a
    p=ic(.                    @   sN
  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/h d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
g d%g 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(ged"e1d.e
d(d)gd*d+gged"e
g d/g d0ged"e1d1e	j6d2ed"e	j6d3ed"d4hd5e1d6e	j37d7d7e	j37d7e1d8e	j37d9d9e	j37d9e1d:d9d;gd<d=ggd;d9gg
7 Z5e5e2d>e1d?e
g d@g d&ged"e
ddged"e1dAe
ddgd d!gdBdCgged"e
g dDed"e1dEe
g d@g d&ged"e
ddged"e1dFe
ddgd d!gdBdCgged"e
g dDed"e1dGe
g dHg dIged"e
d,d(ged"e1dJe
dKdLgdMdNgdOdPgged"e
g dQed"e1dRe
g dHg dIged"e
d,d(ged"e1dSe
dKdLgdMdNgdOdPgged"e
g dQed"e1dTe
g dHg dIged"e
d,d(gdUdVgged"e1dWe
dKdLgdMdNgdOdPgged"e
d,d(gdUdVgdUdVgged"e1dXe	j37d7dYe	j37d7e1dZe	j37d9d[e	j37d9e1d\e	j37d[d9e	j37d[e1d]e	j37dd=e	j37dd4hd5e1d^e	j37d=de	j37d=d4hd5g7 Z5e5e2d_e1d`e
ddgddgged"de1dae
ddgddgged"de1dbe
dd)gdcd9gged"de1dde
dd)gdcd9gged"de1dee	j6d2ed"dd4hd5e1dfd9d;gd;d9ggde1dge
ddgddggde1dhe	j37d9d9dg7 Z5didj Z8e5e8 7 Z5dkdl Z9dmdn Z:e5e: 7 Z5G dodp dpZ;G dqdr dre;Z<G dsdt dte;Z=G dudv dve;Z>G dwdx dxe;Z?G dydz dze;Z@G d{d| 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 ddĄ dedecZeG ddƄ dƃZfG ddȄ debZgG ddʄ debZhG dd̄ debZiG dd΄ deeegZjG ddЄ deeehZkG dd҄ deeeiZlG ddԄ dԃZmddք ZnG dd؄ d؃ZoG ddڄ dڃZpdd܄ Zqddބ Zrdd 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u S N)type
isinstancenpndarray)outin_ r&   o/home/droni/.local/share/virtualenvs/DPS-5Je3_V2c/lib/python3.9/site-packages/numpy/linalg/tests/test_linalg.pyconsistent_subclass   s    r(         c                 K   s8   t | jjttfv 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
    r4   c                 C   s   t ttttttti|  S r   )r   r   r   r   r3   r&   r&   r'   get_complex_dtype1   s
    r5   c                 C   s   | t tfv rdS dS d S )Ngh㈵>gdy=)r   r   r3   r&   r&   r'   get_rtol6   s    r6   >   stridedsize-0	nonsquare	hermitiansquaregeneralizedc                   @   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/   rA   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
        rA   N)r.   r/   rA   )rB   dor&   r&   r'   checkQ   s    zLinalgCase.checkc                 C   s   d| j  dS )Nz<LinalgCase: >)r?   rB   r&   r&   r'   __repr__W   s    zLinalgCase.__repr__N)__name__
__module____qualname__setrC   rF   rI   r&   r&   r&   r'   r=   E   s   r=   c                 C   s,   | t v sJ 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_tagsrA   )tagZcasescaser&   r&   r'   	apply_tag[   s    rQ     r;   r         ?       @      @      @r3   r   Zdouble_2)rT   rS   rV   )rU   rV         @r         ?       @y       @      @y      @      @y      @      @       @      ?r   Z	cdouble_2)rY   rX   y      ?      @)y      ?       y      ?      y      ?      Z0x0r   r   r   r8   rD   Z8x8   Z1x1   Znonarray         r9   Zsingle_nsq_1)rS   rT   rU   Zsingle_nsq_2g      @rW   )rT   rS   rU   Zdouble_nsq_1Zdouble_nsq_2Zcsingle_nsq_1)      ?      ?       @       @      @      )y      @      y      @      "@y      @       @Zcsingle_nsq_2ra   rb   rc   y      @      "y      @      y      @       @)rY   rX   rc   Zcdouble_nsq_1Zcdouble_nsq_2Zcdouble_nsq_1_2y      ?      y       @       Zcdouble_nsq_2_2Z8x11   Z1x5   Z5x1Z0x4Z4x0r:   Z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 u 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 u rd }n$t|jgd d d|jj }t|jd	 |||j	dhB d}| 
| q| S )
Nr^   r_      r)   Z_tile3r<   rD   r_   r^   Z_tile213)CASESr!   r.   r"   r#   r   r/   r=   r?   rA   appendreshapeshape)	new_casesrP   r.   r/   new_caser&   r&   r'   _make_generalized_cases   s*    



$
$
rn   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]   rp   c                 S   s   g | ]\}}t || qS r&   )abs).0r.   r/   r&   r&   r'   
<listcomp>      z%_stride_comb_iter.<locals>.<listcomp>c                 S   s   g | ]}t d d |qS r   )slice)ru   repeatr&   r&   r'   rv     rw   r3   l   >[= .Zstride__c                 S   s   g | ]}d | qS )z%+dr&   )ru   jr&   r&   r'   rv   (  rw   r   )stridesZstride_xxx_0Zstride_xxx_0_xr]   r]   Zstride_xxx_0_0)r!   r"   r#   ndim	itertoolsproducttupleziprk   emptyr,   viewZuint32fill	__class__r   alljoinlistr|   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 )Nrz   r7   rD   )rh   r   r.   r/   r=   r?   rA   ri   )rl   rP   r.   Za_labelr/   Zb_labelrm   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 ]x}|j|@ |krq|j|@ r&qz|| j W q ty| } z.d|d}|t 7 }t||W Y d}~qd}~0 0 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_CASESrA   rF   rE   	Exception	traceback
format_excAssertionError)rB   requireexcluderP   emsgr&   r&   r'   check_casesQ  s    

zLinalgTestCase.check_casesN)rJ   rK   rL   rh   r   rM   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 )Nr;   r<   r8   r   r   r   rH   r&   r&   r'   test_sq_casesg  s    z"LinalgSquareTestCase.test_sq_casesc                 C   s   | j ddhdhd d S )Nr;   r8   r<   r   r   rH   r&   r&   r'   test_empty_sq_casesk  s    
z(LinalgSquareTestCase.test_empty_sq_casesN)rJ   rK   rL   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 )Nr9   r<   r8   r   r   rH   r&   r&   r'   test_nonsq_casesr  s    z(LinalgNonsquareTestCase.test_nonsq_casesc                 C   s   | j ddhdhd d S )Nr9   r8   r<   r   r   rH   r&   r&   r'   test_empty_nonsq_casesv  s    
z.LinalgNonsquareTestCase.test_empty_nonsq_casesN)rJ   rK   rL   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 )Nr:   r<   r8   r   r   rH   r&   r&   r'   test_herm_cases}  s    z!HermitianTestCase.test_herm_casesc                 C   s   | j ddhdhd d S )Nr:   r8   r<   r   r   rH   r&   r&   r'   test_empty_herm_cases  s    
z'HermitianTestCase.test_empty_herm_casesN)rJ   rK   rL   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 )Nr<   r;   r8   r   r   rH   r&   r&   r'   test_generalized_sq_cases  s    
z9LinalgGeneralizedSquareTestCase.test_generalized_sq_casesc                 C   s   | j h dd d S )N>   r<   r8   r;   r   r   rH   r&   r&   r'   test_generalized_empty_sq_cases  s    z?LinalgGeneralizedSquareTestCase.test_generalized_empty_sq_casesN)rJ   rK   rL   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 )Nr<   r9   r8   r   r   rH   r&   r&   r'   test_generalized_nonsq_cases  s    
z?LinalgGeneralizedNonsquareTestCase.test_generalized_nonsq_casesc                 C   s   | j h dd d S )N>   r<   r9   r8   r   r   rH   r&   r&   r'   "test_generalized_empty_nonsq_cases  s    zELinalgGeneralizedNonsquareTestCase.test_generalized_empty_nonsq_casesN)rJ   rK   rL   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 )Nr<   r:   r8   r   r   rH   r&   r&   r'   test_generalized_herm_cases  s    
z8HermitianGeneralizedTestCase.test_generalized_herm_casesc                 C   s   | j h ddhd d S )N>   r<   r8   r:   noner   r   rH   r&   r&   r'   !test_generalized_empty_herm_cases  s    
z>HermitianGeneralizedTestCase.test_generalized_empty_herm_casesN)rJ   rK   rL   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_   rq   r]   zNot implemented...r3   rr   )r   r~   rk   
ValueErrorr"   r   Zcommon_typer   r   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_   r3   rr   .r   )r   r~   r"   r   rk   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(   )rB   r.   r/   rA   r   r&   r&   r'   rE     s    zSolveCases.doNrJ   rK   rL   rE   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]         ?r3   )r"   r   r   r   r   r,   rB   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rJ   rK   rL   r&   r&   r&   r'   ArraySubclass  s   r   r\   r^   r)   r]   r_   r   )r"   r#   arangerj   r   r   r   r   r   r!   r   r   r   rB   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   rj   r   r   r   r   r   r!   r   r&   r&   r'   test_0_size_k  s    ""
"8
zTestSolve.test_0_size_kN)rJ   rK   rL   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(   )rB   r.   r/   rA   Za_invr&   r&   r'   rE     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
u  t|j|j tt|| t jdt jd|}t|}t|jj	t ju  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]   r3   rZ   )r"   r#   zerosint_r   r   r   r   r,   r    float64r   rk   r!   	complex64rB   r   r.   resr&   r&   r'   r     s    

zTestInv.test_0_sizeNrJ   rK   rL   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   )rB   r.   r/   rA   evevaluesevectorsr&   r&   r'   rE   ,  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   r3   rq   )r"   r   r   r   r   r,   r5   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
u  td|j tt|t j t jdt jd|}t|}t|jj	t ju  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   r3   r   r]   rZ   r[   )r"   r#   r   r   r   r   r   r   r,   r    r   r   rk   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   r6   r,   r   r(   )rB   r.   r/   rA   r   r   r&   r&   r'   rE   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,   r5   rB   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
u  t|jj	t j
u  t|j|j td|j tt|t j t jdt jd|}t|\}}t|jj	t ju  t|jj	t ju  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   r3   r   rZ   r[   )r"   r#   r   r   r   r   r   r   r,   r    r   r   rk   r!   r   rB   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   r3   F
compute_uvr:   )r"   r   r   svdr   r,   r4   r:   )rB   r,   r   ur   vhr&   r&   r'   r   ~  s    zSVDBaseTests.test_typesN)rJ   rK   rL   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 )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   r6   r,   r   r(   )rB   r.   r/   rA   r   r   vtr&   r&   r'   rE     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`   rZ   r`   )r   r`   N)r"   r   r   r   r:   r   rk   eye)rB   r   r   r   r   r&   r&   r'   test_empty_identity  s    

zTestSVD.test_empty_identityN)rJ   rK   rL   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r:   .r   c                 S   s<   t t| j}|d |d  |d< |d< ttj| |dS )Nrr   rq   axes)r   r   r~   r"   conj	transpose)matr   r&   r&   r'   r:     s    z'SVDHermitianCases.do.<locals>.hermitianrq   )r   r   r   r   r"   r   r6   r,   r   r	   broadcast_tor   rk   r   sortr   r(   )rB   r.   r/   rA   r   r   r   r:   r&   r&   r'   rE     s    &,,zSVDHermitianCases.doNr   r&   r&   r&   r'   r     s   r   c                   @   s   e Zd ZdZdS )TestSVDHermitianTN)rJ   rK   rL   r:   r&   r&   r&   r'   r     s   r   c                   @   s   e Zd Zdd ZdS )	CondCasesc                 C   s  t |}d|v 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 )Nr8   F)r   ).r   ).rq   re   rd   r0   r1   r^   rr   r]   rq   fro)r   r   r   r   condr   r   r"   r   rt   summaxminr   sqrt)rB   r.   r/   rA   r   r   Zcinvr&   r&   r'   rE     sZ    
&
&&&
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 g dg dg dg}tt|td tt|t d tt|dd tt|dd tt|d	td
 d S )N)rS   r   r]   )r   g       r   )r   r   rU   r`   gUUUUUU?r]   rq   r   r  gUUUUU6@)r   r   r   r  r   r"   r  rB   Ar&   r&   r'   test_basic_nonsvd  s    zTestCond.test_basic_nonsvdc                 C   st   t dt dg}g d}ddg}t||D ]\}}tt||dk q0t||D ]\}}t|| qZd S )Nr^   r^   Nr]   r^   r  rq   rr     4&kC)r"   r   onesr   r   r   r   r  )rB   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   g d}g d}t d}t j|d< |D ].}t||}tt|t j tt | q(t d}t j|d< |D ]t}t||}tt |d  ||v rt|d d	k t|d
 d	k qptt |d   tt |d
   qpd S )N)Nr]   rq   r^   rr   r  r  r  r   )r_   r^   r^   r]   r   r]   r]   r   r  r^   )	r"   r  nanr   r  r   r!   float_isnan)rB   Zpsr  r	  r  r   r&   r&   r'   test_nan  s$    



zTestCond.test_nanc                 C   s   t jd t jdddd}d|d< d|d< dD ]T}t||}t|d t j t|d t j tt 	|d  tt 	|d  q2d S )	NrR   r^   r   rZ   r}   )Nr]   r^   r  rq   rr   r   r]   r   )
r"   randomseedrandr   r  r   r   r   isfinite)rB   r	  r  r   r&   r&   r'   test_stacked_singular  s    zTestCond.test_stacked_singularN)
rJ   rK   rL   r
  r  r   r   xfailr  r  r&   r&   r&   r'   r    s   	

r  c                   @   s   e Zd Zdd ZdS )	PinvCasesc                 C   s<   t |}t}t||||||ddd tt|| d S )Nre   rd   r   r   pinvr   r   r   r(   rB   r.   r/   rA   Za_ginvr   r&   r&   r'   rE   1  s    
zPinvCases.doNr   r&   r&   r&   r'   r   ,  s   r   c                   @   s   e Zd ZdS )TestPinvNr   r&   r&   r&   r'   r$  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   re   rd   r   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 )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v 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 )Nrq   axisr   r]   )r   detslogdetr   r,   r    r   r   astyper   r   r   r   reducer"   expZ
atleast_1drt   r   r   )
rB   r.   r/   rA   dr   ldadr   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 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   rH   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+  r4   )rB   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u  t	|}t|d t|d jjt ju  t|d jjt j
u  t jdt jd}t|}t|d t|jjt ju  t	|}t|d t|d jjt ju  t|d jjt ju  d S )NrZ   r3   rS   r  r   r]   )r"   r   r   r   r*  r   r   r,   r    r+  float32r   )rB   r.   r   r&   r&   r'   r   u  s     







zTestDet.test_0_sizeN)rJ   rK   rL   r5  r   r   r   r   r   r   r   r   r   r&   r&   r&   r'   r3  _  s   
r3  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 )	NFrq   Zrcondr   r^   r(  r]   ro   )r"   r   rk   r   r   lstsqr   r   r   r   r   Z__array_wrap__rt   r  r~   r   r   r    
issubdtyper,   floatingr(   )rB   r.   r/   rA   arrr2  nr   r   r   r   	residualsranksvZexpect_residsr&   r&   r'   rE     s2    




zLstsqCases.doNr   r&   r&   r&   r'   r8    s   r8  c                   @   s:   e Zd Zdd Zejg dg ddd Zdd Zd	S )
	TestLstsqc           	      C   s   t g dg dg dg dgj}t g d}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 d    n1 s0    Y  d S )N)r4  rS   r4  rS   rT   r4  )r4  rT   r4  r4  rS   r4  )rS   r4  rS   r4  r4  rV   )r4  r4  r4  rT   rU   r4  )r]   r   r   r   r   r   z`rcond` parameter will changer`   rq   r9  r_   r]   )
r"   r   Tr   recordFutureWarningr   r:  r   len)	rB   r.   r/   supr   r   r?  r@  r   r&   r&   r'   test_future_rcond  s    
zTestLstsq.test_future_rcond)r2  r>  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 )Nr9  r   r[   rr   r(  )r"   r   rj   r  r   r:  r   r   r   rk   r   r   r  r  )rB   r2  r>  rI  r.   r/   r   r?  r@  r   r   r&   r&   r'   test_empty_a_b  s    
zTestLstsq.test_empty_a_bc                 C   st   t g d}t g d}t |t t|gj}ttd  tj	||d d W d    n1 sf0    Y  d S )N)r   r]   r^   r_   )rq   g?g?g @gffffff
@zIncompatible dimensionsr9  )
r"   r   Zvstackr  rF  rC  r   r   r   r:  )rB   r   yr	  r&   r&   r'   test_incompatible_dims  s
    z TestLstsq.test_incompatible_dimsN)	rJ   rK   rL   rH  r   r   r   rJ  rL  r&   r&   r&   r'   rB    s   	
rB  dtc                 C   s   g | ]}t |qS r&   )r"   r,   )ru   r   r&   r&   r'   rv     rw   rv   z?bBhHiIqQefdgFDGOc                   @   s   e Zd ZedZeg d Zeg d Zeg d 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^   r_   r   r]   )r]   r^   r_   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)rB   rM  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rB   rM  rZ  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   rY  r&   r&   r'   rZ    s    

z-TestMatrixPower.test_power_is_one.<locals>.tzr[  r_  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,   r]  r	   r   r   )r   rY  mmulr&   r&   r'   rZ  
  s    
z-TestMatrixPower.test_power_is_two.<locals>.tzr[  r_  r&   r&   r'   test_power_is_two	  s
    
z!TestMatrixPower.test_power_is_twoc                 C   s0   dd }| j D ]}|| jvr||| qd S )Nc                 S   s4   t | d}| jtkrtnt}t||| t|  d S Nrq   )r   r,   r]  r	   r   r   r   )r   Zinvmatrb  r&   r&   r'   rZ    s
    
z3TestMatrixPower.test_power_is_minus_one.<locals>.tz)r\  dtnoinvr,  r_  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]   )rT  r,  r   	TypeErrorr   rB   rM  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  )rB   rM  r&   r&   r'   test_exceptions_non_square%  s    z*TestMatrixPower.test_exceptions_non_squarec                 C   s,   || j v rd S | j|}ttt|d d S rd  )re  noninvr,  r   r   r   rh  r&   r&   r'   test_exceptions_not_invertible*  s    
z.TestMatrixPower.test_exceptions_not_invertibleN)rJ   rK   rL   r"   r   rT  rS  rU  rV  r\  r   rk  blockr^  r]  r,   re  rW  r`  ra  rc  rf  ri  rj  rl  r&   r&   r&   r'   rN    s    
rN  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Lrq   r(  r   U)r   eigvalshr   r   r   r6   r,   )rB   r.   r/   rA   r   r   r   ev2r&   r&   r'   rE   3  s    zTestEigvalshCases.doNr   r&   r&   r&   r'   rn  1  s   rn  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   rq  r   r,   r4   )rB   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   r3   ZlrongZUPLOlowerupper)r"   r   r7  r   r   r   rq  rB   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]   r3   rq   r   ro  ru  lrp  r   )r"   r   r   r6   r   rq  r   )rB   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
u  td|j tt|t j t jdt jd|}t|}t|jj	t ju  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   r3   r   rZ   r[   )r"   r#   r   r   r   r   rq  r   r,   r    r   r   rk   r!   r   r7  r   r&   r&   r'   r   b  s    

zTestEigvalsh.test_0_sizeNrJ   rK   rL   r   r   r   r   r   r   r   r   ry  r  r   r&   r&   r&   r'   rs  ?  s
   
rs  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 )Nrq   r(  .r   rp  )r   err_msg)r   eighr   r   r   r   r   r"   r   r6   r,   repr)
rB   r.   r/   rA   r   Zevcr   r   rr  Zevc2r&   r&   r'   rE   w  s    

 

 zTestEighCases.doNr   r&   r&   r&   r'   r  u  s   r  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   r  r   r,   r4   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 rt  )r"   r   r7  r   r   r   r  rx  r&   r&   r'   ry    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 rz  )r"   r   r   r6   r   r  r   )rB   r|  r}  r~  r   r   r   r&   r&   r'   r    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
u  t|jj	t j
u  t|j|j td|j tt|t j t jdt jd|}t|\}}t|jj	t ju  t|jj	t ju  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   r3   r   rZ   r[   )r"   r#   r   r   r   r   r  r   r,   r    r   r   rk   r!   r   r7  r   r&   r&   r'   r     s    zTestEigh.test_0_sizeNr  r&   r&   r&   r'   r    s
   
r  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   r<  )r   r   r&   r&   r'   check_dtype  s    z_TestNormBase.check_dtype)rJ   rK   rL   rM  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 )Nr4  r3   )r   r   r   rM  r   rH   r&   r&   r'   
test_empty  s    z_TestNormGeneral.test_emptyc           	   	   C   s  t g d}t jd }t jd }|| }|D ]N}||}t|t j }| || t|d t <}|	t
d t|d}| || t|d W d    n1 s0    Y  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 q.d S )Nr  
AllIntegerZAllFloatr4  divide by zero encounteredrq   r   r^   r]   rT   r   r`   g      ?rS   )r"   r   	typecodesr,  r   r   r  r   r   filterRuntimeWarningr,   r    	rB   r.   Zexact_typesZinexact_typesZ	all_typesZ	each_typeatanrG  r&   r&   r'   test_vector_return_type  s:    





(





z(_TestNormGeneral.test_vector_return_typec                    sv   g d}g d}g d} fdd}|||fD ]}|| q.t | jdt | jdt | jdfD ]}|| qdd S )N)r]   r^   r_   r`   )rq   rr   rs   rp   )rq   r^   rs   r`   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]         $@rq   gQ?r^   rr   gsc?r   r`   )r"   testingr   r   r  r   )r   rH   r&   r'   _test  s0    z+_TestNormGeneral.test_vector.<locals>._testr3   )r   rM  )rB   r.   r/   r   r  r   r&   rH   r'   test_vector  s    
z_TestNormGeneral.test_vectorc           	   	      s  t g dg d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| q4t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r@ttt|d qt|d}|||  ||k rfdd
tj D }n fdd
tj D }t|| qqd S )Nr]   r^   r_   r`   re   r)   r3   rq   r   r]   r^   r_   c                    s$   g | ]}t  d d |f dqS Nordr   ru   kr	  orderr&   r'   rv   '  rw   z._TestNormGeneral.test_axis.<locals>.<listcomp>r  r)  c                    s$   g | ]}t  |d d f dqS r  r  r  r  r&   r'   rv   )  rw      r`   rr   r  c                    s*   g | ]"}t  d d  j|ddqS Nr(  r  )r   taker  Bk_indexr  r&   r'   rv   ?  s   c                    s,   g | ]$}t  d d  j|djdqS r  )r   r  rC  r  r  r&   r'   rv   B  s   )r   rM  r"   Infr   rk   r   r   r   rj   r~   r   combinationsr   r   )	rB   Z	expected0Z	expected1ndr)  Zrow_axisZcol_axisr>  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  r3   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)r  )r]   r]   r]   rq   r   rr   r  nuc)r"   r   rM  rj   r   r   Zsqueezeformatr   rk   r  r   r~   r   r   r   permutations)	rB   r	  Zallclose_errZ	shape_errr   foundZexpected_shaper  r  r&   r&   r'   test_keepdimsF  sN    




 


z_TestNormGeneral.test_keepdimsN)rJ   rK   rL   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 )Nr3   r4  )r   r   r   rM  rH   r&   r&   r'   test_matrix_emptyv  s    z_TestNorm2D.test_matrix_emptyc           	   	   C   s  |  g dg dg}tjd }d}|| }|D ]N}||}t|tj }| || t|d t <}|	t
d t|d}| || t|d W d    n1 s0    Y  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 q0d S )Nr  r   r  ZfdFDrT   r  rq   rS   r]   r^   gLXz?rr   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_   re   rf   r3   gT"@r  r  r  g      (@rV   rq   rW   r^   gW?"@rr   gїʄ?Znofrors   r   )r   rM  r   r   r   r   r   r  r&   r&   r'   test_matrix_2x2  s    z_TestNorm2D.test_matrix_2x2c                 C   s   d| j g dg dg d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   re   )r_   r^   r]   r3   grj=Q0?r  r  gB+pc?g?g333333?r]   rS   rq   g?r^   g&.d?rr   gܸՠ?)r   rM  r   r   r   r  r&   r&   r'   test_matrix_3x3  s     z_TestNorm2D.test_matrix_3x3c                 C   s  | j g dg d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  r3   r]   r  r^   r_   r`   r  r   r  testr   r_   r   )r]   r^   r^   r_   )r   r]   r^   )	r   rM  r"   r   rj   r   r   r   Z	AxisError)rB   r	  r  r  r&   r&   r'   test_bad_args  s    z_TestNorm2D.test_bad_argsN)
rJ   rK   rL   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
   r3   r_   r  gL)@r^   r  )r"   r   Z
longdoubler-   r   rx  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   r3   r_   r  l        re   r  )r"   r   int32r-   r   rx  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^   r3   y      @      @r   y            @r]   gV;'@r_   r  r  r  	   re   )	r"   r   Zclongdoubler-   r   r   r,  
complex128r   )rB   r/  r   r&   r&   r'   test_complex_high_ord  s    z,TestNorm_NonSystematic.test_complex_high_ordN)rJ   rK   rL   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)rJ   rK   rL   r"   r   rM  r  r&   r&   r&   r'   r  	  s   r  c                   @   s   e Zd ZejZdZdS )_TestNormSingleBaser)   N)rJ   rK   rL   r"   r7  rM  r  r&   r&   r&   r'   r    s   r  c                   @   s   e Zd ZejZdZdS )_TestNormInt64Baser*   N)rJ   rK   rL   r"   int64rM  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g dd t ttd	d t tdgd t|tdtdg}t t|tg d
 t tdd d S )Nr`   r4  rq   rq   r_   r   r   )r]   r   r   r   r]   )r`   )r_   r`   r   )r   r   r"   r   r   r   )rB   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   r4  r  r_   g:0yE>g|"BE>)r:   Ztolg;䡈E>)r   r   r"   r   r  r   )rB   r  r&   r&   r'   test_symmetric_rank:  s    
z"TestMatrixRank.test_symmetric_rankN)rJ   rK   rL   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rQ  )(   r  sizer]   r^   r   r  r`   re   r_   r\   )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g ddd Z	dd	 Z
d
d Zdd Zejdg dejdg d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,   rk   r  r   qrr   r!   r   r   rC  r   r"   r   triu)rB   r.   a_typea_dtyper2  r>  r  qr   q1r1r2r&   r&   r'   check_qrY  s8    

zTestQR.check_qrr2  r>  )r_   r   r  rZ   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   rk   )rB   r2  r>  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`   re   r)   r3   r  r  r  r  rg   )	r   r"   r   r   r  r   r,   rk   rC  )rB   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`   re   r)   fd              ?)r   r,  r  rC  )rB   r.   r/   rM  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 )	Nrr   r  r  rq   r^   .r  r   )r    r,   rk   r  r   r  r   r!   r   r	   r"   r   r   r
   r   r  )rB   r.   r  r  r2  r>  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   r  r  
outer_size)r  r  )r^   r_   r`   rM  c                 C   sP   t jj|| d|}t jj|| d|}| | | |d|   d S )Nr  r  )r"   r  r  r,  r  )rB   r  r  rM  r	  r  r&   r&   r'   test_stacked_inputs  s    

zTestQR.test_stacked_inputsN)rJ   rK   rL   r"   r   r  r   r   r   r  r  r  r  r   r   r   r   r  r&   r&   r&   r'   r  U  s   '
-r  c                   @   sL   e Zd Zejdg dejdejejej	ej
fdd Zdd ZdS )	TestCholeskyrk   )r}   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  )rq   rr   rr   r3    
i  r   )r  Zatol)r"   r  r  randnr;  Zcomplexfloatingr   r   rF  r	   r   r   r   r   choleskyr   rk   ZfinfoZeps)rB   rk   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u  t	t|t j t jdt jd|}t|}t|j|j t	|j
jt ju  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   r3   )r]   r   r   )r"   r#   r   r   r   r   r   r   rk   r   r,   r    r   r!   r   r   r&   r&   r'   r     s    

zTestCholesky.test_0_sizeN)rJ   rK   rL   r   r   r   r"   r7  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<rG   r`   r3   S=)sys	byteorderr"   r7  r   r   Znewbyteorderbyteswapr   r,   r   r   r*  r"  r   )nativeZdttr=  Zn_arrZsw_arrZroutiner   r&   r&   r'   test_byteorder_check#  s    

r  c                  C   sl   t ddgddgg} t ddgddgg}t g ddd d }| |d< ||d< tt jjt jj| d S )Nr]   r^   r_   r`   )r`   r`   r^   r^   .rZ   )r"   r   r   r   r   r   r   )Z
invertibleZnon_invertibler   r&   r&   r'    test_generalized_raise_multiloop8  s    r  c                  C   sL  d} zt  }W n  ttfy0   td Y n0 |dkr"t d t d dd l}||j	d zt
jj  W n. ty   Y n ty   t t j Y n0 z0t
dgg}t
jjddd|d||dd	 W n< ty } z"dt|v rt |  W Y d }~n
d }~0 0 t t j n&t  \}}t || krHtd d S )	N   zNot POSIX or fork failed.r   r]   rZ   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  s<    


 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   )rB   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-  )rB   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-  )rB   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   rk   )rB   A1dr  r.  r2  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)   r4  )rB   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&   r4  )rB   r5  r  r.  r7  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}||u sLJ t|||| t|t |t || d S )Nr+  r,  r$   r"   r  r   r   r   r   )rB   r	  r  r.  r$   retr&   r&   r'   test_three_arguments_and_out  s    
z)TestMultiDot.test_three_arguments_and_outc                 C   sd   t jd}t jd}t d}t||g|d}||u s>J t||| t|t || d S )Nr+  r,  )r)   r)   r:  r;  )rB   r	  r  r$   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}||u sZJ t||||| d S )Nr+  r,  r1  )r)   r]   r:  r;  )rB   r	  r  r.  r2  r$   r<  r&   r&   r'   -test_dynamic_programming_optimization_and_out  s    
z:TestMultiDot.test_dynamic_programming_optimization_and_outc              	   C   s  t jdt jdt jdt jdt jdt jdg}t g dg dg d	g d
g dg dg}t jg dg dg dg dg dg d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)   #   )rA     )rB  re   )re   r  )r     )rC  r  )r4  g     @g     þ@g    O@g    1@g    @)r4  r4  g     @g     @g     ջ@g     @)r4  r4  r4  g     p@g     @g     @)r4  r4  r4  r4  g     @@g     X@)r4  r4  r4  r4  r4  g     @)r4  r4  r4  r4  r4  r4  )r   r]   r]   r_   r_   r_   )r   r   r^   r_   r_   r_   )r   r   r   r_   r_   r_   )r   r   r   r   r`   re   )r   r   r   r   r   re   )r   r   r   r   r   r   r3   r]   T)Zreturn_costsrq   )r"   r  r   intr   r   r  )rB   ZarraysZ
m_expectedZ
s_expectedr   r2  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  rH   r&   r&   r'   test_too_few_input_arrays  s    z&TestMultiDot.test_too_few_input_arraysN)rJ   rK   rL   r/  r0  r3  r6  r8  r9  r=  r>  r?  rE  rF  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)   r\   r^   r^   r_   r_   r^   r]   c                 C   s:   t t tj||d W d    n1 s,0    Y  d S )Nind)r   r   r   	tensorinv)rB   r=  rK  r&   r&   r'   test_non_square_handling  s    
z&TestTensorinv.test_non_square_handlingz
shape, ind)r`   r)   r\   r_   r^   )   r\   r_   r]   c                 C   sN   t d}||_tj||d}|j|d  |jd |  }|j}t|| d S )NrP  r.   rK  )r"   r   rk   r   rL  r   )rB   rk   rK  r.   ainvr   actualr&   r&   r'   test_tensorinv_shape%  s    
z"TestTensorinv.test_tensorinv_shaperK  r   rr   c                 C   sJ   t d}d|_tt tj||d W d    n1 s<0    Y  d S )NrP  rN  rQ  )r"   r   rk   r   r   r   rL  )rB   rK  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 )NrP  rO  r]   rJ  )	r"   r   rk   r   rL  r  r   	tensordottensorsolve)rB   r.   rR  r/   r&   r&   r'   test_tensorinv_result;  s
    

z#TestTensorinv.test_tensorinv_resultN)rJ   rK   rL   r   r   r   r"   r  rM  rT  rU  rX  r&   r&   r&   r'   rG    s   


rG  c                   @   sT   e Zd Zejdeddfeddfgdd Zejdg d	d
d Z	dS )TestTensorsolveza, axesrH  NrI  )r   r^   c                 C   sP   t t4 t|jd d }tj|||d W d    n1 sB0    Y  d S Nr^   r   )r   r   r"   r  rk   r   rW  )rB   r.   r   r/   r&   r&   r'   rM  F  s    
z(TestTensorsolve.test_non_square_handlingrk   ))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 rZ  )
r"   r  r  r  rk   r   rW  r   rV  rF  )rB   rk   r.   r/   r   r&   r&   r'   test_tensorsolve_resultO  s    z'TestTensorsolve.test_tensorsolve_result)
rJ   rK   rL   r   r   r   r"   r  rM  r[  r&   r&   r&   r'   rY  D  s   
rY  c                  C   sR   t jddgddggdd} ttd t|  W d    n1 sD0    Y  d S )Nr]   rr   r^   re   float16r3   zunsupported in linalg)r"   r   r   rg  r   r   )r=  r&   r&   r'   test_unsupported_commontypeY  s    r]  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]   r3   )r   rq   )r"   r   r7  r  r   r   )r>  r.   r/   r   r&   r&   r'   test_blas64_dotd  s    r_  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]   r3   rq   r   infor2  r>  r^  l        )
r"   r   r   r  Zdgeqrfr   r   rD  itemr   )
r,   Zlapack_routiner2  r>  Zldar.   Zworkr  resultsZlworkr&   r&   r'   !test_blas64_geqrf_lwork_smoketestn  s    
rc  )r)   r*   )~__doc__r  r  r   r   r!  r#  r   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=   rQ   r  r  rh   r   r  rn   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'  r3  r8  rB  r   r   rN  rn  rs  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r(  r)  rG  rY  r]  r  r_  r  rc  r&   r&   r&   r'   <module>   s  (,
	

#




9 
0

:	
$.C
*4U6; x$ !.1
" )
	
