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r" r r- r9 r; r= �append�reshape�shape)� new_casesrK r, r- �new_caser$ r$ r% �_make_generalized_cases� s& $ $r[ c c s� t | tj�s| dfV dS dg| j }d|d< | jdkr@d|d< | jdkrRd |d < �x�tjt|�� D �]�}d d � t| j|�D �}td d � |D ��}tj || j d�}|� tj �� d� || }| |d< |� | j�}tt�|| k�� |dd�dd � |D �� fV | jdk�rJ| jd dk�rJt| j�}d|d< tjjj| |d�}|dfV | jdk�r�| jd dk�r�t| j�}d|d< tjjj| |d�}|dfV | jdkrd| jdd� dkrdt| j�}d|d< d|d< tjjj| |d�}|dfV qdW dS )z< Generate cartesian product of strides for all axes ZnopN)rN )rN rP ������rN ���rO )rN r\ ���c S s g | ]\}}t || ��qS r$ )�abs)�.0r, r- r$ r$ r% � <listcomp> s z%_stride_comb_iter.<locals>.<listcomp>c S s g | ]}t d d |��qS )N)�slice)ra �repeatr$ r$ r% rb s )r* l �>[= .Zstride_�_c S s g | ] }d | �qS )z%+dr$ )ra �jr$ r$ r% rb ( s r )�stridesZ stride_xxx_0Zstride_xxx_0_x)rN rN Zstride_xxx_0_0)r r! r" �ndim� itertools�product�tuple�ziprX �emptyr* �viewZuint32�fill� __class__r �all�join�listrg �libZ stride_tricksZ as_strided)�xZ stride_setZrepeats� new_shapeZslices�xi�sr$ r$ r% �_stride_comb_iter sF ry c C sz g } xpt D ]h}xbt|j�D ]T\}}xJt|j�D ]<\}}t|jd | d | |||jdhB d�}| �|� q.W qW q W | S )Nre r8 )r= )rU ry r, r- r9 r; r= rV )rY rK r, Za_labelr- Zb_labelrZ r$ r$ r% �_make_strided_cases= s rz c @ s" e Zd ZeZe� e� fdd�ZdS )�LinalgTestCasec C s� x�| j D ]v}|j|@ |kr q|j|@ r(qy|�| j� W q tk r| } z&d|�d�}|t�� 7 }t|�|�W dd}~X Y qX qW dS )zx Run func on each of the cases with all of the tags in require, and none of the tags in exclude zIn test case: z N)� TEST_CASESr= rA r@ � Exception� traceback� format_excrI )r> �require�excluderK �e�msgr$ r$ r% � check_casesQ s zLinalgTestCase.check_casesN)rD rE rF rU r| rG r� r$ r$ r$ r% r{ N s r{ c @ s e Zd Zdd� Zdd� ZdS )�LinalgSquareTestCasec C s | j dhddhd� d S )Nr4 r7 zsize-0)r� r� )r� )r> r$ r$ r% � test_sq_casesg s z"LinalgSquareTestCase.test_sq_casesc C s | j ddhdhd� d S )Nr4 zsize-0r7 )r� r� )r� )r> r$ r$ r% �test_empty_sq_casesk s z(LinalgSquareTestCase.test_empty_sq_casesN)rD rE rF r� r� r$ r$ r$ r% r� e s r� c @ s e Zd Zdd� Zdd� ZdS )�LinalgNonsquareTestCasec C s | j dhddhd� d S )Nr5 r7 zsize-0)r� r� )r� )r> r$ r$ r% �test_nonsq_casesr s z(LinalgNonsquareTestCase.test_nonsq_casesc C s | j ddhdhd� d S )Nr5 zsize-0r7 )r� r� )r� )r> r$ r$ r% �test_empty_nonsq_casesv s z.LinalgNonsquareTestCase.test_empty_nonsq_casesN)rD rE rF r� r� r$ r$ r$ r% r� p s r� c @ s e Zd Zdd� Zdd� ZdS )�HermitianTestCasec C s | j dhddhd� d S )Nr6 r7 zsize-0)r� r� )r� )r> r$ r$ r% �test_herm_cases} s z!HermitianTestCase.test_herm_casesc C s | j ddhdhd� d S )Nr6 zsize-0r7 )r� r� )r� )r> r$ r$ r% �test_empty_herm_cases� s z'HermitianTestCase.test_empty_herm_casesN)rD rE rF r� r� r$ r$ r$ r% r� { s r� c @ s, e Zd Zejjdd� �Zejjdd� �ZdS )� LinalgGeneralizedSquareTestCasec C s | j ddhdhd� d S )Nr7 r4 zsize-0)r� r� )r� )r> r$ r$ r% �test_generalized_sq_cases� s z9LinalgGeneralizedSquareTestCase.test_generalized_sq_casesc C s | j dddhd� d S )Nr7 r4 zsize-0)r� )r� )r> r$ r$ r% � test_generalized_empty_sq_cases� s z?LinalgGeneralizedSquareTestCase.test_generalized_empty_sq_casesN)rD rE rF �pytest�mark�slowr� r� r$ r$ r$ r% r� � s r� c @ s, e Zd Zejjdd� �Zejjdd� �ZdS )�"LinalgGeneralizedNonsquareTestCasec C s | j ddhdhd� d S )Nr7 r5 zsize-0)r� r� )r� )r> r$ r$ r% � test_generalized_nonsq_cases� s z?LinalgGeneralizedNonsquareTestCase.test_generalized_nonsq_casesc C s | j dddhd� d S )Nr7 r5 zsize-0)r� )r� )r> r$ r$ r% �"test_generalized_empty_nonsq_cases� s zELinalgGeneralizedNonsquareTestCase.test_generalized_empty_nonsq_casesN)rD rE rF r� r� r� r� r� r$ r$ r$ r% r� � s r� c @ s, e Zd Zejjdd� �Zejjdd� �ZdS )� HermitianGeneralizedTestCasec C s | j ddhdhd� d S )Nr7 r6 zsize-0)r� r� )r� )r> r$ r$ r% �test_generalized_herm_cases� s z8HermitianGeneralizedTestCase.test_generalized_herm_casesc C s | j dddhdhd� d S )Nr7 r6 zsize-0�none)r� r� )r� )r> r$ r$ r% �!test_generalized_empty_herm_cases� s z>HermitianGeneralizedTestCase.test_generalized_empty_herm_casesN)rD rE rF r� r� r� r� r� r$ r$ r$ r% r� � s r� c C s� t | �} | jdkr�| j|jkr<| jd d� |jdd � }n(| j|jd kr\| jd d� }ntd��tj|t�| |�d�}x8tjt t | jd d� �� D ]}t | | || �||< q�W |S t | |�S d S )NrP r] rN zNot implemented...)r* r^ ) r rh rX � ValueErrorr! rm Z common_typeri rj �map�ranger )r, r- rv �r�cr$ r$ r% �dot_generalized� s r� c C sL t | �} | jdkr:tj| j| jd�}t| jd �|d< |S t| jd �S d S )NrP )r* r^ .r )r rh r! rm rX r* r )r, r� r$ r$ r% �identity_like_generalized� s r� c @ s e Zd Zdd� ZdS )� SolveCasesc C s. t �||�}t|t||�� tt||�� d S )N)r �solver r� r r& )r> r, r- r= ru r$ r$ r% r@ � s z SolveCases.doN)rD rE rF r@ r$ r$ r$ r% r� � s r� c @ s: e Zd Zej�deeee g�dd� �Z dd� Z dd� Z dS ) � TestSolver* c C s2 t jddgddgg|d�}tt�||�j|� d S )NrN g �?)r* )r! r r r r� r* )r> r* ru r$ r$ r% � test_types� s zTestSolve.test_typesc C s. G dd� dt j�}t �d��ddd�}t �d��ddd��|�}t�||�d d �dd�d d �f }t�|d d �dd�dd�f |d d �dd�d d �f �}t||� tt ||�� t tj tj|d d �dd�dd�f |� t t tj||d d �dd�d d �f � t �d��ddd�}t t tj||� t t tj|dd� |dd� � t �d��dd��|�}t�||�d d �dd�f }t�|d d �dd�dd�f |d d �dd�f �}t||� tt ||�� t �d��dd�}t t tj||� t t tj|dd� |dd� � t t tj|d d �dd�dd�f |� d S ) Nc @ s e Zd ZdS )z,TestSolve.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% � ArraySubclass� s r� rM rO r' rN rP r ) r! r" �arangerW rn r r� r r r r r r� )r> r� r, r- �expected�resultr$ r$ r% � test_0_size� s* "8 (& 2 zTestSolve.test_0_sizec C s G dd� dt j�}t �d��ddd�}t �d��ddd��|�}t�||�d d �d d �dd�f }t�||d d �d d �dd�f �}t||� tt ||�� t�||�d d �dd�dd�f }t�|d d �dd�dd�f |d d �dd�dd�f �}t||� tt ||�� d S ) Nc @ s e Zd ZdS )z.TestSolve.test_0_size_k.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� � s r� rQ rN rO r' rP r ) r! r" r� rW rn r r� r r r )r> r� r, r- r� r� r$ r$ r% � test_0_size_k� s "" "8 zTestSolve.test_0_size_kN) rD rE rF r� r� � parametrizer r r r r� r� r� r$ r$ r$ r% r� � s !r� c @ s e Zd Zdd� ZdS )�InvCasesc C s0 t �|�}tt||�t|�� tt||�� d S )N)r �invr r� r� r r& )r> r, r- r= Za_invr$ r$ r% r@ s z InvCases.doN)rD rE rF r@ r$ r$ r$ r% r� s r� c @ s2 e Zd Zej�deeee g�dd� �Z dd� Z dS )�TestInvr* c C s0 t jddgddgg|d�}tt�|�j|� d S )NrN g �?)r* )r! r r r r� r* )r> r* ru r$ r$ r% r� s zTestInv.test_typesc C s� G dd� dt j�}t jdt jd��|�}t�|�}t|jj t j k� t |j |j � tt ||�� t jdt jd��|�}t�|�}t|jj t jk� t |j |j � tt ||�� d S )Nc @ s e Zd ZdS )z*TestInv.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� s r� )r rN rN )r* )r r )r! r" �zeros�int_rn r r� r r* r �float64r rX r � complex64)r> r� r, �resr$ r$ r% r� s zTestInv.test_0_sizeN) rD rE rF r� r� r� r r r r r� r� r$ r$ r$ r% r� s r� c @ s e Zd Zdd� ZdS )� EigvalsCasesc C s& t �|�}t �|�\}}t||� d S )N)r �eigvals�eigr )r> r, r- r= �ev�evalues�evectorsr$ r$ r% r@ , s zEigvalsCases.doN)rD rE rF r@ r$ r$ r$ r% r� * s r� c @ s2 e Zd Zej�deeee g�dd� �Z dd� Z dS )� TestEigvalsr* c C s` t jddgddgg|d�}tt�|�j|� t jddgddgg|d�}tt�|�jt|�� d S )NrN g �?)r* r] )r! r r r r� r* r2 )r> r* ru r$ r$ r% r� 3 s zTestEigvals.test_typesc C s� G dd� dt j�}t jdt jd��|�}t�|�}t|jj t j k� t d|j � tt |t j�� t jdt jd��|�}t�|�}t|jj t jk� t d|j � tt |t j�� d S )Nc @ s e Zd ZdS )z.TestEigvals.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� < s r� )r rN rN )r* )r rN )r r )r )r! r" r� r� rn r r� r r* r r� r rX r r� )r> r� r, r� r$ r$ r% r� : s zTestEigvals.test_0_sizeN) rD rE rF r� r� r� r r r r r� r� r$ r$ r$ r% r� 2 s r� c @ s e Zd Zdd� ZdS )�EigCasesc C sX t �|�\}}tt||�t�|�t�|�dd d d �f t|j�d� tt ||�� d S )N.)�rtol) r r� r r� r! r r3 r* r r& )r> r, r- r= r� r� r$ r$ r% r@ O s z EigCases.doN)rD rE rF r@ r$ r$ r$ r% r� M s r� c @ s2 e Zd Zej�deeee g�dd� �Z dd� Z dS )�TestEigr* c C s� t jddgddgg|d�}t j�|�\}}t|j|� t|j|� t jddgddgg|d�}t j�|�\}}t|jt|�� t|jt|�� d S )NrN g �?)r* r] )r! r r r� r r* r2 )r> r* ru �w�vr$ r$ r% r� X s zTestEig.test_typesc C s� G dd� dt j�}t jdt jd��|�}t�|�\}}t|jj t j k� t|jj t j k� t |j |j � t d|j � tt |t j�� t jdt jd��|�}t�|�\}}t|jj t jk� t|jj t jk� t |j |j � t d|j � tt |t j�� d S )Nc @ s e Zd ZdS )z*TestEig.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� f s r� )r rN rN )r* )r rN )r r )r )r! r" r� r� rn r r� r r* r r� r rX r r� )r> r� r, r� �res_vr$ r$ r% r� d s zTestEig.test_0_sizeN) rD rE rF r� r� r� r r r r r� r� r$ r$ r$ r% r� W s r� c @ s. e Zd ZdZej�deee e g�dd� �Z dS )� SVDBaseTestsFr* c C sx t jddgddgg|d�}t�|�\}}}t|j|� t|jt|�� t|j|� tj|d| jd�}t|jt|�� d S )NrN g �?)r* F)� compute_uvr6 )r! r r �svdr r* r1 r6 )r> r* ru �urx �vhr$ r$ r% r� ~ s zSVDBaseTests.test_typesN) rD rE rF r6 r� r� r� r r r r r� r$ r$ r$ r% r� { s r� c @ s e Zd Zdd� ZdS )�SVDCasesc C sp t �|d�\}}}t|tt�|�t�|�dd d d �f t�|��t|j�d� tt ||�� tt ||�� d S )NF.)r� ) r r� r r� r! r r3 r* r r& )r> r, r- r= r� rx �vtr$ r$ r% r@ � s & z SVDCases.doN)rD rE rF r@ r$ r$ r$ r% r� � s r� c @ s e Zd Zdd� ZdS )�TestSVDc C s� t �d�}tj|d| jd�\}}}t|jd� t|jd� t|t �d�� t �d�}tj|d| jd�\}}}t|jd� t|jd� t|t �d�� dS ) z6 Empty input should put an identity matrix in u or vh )rQ r T)r� r6 )rQ rQ )r r rQ )r rQ N)r! rm r r� r6 r rX �eye)r> ru r� rx r� r$ r$ r% �test_empty_identity� s zTestSVD.test_empty_identityN)rD rE rF r� r$ r$ r$ r% r� � s r� c @ s e Zd Zdd� ZdS )�SVDHermitianCasesc C s� t j|ddd�\}}}t|tt�|�t�|�dd d d �f t�|��t|j�d� dd� }tt� |||��t� t� |j d �|j �� tt� |||��t� t� |j d �|j �� t t�|�dd d d�f |� tt||�� tt||�� d S ) NFT)r6 .)r� c S s< t t| j��}|d |d |d< |d< t�tj| |d��S )Nr^ r] )�axes)rs r� rh r! �conj� transpose)�matr� r$ r$ r% r6 � s z'SVDHermitianCases.do.<locals>.hermitianr] )r r� r r� r! r r3 r* r r Z broadcast_tor� rX r �sortr r& )r> r, r- r= r� rx r� r6 r$ r$ r% r@ � s & ,, zSVDHermitianCases.doN)rD rE rF r@ r$ r$ r$ r% r� � s r� c @ s e Zd ZdZdS )�TestSVDHermitianTN)rD rE rF r6 r$ r$ r$ r% r� � s r� c @ s e Zd Zdd� ZdS )� CondCasesc C s� t |�}d|kr"tttj|� d S tj|dd�}tt�|�|d |d ddd� tt�|d �|d |d ddd� tt�|d �|d |d ddd� tj�|�}tt�|d �t |�� d �� d �t |�� d �� d � ddd� tt�|d �t |�� d �� d �t |�� d �� d � ddd� tt�|tj �t |�� d �� d �t |�� d �� d � ddd� tt�|tj �t |�� d �� d �t |�� d �� d � ddd� tt�|d �t�t |�d � d �� d �t |�d � d �� d � �ddd� d S )Nzsize-0F)r� ).r ).r] rS rR )r. r/ rO r^ rN r] �fro)r r r r �condr� r r! r� r` �sum�max�minr �sqrt)r> r, r- r= r� rx Zcinvr$ r$ r% r@ � sH & & & & z CondCases.doN)rD rE rF r@ r$ r$ r$ r% r� � s r� c @ s> e Zd Zdd� Zdd� Zejjdddd�d d � �Zd d � Z d S )�TestCondc C s� t dddgdddgdddgg�}tt�|t�d� tt�|t �d� tt�|d�d� tt�|d�d � tt�|d �t�d �� d S ) Ng �?r rN g �g @rQ gUUUUUU�?r] g �?r� gUUUUU6@)r r r r� r r! r� )r> �Ar$ r$ r% �test_basic_nonsvd� s zTestCond.test_basic_nonsvdc C s� t �d�t �d�g}d dddg}ddg}x,t�||�D ] \}}tt�||�dk� q6W x$t�||�D ]\}}t�||� qdW d S )N)rO rO rN rO r� r] r^ g 4&�k C)r! r� �onesri rj r r r� )r> ZAs�p_posZp_negr� �pr$ r$ r% � test_singular� s zTestCond.test_singularTFz/Platform/LAPACK-dependent failure, see gh-18914)�run�reasonc C s� d dddddg}d dddg}t �d�}t j|d< x6|D ].}t�||�}tt|t j�� tt �|�� q6W t �d�}t j|d < x||D ]t}t�||�}tt �|d �� ||kr�t|d d k� t|d d k� q�tt �|d � � tt �|d � � q�W d S ) NrN r] rO r^ r� )rO rO )r rN )rP rO rO )rN r rN r g 4&�k C) r! r� �nanr r� r r Zfloat_�isnan)r> Zpsr� r� r� r� r$ r$ r% �test_nan s$ zTestCond.test_nanc C s� t j�d� t j�dddd�}d|d< d|d< x\dD ]T}t�||�}t|d t j� t|d t j� tt � |d �� tt � |d �� q4W d S ) Ni� rO r )r r )rN rN )NrN rO r� r] r^ )r rN )rN r ) r! �random�seed�randr r� r r r �isfinite)r> r� r� r� r$ r$ r% �test_stacked_singular s z TestCond.test_stacked_singularN) rD rE rF r� r� r� r� �xfailr� r� r$ r$ r$ r% r� � s r� c @ s e Zd Zdd� ZdS )� PinvCasesc C s< t �|�}t}t||||�|�|ddd� tt||�� d S )NrS rR )r. r/ )r �pinvr� r r r& )r> r, r- r= �a_ginvr r$ r$ r% r@ 1 s z PinvCases.doN)rD rE rF r@ r$ r$ r$ r% r� , s r� c @ s e Zd ZdS )�TestPinvN)rD rE rF r$ r$ r$ r% r� 9 s r� c @ s e Zd Zdd� ZdS )�PinvHermitianCasesc C s@ t j|dd�}t}t||||�|�|ddd� tt||�� d S )NT)r6 rS rR )r. r/ )r r� r� r r r& )r> r, r- r= r� r r$ r$ r% r@ ? s zPinvHermitianCases.doN)rD rE rF r@ r$ r$ r$ r% r� = s r� c @ s e Zd ZdS )�TestPinvHermitianN)rD rE rF r$ r$ r$ r% r� G s r� c @ s e Zd Zdd� ZdS )�DetCasesc C s� t �|�}t �|�\}}t|�jjttfkr<t|��t�}nt|��t �}t � |�}t |t j |dd�� t |t�|� t j |dd�� t�|�}t�|�}|dk} t t�|| �d� t|| t � d S )Nr] )�axisr rN )r �det�slogdetr r* r r r �astyper r� r r �reducer! �expZ atleast_1dr` r r ) r> r, r- r= �drx �ld�adr� �mr$ r$ r% r@ M s z DetCases.doN)rD rE rF r@ r$ r$ r$ r% r� K s r� c @ s: e Zd Zdd� Zej�deee e g�dd� �Z dd� Z dS ) �TestDetc C s t t�dgg�d� t tt�dgg��t� t t�dgg�d� t tt�dgg��t� t t�dgg�dt f� t tt�dgg�d �t� t tt�dgg�d �t� t t�dgg�dt f� t tt�dgg�d �t� t tt�dgg�d �t� d S )Ng y r rN )r r r� r r r r� r )r> r$ r$ r% � test_zero` s zTestDet.test_zeror* c C s^ t jddgddgg|d�}tt j�|�j|� t j�|�\}}t|jt|�� t|j|� d S )NrN g �?)r* )r! r r r r� r* r� r1 )r> r* ru �phrx r$ r$ r% r� m s zTestDet.test_typesc C s� t jdt jd�}t�|�}t|d� t|jjt jk� t� |�}t|d� t|d jjt jk� t|d jjt j k� t jdt j d�}t�|�}t|d� t|jjt j k� t� |�}t|d� t|d jjt j k� t|d jjt j k� d S )N)r r )r* g �?)rN r r rN ) r! r� r� r r� r r r* r r� �float32r� )r> r, r� r$ r$ r% r� u s zTestDet.test_0_sizeN) rD rE rF r� r� r� r� r r r r r� r� r$ r$ r$ r% r� _ s r� c @ s e Zd Zdd� ZdS )� LstsqCasesc C sL t �|�}|j\}}t�|d�\}}} tj||dd�\} } } } |dkrVt| dk�� � ||krzt|t || �� t | |� n t | |� t| | � |�� | |kr�||kr�t �t t � || �| ��d j dd�}t �|�}t �|�jdkr�d|_t | j|j� nt �g ��t| ��}t| |� tt �| jt j�� tt| |�� tt| |�� d S ) NFr] )�rcondr rO )r� rN )rN )r! r rX r r� �lstsqr rq r r r Z__array_wrap__r` r� rh r rn r � issubdtyper* �floatingr& )r> r, r- r= �arrr� �nr� rx r� ru � residuals�rank�svZ expect_residsr$ r$ r% r@ � s, & z LstsqCases.doN)rD rE rF r@ r$ r$ r$ r% r � s r c @ sF e Zd Zdd� Zej�dddgdddd d d d g�d d� �Zdd� ZdS )� TestLstsqc C s� t �ddddddgddddddgddddddgddddddgg�j}t �ddddddg�}t� ��}|�td�}t�||�\}}}}t|d k� tj||d d �\}}}}t|d k� tj||d d �\}}}}t|d k� tt |�dk� W d Q R X d S ) Ng g �?g @g @g @rN r z `rcond` parameter will changerQ r] )r rP ) r! r �Tr �record� FutureWarningr r r �len) r> r, r- �supr� ru r r rx r$ r$ r% �test_future_rcond� s zTestLstsq.test_future_rcondr� r �n_rhs)rQ rO rO )r rQ rN )r rQ rO )rQ r rN )rQ r rO )rQ rO r )r r r c C s� t �|| ��||�}t �||f�}tj||d d�\}}}} |dkrTt|dk�� � t|j ||f� t|j ||krx|fnd� ||kr�|dkr�|t � ||� } t || | j dd�� t|t ||�� t| j t ||�f� d S )N)r r )r r^ )r� )r! r� rW r� r r r rq r rX r r r� r� ) r> r� r r r, r- ru r r rx r� r$ r$ r% �test_empty_a_b� s zTestLstsq.test_empty_a_bc C sj t �ddddg�}t �ddddd g�}t �|t �t|��g�j}ttd �� tj ||d d � W d Q R X d S ) Nr rN rO rP r] g�������?g�������?g������ @gffffff @zIncompatible dimensions)r ) r! r Zvstackr� r r r r r r )r> ru �yr� r$ r$ r% �test_incompatible_dims� s z TestLstsq.test_incompatible_dimsN) rD rE rF r r� r� r� r r r$ r$ r$ r% r � s r �dtc C s g | ]}t �|��qS r$ )r! r* )ra r� r$ r$ r% rb � s rb z?bBhHiIqQefdgFDGOc @ s� e Zd Ze�d�Zeddddg Zeddddg Zeddddg ZeeeegZ e ddgddgg�Z e� egggd �Z ee�d�e�d�e�d�gZd d � Zd d � Zd d� Zdd� Zdd� Zdd� Zdd� Zdd� ZdS )�TestMatrixPowerrQ rP r rN rO r� �g�Gc C s� | j �|�}tt|dd d d d �| j� tt|dd d d d �| j � tt|dd d d d �| j� tt|dd d d d �| j� d S )NrO �d i � r rN rP )�rshft_1r� r r �rshft_0�rshft_2�rshft_3)r> r Zrshftr$ r$ r% �test_large_power� s z TestMatrixPower.test_large_powerc C sB dd� }x4| j D ]*}||�|�� |tkr|| j�|�� qW 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)r> r r# r� r$ r$ r% �test_power_is_zero� s z"TestMatrixPower.test_power_is_zeroc C sB dd� }x4| j D ]*}||�|�� |tkr|| j�|�� qW d S )Nc S s& t | d�}t|| � t|j| j� d S )NrN )r r r* )r� r" r$ r$ r% r# � s z-TestMatrixPower.test_power_is_one.<locals>.tz)r$ r� r% r& )r> r r# r� r$ r$ r% �test_power_is_one� s z!TestMatrixPower.test_power_is_onec C sB dd� }x4| j D ]*}||�|�� |tkr|| j�|�� qW d S )Nc S s> t | d�}| jtkrtnt}t||| | �� t|j| j� d S )NrO )r r* r% r r r )r� r" �mmulr$ r$ r% r# s z-TestMatrixPower.test_power_is_two.<locals>.tz)r$ r� r% r& )r> r r# r� r$ r$ r% �test_power_is_two s z!TestMatrixPower.test_power_is_twoc C s4 dd� }x&| j D ] }|| jkr||�|�� qW d S )Nc S s4 t | d�}| jtkrtnt}t||| �t| �� d S )Nr] )r r* r% r r r r� )r� Zinvmatr) r$ r$ r% r# s z3TestMatrixPower.test_power_is_minus_one.<locals>.tz)r$ �dtnoinvr� )r> r r# r� r$ r$ r% �test_power_is_minus_one s z'TestMatrixPower.test_power_is_minus_onec C s. | j �|�}ttt|d� ttt|dg� d S )Ng �?rN )r r� r � TypeErrorr )r> r r� r$ r$ r% �test_exceptions_bad_power s z)TestMatrixPower.test_exceptions_bad_powerc C sP t ttt�dg|�d� t ttt�dgdgg|�d� t ttt�d|�d� d S )NrN rO )rQ rP rO )r r r r! r r� )r> r r$ r$ r% �test_exceptions_non_square% s z*TestMatrixPower.test_exceptions_non_squarec C s, || j krd S | j�|�}ttt|d� d S )Nr] )r+ �noninvr� r r r )r> r r� r$ r$ r% � test_exceptions_not_invertible* s z.TestMatrixPower.test_exceptions_not_invertibleN)rD rE rF r! r� r r r r r$ r r0 �blockr& r% r* r+ r r' r( r* r, r. r/ r1 r$ r$ r$ r% r � s r c @ s e Zd Zdd� ZdS )�TestEigvalshCasesc C s^ t �|d�}t �|�\}}|jdd� t||t|j�d� t �|d�}t||t|j�d� d S )N�Lr] )r� )r� �U)r �eigvalshr� r� r r3 r* )r> r, r- r= r� r� r� �ev2r$ r$ r% r@ 4 s zTestEigvalshCases.doN)rD rE rF r@ r$ r$ r$ r% r3 2 s r3 c @ sB e Zd Zej�deeee g�dd� �Z dd� Z dd� Z dd � Z d S ) � TestEigvalshr* c C s: t jddgddgg|d�}t j�|�}t|jt|�� d S )NrN g �?)r* )r! r r r6 r r* r1 )r> r* ru r� r$ r$ r% r� A s zTestEigvalsh.test_typesc C sX t jddgddggt jd�}ttt jj|dd� ttt jj|d� ttt jj|d� d S )NrN g �?)r* �lrong)�UPLO�lower�upper)r! r r r r� r r6 )r> ru r$ r$ r% � test_invalidG s zTestEigvalsh.test_invalidc C s� t jddgddggt jd�}t jddgddggt jd�}t jddgt jd�}tt j�}t j�|�}t|||d� t jj|dd�}t|||d� t jj|dd�}t|||d� t jj|d d�}t|||d� t jj|d d�}t|||d� d S ) Nr rN )r* r] )r� r4 )r: �lr5 r� )r! r r r3 r r6 r )r> �Klo�Kup�tgtr� r� r$ r$ r% � test_UPLOM s zTestEigvalsh.test_UPLOc C s� G dd� dt j�}t jdt jd��|�}t�|�}t|jj t j k� t d|j � tt |t j�� t jdt jd��|�}t�|�}t|jj t jk� t d|j � tt |t j�� d S )Nc @ s e Zd ZdS )z/TestEigvalsh.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� e s r� )r rN rN )r* )r rN )r r )r )r! r" r� r� rn r r6 r r* r r� r rX r r� r )r> r� r, r� r$ r$ r% r� c s zTestEigvalsh.test_0_sizeN)rD rE rF r� r� r� r r r r r� r= rB r� r$ r$ r$ r% r8 @ s r8 c @ s e Zd Zdd� ZdS )� TestEighCasesc C s� t �|�\}}t �|�\}}|jdd� t||� tt||�t�|�dd d d �f t�|� t |j �d� t �|d�\}} t||� tt|| �t�|�dd d d �f t�| � t |j �t |�d� d S )Nr] )r� .)r� r5 )r� �err_msg) r �eighr� r� r r r� r! r r3 r* �repr) r> r, r- r= r� Zevcr� r� r7 Zevc2r$ r$ r% r@ x s zTestEighCases.doN)rD rE rF r@ r$ r$ r$ r% rC v s rC c @ sB e Zd Zej�deeee g�dd� �Z dd� Z dd� Z dd � Z d S ) �TestEighr* c C sJ t jddgddgg|d�}t j�|�\}}t|jt|�� t|j|� d S )NrN g �?)r* )r! r r rE r r* r1 )r> r* ru r� r� r$ r$ r% r� � s zTestEigh.test_typesc C sX t jddgddggt jd�}ttt jj|dd� ttt jj|d� ttt jj|d� d S )NrN g �?)r* r9 )r: r; r< )r! r r r r� r rE )r> ru r$ r$ r% r= � s zTestEigh.test_invalidc C s t jddgddggt jd�}t jddgddggt jd�}t jddgt jd�}tt j�}t j�|�\}}t|||d� t jj|dd�\}}t|||d� t jj|dd�\}}t|||d� t jj|d d�\}}t|||d� t jj|d d�\}}t|||d� d S ) Nr rN )r* r] )r� r4 )r: r> r5 r� )r! r r r3 r rE r )r> r? r@ rA r� r� r� r$ r$ r% rB � s zTestEigh.test_UPLOc C s� G dd� dt j�}t jdt jd��|�}t�|�\}}t|jj t j k� t|jj t j k� t |j |j � t d|j � tt |t j�� t jdt jd��|�}t�|�\}}t|jj t jk� t|jj t jk� t |j |j � t d|j � tt |t j�� d S )Nc @ s e Zd ZdS )z+TestEigh.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� � s r� )r rN rN )r* )r rN )r r )r )r! r" r� r� rn r rE r r* r r� r rX r r� r )r> r� r, r� r� r$ r$ r% r� � s zTestEigh.test_0_sizeN)rD rE rF r� r� r� r r r r r� r= rB r� r$ r$ r$ r% rG � s rG c @ s e Zd ZdZdZdS )� _TestNormBaseN)rD rE rF r �decr$ r$ r$ r% rH � s rH c @ s4 e Zd Zdd� Zdd� Zdd� Zdd� Zd d � Zd S ) �_TestNormGeneralc C sF t tg �d� t ttg | jd��d� t tttg | jd���d� d S )Ng )r* )r r r r r )r> r$ r$ r% � test_empty� s z_TestNormGeneral.test_emptyc C s� t �dddg�}t jd }t jd }|| }�x||D �]r}|�|�}t|t j �}tt|jj t j �� t |d� t � �:}|� td� t|d�}tt|jj t j �� t |d� W d Q R X t|d�}tt|jj t j �� t |d� t|d�}tt|jj t j �� t |d � t|d�}tt|jj t j �� t ||j� d �|j� d � � t|d �}tt|jj t j �� t ||j� d �|j� d � � t|t j�}tt|jj t j �� t |d � q4W d S )NrN r � AllIntegerZAllFloatg zdivide by zero encounteredr] rO g @g �?rQ g �?g �?)r! r � typecodesr� r r r � issubclassr* r r r r �filter�RuntimeWarning) r> r, � exact_types� inexact_types� all_types�each_inexact_types�at�anr r$ r$ r% �test_vector_return_type� s: z(_TestNormGeneral.test_vector_return_typec s� ddddg}ddddg}ddddg}� fd d �}x|||fD ] }||� q<W x8t |� jd �t |� jd �t |� jd �fD ] }||� qvW d S ) NrN rO rP rQ r] r^ r_ r\ c s� t jjt| �d� jd� t jjt| t�d� jd� t jjt| t �d� jd� t jjt| d�d� jd� t jjt| d�d� jd� t jjt| d �d� jd� t jjt| d �d � jd� t jjt| d �d � jd� d S )Ng��6ҭ�@)r) g @g �?rN g $@r] g� ��Q��?rO r^ g�s�c���?r rQ )r! �testingr r rI r )r� )r> r$ r% �_test s z+_TestNormGeneral.test_vector.<locals>._test)r* )r r )r> r, r- r� rY r� r$ )r> r% � test_vector� s z _TestNormGeneral.test_vectorc s� t dddgdddgg| jd�� x�d dd dddtjtj gD ]h�� �fd d �t� jd �D �}tt� �d d �|� � �fd d �t� jd �D �}tt� �dd �|� q:W tjdd| jd�� ddd���j }x�d ddddtjtj dgD ]܉x�t � t| |�d�D ]�}|\}}|d k �r ||7 }|d k �r.||7 }||k�rLt tt��|d � q�t��|d �}||| �||k �r����fdd �t�j� �D �}n ���fdd �t�j� �D �}t||� q�W q�W d S )NrN rO rP rQ rS r' )r* r] r c s$ g | ] }t � d d �|f �d��qS )N)�ord)r )ra �k)r� �orderr$ r% rb s z._TestNormGeneral.test_axis.<locals>.<listcomp>)r[ r� c s$ g | ] }t � |d d �f �d��qS )N)r[ )r )ra r\ )r� r] r$ r% rb " s � r^ r� c s* g | ]"}t � d d � j|�d��d��qS )N)r� )r[ )r �take)ra r\ )�B�k_indexr] r$ r% rb 8 s c s, g | ]$}t � d d � j|�d�j�d��qS )N)r� )r[ )r r_ r )ra r\ )r` ra r] r$ r% rb ; s )r r r! 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rM r� r r r rN r* r r r r rO rP rX ) r> r, rQ rR rS rT rU rV r r$ r$ r% �test_matrix_return_typer s@ z#_TestNorm2D.test_matrix_return_typec C s� | j ddgddgg| jd�}tt|�d� tt|d�d� tt|d�d � tt|t�d � tt|t �d � tt|d�d � tt|d �d � tt|d�d� tt|d�d� ttt|d� ttt|d� ttt|d� d S )NrN rP rS rT )r* g� ��T"@r� rf g $@g (@g @r] g @rO g��W�?"@r^ gї�ʄ�?Znofror_ r )r r r r r r r� )r> r� r$ r$ r% �test_matrix_2x2� s z_TestNorm2D.test_matrix_2x2c C s� d| j dddgdddgdddgg| jd� }tt|�d � tt|d �d � tt|d �d � tt|t�d � tt|t �d� tt|d�d� tt|d�d� tt|d�d� tt|d�d� d S )Ng�������?rN rO rP r' r rS )r* grj=Q0�?r� rf g�B+pc�?g�������?g333333�?g �?r] g�������?g�&��.d�?r^ gܸՠ���?)r r r r r )r> r� r$ r$ r% �test_matrix_3x3� s *z_TestNorm2D.test_matrix_3x3c C s | j dddgdddgg| jd�}tjdd| jd��ddd�}ttt|d d � ttt|d d � tttddgd d � tttddgd d � tttddgd d � x<d D ]4}ttt||d � ttt||d� ttt||d� q�W ttjt|d d� ttjt|d d� ttt|d d� d S )NrN rO rP rQ rS r' )r* r^ r� r rf �test)r rP )r rN )rN rO )rO rP )r rN rO ) r r r! r� rW r r� r Z AxisError)r> r� r` r] r$ r$ r% � test_bad_args� s z_TestNorm2D.test_bad_argsN) rD rE rF r! r rl rm rn ro rq r$ r$ r$ r% rk j s 3rk c @ s e Zd ZdS )� _TestNormN)rD rE rF r$ r$ r$ r% rr � s rr c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )�TestNorm_NonSystematicc C s* t jdt jd�}tt|dd�ddd� d S )N� )r* rP )r[ g�����L)@rO )r) )r! r� Z longdoubler+ r )r> ru r$ r$ r% �test_longdouble_norm� s z+TestNorm_NonSystematic.test_longdouble_normc C s, t jdgt jd�}tt|dd�ddd� d S )Ni �)r* rP )r[ l rS )r) )r! r Zint32r+ r )r> ru r$ r$ r% � test_intmin� s z"TestNorm_NonSystematic.test_intminc C s� t jdt jd�}d|d< d|d< d}tt jj|dd �|d d � |�t j�}tt jj|dd �|d d � |�t j�}tt jj|dd �|d d � d S )N)rO )r* y @ @r y � @rN g���V;'@rP )r[ rt )r) � rS ) r! rm Z clongdoubler+ r r r� � complex128r� )r> r� r� r$ r$ r% �test_complex_high_ord� s z,TestNorm_NonSystematic.test_complex_high_ordN)rD rE rF ru rv ry r$ r$ r$ r% rs � s rs c @ s e Zd ZejZdZdS )�_TestNormDoubleBaser( N)rD rE rF r! r r rI r$ r$ r$ r% rz s rz c @ s e Zd ZejZdZdS )�_TestNormSingleBaser' N)rD rE rF r! r r rI r$ r$ r$ r% r{ s r{ c @ s e Zd ZejZdZdS )�_TestNormInt64Baser( N)rD rE rF r! Zint64r rI r$ r$ r$ r% r| s r| c @ s e Zd ZdS )�TestNormDoubleN)rD rE rF r$ r$ r$ r% r} s r} c @ s e Zd ZdS )�TestNormSingleN)rD rE rF r$ r$ r$ r% r~ s r~ c @ s e Zd ZdS )� TestNormInt64N)rD rE rF r$ r$ r$ r% r s r c @ s e Zd Zdd� Zdd� ZdS )�TestMatrixRankc C s� t dtt�d��� t�d�}d|d< t t|�d� t tt�d��d� t tddddg�d� t tt�d��d� t tdg�d� t�|t�d�t�d�g�}t t|�t�dddg�� t td�d� d S ) NrQ g )r] r] rP )rQ rQ r rN )rQ )r r r! r� r� r )r> �I�msr$ r$ r% �test_matrix_rank s z TestMatrixRank.test_matrix_rankc C s� t dtt�d�dd�� t dtt�d�dd�� t dtt�d�dd�� t�d�}d|d< t d t|dd�� d |d< t dt|dd d �� t d t|dd d �� d S )NrQ T)r6 rN )rQ rQ r g )r] r] rP g:�0�yE>g��|"�BE>)r6 Ztolg�;䡈�E>)r r r! r� r� r� )r> r� r$ r$ r% �test_symmetric_rank3 s z"TestMatrixRank.test_symmetric_rankN)rD rE rF r� r� r$ r$ r$ r% r� s r� c C s� t j�d�} x�td�D ]�}| jdd�}|d d �df |d d �df |d d �df< tt|�d� |d d �d f |d d �d f |d d �d f< tt|�d � qW d S ) Ni�3r )�( rt )�sizerN rO r rw rQ rS rP rM )r! r� Z RandomStater� �normalr r )�rng�i�Xr$ r$ r% �test_reduced_rankA s ,,r� c @ sJ e Zd ZejZdd� Zej�ddgdddg�dd � �Z d d � Z d d � Z dS )�TestQRc C s� t |�}|j}|j\}}t||�}tj|dd�\}}t|j|k� t|j|k� tt||�� tt||�� t|j||fk� t|j||fk� tt ||�|� tt |j � � |�t � |�� tt �|�|� tj|dd�\} } t| j|k� t| j|k� tt| |�� tt| |�� t| j||fk� t| j||fk� tt | | �|� tt | j � � | �t � |�� tt �| �| � tj|dd�} t| j|k� tt| |�� t| | � d S )NZcomplete)�modeZreducedr� )r r* rX r� r �qrr r r r r r� r! r� �triu) r> r, �a_typeZa_dtyper� r r\ �qr� �q1�r1�r2r$ r$ r% �check_qrR s8 zTestQR.check_qrr� r )rP r )r rP )r r c C st t ||�}t�||f�}| �|� tjj|dd�\}}t|jtj� t|jtj� t|j ||f� t|j |f� d S )N�raw)r� ) r� r! rm r� r r� r r* r rX )r> r� r r\ r, �h�taur$ r$ r% � test_qr_emptyy s zTestQR.test_qr_emptyc C s� | j ddgddgddggtjd�}tj|dd �\}}t|jtjk� t|jtjk� t|jd k� t|jd k� tj|jdd �\}}t|jtjk� t|jtjk� t|jd k� t|jd k� d S ) NrN rO rP rQ rS r' )r* r� )r� )rO rP )rO )rP rO ) r r! r r r� r r* rX r )r> r, r� r� r$ r$ r% � test_mode_raw� s "zTestQR.test_mode_rawc C s� | � ddgddgg�}| � ddgddgddgg�}x@dD ]8}|�|�}|�|�}| �|� | �|� | �|j� q8W xPdD ]H}dd|�|� }dd|�|� }| �|� | �|� | �|j� qzW d S ) NrN rO rP rQ rS r' �fdy �?)r r� r� r )r> r, r- r �m1�m2r$ r$ r% �test_mode_all_but_economic� s z!TestQR.test_mode_all_but_economicN) rD rE rF r! r r� r� r� r� r� r� r� r$ r$ r$ r% r� N s ' r� c @ s e Zd Zdd� Zdd� ZdS )� TestCholeskyc C s dddddg}t jt jt jt jf}x�t�||�D ]�\}}t j�d� t jj |� }t � |t j �rr|dt jj |� }t t t|���}d|d d �< t �|�|��� |�}t j||d �}t j�|�}t �||�|��� �}t|||� d |� d |� d |� �d |jd t �|�j d� q0W d S )N)rN rN )rO rO )rP rP )�2 r� )rP rt rt rN y �?)r] r^ r^ )r* � � i� r )rD Zatol)r! r r� r� rx ri rj r� r� Zrandnr Zcomplexfloatingrs r� r r r� r� r r �choleskyr rX ZfinfoZeps) r> ZshapesZdtypesrX r* r, �tr� r- r$ r$ r% �test_basic_property� s z TestCholesky.test_basic_propertyc C s� G dd� dt j�}t jdt jd��|�}t�|�}t|j|j� t |j j t j k� t t |t j�� t jdt jd��|�}t�|�}t|j|j� t |j j t jk� t t |t j�� d S )Nc @ s e Zd ZdS )z/TestCholesky.test_0_size.<locals>.ArraySubclassN)rD rE rF r$ r$ r$ r% r� � s r� )r rN rN )r* )rN r r )r! r" r� r� rn r r� r rX r r* r r� r r� )r> r� r, r� r$ r$ r% r� � s zTestCholesky.test_0_sizeN)rD rE rF r� r� r$ r$ r$ r% r� � s r� c C s� t jdkrd} nd} x�tjtjfD ]v}tjd|d�}|�| �}|�d��� }t|j jd� x<t j t j t j fD ](}||�}t|||�� t|||�� qlW q"W d S )N�little�<rB rQ )r* �S�=)�sys� byteorderr! r r� r� Z newbyteorder�byteswapr r* r r� r� r� r )�nativeZdttr Zn_arrZsw_arrZroutiner� r$ r$ r% �test_byteorder_check� s r� c C sp t �ddgddgg�} t �ddgddgg�}t �ddddg�dd d� }| |d< ||d< tt jjt jj|� d S )NrN rO rP rQ .)r r )r! r r� r r r r� )Z invertibleZnon_invertibleru r$ r$ r% � test_generalized_raise_multiloop� s r� c C sR d} y t �� }W n" ttfk r2 t�d� Y nX |dk�r(t �d� t �d� dd l}|�|j d� yt j j � � W n2 tk r� Y n tk r� t �t j� Y nX y0t �dgg�}t j j �ddd|d||dd� W n< tk �r } z dt|�k�rt �| � W d d }~X Y nX t �t j� n&t �� \}}t �|�| k�rNt�d� d S ) N� zNot POSIX or fork failed.r rN )r r g �?zDORGQR parameter number 5zNumpy xerbla not linked in.)�os�fork�OSError�AttributeErrorr� �skip�close�resourceZ setrlimitZ RLIMIT_COREr! 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r� r r r )r> r� r` r� �Dr$ r$ r% �8test_basic_function_with_dynamic_programing_optimizationi s zETestMultiDot.test_basic_function_with_dynamic_programing_optimizationc C sL t j�d�}t j�d�}t j�d�}t j�d�}tt||||g�jd� d S )NrO )rO r' )r' rO )rO rO )rO )r! r� r r rX )r> �A1dr` r� r� r$ r$ r% � test_vector_as_first_argumentr s z*TestMultiDot.test_vector_as_first_argumentc C sL t j�d�}t j�d�}t j�d�}t j�d�}tt||||g�jd� d S )N)r' rO )rO r' rO )r' )r! r� r r rX )r> 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�}tt||||g�jd� d S )NrO )rO r' )r' rO r$ )r! r� r r rX )r> 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�}||ksLt�t||�|��|�� t|t �|t �||��� d S )N)r' rO )rO r' )r# )r! r� r� r rI r r )r> 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�}||ks>t�t||�|�� t|t �||�� d S )N)r' rO )rO r' )r' r' )r# )r! 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r� rX r r� r )r> rX r� r, �ainvr� �actualr$ r$ r% �test_tensorinv_shape� s z"TestTensorinv.test_tensorinv_shaper� r r^ c C s6 t �d�}d|_tt�� tj||d� W d Q R X d S )Nr� )rQ r' rM rP )r, r� )r! r� rX r r� r r� )r> r� r, r$ r$ r% �test_tensorinv_ind_limit� s z&TestTensorinv.test_tensorinv_ind_limitc C sJ t �d�}d|_tj|dd�}t �d�}tt �||d�t j�||�� d S )Nr� )r� rM rP rN )r� ) r! r� rX r r� r� r Z tensordotZ tensorsolve)r> r, r� r- r$ r$ r% �test_tensorinv_result� s z#TestTensorinv.test_tensorinv_resultN) rD rE rF r� r� r� r! r� r� r� r� r� r$ r$ r$ r% r� � s r� c C s> t jddgddggdd�} ttd�� t�| � W d Q R X d S )NrN r^ rO rS Zfloat16)r* zunsupported in linalg)r! r r r- r r� )r r$ r$ r% �test_unsupported_commontype� s r� Fz*Numpy not compiled with 64-bit BLAS/LAPACK)r� r� g e� B)Z free_bytesc C sR d} t jd| gt jd�}t jddgt jd�}d|d< t �||�}t|d d� d S )Nl rN )r* )r r] )r! r� r r� r r )r r, r- r� r$ r$ r% �test_blas64_dot s r� )r� c C s� t j} t jjj}d}d}|}t jddg| d�}t jdg| d�}t jdg| d�}|||||||dd�}t|d d� t|d |� t|d |� t|�� �} t d | k o�d k n � d S ) Nl rN )r* r] r �infor� r l l ) r! 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