a
    CCCfE                    @   s  d dl Z d dlmZ d dlmZmZmZmZmZm	Z	 d dl
Z
d dl
m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mZmZ d dlmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z( d dl)m*Z* d d	l+m,Z,m-Z- d dl.m/Z0 zd d
l1m2Z2 W n e3y   dZ2Y n0 zd dlm4Z5 W n e3y>   dZ5Y n0 d dl)m6Z6 d dl7m8Z8 ej9ej:gZ;ej<ej=gZ>e;e> Z?d Z@ZAe2dure2d d d Z@e2d d d ZAdd ZBdd ZCG dd dZDG dd dZEG dd dZFe
jGHde?e
jGHdg ddd  ZIG d!d" d"ZJG d#d$ d$ZKG d%d& d&ZLG d'd( d(ZMd)d* ZNd+d, ZOd-d. ZPd/d0 ZQG d1d2 d2ZRG d3d4 d4ZSd5d6 ZTd7d8 ZUd9d: ZVd;d< ZWd=d> ZXd?d@ ZYdAdB ZZdCdD Z[dEdF Z\dGdH Z]dIdJ Z^dKdL Z_dMdN Z`dOdP ZaG dQdR dRZbdSdT ZcdUdV ZddWdX ZedYdZ Zfe
jGjgd[d\d]d^d_ Zhd`da Zie
jGHdbdcddge
jGHde;e
jGHdeejdfe
jGHdgejdhe
jGHdiejdhe
jGHdjd dkge
jGHdld dkgddmdnZke
jGHde;dodp Zle
jGHdqdedridgdrididridjdridsdridldrifdtdu Zme
jGHdveng dwg dxg dyg dzg d{g d|geng d}eng d~g dg dg dg dg dgeng dg dg dg dgfgdd Zoe
jGHde?dd Zpe
jGHdeng deng deng deng deng deng deng denddgddgddgddgddggenddgddgddgddgddkggf	eng deng deng deng deng deng deng denddgddgddgddgddggenddgddgddgddgddggf	gdd Zqe
jGHde?e
jGHdg ddd Zre
jGHdese;e; e?ddĄ Zte
jGHdese;e; e?ddƄ Zue
jGHdese;e; e?ddȄ Zve
jGHdeng dʢeng dˢeng d̢eng d͢endfdgdrdhgddrgddgddggenddgddgdkdgddfgddggfeng d֢eng dעeng dآeng d٢enddgddgddgddggenddgddgddgddggfgdd Zwdd Zxe
jGHdese?e;e; e
jGHdejddd Zye
jGHdese?e;e; e
jGHdejddd Zze
jGHdese?e;e; e
jGHdejddd Z{e
jGHdese?e;e; e
jGHdejddd Z|e
jGHddeng deng deng deng dg dg dg dgfgdd Z}e
jGHde?e
jGHdg ddd Z~d d Ze
jGHdg de
jGHdddgdd Ze
jGHdd	d
ge
jGHdddgdd Ze
jGHde?e
jGHdg ddd Ze
jGHde?dd Ze
jGHde?e
jGHddd[ge
jGHdddgdd Ze
jGHde?e
jGHdd dkge
jGHdddgdd Ze
jGHde?d e
jGHddd[ge
jGHdddgdd Ze
jGHdeng deng deng denddgddgddgddgddggenddgddgddgddgddkggfeng deng deng denddgddgddgddgddggenddgddgddgddgddggfgd d! Ze
jGHdese?e;e; e
jGHd"dd#d$ fdd%d$ fgd&d' Ze
jGHdese?e;e; e
jGHd"dd(d$ fdd)d$ fgd*d+ Ze
jGHdese?e;e; e
jGHd"dd,d$ fdd-d$ fgd.d/ Ze
jGHd0eng dʢeng dˢendfdgdrdhgddrgddgddggenddgddgdkdgddfgddggfeng d֢eng dעenddgddgddgddggenddgddgddgddggfgd1d2 Ze
jGHd3dd[ge
jGHde?d4d5 Ze
jGHde?d6d7 Ze
jGHd8eng d9g d:g d;g d<geng d=g d>g d?g d<gddkfeng d@g dAg dBg dCgeng dDg dEg dFg dGgdkdhfgdHdI Ze
jGHde?dJdK Ze
jGHde?dLdM Ze
jGHdNeng dOg dPg dQg dRgeng dSg dTg dUg dVgeng dWg dXg dYg dZgeng d[d\d]feng d^g d_g d`g dageng dbg dcg ddg degeng dfg dgg dhg digeng d[djdkfgdldm Ze
jGHde?dndo Ze
jGHdpeng dqg drg dsg dtgeng dug drg dsg dvgeng dwg dxg dyg dzgeng d{g d|g d}g d~geng dg dg d}g dgeng dg dg dg dgeng dug dg dg dgeng dg dg dg dgfge
jGHde;dd Ze
jGHde;e
jGHdde
jGHdg ddd ZdS (      N)reduce)assert_equalassert_array_almost_equalassert_assert_allcloseassert_almost_equalassert_array_equal)raises)eyeoneszeros
zeros_liketriutriltril_indicestriu_indices)randrandintseed)_flapacklapackinvsvdcholeskysolveldlnorm
block_diagqreighqz)_compute_lwork)ortho_groupunitary_group)CONFIG)_clapack)get_lapack_funcs)get_blas_funcszBuild DependenciesZblasnameversionc                 C   s<   |t v r*tjj|  tjj|  d  |S tjj|  |S )N              ?)COMPLEX_DTYPESnprandomr   astype)shapedtype r1   Z/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/linalg/tests/test_lapack.pygenerate_random_dtype_array1   s    
r3   c                  C   sv   t jdu rtd tt j } h d}t }tt D ](}|ds8||vr8|| vr8|	| q8|g ksrJ ddS )z%Test that all entries are in the doc.Nzlapack.__doc__ is None>   absolute_importflapackclapackZ	HAS_ILP64Zfind_best_lapack_typeprint_functiondivision_z2Name(s) missing from lapack.__doc__ or ignore_list)
r   __doc__pytestskipsetsplitlistdir
startswithappend)namesZignore_listmissingr(   r1   r1   r2   test_lapack_documented9   s    

rE   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestFlapackSimplec           
      C   s   g dg dg dg}g dg dg dg dg}dD ]}t t|d	 d }|d u rTq6||\}}}}}	t|	 t|	 t|| t||fd
t|d
 d f t|tt| ||ddd\}}}}}	t|	 t|	 q6d S )N)         )         )      	   )rG   r   r   ga2U0*3?)rJ   r   r   gMb`?)rM   rG   r   r   )r   rG   r   r   ZsdzcZgebalr   rG   )Zpermutescale)	getattrr5   r   reprr   r   lenr,   r   )
selfaa1pfbalohiZpivscaleinfor1   r1   r2   
test_gebalL   s"    
zTestFlapackSimple.test_gebalc                 C   s\   g dg dg dg}dD ]<}t t|d d }|d u r8q||\}}}t| t| qd S )Nikiifi     i"  iiidZgehrd)rQ   r5   r   rR   )rT   rU   rW   rX   Zhttaur\   r1   r1   r2   
test_gehrda   s    zTestFlapackSimple.test_gehrdc                 C   s\  t ddgddgg}t ddgddgg}t dd	gd
dgg}d}dD ]
}||||||  }}}td|f\}	| r|d  d7  < d}|	|||\}
}}tt ||
t |
| ||  |	|||||d\}
}}tt | j|
t |
| j || dd |	|||dd\}
}}tt ||
t |
| || dd qJd S )NrG   rH   r   rJ   rK   rL   rN   rO   
         TfdFD)trsylr*   C)ZtranaZtranbdecimal)Zisgn)	r,   arrayr.   r&   isupperr   dot	conjugaterh   )rT   rU   bctransr0   rV   b1c1rj   xrP   r\   r1   r1   r2   
test_trsyll   s.    
""zTestFlapackSimple.test_trsylc           	      C   s  t g dg dg dg}dD ]}dD ]}||}| rN|d  d7  < td|f\}|||}|d	v r|d
v r|d}nd}t t t t |}t	||| q(|dv rt 
t |}nH|dv rt 
t jt |dd}n$|dv rt 
t jt |dd}t|| q(q d S )Nr^   r_   ra   ri   ZMm1OoIiFfEer   r   r*   )langeZFfEeZFfrI   rM   ZMmZ1Oor   ZaxisZIirG   )r,   ro   r.   rp   r&   sqrtsumZsquareabsr   maxr   )	rT   rU   r0   Znorm_strrV   r{   valuerm   refr1   r1   r2   
test_lange   s2    


zTestFlapackSimple.test_langeN)__name__
__module____qualname__r]   rd   ry   r   r1   r1   r1   r2   rF   J   s   rF   c                   @   s   e Zd Zdd Zdd ZdS )
TestLapackc                 C   s   t tdr
d S NZempty_module)hasattrr5   rT   r1   r1   r2   test_flapack   s    
zTestLapack.test_flapackc                 C   s   t tdr
d S r   )r   r6   r   r1   r1   r2   test_clapack   s    
zTestLapack.test_clapackN)r   r   r   r   r   r1   r1   r1   r2   r      s   r   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestLeastSquaresSolversc                 C   sz  t d ttD ]\}}d}d}d}t|||}t||}td|d\}}	t|	|||}
||||
d\}}}t|dk |||d	| |
d
\}}}t|dk qtD ]}t	j
ddgddgddgg|d}t	j
g d|d}td||f\}}}|j\}}t|jdkr|jd }nd}t||||}
||||
d\}}}t|d d t	j
ddg|ddt	|j d ||\}}}}t|| qtD ]}t	j
ddgddgddgg|d}t	j
g d|d}td||f\}}}|j\}}t|jdkr|jd }nd}t||||}
||||
d\}}}t|d d t	j
dd g|ddt	|j d ||\}}}}t|| qd S )!N  re      rG   )gels
gels_lworkr0   lworkr   ZTTCCru   r         ?       @      @      @      @       @      0@g      1@g      4@)r   r   geqrfrH   rn   祪,-@   rtol      ?      @      @      ?      @            @              @ffffff?r   y      1@       @y      4@      R ?\j,? W?)r   	enumerateDTYPESr   r.   r&   r!   r   REAL_DTYPESr,   ro   r/   rS   r   finfoepsr   r+   )rT   indr0   mnnrhsrV   rv   ZglsZglslwr   r9   r\   r   r   r   Zlqrrx   Z	lqr_truthr1   r1   r2   	test_gels   s    





z!TestLeastSquaresSolvers.test_gelsc              
   C   s8  t D ]
}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
krr|jd }nd}||||d\}	}
}tt|	}|
}|||||ddd\}}}}t|d d tjddg|ddt	|j
 d t|tjddg|ddt	|j
 d qtD ]}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
kr|jd }nd}||||d\}	}}
}tt|	}t|}|
}||||||ddd\}}}}t|d d tjddg|ddt	|j
 d t|tjddg|ddt	|j
 d qd S )Nr   r   r   r   r   r   r   r   )gelsdgelsd_lworkrH   rG   rn   Fr   r   r   r   YN))1)@*@.?r   r   r   r   r   r   r   r   U.*@_Y@r   r,   ro   r&   r/   rS   intrealr   r   r   r+   )rT   r0   rV   rv   r   r   r   r   r   workiworkr\   r   Z
iwork_sizerx   srankZrworkZ
rwork_sizer1   r1   r2   
test_gelsd   s    








z"TestLeastSquaresSolvers.test_gelsdc                 C   s$  t D ]}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
krr|jd }nd}||||d\}	}
tt|	}|||d|dd\}}}}}	}
t|d d tjddg|ddt	|j
 d t|tjddg|ddt	|j
 d qtD ]
}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
kr|jd }nd}||||d\}	}
tt|	}|||d|dd\}}}}}	}
t|d d tjddg|ddt	|j
 d t|tjddg|ddt	|j
 d qd S )Nr   r   r   r   r   r   r   r   )gelssgelss_lworkrH   rG   rn   Fr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )rT   r0   rV   rv   r   r   r   r   r   r   r\   r   vrx   r   r   r1   r1   r2   
test_gelss9  s    







z"TestLeastSquaresSolvers.test_gelssc              	   C   s0  t D ]}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
krr|jd }nd}||||dt|j \}	}
tt	|	}tj
|jd dftjd}||||t|j|dd\}}}}}
t|d d tjddg|ddt|j d qtD ]}tjddgddgddgg|d}tjg d|d}td	||f\}}|j\}}t|jd
kr|jd }nd}||||dt|j \}	}
tt	|	}tj
|jd dftjd}||||t|j|dd\}}}}}
t|d d tjddg|ddt|j d qd S )Nr   r   r   r   r   r   r   r   )gelsyr   rH   rG   re   Frn   r   r   r   r   r   r   r   r   r   r   r   r   )r   r,   ro   r&   r/   rS   r   r   r   r   r   Zint32r   r+   )rT   r0   rV   rv   r   Zgelsy_lworkr   r   r   r   r\   r   Zjptvr   rx   jr   r1   r1   r2   
test_gelsyr  sr    





z"TestLeastSquaresSolvers.test_gelsyN)r   r   r   r   r   r   r   r1   r1   r1   r2   r      s   D<9r   r0   r/   )rI   rJ   )rK   rH      r   c                 C   s2   t d| d}|\}}|||d\}}t|d d S )Ngeqrf_lworkr   r   r   r   r&   r   )r0   r/   r   r   r   r   r\   r1   r1   r2   test_geqrf_lwork  s    r   c                   @   s   e Zd Zdd ZdS )TestRegressionc           
      C   s   t D ]}tjd|d}tdg|g\}tt||dd ||\}}}}|tv rtdg|g\}tt||dd  |dd ||dd  |dd q|tv rtd	g|g\}	tt|	|dd  |dd |	|dd  |dd qd S )
N)i,  rH   r   gerqfrH   r   orgrqrG   ungrq)r   r,   r   r&   assert_raises	Exceptionr   r+   )
rT   r0   rU   r   Zrqrc   r   r\   r   r   r1   r1   r2   test_ticket_1645  s    zTestRegression.test_ticket_1645N)r   r   r   r   r1   r1   r1   r2   r     s   r   c                   @   s   e Zd Zdd ZdS )	TestDpotrc           
      C   s   dD ]}dD ]}t jd t jjdd}||j}td|f\}}||||d\}}|||d }	|rtt |	t t	| qtt 
|	t 
t	| qqd S )N)TF*   )rI   rI   )size)potrfZpotri)cleanr   )r,   r-   r   normalrq   rh   r&   r   r   r   r   )
rT   lowerr   rx   rU   ZdpotrfZdpotrirt   r\   Zdptr1   r1   r2   test_gh_2691  s    zTestDpotr.test_gh_2691N)r   r   r   r   r1   r1   r1   r2   r     s   r   c                   @   s   e Zd Zdd ZdS )
TestDlasd4c              
   C   sl  t g d}t g d}t t t |dd t dt|d ff|d d t jf f}t|ddddd}t|}t 	|d d d |d |t
|  gf}t 	|d d d df}td	|f}g }	td|D ]4}
||
||}|	|d  t|d
 dkd|
  qt |	d d d }	tt t |	 df t||	dt t jj dt t jj d d S )N)r         @r   r   )g(\@g@g333333皙r   rn   rG   F)full_matrices
compute_uvoverwrite_aZcheck_finiter   lasd4rI   zcLAPACK root finding dlasd4 failed to find                                     the singular value %izThere are NaN rootsd   atolr   )r,   ro   hstackZvstackdiagr   rS   Znewaxisr   concatenater   r&   rangerB   r   anyisnanr   r   float64r   )rT   ZsigmasZm_vecMZSMZit_lenZsgmZmvcr   rootsiresr1   r1   r2   test_sing_val_update  s4    
*zTestDlasd4.test_sing_val_updateN)r   r   r   r   r1   r1   r1   r2   r     s   r   c                   @   s   e Zd Zejdedd Zejddd eD ejddd	gejd
ddgdd Zejdg dg dg dgdd Z	dd Z
ejdddgdd ZdS )	TestTbtrsr0   c                 C   s2  |t v rptjg dg dg|d}tjddgddgdd	gd
dgg|d}tjddgddgddgddgg|d}n|tv rtjg dg dg dg|d}tjddgddgddgddgg|d}tjddgd d!gd"d#gd$d%gg|d}ntd&| d'td(|d}|||d)d*\}}t|d+ t||d+d,d- d.S )/zTest real (f07vef) and complex (f07vsf) examples from NAG

        Examples available from:
        * https://www.nag.com/numeric/fl/nagdoc_latest/html/f07/f07vef.html
        * https://www.nag.com/numeric/fl/nagdoc_latest/html/f07/f07vsf.html

        )p=
ףgQ@gHzG@g{Gz?)g      gq=
ףp@gHzGr   r   gp=
ף0r   g(\+gףp=
0g333333*@g(\gHzG,gQ#rJ   rG   rn   rI   rH   r   )y
ףp=
Q@y{Gz@GzyQ?HzGy)\(??)yQQ@yq=
ףpGz@yףp=
?{Gzr   )yQ?q=
ףp@y)\(zGr   r   yQ!
ףp=
yףp=
8Gzyp=
#/)\h7y\(LHzG @yQHz6@yףp=
3@(\=y{Gz-333333yQ+3@GzT5@y               @y      ?      @y      ?      y             yt&m=#yi6@Ug$B@y[a^C?b->y-@ji& *!z	Datatype z not understood.tbtrsLabrs   uplor   h㈵>r   r   N)r   r,   ro   r+   
ValueErrorr&   r   r   )rT   r0   r   rs   Zx_outr   rx   r\   r1   r1   r2   test_nag_example_f07vef_f07vsf  s\    	






z(TestTbtrs.test_nag_example_f07vef_f07vsfzdtype,transc                 C   s.   g | ]&}d D ]}|dkr |t v s||fqqS ))Nrh   rk   rk   )r   ).0r0   ru   r1   r1   r2   
<listcomp>-  s   
zTestTbtrs.<listcomp>r   Ur   r   r  c                    sz  t d d\}}td d}|dk}|| }	||	 }
t|	|
 d d}fdd	|D } fd
d	|D }|dkrtj d||	< tj||dd}t|d f }t|D ].\}}|	|||t
|dt| f< qt|f }||||||d\}}t|d |dkr.t|| |dd nH|dkrNt|j| |dd n(|dkrnt|j| |dd ntdd S )Ni  )rJ   rI   rH   r   r   r  rG   rn   c                    s   g | ]} t | qS r1   )r   r  rx   r   r1   r2   r  A      z2TestTbtrs.test_random_matrices.<locals>.<listcomp>c                    s   g | ]}t |f qS r1   )r3   )r  widthr   r1   r2   r  B  s   Zdia)formatr   )r   rs   r   ru   r   r  g-C6
?r   rh   rk   zInvalid trans argument)r   r&   r   r,   r   spsZdiagsr   r   Zdiagonalr   minr3   r   r   rh   Hr  )rT   r0   ru   r   r   r   kdr   Zis_upperZkuklZband_offsetsZband_widthsZbandsrU   r   rowkrs   rx   r\   r1   )r0   r   r2   test_random_matrices,  s6    

(



zTestTbtrs.test_random_matriceszuplo,trans,diag)r  r  Invalid)r  r  r  )r  r  r  c                 C   s:   t dtjd}tdd}tdd}tt|||||| dS )z?Test if invalid values of uplo, trans and diag raise exceptionsr   r   rJ   rH   N)r&   r,   r   r   r   r   )rT   r   ru   r   r   r   rs   r1   r1   r2   &test_invalid_argument_raises_exception_  s    

z0TestTbtrs.test_invalid_argument_raises_exceptionc                 C   sP   t jdtd}t jdtd}tdtd}d|d< |||dd\}}t|d d	S )
aH  Test if a matrix with a zero diagonal element is singular

        If the i-th diagonal of A is zero, ?tbtrs should return `i` in `info`
        indicating the provided matrix is singular.

        Note that ?tbtrs requires the matrix A to be stored in banded form.
        In this form the diagonal corresponds to the last row.r   r   rJ   r   r   )rn   rI   r  r   N)r,   r   floatr&   r   )rT   r   rs   r   r9   r\   r1   r1   r2   test_zero_element_in_diagonall  s    z'TestTbtrs.test_zero_element_in_diagonalzldab,n,ldb,nrhs)rK   rK   r   rK   )rK   rK   rI   rK   c                 C   sB   t j||ftd}t j||ftd}tdtd}tt||| dS )z2Test ?tbtrs fails correctly if shapes are invalid.r   r   Nr,   r   r  r&   r   r   )rT   Zldabr   Zldbr   r   rs   r   r1   r1   r2   test_invalid_matrix_shapes|  s    z$TestTbtrs.test_invalid_matrix_shapesN)r   r   r   r;   markparametrizer   r  r  r  r  r  r1   r1   r1   r2   r     s.   
--
	r   c                  C   s   dD ]} t d| d}td| }td| }t|r>|d9 }|||\}}}t|d t|d t|rt|d	 tt|t tt|t qt|d
 qd S )Nri   lartgr   rI   rJ   r*   333333?r   y       皙?)	r&   r,   ro   iscomplexobjr   r   
isinstancecomplexr  )r0   r  rX   gcsZsnrr1   r1   r2   
test_lartg  s    




r'  c            
      C   s  dD ]} d}d}t dd| }t dd| }dt | jd   }| dv r^td	| d
}d}n td	| d
}|d9 }|d9 }d}t|||||g dg dg|d t|||||ddg ddd||gg|d t|||||dddg d||ddgg|d t|||||ddddg d||ddgg|d t|||||ddddg dd|d|gg|d t|||||dddddd	g d||d|gg|d t|||||ddddg dd|d|gg|d |||||ddd\}}	t||u  t|	|u  t|g d|d t|	g d|d qd S )Nri   r  r   rJ   rI   re   rG   fdrotr   y             r*   y              @)rK   rK   rK   rK   )r   r   r   r   r   rH   r
  )rK   rK   rI   rI   r   )offxoffy)rI   rI   rK   rK   )incxr,  r   )rK   rI   rK   rI   )r+  incyr   )r+  r-  r,  r.  r   )rI   rI   rK   rI   r   )r-  r.  r   )Zoverwrite_xZoverwrite_y)r,   fullr   	precisionr'   r&   r   r   )
r0   rt   r   ur   r   r)  rX   rU   rs   r1   r1   r2   test_rot  sV    

r2  c               	   C   s  t jd t jd} | j| } t jddt jd  }|j |}dD ]b}tddg|d\}}|dv r| }n|  }||jd	 d
 |d |dd d	f \}}}t 	|d d d	f }	|d |	d	< ||	d
< t 	|d
d d	f }
d|
d	< ||
d
d < ||
|
 |d
d d d f t |jd
 |d
d d d f< ||
||d d d
d f t |jd	 dd|d d d
d f< t|d d d	f |	dd t|d	d d f |	dd qTd S )Nr   )rJ   rJ   r*   ri   larfglarfr   ZFDr   rG   rG   r   rH   rz   r   Rsider  r*  )r,   r-   r   rh   rq   conjr&   copyr/   r   rr   r   r   )Za0Za0jr0   r3  r4  rU   alpharx   rc   expectedr   r1   r1   r2   test_larfg_larf  s*    

,>>r=  c                  C   s>   t dtjdd} d}t| ||ddd}|dks:|dks:J d S )	NZgesdd_lwork	preferredr0   Zilp64iA%  T)r   r   i`DiD)r&   r,   float32r!   )Zsgesdd_lworkr   r   r1   r1   r2    test_sgesdd_lwork_bug_workaround  s    rA  c                   @   sF   e Zd Zejdedd Zejdeejdddd ZdS )		TestSytrdr0   c                 C   s*   t jd|d}td|f}tt|| d S )Nrz   r   sytrdr,   r   r&   r   r  )rT   r0   ArC  r1   r1   r2   test_sytrd_with_zero_dim_array  s    z(TestSytrd.test_sytrd_with_zero_dim_arrayr   rG   rI   c                 C   s  t j||f|d}td|f\}}t jd||d  d d |d|t |< ||\}}t|d ||d|d\}}	}
}}t|d t||dt |j dd	 t|	t 	| t|
d
 t|d
 |||d\}}	}
}}t|d t j
||d}t |jd }|	|||f< t |jd d }|
||d |f< |
|||d f< t j|||d}t|d D ]h}t j||d}|d ||d f |d |< d||< t j|||d|| t ||  }t ||}q^t |d}|j| ||< t |jt ||}t||dt |j dd	 d S )Nr   )rC  sytrd_lworkrG   rH   r   r   r   rK   r   r           r   rn   )r,   r   r&   arangetriu_indices_fromr   r   r   r   r   r   r/   r
   r   outerrq   r   rh   )rT   r0   r   rE  rC  rH  r   r\   datarb   erc   rh   r  k2Qr   r   r  i_lowerZQTAQr1   r1   r2   
test_sytrd  s@    





$zTestSytrd.test_sytrdN)	r   r   r   r;   r  r  r   rF  rS  r1   r1   r1   r2   rB    s
   
rB  c                   @   sL   e Zd Zejdedd Zejdee	eejdddd Z
d	S )
	TestHetrdcomplex_dtypec                 C   s*   t jd|d}td|f}tt|| d S )Nrz   r   hetrdrD  )rT   rU  rE  rV  r1   r1   r2   test_hetrd_with_zero_dim_arrayT  s    z(TestHetrd.test_hetrd_with_zero_dim_arrayzreal_dtype,complex_dtyper   rG  c              	   C   s  t j||f|d}td|f\}}t jd||d  d d |ddt jd||d  d d |d  |t |< t |t t | dD ]}|||d\}}	t|	d qt	||}
||d|
d	\}}}}}	t|	d t
||d
t |j dd t
|t t | t
|d t
|d |||
d\}}}}}	t|	d t j||d}t j|jd td}||||f< t j|jd d td}|||d |f< ||||d f< t j|||d}t|d D ]n}t j||d}|d ||d f |d |< d||< t j|||d|| t |t |  }t ||}qt |d}t |j| ||< t t |jt ||}t
||dt |j dd d S )Nr   )rV  hetrd_lworkrG   rH   r*   )r   rG   r   r   rI  rK   r   r   rJ  r   rn   re   )r,   r   r&   rK  rL  Zfill_diagonalr   r   r   r!   r   r   r   r   r/   r   r
   r   rM  r9  rq   r   rh   )rT   r   Z
real_dtyperU  rE  rV  rX  rx   r9   r\   r   rN  rb   rO  rc   rh   r  rP  rQ  r   r   r  rR  ZQHAQr1   r1   r2   
test_hetrd[  sR    
"




zTestHetrd.test_hetrdN)r   r   r   r;   r  r  r+   rW  zipr   rZ  r1   r1   r1   r2   rT  S  s   
rT  c               
   C   sb  t tD ]R\} }td|d\}}t|dddd}| dk rtjg dg dg d	g d
g dg dg|d}tjg d|d}tjddg|d}n^tg dg dg dg dg dg dg}tdgdgdgdgdgdgg}tjd|d}tjg dg dg|d}||||||d\}	}	}	}
}	| dk r@tg d}ntg d}t|
|dd  qd S )!N)ZgglseZgglse_lworkr   rL   rJ   rH   )r   r   rW   )g=
ףp=g{Gzg(\ؿ      ?)zGgHzG?gףp=
ӿQ)ffffff@gQ?g?gffffffֿ)r]  g{Gz?Qg{Gz?)333333?g333333?ra  g
ףp=
)g{Gz{Gz?gzG      ?)g      r^  gGz?gHzGgzGg=
ףp=?rJ  )yQ?QyQQ?yQ{Gz @y=
ףp=?)y\(\￮Gz?y333333RQ?yQzG?yQQ?)yףp=
?q=
ףpݿy)\(?{Gz?y)\(?(\ſy(\333333?)yGz?RQ?yRQ?HzGy\(\
ףp=
׿y)\(?ɿ)y(\?RQ?y?{Gz?y(\ſq=
ףpݿyQ?q=
ףp?)yHzG?Qѿy?QyQ뱿Gz?yp=
ף?p=
ף?yRQ
ףp=
?yffffff?GzyzG GzyQ?ffffff
@yp=
ף)\(@y(\ @Q?)r   rJ        rJ  )rJ  r   rJ  rd  r   )^"L?\}?re  rf  )y!f?$_Kdy^gŵ翸F@y!f?}dy61ŵe_@rl   )r   r   r&   r!   r,   ro   r   r   )r   r0   func
func_lworkr   rU   rt   rb   rs   r9   resultr<  r1   r1   r2   
test_gglse  sL    



rj  c                  C   s   t d ttt D ]\} }d}| dk rXtd|d}td|d\}}t|||}n:td|d}td|d\}}t||t||d	  |}|| j d
 d
t	j
||d  }t|d}t||}|||dd\}	}
}||	|
|dd\}}ttd| t	jj|dd | dk  qd S )Nr   re   rJ   sytrf_lworkr   )ZsyconsytrfZhetrf_lwork)ZheconZhetrfr*   rH   rG   )r   r   )rU   ipivanormr   rW   )r   r   r   r+   r&   r   r.   r9  rh   r,   r
   r   r!   r   r   linalgcond)r   r0   r   rh  ZfunconZfunctrfrE  rn  r   ldurm  r9   rcondr1   r1   r2   test_sycon_hecon  s     $

rt  c                  C   s   t d ttD ]\} }d}td|d\}}}}t|||}||j d }t|||}||j d dtj||d  }|||\}	}
}t	|dk ||\}}t	|dk |||\}}t	|dk ||\}}
}t	|dk t
||	dd qd S )	Nr   re   )r   sygstsyevdsygvdr   rH   r   giUMu?r   )r   r   r   r&   r   r.   rh   r,   r
   r   r   )r   r0   r   r   ru  rv  rw  rE  Beig_gvdr9   r\   rs   rU   eigr1   r1   r2   
test_sygst  s&     r{  c                  C   s,  t d ttD ]\} }d}td|d\}}}}t|||dt|||  }|| j d }t|||dt|||  }|| j d dtj	||d  }|||\}	}
}t
|dk ||\}}t
|dk |||\}}t
|dk ||\}}
}t
|dk t||	dd	 qd S )
Nr   re   )r   hegstheevdhegvdr   r*   rH   r   -C6?r   )r   r   r+   r&   r   r.   r9  rh   r,   r
   r   r   )r   r0   r   r   r|  r}  r~  rE  rx  ry  r9   r\   rs   rU   rz  r1   r1   r2   
test_hegst  s&    $$$r  c               	      sn  t d d\} }ttD ]N\}}td|d\}}t|| |}|dk r\tt| ||}n"tt| |t| |d  |}tt	||j
 |||d\}}	t|	dk t|d	d	d	| f tj| ||  f|df}
ttj| |d|d	d	| d	f ftj||d  fd
dt| D }ttj|}t|
|| t||ddt|dj dd qd	S )z
    This test performs an RZ decomposition in which an m x n upper trapezoidal
    array M (m <= n) is factorized as M = [R 0] * Z where R is upper triangular
    and Z is unitary.
    r   re      tzrzfZtzrzf_lworkr   rH   r*   r   r   Nc              
      sD   g | ]<} | |gd d f j |gd d f    qS Nrh   rq   r9  r	  ZIdVrc   r1   r2   r  H  r  ztest_tzrzf.<locals>.<listcomp>re   r   rJ  r   )r   r   r   r&   r!   r   r   r.   r   r   rh   r   r,   r   r   r
   r   r   rq   r   r   spacingr   )r   r   r   r0   r  tzrzf_lwr   rE  rzr\   r6  r   Zr1   r  r2   
test_tzrzf,  s*    
"0(r  c               	   C   s  t d ttD ]\} }d}| dkrVtt||t||d  t| |}d}n tt||t| |}d}td|d\}}}||\}}	t|d	|}
|d
||
}t|t	| |
| d	 dkrdndd |d
||
|d}t|t	|
 j |
| d	 dkrdndd |d|t|t|f< |d
||
|dd}t|t	|
 j |
| d	 dkrhdndd td||}|d
|||ddd}t|t	| |j
 j| d	 dkrdndd qdS )z
    Test for solving a linear system with the coefficient matrix is a
    triangular array stored in Full Packed (RFP) format.
    r   r   rG   r*   rk   rh   )trttftfttrtfsmr   rH   rn   r   rJ   rL   rl   ru   r   r  )ru   r   rI   r6  )ru   r   r8  N)r   r   r   r   r   r
   r.   r&   r   r   r9  rh   r,   rK  )r   r0   r   rE  ru   r  r  r  Afpr9   rx  solnZB2r1   r1   r2   	test_tfsmN  s>    *r  c               	      s  t d d\} }}ttD ]^\}}td|d\}}t|| |}|dk r~tt| ||}t|||}	td|d\}
}nPtt| |t| |d  |}t||t||d  |}	td|d\}
}t|||}|||d	\}}t	tj
| |d|d
d
| d
f ftj
||d  fddt| D }ttj|}|dk rVdnd}dt|dj }|
||	|d	\}}t|dk t|||	 t|	|dd |
||	||d\}}t|dk t|| j|	 t|	|dd |
||	d|d\}}t|dk t||	| t|	|dd |
||	d||d\}}t|dk t||	| j t|	|dd qd
S )a  
    This test performs a matrix multiplication with an arbitrary m x n matrix C
    and a unitary matrix Q without explicitly forming the array. The array data
    is encoded in the rectangular part of A which is obtained from ?TZRZF. Q
    size is inferred by m, n, side keywords.
    r   )re   r  r  r  r   rH   )ZormrzZormrz_lworkr*   )ZunmrzZunmrz_lworkr   Nc              
      sD   g | ]<} | |gd d f j |gd d f    qS r  r  r	  r  r1   r2   r    r  z$test_ormrz_unmrz.<locals>.<listcomp>rh   rk   re   r   r   rJ  r   r   r6  )r8  r   )r8  ru   r   )r   r   r   r&   r!   r   r   r.   r,   r   r
   r   r   rq   r  r   r   r   r   r9  rh   )ZqmqnZcnr   r0   r  r  Zlwork_rzrE  rk   Zorun_mrzZorun_mrz_lwZ	lwork_mrzr  r\   r   rQ  ru   tolZcqr1   r  r2   test_ormrz_unmrzw  sT    

"
(r  c               	   C   s   t d ttD ]\} }d}| dkrJt||t||d  |}d}nt|||}d}td|d\}}||\}}t|d	k ||d
d\}	}t|d	k |||dd\}
}t|d	k |||d
d\}}t|d	k t|d |d f|d}t|dd|d df |ddddf< ||d d dddf  t|d|d d|d f 	 j
7  < t|d |d f|d}t|ddd|d f |ddddf< |d|d ddf  t||d d|d df 	 j
7  < t||jddd t|
|	 j
jddd t|	|jddd t||	 j
jddd |||\}}t|d	k |||	d
d\}}t|d	k |||
|dd\}}t|d	k ||||d
d\}}t|d	k t|t| t|t| t|t| t|t| qdS )z
    Test conversion routines between the Rectengular Full Packed (RFP) format
    and Standard Triangular Array (TR)
    r   r   rG   r*   rk   rh   )r  r  r   r   r   r   r  )transrr   rH   Nrn   F)order)r   r   r   r   r.   r&   r   r   r   r9  rh   r   r   reshape)r   r0   r   A_fullr  r  r  ZA_tf_Ur\   ZA_tf_LZA_tf_U_TZA_tf_L_TZA_tf_U_mZA_tf_L_mA_tr_UA_tr_LZA_tr_U_TZA_tr_L_Tr1   r1   r2   test_tfttr_trttf  sV    ,F,Br  c                  C   st  t d ttD ]\\} }d}| dkrFt||t||d  |}nt|||}td|d\}}||\}}t|dk ||dd	\}}t|dk t|}	t||d  d
 |d}
t	|j
|	 |
dd< t|}	t||d  d
 |d}t|j
|	 |dd< t||
 t|| |||\}}t|dk |||dd	\}}t|dk t|t	| t|t| qdS )r  r   r   rG   r*   )trttptpttrr   r   r   r  rH   N)r   r   r   r   r.   r&   r   r   r   r   rh   r   r   r   )r   r0   r   r  r  r  ZA_tp_Ur\   ZA_tp_LindsZA_tp_U_mZA_tp_L_mr  r  r1   r1   r2   test_tpttr_trttp  s2     

r  c                  C   s   t d ttD ]\} }d}| dkr^t||t||d  |}|| j |t|  }n&t|||}||j |t|  }td|d\}}}||\}}|||\}	}t	|dk |||	\}
}t
|}t|
| qdS )	zk
    Test Cholesky factorization of a positive definite Rectengular Full
    Packed (RFP) format array
    r   r   rG   r*   )pftrfr  r  r   r   N)r   r   r   r   r.   r9  rh   r
   r&   r   r   r   )r   r0   r   rE  r  r  r  r  r\   Z	Achol_rfpZA_chol_rr9   ZAcholr1   r1   r2   
test_pftrf  s"    r  c                  C   s
  t d ttD ]\} }d}| dkr^t||t||d  |}|| j |t|  }n&t|||}||j |t|  }td|d\}}}}||\}}	|||\}
}	|||
\}}	t	|	dk |||\}}t
|}t|t|| d dkrd	nd
d qdS )z
    Test Cholesky factorization of a positive definite Rectengular Full
    Packed (RFP) format array to find its inverse
    r   r   rG   r*   )pftrir  r  r  r   r   rH   rJ   rL   rl   N)r   r   r   r   r.   r9  rh   r
   r&   r   r   r   r   )r   r0   r   rE  r  r  r  r  r  r\   
A_chol_rfpZ	A_inv_rfpZA_inv_rr9   ZAinvr1   r1   r2   
test_pftri/  s(    
r  c                  C   s`  t d ttD ]H\} }d}| dkr`t||t||d  |}|| j |t|  }n&t|||}||j |t|  }t|df|d}t|d df|d}t|d df|d}t	d|d\}}}	}
|	|\}}|||\}}||||\}}t
|d	k tt|||| ||||\}}t
|d	k tt|||| d d	krRd
ndd qdS )z
    Test Cholesky factorization of a positive definite Rectengular Full
    Packed (RFP) format array and solve a linear system
    r   r   rG   r*   rI   r   rH   )pftrsr  r  r  r   rJ   rL   rl   N)r   r   r   r   r.   r9  rh   r
   r   r&   r   r   r   r   r   )r   r0   r   rE  rx  ZBf1ZBf2r  r  r  r  r  r\   r  r  r1   r1   r2   
test_pftrsO  s0    r  c                  C   s4  t d ttD ]\} }d}| dkr`t||t||d  |}|| j |t|  }n&t|||}||j |t|  }| dk rdnd}tdd	| d
f|d\}}}||\}}	t	j
|d|}
||dd|
d|}|||\}}	t|t|
|
 j d|  | d dkr&dndd qdS )zT
    Test for performing a symmetric rank-k operation for matrix in RFP format.
    r   r   rG   r*   rH   r   hr  r  Zfrkr   rn   r   rJ   rL   rl   N)r   r   r   r   r.   r9  rh   r
   r&   r,   r-   r   r   rq   )r   r0   r   rE  prefixr  r  Zshfrkr  r9   rk   ZAfp_outZA_outr1   r1   r2   test_sfrk_hfrkt  s&     r  c                  C   s  t d ttD ]\} }d}| dkr`tdd||ftdd||fd  |}|| j }n,tdd||f|}||j |t|  }dt	|dj
 }td	|d
\}}}t||dd}t|ddd\}	}
}t||dd}||d|d\}}}|||dd\}}}tt|dt|	|ddf d|dd t|ddd\}}
}||dd\}}}|||dd\}}}tt|dt||ddf d|dd qdS )zt
    Test for going back and forth between the returned format of he/sytrf to
    L and D factors/permutations.
    r   re   rG   i   r*   r   r   )syconvrl  rk  r   rY  F)r   Z	hermitianrI  rn   NrJ  r   r   )r   r   r   r   r.   r9  rh   r
   r,   r  r   r&   r!   r   r   r   r   )r   r0   r   rE  r  r  ZtrfZ	trf_lworklwr   Dpermrr  rm  r\   rU   rO  r  r1   r1   r2   test_syconv  s4    (r  c                   @   s    e Zd ZdZdd Zdd ZdS )TestBlockedQRzd
    Tests for the blocked QR factorization, namely through geqrt, gemqrt, tpqrt
    and tpmqr.
    c              
   C   s>  t d ttD ]&\}}d}|dkrFt||t||d  |}nt|||}dt|dj }td|d\}}|||\}}	}
|
d	ksJ t	|d
tj
||d }tj
||d||	 |j   }t|}t|j | tj
||d|dd t|| ||dd |dkr@t||t||d  |}d}nt|||}d}dD ]}d|fD ]}|||	|||d\}}
|
d	ksJ ||kr|j }n|}|dkr|| }n|| }t|||dd ||fdkrd|||	|\}}
|
d	ksJ t|| qdqXtt|||	|dd tt|||	|dd qd S )Nr   r   rG   r*   r   r   )geqrtgemqrtr   r   rn   rJ  r   rk   rh   r   r6  r  r8  ru   r   r   r  rE  r7  r  )r   r   r   r   r.   r,   r  r   r&   r   r
   rh   r9  r   r   r   r   r   )rT   r   r0   r   rE  r  r  r  rU   tr\   r   rQ  r6  rk   	transposer8  ru   rt   qZqC	c_defaultr1   r1   r2   test_geqrt_gemqrt  sN      




zTestBlockedQR.test_geqrt_gemqrtc                  C   s  t d ttD ]\}}d}|dkrdt||t||d  |}t||t||d  |}n t|||}t|||}dt|dj }td|d\}}d	|d
 |fD ]}	||	|||\}
}}}|d	ksJ t	t
|
dt
|d t	t
||	| d t
||	| d  t||	| t||	|  }}ttj||d|f}tjd
| |d|| |j   }tt|
t|
f}t|j | tjd
| |d|dd t|| tt||f|dd |dkr2t||t||d  |}t||t||d  |}d}n$t|||}t|||}d}dD ]}d|fD ]}||	||||||d\}}}|d	ksJ ||kr|j }n|}|dkrtj||fd	d}tj||fd	d}|| }n,tj||fdd}tj||fdd}|| }t|||dd ||fdkrh||	||||\}}}|d	ksXJ t	|| t	|| qhqZtt||	||||dd tt||	||||dd qqd S )Nr   r   rG   r*   r   r   )tpqrttpmqrtr   r   rH   rn   rJ  r   rk   rh   r  r  r  r   r|   r  rE  r7  r  )r   r   r   r   r.   r,   r  r   r&   r   r   r   r   r
   rh   r9  r   r   r   r   ) rT   r   r0   r   rE  rx  r  r  r  lrU   rs   r  r\   ZB_pentZb_pentr   rQ  r6  rk   r  r  r8  ru   rt   rb   r  cdZCDZqCDr  Z	d_defaultr1   r1   r2   test_tpqrt_tpmqrt  sp     *"$





zTestBlockedQR.test_tpqrt_tpmqrtN)r   r   r   r:   r  r  r1   r1   r1   r2   r    s   >r  c                  C   s  t d ttD ]\} }d}d}td|d}| dkrrt||| |dt||| |  }|| j }nt||| |}||j }||\}}}}	t|}
d|
|| d || d f< t	|	d d	t
t
jj }d	t
t
jj }| d
v r|n|}t||d  d d |d f |
 j|
 d|d ||dd\}}}}	t|}d||| d || d f< t	|	d d	t
t
jj }d	t
t
jj }| d
v r|n|}t||d  d d |d f || j d|d qd S )Nr   re   rH   pstrfr   rG   r*   rJ    r   rH   r  rY  r   r   r   r&   r   r.   r9  rh   r   r   r,   r   r@  r   r   r   r   )r   r0   r   r&  r  rE  rt   pivr_cr\   r  single_atoldouble_atolr   r   r1   r1   r2   
test_pstrfI  s4    ,

2
r  c                  C   s  t d ttD ]\} }d}d}td|d}| dkrrt||| |dt||| |  }|| j }nt||| |}||j }||\}}}}	t|}
d|
|| d || d f< t	|	d d	t
t
jj }d	t
t
jj }| d
v r|n|}t||d  d d |d f |
 j|
 d|d ||dd\}}}}	t|}d||| d || d f< t	|	d d	t
t
jj }d	t
t
jj }| d
v r|n|}t||d  d d |d f || j d|d qd S )Nr   re   rH   pstf2r   rG   r*   rJ  r  r  r  rY  r  )r   r0   r   r&  r  rE  rt   r  r  r\   r  r  r  r   r   r1   r1   r2   
test_pstf2q  s4    ,

2
r  c                  C   sZ  t g dg dg dg dg} t g dg dg dg}ttD ]\}}|dk rt g d	g d
g dg dg}||}nNt jg dg dg dg|d}|t g dg dg dgd 7 }||}td|d}||\}}}}	}
}|dk r*t| ||d d d f | | ddd qFt|||d d d f | | ddd qFd S )N)g      ?r   g1w-!?gd`TRۿ)r   gsrd  rd  )gs?rd  g2%䃮g,eX)rd  gsFg%ug??)y/nҿ&?yDioɴ?Af?y o_[ Acп)ysֿAfҿyPkw?JY8y5;NёCl?)yYڊ?1*?y=yXѿ@a+?yh oſFxrH   )g   ЈBg   tBgffffff @g   ٓ )      @gg#fDgffffff)gHzG?gQg'Vgp=
ף)g(\r`  gS7нr   )gq=
ףpg   Ag(\)g333333g   Bg333333ÿ)gZ9=gQgֽr   )gffffff@g   tޅBr   )g(\g   Zgq=
ףp?)gEop=gQ?gZEqҽr*   geequr   r  r  )r,   ro   r   r   r.   r&   r   )desired_realdesired_cplxr   r0   rE  r  r&  rt   ZrowcndZcolcndamaxr\   r1   r1   r2   
test_geequ  sN    






  r  c            
         s   t g d} ttD ]\}}t jd|d}||dk r:dnd t j fddtd	d
D |d}|t t |7 }td|d}||\}}}}	t	t 
|t|  qd S )N)
r   r   r   r   r   r   rn   rn   r   r   re   r   rH   r   r*   c                    s   g | ]} d |  qS )r   r1   r	  r;  r1   r2   r    r  ztest_syequb.<locals>.<listcomp>rK   syequb)r,   ro   r   r   r
   r   Zrot90r   r&   r   log2r.   r   )
Zdesired_log2sr   r0   rE  rb   r  r   scondr  r\   r1   r  r2   test_syequb  s    "r  Tz.Failing on some OpenBLAS version, see gh-12276)reasonc               	   C   s   t dgd dgd  t jt dddd  } t| \}}}}t|d tt |d	d
gd d	g dgd   t dt t 	dd d } d| d< d| d< tj
| t jdd\}}}}t|d tt |g d d S )NrH   rK   i  rO   rG   )r  r*   r   rJ  rd  r  rL                   i   rK   rK   y              0@)rK   r   rY  )r   rn   rn   r   r   r  r   rn   rn   r   r   )r,   r   r   r   Zzheequbr   r   r  r   rK  Zcheequbr.   	complex64)rE  r   r  r  r\   r1   r1   r2   test_heequb  s    2
( 
r  c                  C   s<  t jd d} t j| }t j| t j| d  }ttD ]\}}|dk r|t j| | }||}|| }||}n<t j| | t j| | d  }||}|| }||}td|d}td|d}||dd	\}	}
}}||	||
|dd
\}}|dk rt|||| dd q@t|||| dd q@d S )Nr   re   r*   rH   getc2r   gesc2r   r   )Zoverwrite_rhsrJ   rl   )	r,   r-   r   r   r   r   r.   r&   r   )r   r  r  r   r0   rE  rs   r  r  Zlurm  Zjpivr\   rx   rP   r1   r1   r2   test_getc2_gesc2  s2    
 




r  r   )rL   rK   r  jobarL   joburJ   jobvjobrrG   jobpc              
   C   s  t d | \}}	dt|j }
t| |}td|d}|dk }|dk }|dkoT||	k}t|}|dkor| or| }|dko|o| o|}|dko|o| o|}|rd}n|s|rd}nd	}|dkr|dkrtt||||||||	 n0||||||||d
\}}}}}}t	|| |s|d	 |d  |d|	  }t
|t|dd|
d |dkrj|ddd|	f }|r|rt
|t| | j ||
d |rt
| j| t|	|
d |rt
| j| t|	|
d t	|d	 tj| t	|d t| t	|d d	 dS )a  Test the lapack routine ?gejsv.

    This function tests that a singular value decomposition can be performed
    on the random M-by-N matrix A. The test performs the SVD using ?gejsv
    then performs the following checks:

    * ?gejsv exist successfully (info == 0)
    * The returned singular values are correct
    * `A` can be reconstructed from `u`, `SIGMA`, `v`
    * Ensure that u.T @ u is the identity matrix
    * Ensure that v.T @ v is the identity matrix
    * The reported matrix rank
    * The reported number of singular values
    * If denormalized floats are required

    Notes
    -----
    joba specifies several choices effecting the calculation's accuracy
    Although all arguments are tested, the tests only check that the correct
    solution is returned - NOT that the prescribed actions are performed
    internally.

    jobt is, as of v3.9.0, still experimental and removed to cut down number of
    test cases. However keyword itself is tested externally.
    r   r   gejsvr   rH   rG   r   r   r   )r  r  r  r  jobtr  NF)r   r*  )r   r,   r   r   r3   r&   r!  r   r   r   r   r   r   r9  rh   identityrp  Zmatrix_rankZcount_nonzero)r   r0   r  r  r  r  r  r  r   r   r   rE  r  ZlsvecZrsvecZl2tranZ
is_complexZinvalid_real_jobvZinvalid_cplx_jobuZinvalid_cplx_jobvZexit_statussvar1  r   r   r   r\   sigmar1   r1   r2   test_gejsv_general  sT    !

	

"r  c                 C   sX  t d| d}|d\}}}}}}t|d t|jd t|jd t|tjdg| d tjd| d}||\}}}}}}t|d t|jd t|jd t|tjdg| d tjd| d}||\}}}}}}t|d t|jd t|jd t|tjg | d ttdd	d		| }t
||j }|d
}	||}
t||	 dS )z*Test edge arguments return expected statusr  r   r   r   rG   rG   rG   r5  r   re   rE  N)r&   r   r/   r,   ro   r   sinrK  r  r.   Zasfortranarrayrh   r:  r   )r0   r  r  r1  r   r   r   r\   rE  ZAcr9   r1   r1   r2   test_gejsv_edge_argumentst  s.    



r  kwargsrO   r  c                 C   s2   t jdtd}tdtd}tt||fi |  dS )z-Test invalid job arguments raise an Exception)rH   rH   r   r  Nr  )r  rE  r  r1   r1   r2    test_gejsv_invalid_job_arguments  s    
r  zA,sva_expect,u_expect,v_expect)g)\(@gp=
ףgffffff?g
ףp=
)gQ?gQgGz?g(\)gQ޿gQgGz?gzGʿ)gQ?gQ?gHzG?g)\(?)ggq=
ףp@g333333r_  )ףp=
?g(\rb  g(\)g cZB#@gI.!v@g?ܵ?rc  )gC?g=yX5gc=yXga4?)gB`"?g:pΈҞgʡE?gn4@?)g[B>٬?g٬\m?gJ{/L?gOe?)gc]Fgꕲq׿g\m?fc]F)g؁sFڿgZB>?g0L
F%?gq=
ףp)g ?gR!u?guVſg&Sٿ)gǘ?gV-g	^)p?g()gFx$g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ?g_vO?)g}?5^Iؿg58EGr?gi o?g7[ Ac                 C   sT   d}t d| jd}|| \}}}}	}
}t|||d t|||d t|||d dS )z~
    This test implements the example found in the NAG manual, f08khf.
    An example was not found for the complex case.
    r  r  r   r*  N)r&   r0   r   )rE  Z
sva_expectZu_expectZv_expectr   r  r  r1  r   r   r   r\   r1   r1   r2   test_gejsv_NAG  s    r  c           !   	   C   s  t d d}dt| j }t|d f| d}t|f| d}t|d f| d}| | | g}t|t|d t|d }tj|}|| }	t	d| d\}
}|
|||\}}}}}}t
||d  t
||d  t
||d	  t|dt|d t|d	 }tj|| d}t|D ]f\}}|| d }|d d ||gf |d d ||gf< |d d |f  |d d |d f | 7  < q&d|d d  }}|d d ||gf |d d ||gf< t||| |d
 |	 }|||||||	\}}t
|	| t|||d
 | tv r&d}|j| }nd}| j| }||||||||d\}}t|||d
 tt$ |
|d d || W d    n1 s0    Y  tt$ |
||d d | W d    n1 s0    Y  tt$ |
|||d d  W d    n1 s0    Y  tt, |
|d |d d |d  W d    n1 sV0    Y  d|d< d|d< |
|||\}}}}}} tj||d  dkd||d   d S )Nr   re   r   rG   r   rn   gttrfgttrsr   rH   r*  rh   rk   r  z3?gttrf: _d[info-1] is {}, not the illegal value :0.)r   r,   r   r   r3   r:  r   r-   r   r&   r   r
   r   r   r   rh   r9  r   r  r   testingr   r  )!r0   r   r   durb   dldiag_cpyrE  rx   rs   r  r  _dl_d_dudu2rm  r\   r  r   r   r   r  Zb_cpyx_gttrsru   Zb_transZ__dlZ__dZ__duZ_du2Z_ipiv_infor1   r1   r2   test_gttrf_gttrs  sf    "$$0$


4
4
4
<
r  z1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g @rd  ffffff?r   )r   r_        ffffff@)333333@@r         )r_  r  r  r  )r  r  rM   gC>)rn   r	  rN   )rH   rI   rJ   rK   rK   g@gffffff@      g%@g@g	r  gffffff&g3@r  rK   rM   rI   r   r   )       @             @      ?            ?      ?      )?r  ffffff
@333333ӿ333333@ffffff
?)      ?             ?      ?       @      r  )r  r  r  r  )r  r  r  r  y ~:pffffff?)r  r  r  y333333@      y@@y333333@3333332@y333333yffffff-ffffff#@y      333333yfffff?@y333333"@y      𿚙?y      ffffff(@r  r  y      @      y      ?       @y      @      @r  y             r  r  y       @       c	                 C   s   t d| d | d f\}	}
|	||| \}}}}}}t|| t|| t||dd t|| |
||||||\}}t|| d S )Nr  r   r  r*  )r&   r   )r  rb   r   Zdu_expZd_expZdu2_expZipiv_exprs   rx   r  r  r  r  r  r  rm  r\   r  r1   r1   r2   0test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csf&  s    2


r  ))rI   rM   )rM   rI   r   c                 C   s2   t d| d}|\}}|||d\}}t|d d S )Ngeqrfp_lworkr   r   r   r   )r0   r/   r  r   r   r   r\   r1   r1   r2   test_geqrfp_lworke  s    r  zddtype,dtypec                 C   s`  t d dt|j }d}t|f| d }t|d f|}t|t|d tt|d }| | g}td|d}|||\}	}
}t	||d	  t	||d  t
|d	d
| dd t|
dtt| }t|	}t||| | j |d t|f|}|| }td|d}||	|
 |\}}t
|d	d| dd t|||d d S )Nr   r   re   rJ   rG   rn   pttrfr   r   zpttrf: info = z, should be 0)err_msgr*  pttrszpttrs: info = )r   r,   r   r   r3   r   r9  r:  r&   r   r   r   r   rr   rh   )ddtyper0   r   r   rb   rO  rE  r  r   r  _er\   r   r  rx   rs   r"  _xr1   r1   r2   test_pttrf_pttrsn  s*    (
r&  c                 C   s`   d}t d|d}t|f| d }t|d f|}tt||d d | tt|||d d  d S )Nre   r   r   rH   rG   rn   )r&   r3   r   r  )r#  r0   r   r   rb   rO  r1   r1   r2   *test_pttrf_pttrs_errors_incompatible_shape  s    r'  c           	      C   s   d}t d|d}t|f| d }t|d f|}d|d< d|d< |||\}}}t||d  dd||d   d t|f| }|||\}}}t|dkd	 d S )
Nre   r   r   rH   rG   r   z?pttrf: _d[info-1] is z, not the illegal value :0.z2?pttrf should fail with non-spd matrix, but didn't)r&   r3   r   r   )	r#  r0   r   r   rb   rO  r  r$  r\   r1   r1   r2   'test_pttrf_pttrs_errors_singular_nonSPD  s    r(  z%d, e, d_expect, e_expect, b, x_expect)rJ   re      r   rK   )r   r  r  rN   )rJ   rO   r      rG   )r  gK=Ur  rc  re   rH      A      g      @rn   r  )r*  )   .      )y      0@      0@y      2@      "      ?      )r*  rO   rG   rJ   )r  r  r1  y      P@      0@y      0      @y     @W@      O@y     N@     Py     S@      Ty     Q@     Ry      ,@      ;y     A@      .@y             r  c                 C   s   d}t d|d d}|| |\}}	}
t|||d t|	||d t d|d d}|||	 |\}}
t|||d |jtv r|||	|dd\}}
t|||d d S )	Nr  r   r   r   r*  r"  rG   rY  )r&   r   r9  r0   r+   )rb   rO  d_expectZe_expectrs   Zx_expectr   r   r  r$  r\   r"  r%  r1   r1   r2   test_pttrf_pttrs_NAG  s    
r3  c                 C   s  |dkrt ||f| }|tt|d|   }|| j d }t|d }t |f|d }t |d f|}t|t|d t|d }|| | j }	|}
nht |f|}t |d f|}|d }t|t|d t|d }	t|t|d t|d }
|||	|
fS )NrG   rJ   rH   rn   )r3   r,   r   r   r9  rh   r   )r0   realtyper   	compute_zZA_eigZvrrb   rO  ZtrirE  zr1   r1   r2   pteqr_get_d_e_A_z  s     """r7  zdtype,realtyper5  c                 C   s   t d dt| j }td| d}d}t| |||\}}}}	||||	|d\}
}}}t|dd| d	 ttt	|d t|
|d
 |rt|t
|j t||d
 t|t|
 t
|j ||d
 dS )a  
    Tests the ?pteqr lapack routine for all dtypes and compute_z parameters.
    It generates random SPD matrix diagonals d and e, and then confirms
    correct eigenvalues with scipy.linalg.eig. With applicable compute_z=2 it
    tests that z can reform A.
    r   r  pteqrr   re   rb   rO  r6  r5  r   zinfo = z, should be 0.r*  N)r   r,   r   r   r&   r7  r   r   sortr   r9  rh   r  r   )r0   r4  r5  r   r8  r   rb   rO  rE  r6  d_pteqre_pteqrz_pteqrr\   r1   r1   r2   
test_pteqr	  s    
"r>  c                 C   sZ   t d td| d}d}t| |||\}}}}||d |||d\}	}
}}|dksVJ d S )Nr   r8  r   re   rJ   r6  r5  r   r   r&   r7  r0   r4  r5  r8  r   rb   rO  rE  r6  r;  r<  r=  r\   r1   r1   r2   test_pteqr_error_non_spd)	  s    rB  c           	      C   s   t d td| d}d}t| |||\}}}}tt||d d |||d tt|||d d ||d |rtt||||d d |d d S )Nr   r8  r   re   rn   r?  )r   r&   r7  r   r  )	r0   r4  r5  r8  r   rb   rO  rE  r6  r1   r1   r2   "test_pteqr_raise_error_wrong_shape8	  s    rC  c                 C   sf   t d td| d}d}t| |||\}}}}d|d< d|d< |||||d\}	}
}}|dksbJ d S )Nr   r8  r   re   r   r?  r@  rA  r1   r1   r2   test_pteqr_error_singularG	  s    rD  zcompute_z,d,e,d_expect,z_expect)gp=
ף@r  gq=
ףp?r  )g\(\	@g
ףp=
g?)gŏ1w- @gR'?g/n?g&䃞ͪ?)g cZB>?gCl?g:pΈڿg??)gaTR'?gSۿg}гY?g%uο)g\mg٬\m?gAf?gL
F%u)gǘgŏ1w-!?g333333?gz6?c                 C   sx   d}t d|jd}t|t|d t|d }||||| d\}}	}
}t|||d tt|
t||d dS )	zb
    Implements real (f08jgf) example from NAG Manual Mark 26.
    Tests for correct outputs.
    r  r8  r   rG   rn   r9  r*  N)r&   r0   r,   r   r   r   )r5  rb   rO  r2  Zz_expectr   r8  r6  r  r$  Z_zr\   r1   r1   r2   test_pteqr_NAG_f08jgfV	  s    "rE  matrix_size)r   )rM   rL   rL   rL   c              
   C   s  t jd dt | j }dt | j }td| d}td| d}|\}}t||f| d}||\}	}
}t |	}||krt j||f| d}|	|d d d |f< |||
|dd }n"||	d d d |f |
|dd }t	|| ||d	 t	t 
|jd || j ||d
 t	|t ||d	 tt t |t tt |k t|dk t||f| dd }t|\}}||\}}}tt t |dk ot t |dk d S )Nr      r   geqrfpr   Zorgqr)rc   r   r   r   r  rn   )r,   r-   r   r   r   r&   r3   r   r   r   r
   r/   r9  rh   r   allr   rS   r   r   )r0   rF  r   r   rI  Zgqrr   r   rE  Zqr_Arc   r\   r&  Zqqrr  Z
A_negativeZr_rq_negZq_rq_negZrq_A_negZtau_negZinfo_negr1   r1   r2   test_geqrfpo	  s6    
"(rK  c                  C   s(   t g } td| jd}tt||  d S )NrI  r   )r,   ro   r&   r0   r   r   )ZA_emptyrI  r1   r1   r2   #test_geqrfp_errors_with_empty_array	  s    
rL  driver)ZevZevdZevrZevxpfxsyhec              
   C   s   d}| dkrt nt}t| | d |d d}t| | d |d d}z t||dd t||dd W n< ty } z$t| |  d|  W Y d }~n
d }~0 0 d S )	N  rO  _lworkr   r   rG   rY  $_lwork raised unexpected exception: r   r+   r&   r!   r   r;   ZfailrN  rM  r   r0   Zsc_dlwZdz_dlwrO  r1   r1   r2   test_standard_eigh_lworks	  s    rV  gvZgvxc              
   C   s   d}| dkrt nt}t| | d |d d}t| | d |d d}z t||dd t||dd W n< ty } z$t| |  d	|  W Y d }~n
d }~0 0 d S )
NrQ  rO  rR  r   r   rG   r   r  rS  rT  rU  r1   r1   r2   test_generalized_eigh_lworks	  s    rX  dtype_r   )rG   re   r   r  c                 C   sx   t d td|}|| }| tv r&dnd}|d }t|| d}t||||}|dkrX|n|f}tdd |D stJ d S )	Nr   r   orun	csd_lworkr   c                 S   s   g | ]}|d kqS r   r1   r	  r1   r1   r2   r  	  r  z*test_orcsd_uncsd_lwork.<locals>.<listcomp>)r   r   r   r&   r!   rJ  )rY  r   rW   r  rN  dlwr  lwvalr1   r1   r2   test_orcsd_uncsd_lwork	  s    
r_  c              
   C   s  d\}}}| t v rdnd}|dkr,t|nt|}t|d |d f| d\}}t||||}|dkrpd|inttddg|}	||d |d |f |d ||d f ||d d |f ||d |d f fi |	\
}
}}}}}}}}}|d	ksJ t||}t||}t	t	||t	|| || }t	||| }t	||| | }t	|| || }t	|| || | }t
j||f| d}| d
}t|D ]}||||f< qt|D ]}|||| || f< qt|D ]0}| ||| | || | | | | f< qt|D ]&}|||| | | || | f< qt|D ]}t
|| ||| || f< t
|| ||| | || | | f< t
||  ||| || | | | f< t
|| ||| | || f< q>|| | }t||ddt
| j d d S )N)rH  P      rZ  r[  csdr\  r   r   Zlrworkr   r   rJ  g     @r  )r   r"   Zrvsr#   r&   r!   dictr[  r   r  r,   r   r   cosr  r   r   r   )rY  r   rW   r  rN  Xdrvr]  r^  ZlwvalsZcs11Zcs12Zcs21Zcs22thetau1u2Zv1tZv2tr\   r  ZVHr&  Zn11Zn12Zn21Zn22Soner   ZXcr1   r1   r2   test_orcsd_uncsd	  sJ    
T

.$*,&rl  
trans_boolFfactr  r  c                  C   s  t d dt| j }td| d\}}d}t|d f| d}t|f| d}t|d f| d}	t|dt| t|	d }
t|df| d}|r| tv rd	qd
nd}|r|
 j	n|
| }|
 |
 |	
 |
 g}|dkr||||	ndgd \}}}}}}||||	||||||||d}|\
}}}}}}}}}}t|dkd| d t||d  t||d  t|	|d  t||d  t|||d tt|ddud|  t|jd |jd kd|jd |jd  t|jd |jd kd|jd |jd  dS )aS  
    These tests uses ?gtsvx to solve a random Ax=b system for each dtype.
    It tests that the outputs define an LU matrix, that inputs are unmodified,
    transposal options, incompatible shapes, singular matrices, and
    singular factorizations. It parametrizes DTYPES and the 'fact' value along
    with the fact related inputs.
    r   r   gtsvxr  r   re   rG   rn   rH   rh   rk   r  r  NrL   rn  ru   dlfdfdufr  rm  r   z?gtsvx info = z, should be zerorI   r*  __len__Trcond should be scalar but is z"ferr.shape is {} but should be {},z"berr.shape is {} but should be {},)r   r,   r   r   r&   r3   r   r   r9  rh   r:  r   r   r   r   r/   r  ) r0   rm  rn  r   rp  r  r   r   rb   r  rE  rx   ru   rs   Z
inputs_cpydlf_df_duf_du2f_ipiv_info_	gtsvx_outrr  rs  rt  du2frm  x_solnrs  ferrberrr\   r1   r1   r2   
test_gtsvx
  sB    "r  c                 C   s  t d td| d\}}d}t|d f| d}t|f| d}t|d f| d}t|dt| t|d }	t|df| d}
| tv rdnd	}|r|	 jn|	|
 }|d
kr||||nd gd \}}}}}}||||||||||||d}|\
}}}}}}}}}}|dkrZd|d< d|d< |||||}|\
}}}}}}}}}}|dksJ dnh|d
krd|d< d|d< d|d< |||||||||||d
}|\
}}}}}}}}}}|dksJ dd S )Nr   ro  r   re   rG   rn   rH   rh   rk   r  rL   rq  r  r   z&info should be > 0 for singular matrix)rn  rr  rs  rt  r  rm  )r   r&   r3   r,   r   r   r9  rh   )r0   rm  rn  rp  r  r   r   rb   r  rE  rx   ru   rs   rw  rx  ry  rz  r{  r|  r}  rr  rs  rt  r~  rm  r  rs  r  r  r\   r1   r1   r2   test_gtsvx_error_singularO
  s>    "

r  c                 C   s0  t d td| d\}}d}t|d f| d}t|f| d}t|d f| d}t|dt| t|d }	t|df| d}
| tv rdnd	}|r|	 jn|	|
 }|d
kr||||nd gd \}}}}}}|dkrtt	||d d ||||||||||d tt	|||d d |||||||||d tt	||||d d ||||||||d tt
|||||d d |||||||d ntt	||||||||d d ||||d tt	|||||||||d d |||d tt	||||||||||d d ||d tt	|||||||||||d d |d d S )Nr   ro  r   re   rG   rn   rH   rh   rk   r  rL   r  rq  )r   r&   r3   r,   r   r   r9  rh   r   r  r   )r0   rm  rn  rp  r  r   r   rb   r  rE  rx   ru   rs   rw  rx  ry  rz  r{  r|  r1   r1   r2   "test_gtsvx_error_incompatible_size
  sZ    "
r  zdu,d,dl,b,xc              
   C   sB   t d|jd}|||| |}|\
}}}	}
}}}}}}t|| d S )Nrp  r   r&   r0   r   )r  rb   r   rs   rx   rp  r}  rr  rs  rt  r~  rm  r  rs  r  r  r\   r1   r1   r2   test_gtsvx_NAG
  s    r  zfact,df_de_lambdac                 C   s   t d|jd| |S Nr   r   r&   r0   rb   rO  r1   r1   r2   <lambda>
  s   r  c                 C   s   dS N)NNNr1   r  r1   r1   r2   r  
  r  c                 C   s  t d dt| j }td| d}d}t|f|d }t|d f| }t|t|d tt|d }	t|d	f| d}
|	|
 }|||\}}}| | | g}|||||||d
\}}}}}}}t	||d  t	||d  t	||d	  t
|dkd| d t|
| t|dtt| }t|}t|	|| t|j |d t|drxJ d| t
|jdkd|j|
jd  t
|jdkd|j|
jd  dS )a  
    This tests the ?ptsvx lapack routine wrapper to solve a random system
    Ax = b for all dtypes and input variations. Tests for: unmodified
    input parameters, fact options, incompatible matrix shapes raise an error,
    and singular matrices return info of illegal value.
    r   r   ptsvxr   rK   rJ   rG   rn   rH   rn  rs  efr   zinfo should be 0 but is .r*  ru  rv  )rH   z$ferr.shape is {} but should be ({},)z$berr.shape is {} but should be ({},)N)r   r,   r   r   r&   r3   r   r9  r:  r   r   r   r   r   rh   r   r/   r  )r0   r4  rn  df_de_lambdar   r  r   rb   rO  rE  r  rs   rs  r  r\   r  rx   rs  r  r  r   r  r1   r1   r2   
test_ptsvx
  s>    (


r  c                 C   s   t d|jd| |S r  r  r  r1   r1   r2   r    s   c                 C   s   dS r  r1   r  r1   r1   r2   r    r  c              
   C   s   t d td| d}d}t|f|d }t|d f| }t|t|d tt|d }t|df| d}	||	 }
|||\}}}tt||d d ||
|||d	 tt|||d d |
|||d	 tt||||
d d |||d	 d S )
Nr   r  r   rK   rJ   rG   rn   rH   r  )	r   r&   r3   r,   r   r9  r   r  r   )r0   r4  rn  r  r  r   rb   rO  rE  r  rs   rs  r  r\   r1   r1   r2   test_ptsvx_error_raise_errors  s    (  r  c                 C   s   t d|jd| |S r  r  r  r1   r1   r2   r  .  s   c                 C   s   dS r  r1   r  r1   r1   r2   r  0  r  c                 C   sl  t d td| d}d}t|f|d }t|d f| }t|t|d tt|d }t|df| d}	||	 }
|||\}}}|d	krd
|d< |||\}}}||||
\}}}}}}}|d
kr||ksJ t|f|}||||
\}}}}}}}|d
kr||kshJ nP|||\}}}d
|d
< d
|d
< ||||
|||d\}}}}}}}|d
kshJ d S )Nr   r  r   rK   rJ   rG   rn   rH   r  r   rI   r  )r   r&   r3   r,   r   r9  )r0   r4  rn  r  r  r   rb   rO  rE  r  rs   rs  r  r\   rx   rs  r  r  r1   r1   r2   test_ptsvx_non_SPD_singular*  s0    (

r  zd,e,b,xc                 C   s6   t d|jd}|| ||\}}}}}	}
}t|| d S )Nr  r   r  )rb   rO  rs   rx   r  rs  r  Zx_ptsvxrs  r  r  r\   r1   r1   r2   test_ptsvx_NAGV  s    r  r   c                    s  t d t| jd }d\ }t  g| d}t |g| d}| j| tj | d| d  }|r fddt D  fddt D f}n0d	d td
 d
 D dd td
 d
 D f}|| }t	d| dd\}}	}
}}|	 ||d\}}t
|d t||d| }t||d|d | ||d\}}t
|d t|| }t||d|d |
 |||d\}}t
|d t||}t||d|d | |||d\}}t
|d t||d|d tj|d
}| |||d\}}t
|d ttd
| tjj|d
d | d
k  d S )Nr   r   )re   rJ   r   r   c                    s    g | ]}t | D ]}|qqS r1   r   r  yrx   r
  r1   r2   r    r  z5test_pptrs_pptri_pptrf_ppsv_ppcon.<locals>.<listcomp>c                    s    g | ]}t | D ]}|qqS r1   r  r  r
  r1   r2   r    r  c                 S   s   g | ]}t |D ]}|qqS r1   r  r  r1   r1   r2   r    r  rG   c                 S   s"   g | ]}t |D ]}|d  qqS r  r  r  r1   r1   r2   r    r  )ppsvpptrfpptrspptrippconr>  r?  rY  r   r  )rn  r   ro  )r   r,   r   r   r3   r9  rh   r
   r   r&   r   r   r   r   r   rp  r   r   r   rq  )r0   r   r   r   rU   rs   r  Zapr  r  r  r  r  Zulr\   ZaulZuliZaulirx   bxZxvrn  rs  r1   r
  r2   !test_pptrs_pptri_pptrf_ppsv_ppcont  sL    $





r  c           
      C   s0  t d t| jd }d}t||g| d}td| d\}}|dd |dd	}t|d
 d |d }|d }|d }	| tv rt|t	|d|d t|| |
 j |d|d |||dd}t|d
 d |d }|d }| tv rt|t	|d|d t|| |
 j |d|d t|d |	d|d d S )Nr   r   re   r   )geestrexcc                 S   s   d S r  r1   rx   r1   r1   r2   r    r  z!test_gees_trexc.<locals>.<lambda>Fr  rn   r   r   rG  r  rM   rG   r   rz   )r   r,   r   r   r3   r&   r   r+   r   r   r9  rh   )
r0   r   r   rU   r  r  ri  r  r6  d2r1   r1   r2   test_gees_trexc  s*    r  zt, expect, ifst, ilst)r   g)\({Gz?gQ?)rJ  皙r\  ffffff?)rJ  gr  g?)rJ  rJ  rJ  r  )r  lV}gV_?g|?5^?)g?r  gV/?g;On?)rJ  rJ  r   ggj+)            y
ףp=
?
ףp=
׿yRQȿQ?y)\(?      п)r               @yQ
ףp=
yq=
ףpͿp=
ף?)r  r         @      yGz?(\?)r  r  r        @      )r  y1%Ŀq?ys??ܵ|ȿyHzG??ܵ?)r  r  yV/?ݓ?yjt?vտ)r  r  r  yB>٬?=U?)r  r  r  r  c                 C   sL   d}t d| jd}|| | ||dd}t|d d |d } t|| |d dS )	zg
    This test implements the example found in the NAG manual,
    f08qfc, f08qtc, f08qgc, f08quc.
    r  r  r   r   )Zwantqrn   r*  N)r&   r0   r   r   )r  ZifstZilstexpectr   r  ri  r1   r1   r2   test_trexc_NAG  s    r  c                 C   s>  | t jkr.tjdkr.tdkr.tdk r.td td t 	| j
d }d}t||g| d}t||g| d}td	| d\}}|d
d ||ddd}t|d d |d }|d }	|d }
|d }|d |	d  }|d |	d  }| tv rt|t |d|d t|	t |	d|d t|
| | j |d|d t|
|	 | j |d|d |||	|
|dd}t|d d |d }|d }	|d }
|d }| tv rt|t |d|d t|	t |	d|d t|
| | j |d|d t|
|	 | j |d|d t|d |	d  |d|d t|d |	d  |d|d d S )Ndarwinopenblas
0.3.21.dev8gges[float32] broken for OpenBLAS on macOS, see gh-16949r   r   re   r   )ggestgexcc                 S   s   d S r  r1   r  r1   r1   r2   r    r  z!test_gges_tgexc.<locals>.<lambda>Fr   Zoverwrite_brn   r   rG   r  r   rz   rG  r  rM   rH   rI   r  )r,   r@  sysplatformblas_providerblas_versionr;   xfailr   r   r   r3   r&   r   r+   r   r   r9  rh   )r0   r   r   rU   rs   r  r  ri  r   r  r  r6  d1r  r1   r1   r2   test_gges_tgexc  sR    


r  c                 C   st  t d t| jd }d}t||g| d}td| d\}}}|dd |dd	}t|d
 d |d }|d }	|d }
| tv rt|t	|d|d t|	| |	
 j |d|d t|}d|d< t|||}| tv r||||	|d}n||||	||d d}t|d
 d |d }|d }	| tv r>t|t	|d|d t|	| |	
 j |d|d t|d |
d|d d S )Nr   r   re   r   )r  trsentrsen_lworkc                 S   s   d S r  r1   r  r1   r1   r2   r  4  r  z!test_gees_trsen.<locals>.<lambda>Fr  rn   r   r   rG  r  rG   rL   r   r   Zliworkrz   )r   r,   r   r   r3   r&   r   r+   r   r   r9  rh   r   r!   )r0   r   r   rU   r  r  r  ri  r  r6  r  selectr   r1   r1   r2   test_gees_trsen)  s8    

r  z*t, q, expect, select, expect_s, expect_sep)g/$?gQIg~jtx?gJ4?)rJ  58EGrgGr?gyX5;?)rJ  g?߾r  gt?)rJ  rJ  rJ  gyǹ)g؁sF?g_L?gGz?gUN@?)goT?g0*g'gz6>W)g(g&䃞ͪӿgbX9ҿg-!lV?)gb=y?gۊe?r  g8EGr?)r  g?gQg(\ſ)g
ףp=
?gQ?r  r  )g)\(ܿgQտgQg(\?)r\  g{GzԿgp=
ףg)\(?)rG   r   r   rG   g      ?g(\	@)yqh yfc]F?ڊe׿yMbȿ&S?y&1??п)r  y      ?5^I @yo0*yZd;OͿ~:p?)r  r  yx$(@4@y[ A?&?)r  r  r  y?ܵ@St$)y?ܵ꿽R!uy2U0*6[?yV-?=yXy8m4?1%̿)ySt$?\mҿyʡE?S㥛?y~:p	cڿyK7A`?[ A?)y:pΈ~jtԿyH}?9#J{yH}?	cZy+eXw?-ٿ)y"u?	c?y?տN@ayRQȿ{GzĿyh"lxz?EGrǿ)y47)yS!uqF%u@yyտGx$(?y3ı.n?rh|)yv?
F%uyd`TR?I&ۿyN@?ݓy4@
@	^)?)ys{
@ o_yH.@|Pk@y0*?*:Hy]m{?Gz)y)0[<?yI.!? ryqh 
@ׁsF?y1w-!?h ogRQ?gK?c                 C   s   d}d}t d| jd\}}	t|	|| }
| jtv rB||| ||
d}n||| ||
|
d d}t|d d	 |d	 } |d }| jtv r|d
 }|d }n|d }|d }t|||  | j |d t|d| |d t|d| |d dS )zW
    This test implements the example found in the NAG manual,
    f08qgc, f08quc.
    r  r  )r  r  r   r   rG   r  rn   r   rJ   rK   rL   r*  N)r&   r0   r!   r+   r   r   r9  rh   )r  r  r  r  Zexpect_sZ
expect_sepr   Zatol2r  r  r   ri  r   sepr1   r1   r2   test_trsen_NAGW  s(    0



r  c                 C   sv  | t jkr.tjdkr.tdkr.tdk r.td td t 	| j
d }d}t||g| d}t||g| d}td	| d\}}}|d
d ||ddd}t|d d |d }	|d }
|d }|d }|	d |
d  }|	d |
d  }| tv rt|	t |	d|d t|
t |
d|d t||	 | j |d|d t||
 | j |d|d t |}d|d< t|||	|
}|d d |d f}|||	|
|||d}t|d d |d }	|d }
|d }|d }| tv rt|	t |	d|d t|
t |
d|d t||	 | j |d|d t||
 | j |d|d t|	d |
d  |d|d t|	d |
d  |d|d d S )Nr  r  r  r  r   r   re   r   )r  tgsentgsen_lworkc                 S   s   d S r  r1   r  r1   r1   r2   r    r  z!test_gges_tgsen.<locals>.<lambda>Fr  rn   r   rG   r  r   rz   rG  r  rL   r   ir  r  )r,   r@  r  r  r  r  r;   r  r   r   r   r3   r&   r   r+   r   r   r9  rh   r   r!   )r0   r   r   rU   rs   r  r  r  ri  r   r  r  r6  r  r  r  r   r1   r1   r2   test_gges_tgsen  s^    



r  za, b, c, d, e, f, rans, lans)r   r   r   r   )rJ  r   r   r   )rJ  r   r   r   )rJ  rJ  rJ  g      @)r   r   r   r   )rJ  rJ  rJ  r   )      r   r   g      (@)g      "r          r  )r  r   r  r   )      r   r  g      3@)r   r   r   r   )rJ  r   r   r   )rJ  rJ  r   r   )rJ  rJ  rJ  r   )r   r   r   r   )rJ  r   r   r   )rJ  rJ  rJ  r   )r  r   rJ  r   )r
  r   g       rJ  )rd  r         r   )r  r   rJ  r   )rd  r   rd  rd  )rd  r   r   r   )rd  r   rd  r   )r   rd  r   rd  )r   r   rd  r   )rd  r   r   rd  )r   rd  r   r   c	                 C   s   d}	t d|d}
|
| |||||\}}}}}t|d t|ddt|jd dd t|d	dt|jd d
d t|||	dd t|||	dd d S )Nr  tgsylr   r   r   r   zSCALE must be 1.0r   r   r!  rJ  zDIF must be nearly 0zSolution for R is incorrect)r   r!  zSolution for L is incorrect)r&   r   r   r,   r   r   )rU   rs   rt   rb   rO  rX   ZransZlansr0   r   r  routloutrP   difr\   r1   r1   r2   test_tgsyl_NAG  s     $
r  ru   )r  rh   ijob)r   rG   rH   rI   rJ   c              
   C   s   | t jkrdnd}t jd}d\}}t|dd||g| |dd||g| dd^}}}	t|dd||g| |dd||g| dd^}
}}	|d	d
||g| }|d	d
||g| }td| d}|||
||||||d\}}}}}|dksJ d|dks J d|dkrJt|ddt 	| j
d dd n|dks\J d|d
kr|dkr|| ||
  }|| }|| ||  }|| }nV|dkrt || t ||  }|| }|t |
 |t |  }d| | }t|||ddd t|||ddd d S )NgMbP?g|=l   OElt/ r  ire   r   )outputr   rH   r  r   )ru   r  r   zINFO is non-zerorJ  zSCALE must be non-negativer   zDIF must be 0 for ijob =0r  zDIF must be non-negativer  rh   rd  zlhs1 and rhs1 do not match)r   r   r!  zlhs2 and rhs2 do not match)r,   r@  r-   Zdefault_rngr    uniformr.   r&   r   r   r   r  )r0   ru   r  r   rngr   r   rU   rb   r9   rs   rO  rt   rX   r  r  r  rP   r  r\   Zlhs1Zrhs1Zlhs2Zrhs2r1   r1   r2   
test_tgsyl  sR    






r  )r   )r  	functoolsr   Znumpy.testingr   r   r   r   r   r   r;   r	   r   numpyr,   r
   r   r   r   r   r   r   r   Znumpy.randomr   r   r   Zscipy.linalgr   r5   r   r   r   r   r   r   r   r   r   r   r    Zscipy.linalg.lapackr!   Zscipy.statsr"   r#   Zscipy.sparsesparser  Zscipy.__config__r$   ImportErrorr%   r6   r&   Zscipy.linalg.blasr'   r@  r   r   r  Z
complex128r+   r   r  r  r3   rE   rF   r   r   r  r  r   r   r   r   r   r'  r2  r=  rA  rB  rT  rj  rt  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zskipifr  r  r   r  r  r  ro   r  r  r  r  r[  r&  r'  r(  r3  r7  r>  rB  rC  rD  rE  rK  rL  rV  rX  r_  rl  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r1   r1   r1   r2   <module>   s   (8


` t  **DO1")::) %# ((-
e
#





\



+

/


	



@.:00



4



%


.$	7-*!@"