rf  r   )rA   KloKuptgtr   r   r%   r%   r&   	test_UPLOL  s    
zTestEigvalsh.test_UPLOc                 C   s   G dd dt j}t jdt jd|}t|}t|jj	t j
k td|j tt|t j t jdt jd|}t|}t|jj	t jk td|j tt|t j d S )Nc                   @   s   e Zd ZdS )z/TestEigvalsh.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r   d  s   r   r   r2   r   rX   rY   )r"   r#   r   r   r~   r   rf  r   r+   r    r   r   rf   r!   r   r,  r   r%   r%   r&   r   b  s    

zTestEigvalsh.test_0_sizeNrI   rJ   rK   r   r   r   r   r   r   r   r   rn  rt  r   r%   r%   r%   r&   rh  ?  s
   
rh  c                   @   s   e Zd Zdd ZdS )TestEighCasesc           
      C   s   t |\}}t |\}}|jdd t|| tt||t|dd d d f t| t	|j
d t |d\}}	t|| tt||	t|dd d d f t|	 t	|j
t|d d S )Nrl   r  .r   re  )r   err_msg)r   eighr   r   r   r   r   r"   r   r5   r+   repr)
rA   r-   r.   r@   r   Zevcr   r   rg  Zevc2r%   r%   r&   rD   w  s    

 

  zTestEighCases.doNr   r%   r%   r%   r&   rv  u  s   rv  c                   @   sB   e Zd Zejdeeee	gdd Z
dd Zdd Zdd	 Zd
S )TestEighr+   c                 C   sJ   t jddgddgg|d}t j|\}}t|jt| t|j| d S r   )r"   r   r   rx  r   r+   r3   r   r%   r%   r&   r     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 ttt jj|d d S ri  )r"   r   r,  r   r   r   rx  rm  r%   r%   r&   rn    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}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 ro  )r"   r   r   r5   r   rx  r   )rA   rq  rr  rs  r   r   r   r%   r%   r&   rt    s    
zTestEigh.test_UPLOc                 C   s   G dd dt j}t jdt jd|}t|\}}t|jj	t j
k t|jj	t j
k t|j|j td|j tt|t j t jdt jd|}t|\}}t|jj	t jk t|jj	t jk t|j|j td|j tt|t j d S )Nc                   @   s   e Zd ZdS )z+TestEigh.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r     s   r   r   r2   r   rX   rY   )r"   r#   r   r   r~   r   rx  r   r+   r    r   r   rf   r!   r   r,  r   r%   r%   r&   r     s    zTestEigh.test_0_sizeNru  r%   r%   r%   r&   rz    s
   
rz  c                   @   s    e Zd ZdZdZedd ZdS )_TestNormBaseNc                 C   s:   t | jjtjr"t|j| jj ntt |jjtj d S r   )	
issubclassr+   r    r"   Zinexactr   realr   r1  )r   r   r%   r%   r&   check_dtype  s    z_TestNormBase.check_dtype)rI   rJ   rK   rB  decstaticmethodr~  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 )_TestNormGeneralc                 C   sF   t tg d t ttg | jdd t tttg | jdd d S )Nr)  r2   )r   r   r   rB  r   rG   r%   r%   r&   
test_empty  s    z_TestNormGeneral.test_emptyc           	   
   C   sr  t dddg}t jd }t jd }|| }|D ]:}||}t|t j }| || t|d t 2}|	t
d t|d}| || t|d W 5 Q R X t|d}| || t|d t|d}| || t|d	 t|d}| || t||jd	|jd
  t|d}| || t||jd	|jd  t|t j}| || t|d q0d S )Nr[   r   
AllIntegerZAllFloatr)  divide by zero encounteredrl   r\   rT   r   r^   g      ?rS   )r"   r   	typecodesr"  r   r   r~  r   r   filterRuntimeWarningr+   r    	rA   r-   Zexact_typesZinexact_typesZ	all_typesZ	each_typeatZanr<  r%   r%   r&   test_vector_return_type  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 ]}|| q:t | jdt | jdt | jdfD ]}|| qpd S )Nr[   r\   r]   r^   rl   rm   rn   rk   c                    s   t jjt| d jd t jjt| td jd t jjt| t d jd t jjt| dd jd t jjt| dd jd t jjt| d	d jd t jjt| d
d jd t jjt| dd jd d S )Ng6ҭ@r*   rV   rS   r[         $@rl   gQ?r\   rm   gsc?r   r^   )r"   testingr   r   r  r   )r   rG   r%   r&   _test  s0    z+_TestNormGeneral.test_vector.<locals>._testr2   )r   rB  )rA   r-   r.   r   r  r   r%   rG   r&   test_vector  s    
z_TestNormGeneral.test_vectorc           	   	      s  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 jd D }tt d	d|  fddt jd	 D }tt dd| q8tjdd| jd	dddj
}d ddddtjtj dfD ]؉tt| |dD ]}|\}}|d	k r||7 }|d	k r&||7 }||krDttt|d qt|d}|||  ||k rfddtj D }n fddtj D }t|| qqd S )Nr[   r\   r]   r^   r`   r(   r2   rl   r   c                    s$   g | ]}t  d d |f dqS Nordr   rp   kr  orderr%   r&   rq   '  s     z._TestNormGeneral.test_axis.<locals>.<listcomp>r  r  c                    s$   g | ]}t  |d d f dqS r  r  r  r  r%   r&   rq   )  s        rm   r   c                    s*   g | ]"}t  d d  j|ddqS Nr  r  )r   taker  Bk_indexr  r%   r&   rq   ?  s   c                    s,   g | ]$}t  d d  j|djdqS r  )r   r  r8  r  r  r%   r&   rq   B  s   )r   rB  r"   Infr   rf   r   r   r   re   rx   ry   combinationsr   r   )	rA   Z	expected0Z	expected1Zndr  Zrow_axisZcol_axisr3  r   r%   )r  r  r  r  r&   	test_axis!  s6    



z_TestNormGeneral.test_axisc           	   
   C   s  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  d dddddt j
t j
 fD ]}t|jD ]v}t|||d	}t|||d
d}tt |||||d t|j	}d||< t|}t|j	|k||j	||| qqd ddddt j
t j
 ddf	D ]}tt|jdD ]}t|||d	}t|||d
d}tt |||||d t|j	}d||d < d||d < t|}t|j	|k||j	||| qTq>d S )Nr[   r  r2   r\   r]   r^   zorder {0}, axis = {1}z;Shape mismatch found {0}, expected {1}, order={2}, axis={3}r  T)r  r  Zkeepdims)rw  )r[   r[   r[   rl   r   rm   r   nuc)r"   r   rB  re   r   r   Zsqueezeformatr   rf   r  r   rx   r   r{   ry   permutations)	rA   r  Zallclose_errZ	shape_errr   foundZexpected_shaper  r  r%   r%   r&   test_keepdimsF  sN    




 


z_TestNormGeneral.test_keepdimsN)rI   rJ   rK   r  r  r  r  r  r%   r%   r%   r&   r    s
   )%r  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 )_TestNorm2Dc                 C   s    t t| jg g| jdd d S )Nr2   r)  )r   r   r   rB  rG   r%   r%   r&   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 }| || t|d t 2}|	t
d t|d}| || t|d W 5 Q R X t|d}| || t|d t|d	}| || t|d
 t|d}| || t|d t|tj}| || t|d t|d}| || t|d t|d}| || tjj|ddd q4d S )Nr[   r   r  ZfdFDrT   r  rl   rS   r\   gLXz?rm   r   r  gU&,t=@r(   r  )r   r"   r  r"  r   r   r~  r   r   r  r  r  r  r%   r%   r&   test_matrix_return_typey  s@    














z#_TestNorm2D.test_matrix_return_typec                 C   s   | j ddgddgg| jd}tt|d tt|dd tt|dd	 tt|td
 tt|t d tt|dd	 tt|dd tt|dd tt|dd ttt|d ttt|d ttt|d d S )Nr[   r]   r`   ra   r2   gT"@r   r  r  g      (@rV   rl   rW   r\   gW?"@rm   gїʄ?Znofrorn   r   )r   rB  r   r   r   r   r   r  r%   r%   r&   test_matrix_2x2  s    z_TestNorm2D.test_matrix_2x2c                 C   s   d| j dddgdddgdddgg| jd }tt|d	 tt|d
d	 tt|dd tt|td tt|t d tt|dd tt|dd tt|dd tt|dd d S )Ng?r[   r\   r]   r(   r   r`   r2   grj=Q0?r   r  gB+pc?g?g333333?rS   rl   g?g&.d?rm   gܸՠ?)r   rB  r   r   r   r  r%   r%   r&   test_matrix_3x3  s    &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
 ttt|dd
 tttddgd	d  tttddgdd  tttddgdd  dD ]4}ttt||d  ttt||d ttt||d qttjt|d d ttjt|d d ttt|d d d S )Nr[   r\   r]   r^   r`   r(   r2   r  r   r   r  testr   r]   r   )r[   r\   r\   r]   )r   r[   r\   )	r   rB  r"   r   re   r   r   r   Z	AxisError)rA   r  r  r  r%   r%   r&   test_bad_args  s     z_TestNorm2D.test_bad_argsN)
rI   rJ   rK   r"   r   r  r  r  r  r  r%   r%   r%   r&   r  q  s   3r  c                   @   s   e Zd ZdS )	_TestNormNr   r%   r%   r%   r&   r    s   r  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestNorm_NonSystematicc                 C   s*   t jdt jd}tt|ddddd d S )N
   r2   r]   r  gL)@r\   r  )r"   r   Z
longdoubler,   r   rm  r%   r%   r&   test_longdouble_norm  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   r2   r]   r  l        r`   r  )r"   r   Zint32r,   r   rm  r%   r%   r&   test_intmin  s    z"TestNorm_NonSystematic.test_intminc                 C   s   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\   r2   y      @      @r   y            @r[   gV;'@r]   r  r  r  	   r`   )	r"   r}   Zclongdoubler,   r   r   r"  
complex128r   )rA   r%  r   r%   r%   r&   test_complex_high_ord  s    z,TestNorm_NonSystematic.test_complex_high_ordN)rI   rJ   rK   r  r  r  r%   r%   r%   r&   r    s   r  c                   @   s   e Zd ZejZdZdS )_TestNormDoubleBaser)   N)rI   rJ   rK   r"   r   rB  r  r%   r%   r%   r&   r  	  s   r  c                   @   s   e Zd ZejZdZdS )_TestNormSingleBaser(   N)rI   rJ   rK   r"   r,  rB  r  r%   r%   r%   r&   r    s   r  c                   @   s   e Zd ZejZdZdS )_TestNormInt64Baser)   N)rI   rJ   rK   r"   Zint64rB  r  r%   r%   r%   r&   r    s   r  c                   @   s   e Zd ZdS )TestNormDoubleNr   r%   r%   r%   r&   r    s   r  c                   @   s   e Zd ZdS )TestNormSingleNr   r%   r%   r%   r&   r    s   r  c                   @   s   e Zd ZdS )TestNormInt64Nr   r%   r%   r%   r&   r     s   r  c                   @   s   e Zd Zdd Zdd ZdS )TestMatrixRankc                 C   s   t dttd td}d|d< t t|d t ttdd t tddddgd t ttdd t tdgd t|tdtdg}t t|tdddg t tdd d S )	Nr^   r)  rl   rl   r]   r   r   r[   )r^   )r   r   r"   r   r   r   )rA   Imsr%   r%   r&   test_matrix_rank&  s    
zTestMatrixRank.test_matrix_rankc                 C   s   t dttddd t dttddd t dttddd td}d|d< t d	t|dd d
|d< t dt|ddd t d	t|ddd d S )Nr^   Tr   r[   r   r   r)  r  r]   g:0yE>g|"BE>)r8   Ztolg;䡈E>)r   r   r"   r   r  r   )rA   r  r%   r%   r&   test_symmetric_rank:  s    
z"TestMatrixRank.test_symmetric_rankN)rI   rJ   rK   r  r  r%   r%   r%   r&   r  $  s   r  c                  C   s   t jd} tdD ]}| jdd}|d d df |d d df  |d d df< tt|d |d d d	f |d d d
f  |d d df< tt|d qd S )Ni3rF  )(   r  sizer[   r\   r   r  r^   r`   r]   rZ   )r"   r  ZRandomStater   normalr   r   )rngiXr%   r%   r&   test_reduced_rankH  s    ,,r  c                	   @   s   e Zd ZejZdd Zejddgdddgdd	 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 ZdS )TestQRc                 C   s  t |}|j}|j\}}t||}tj|dd\}}t|j|k t|j|k tt|| tt|| t|j||fk t|j||fk tt	||| tt	|j
 |t| tt|| tj|dd\}	}
t|	j|k t|
j|k tt|	| tt|
| t|	j||fk t|
j||fk tt	|	|
| tt	|	j
 |	t| tt|
|
 tj|dd}t|j|k tt|| t||
 d S )Ncompletemodereducedr   )r    r+   rf   r   r   qrr   r!   r   r   r8  r   r"   r   triu)rA   r-   a_typea_dtyper'  r3  r  qr   q1r1r2r%   r%   r&   check_qrY  s8    

zTestQR.check_qrr'  r3  )r]   r   r  rX   c                 C   st   t ||}t||f}| | tjj|dd\}}t|jtj t|jtj t|j	||f t|j	|f d S )Nrawr  )
r   r"   r}   r  r   r  r   r+   r   rf   )rA   r'  r3  r  r-   htaur%   r%   r&   test_qr_empty  s    

zTestQR.test_qr_emptyc                 C   s   | j ddgddgddggtjd}tj|dd	\}}t|jtjk t|jtjk t|jd
k t|jdk tj|jdd	\}}t|jtjk t|jtjk t|jdk t|jdk d S )Nr[   r\   r]   r^   r`   r(   r2   r  r  r  r  rb   )	r   r"   r   r   r  r   r+   rf   r8  )rA   r-   r  r  r%   r%   r&   test_mode_raw  s    "zTestQR.test_mode_rawc                 C   s   |  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^   r`   r(   fd              ?)r   r"  r  r8  )rA   r-   r.   rB  m1m2r%   r%   r&   test_mode_all_but_economic  s    





z!TestQR.test_mode_all_but_economicc                 C   sf  t |}|j}|jdd  \}}t||}tj|dd\}}t|j|k t|j|k tt|| tt|| t|jdd  ||fk t|jdd  ||fk tt	||| t
|jd }	t
|	|jd d |jd fd  }
tt	t|dd ||
 tt
|dd d d d f | tj|dd\}}t|j|k t|j|k tt|| tt|| t|jdd  ||fk t|jdd  ||fk tt	||| t
|jd }	t
|	|jd d |jd fd  }
tt	t|dd ||
 tt
|dd d d d f | tj|dd}t|j|k tt|| t|| d S )	Nrm   r  r  rl   r\   .r  r   )r    r+   rf   r   r   r  r   r!   r   r	   r"   r   r   r
   r   r  )rA   r-   r  r  r'  r3  r  r  r   ZI_matZstack_I_matr  r  r  r%   r%   r&   check_qr_stacked  sL    
""zTestQR.check_qr_stackedr  )r]   r^   )r^   r]   r   
outer_sizer  r  )r\   r]   r^   rB  c                 C   sP   t jj|| d|}t jj|| d|}| | | |d|   d S )Nr  r  )r"   r  r  r"  r  )rA   r  r  rB  r  r  r%   r%   r&   test_stacked_inputs  s    

zTestQR.test_stacked_inputsN)rI   rJ   rK   r"   r   r  r   r   r   r  r  r  r  r   r   r   r   r  r%   r%   r%   r&   r  U  s<   '
-       r  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	 Zd
d ZdS )TestCholeskyrf   rw   r  r]   r]   )2   r  )r]   r  r  r+   c              
   C   s   t jd t jj| }t |t jr:|dt jj|   }ttt|}d|dd < t 	|
| |}t j||d}t j|}t 	||
| }t||| d| d| d| d|jd	  t |j d
 d S )Nr[   r  )rl   rm   rm   r2    
i  r   )rw  Zatol)r"   r  r  randnr0  Zcomplexfloatingr   r   r;  r	   r   r   r   r   choleskyr   rf   ZfinfoZeps)rA   rf   r+   r-   tr   r.   r%   r%   r&   test_basic_property  s    z TestCholesky.test_basic_propertyc                 C   s   G dd dt j}t jdt jd|}t|}t|j|j t	|j
jt jk t	t|t j t jdt jd|}t|}t|j|j t	|j
jt jk t	t|t j d S )Nc                   @   s   e Zd ZdS )z/TestCholesky.test_0_size.<locals>.ArraySubclassNr   r%   r%   r%   r&   r     s   r   r   r2   )r[   r   r   )r"   r#   r   r   r~   r   r  r   rf   r   r+   r    r   r!   r   r   r%   r%   r&   r     s    

zTestCholesky.test_0_sizeN)rI   rJ   rK   r   r   r   r"   r,  r   r   r  r  r   r%   r%   r%   r&   r    s     r  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 t
jt
jt
jfD ](}||}t||| t||| qhq d S )Nlittle<rF   r^   r2   S=)sys	byteorderr"   r,  r   r   ZnewbyteorderZbyteswapr   r+   r   r   r   r  r   )ZnativeZdttr2  Zn_arrZsw_arrZroutiner   r%   r%   r&   test_byteorder_check#  s    

r  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| d S )Nr[   r\   r]   r^   .rX   )r"   r   r   r   r   r   r   )Z
invertibleZnon_invertibler   r%   r%   r&    test_generalized_raise_multiloop8  s    r  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
r   Y n  tk
r   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|krt |  W 5 d }~X Y nX t t j n&t  \}}t || krNtd d S )	N   zNot POSIX or fork failed.r   r[   rX   rS   zDORGQR parameter number 5zNumpy xerbla not linked in.)osforkOSErrorAttributeErrorr   skipcloseresourceZ	setrlimitZRLIMIT_COREr"   r   lapack_liteZxerblar   r   _exit	EX_CONFIGr   Zdorgqrr=   waitWEXITSTATUS)Z	XERBLA_OKpidr   r-   r   statusr%   r%   r&   test_xerbla_overrideF  sH    


      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IPythonz
    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 np )beforeafterbad_libz-c)r  r
  r  )textwrapdedentr  
subprocess
check_callr  
executable)Zbad_libstemplater  coder%   r%   r&   test_sdot_bug_8577w  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 )TestMultiDotc              	   C   sl   t jd}t jd}t jd}tt|||g||| tt|||gt |t || d S Nr(   r\   r\   r(   r"   r  r   r   r   )rA   r  r  Cr%   r%   r&   (test_basic_function_with_three_arguments  s
     z5TestMultiDot.test_basic_function_with_three_argumentsc                 C   sN   t jd}t jd}tt||g|| tt||gt || d S r  r  )rA   r  r  r%   r%   r&   &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|||| d S )Nr  r  r\   r[   r  )rA   r  r  r  Dr%   r%   r&   9test_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jd d S )Nr\   r  r  r  r  r"   r  r   r   rf   )rA   A1dr  r  r  r%   r%   r&   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jd d S )Nr  r  r\   )r(   r   )rA   r  r  r  D1dr%   r%   r&   test_vector_as_last_argument  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jd d S )Nr\   r  r  r%   r   )rA   r!  r  r  r#  r%   r%   r&   &test_vector_as_first_and_last_argument  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|||| t|t |t || d S )Nr  r  r$   r"   r  r   r   rN   r   r   )rA   r  r  r  r$   retr%   r%   r&   test_three_arguments_and_out  s    
z)TestMultiDot.test_three_arguments_and_outc                 C   sd   t jd}t jd}t d}t||g|d}||ks>tt||| t|t || d S )Nr  r  )r(   r(   r&  r'  )rA   r  r  r$   r(  r%   r%   r&   test_two_arguments_and_out  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||||| d S )Nr  r  r  )r(   r[   r&  r'  )rA   r  r  r  r  r$   r(  r%   r%   r&   -test_dynamic_programming_optimization_and_out  s    
z:TestMultiDot.test_dynamic_programming_optimization_and_outc                 C   sh  t jdt jdt jdt jdt jdt jdg}t ddd	d
ddgddddddgddddddgddddddgddddddgddddddgg}t jddddddgddddddgddddddgddddddgddddddgddddddggtd}|d8 }t|dd\}}tt |d d dd f t |d d dd f  tt |t | d S )!N)   #   )r-     )r.  r`   )r`   r  )r     )r/  r  r)  g     @g     þ@g    O@g    1@g    @g     @g     @g     ջ@g     @g     p@g     @g     @g     @@g     X@g     @r   r[   r]   r\   r^   r`   r2   T)Zreturn_costsrl   )r"   r  r   intr   r   r  )rA   ZarraysZ
m_expectedZ
s_expectedr   r'  r%   r%   r&   test_dynamic_programming_logic  s:    





z+TestMultiDot.test_dynamic_programming_logicc                 C   s&   t ttg  t tttjdg d S )Nr  )r   r   r   r"   r  rG   r%   r%   r&   test_too_few_input_arrays  s    z&TestMultiDot.test_too_few_input_arraysN)rI   rJ   rK   r  r  r  r"  r$  r%  r)  r*  r+  r1  r2  r%   r%   r%   r&   r    s   
	



r  c                   @   sv   e Zd Zejdeddfeddfgdd Zejdd	d
gdd Z	ejdddgdd Z
dd ZdS )TestTensorinvzarr, indr^   r(   rZ   r\   r\   r]   r]   r\   r[   c              	   C   s&   t t tj||d W 5 Q R X d S )Nind)r   r   r   	tensorinv)rA   r2  r7  r%   r%   r&   test_non_square_handling  s    
z&TestTensorinv.test_non_square_handlingz
shape, ind)r^   r(   rZ   r]   r\   )   rZ   r]   r[   c                 C   sN   t d}||_tj||d}|j|d  |jd |  }|j}t|| d S )Nr<  r-   r7  )r"   r   rf   r   r8  r   )rA   rf   r7  r-   ainvr   actualr%   r%   r&   test_tensorinv_shape%  s    
z"TestTensorinv.test_tensorinv_shaper7  r   rm   c              	   C   s6   t d}d|_tt tj||d W 5 Q R X d S )Nr<  r:  r=  )r"   r   rf   r   r   r   r8  )rA   r7  r-   r%   r%   r&   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|| d S )Nr<  r;  r[   r6  )	r"   r   rf   r   r8  r  r   	tensordottensorsolve)rA   r-   r>  r.   r%   r%   r&   test_tensorinv_result;  s
    

z#TestTensorinv.test_tensorinv_resultN)rI   rJ   rK   r   r   r   r"   r  r9  r@  rA  rD  r%   r%   r%   r&   r3    s    

 
r3  c                   @   sV   e Zd Zejdeddfeddfgdd Zejdd	d
dgdd Z	dS )TestTensorsolveza, axesr4  Nr5  )r   r\   c              	   C   s<   t t* t|jd d }tj|||d W 5 Q R X d S Nr\   r   )r   r   r"   r  rf   r   rC  )rA   r-   r   r.   r%   r%   r&   r9  F  s    
z(TestTensorsolve.test_non_square_handlingrf   )r\   r]   r(   )r]   r^   r^   r]   )r   r]   r]   r   c                 C   sN   t jj| }t |jd d }t j||}tt j||t	|jd| d S rF  )
r"   r  r  r  rf   r   rC  r   rB  r;  )rA   rf   r-   r.   r   r%   r%   r&   test_tensorsolve_resultO  s    z'TestTensorsolve.test_tensorsolve_result)
rI   rJ   rK   r   r   r   r"   r  r9  rG  r%   r%   r%   r&   rE  D  s   
rE  c               	   C   s>   t jddgddggdd} ttd t|  W 5 Q R X d S )Nr[   rm   r\   r`   Zfloat16r2   zunsupported in linalg)r"   r   r   r\  r   r  )r2  r%   r%   r&   test_unsupported_commontypeY  s    rH  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 d S )N        r[   r2   )r   rl   )r"   r   r,  r  r   r   )r3  r-   r.   r   r%   r%   r&   test_blas64_dotd  s    rJ  z*Numpy not compiled with 64-bit BLAS/LAPACKc            
   	   C   s   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}t|d d t|d | t|d | t| }	t	d	|	  k od
k n   d S )Nl       r[   r2   rl   r   infor'  r3  rI  l        )
r"   r   r   r  Zdgeqrfr   r   r0  itemr   )
r+   Zlapack_routiner'  r3  Zldar-   Zworkr  resultsZlworkr%   r%   r&   !test_blas64_geqrf_lwork_smoketestn  s    
rN  )r(   r)   )~__doc__r  r  ry   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,   r3   r4   r5   rM   r<   rQ   r  r  rc   r}   r  ri   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r(  r-  r7  r   r   rC  rc  rh  rv  rz  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r3  rE  rH  r  rJ  r  rN  r%   r%   r%   r&   <module>   s   (,

    

#      




9 
0

:	
$.C
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