o
    h!                    @   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' d dl(m)Z) d d	l*m+Z+m,Z, d dl-m.Z/ zd d
l0m1Z1 W n e2y   dZ1Y nw zd dlm3Z4 W n e2y   dZ4Y nw d dl(m5Z5 d dl6m7Z7 ej8ej9gZ:ej;ej<gZ=e:e= Z>d Z?Z@e1dure1d d d Z?e1d d d Z@dd ZAdd ZBG dd dZCG dd dZDG dd dZEe
jFGde>e
jFGdg ddd  ZHG d!d" d"ZIG d#d$ d$ZJG d%d& d&ZKG d'd( d(ZLd)d* ZMd+d, ZNd-d. ZOd/d0 ZPG d1d2 d2ZQG d3d4 d4ZRd5d6 ZSd7d8 ZTd9d: ZUd;d< ZVd=d> ZWd?d@ ZXdAdB ZYdCdD ZZdEdF Z[dGdH Z\dIdJ Z]dKdL Z^dMdN Z_dOdP Z`G dQdR dRZadSdT ZbdUdV ZcdWdX ZddYdZ Zee
jFjfd[d\d]d^d_ Zgd`da Zhe
jFGdbdcddge
jFGde:e
jFGdeeidfe
jFGdgeidhe
jFGdieidhe
jFGdjd dkge
jFGdld dkgdpdmdnZje
jFGde:dodp Zke
jFGdqdedridgdrididridjdridsdridldrifdtdu Zle
jFGdvemg dwg dxg dyg dzg d{g d|gemg d}emg d~g dg dg dg dg dgemg dg dg dg dgfgdd Zne
jFGde>dd Zoe
jFGdemg demg demg demg demg demg demg demddgddgddgddgddggemddgddgddgddgddkggf	emg demg demg demg demg demg demg demddgddgddgddgddggemddgddgddgddgddggf	gdd Zpe
jFGde>e
jFGdg ddd Zqe
jFGdere:e: e>ddĄ Zse
jFGdere:e: e>ddƄ Zte
jFGdere:e: e>ddȄ Zue
jFGdemg dʢemg dˢemg d̢emg d͢emdfdgdrdhgddrgddgddggemddgddgdkdgddfgddggfemg d֢emg dעemg dآemg d٢emddgddgddgddggemddgddgddgddggfgdd Zvdd Zwe
jFGdere>e:e: e
jFGdeiddd Zxe
jFGdere>e:e: e
jFGdeiddd Zye
jFGdere>e:e: e
jFGdeiddd Zze
jFGdere>e:e: e
jFGdeiddd Z{e
jFGddemg demg demg demg dg dg dg dgfgdd Z|e
jFGde>e
jFGdg ddd Z}d d Z~e
jFGdg de
jFGdddgdd Ze
jFGdd	d
ge
jFGdddgdd Ze
jFGde>e
jFGdg ddd Ze
jFGde>dd Ze
jFGde>e
jFGddd[ge
jFGdddgdd Ze
jFGde>e
jFGdd dkge
jFGdddgdd Ze
jFGde>d e
jFGddd[ge
jFGdddgdd Ze
jFGdemg demg demg demddgddgddgddgddggemddgddgddgddgddkggfemg demg demg demddgddgddgddgddggemddgddgddgddgddggfgd d! Ze
jFGdere>e:e: e
jFGd"dd#d$ fdd%d$ fgd&d' Ze
jFGdere>e:e: e
jFGd"dd(d$ fdd)d$ fgd*d+ Ze
jFGdere>e:e: e
jFGd"dd,d$ fdd-d$ fgd.d/ Ze
jFGd0emg dʢemg dˢemdfdgdrdhgddrgddgddggemddgddgdkdgddfgddggfemg d֢emg dעemddgddgddgddggemddgddgddgddggfgd1d2 Ze
jFGd3dd[ge
jFGde>d4d5 Ze
jFGde>d6d7 Ze
jFGd8emg d9g d:g d;g d<gemg d=g d>g d?g d<gddkfemg d@g dAg dBg dCgemg dDg dEg dFg dGgdkdhfgdHdI Ze
jFGde>dJdK Ze
jFGde>dLdM Ze
jFGdNemg dOg dPg dQg dRgemg dSg dTg dUg dVgemg dWg dXg dYg dZgemg d[d\d]femg d^g d_g d`g dagemg dbg dcg ddg degemg dfg dgg dhg digemg d[djdkfgdldm Ze
jFGde>dndo ZdS (q      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)_compute_lwork)ortho_groupunitary_group)CONFIG)_clapack)get_lapack_funcs)get_blas_funcszBuild Dependencies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   Y/var/www/html/scripts/venv/lib/python3.10/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s0||vr0|| vr0|	| q|g ks9J ddS )z%Test that all entries are in the doc.Nzlapack.__doc__ is None>   clapackflapackdivision	HAS_ILP64print_functionabsolute_importfind_best_lapack_type_z2Name(s) missing from lapack.__doc__ or ignore_list)
r   __doc__pytestskipsetsplitlistdir
startswithappend)namesignore_listmissingr(   r1   r1   r2   test_lapack_documented9   s   


rH   c                   @   ,   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 ]R}t t|d	 d }|d u r*q||\}}}}}	t|	 t|	 t|| t||fd
t|d
 d f t|tt| ||ddd\}}}}}	t|	 t|	 qd S )N)         )         )      	   )rK   r   r   ga2U0*3?)rN   r   r   gMb`?)rQ   rK   r   r   )r   rK   r   r   sdzcgebalr   rK   )permutescale)	getattrr5   r   reprr   r   lenr,   r   )
selfaa1pfbalohi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 rq||\}}}t| t| qd S )Nikiifi     i"  iiidgehrd)rX   r5   r   rY   )r[   r\   r^   r_   httaurd   r1   r1   r2   
test_gehrda   s   zTestFlapackSimple.test_gehrdc                 C   sZ  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\}	| rM|d  d7  < d}|	|||\}
}}tt ||
t |
| ||  |	|||||d\}
}}tt | j|
t |
| j || dd |	|||dd\}
}}tt ||
t |
| || dd q%d S )NrK   rL   r   rN   rO   rP   rR   rS   
         TfdFD)trsylr*   C)tranatranbdecimal)isgn)	r,   arrayr.   r%   isupperr   dot	conjugaterr   )r[   r\   bctransr0   r]   b1c1rt   xrW   rd   r1   r1   r2   
test_trsyll   s0   ""zTestFlapackSimple.test_trsylc           	      C   s  t g dg dg dg}dD ]{}dD ]v}||}| r'|d  d7  < td|f\}|||}|d	v rU|d
v r>d}nd}t t t t |}t	||| q|dv rbt 
t |}n#|dv rtt 
t jt |dd}n|dv rt 
t jt |dd}t|| qqd S )Nrf   rg   ri   rs   Mm1OoIiFfEer   r   r*   )langeFfEeFfrM   rQ   Mm1Oor   axisIirK   )r,   r|   r.   r}   r%   sqrtsumsquareabsr   maxr   )	r[   r\   r0   norm_strr]   r   valuery   refr1   r1   r2   
test_lange   s6   

zTestFlapackSimple.test_langeN)__name__
__module____qualname__re   rn   r   r   r1   r1   r1   r2   rJ   J   s
    rJ   c                   @   s   e Zd Zdd Zdd ZdS )
TestLapackc                 C      t tdr	 d S d S Nempty_module)hasattrr5   r[   r1   r1   r2   test_flapack      
zTestLapack.test_flapackc                 C   r   r   )r   r4   r   r1   r1   r2   test_clapack   r   zTestLapack.test_clapackN)r   r   r   r   r   r1   r1   r1   r2   r      s    r   c                   @   rI   )
TestLeastSquaresSolversc                 C   st  t d ttD ]K\}}d}d}d}t|||}t||}td|d\}}	t|	|||}
||||
d\}}}t|dk |||d	| |
d
\}}}t|dk qtD ]o}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|| qVtD ]o}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  ro      rK   )gels
gels_lworkr0   lworkr   TTCCr   r         ?       @      @      @      @       @      0@g      1@g      4@)r   r   geqrfrL   rz   祪,-@   rtol      ?      @      @      ?      @            @              @ffffff?r   y      1@       @y      4@      R ?\j,? W?)r   	enumerateDTYPESr   r.   r%   r    r   REAL_DTYPESr,   r|   r/   rZ   r   finfoepsr   r+   )r[   indr0   mnnrhsr]   r   glsglslwr   r;   rd   r   r   r   lqrr   	lqr_truthr1   r1   r2   	test_gels   s   





z!TestLeastSquaresSolvers.test_gelsc              
   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r8|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 qd S )Nr   r   r   r   r   r   r   r   )gelsdgelsd_lworkrL   rK   rz   Fr   r   r   r   YN))1)@*@.?r   r   r   r   r   r   r   r   U.*@_Y@r   r,   r|   r%   r/   rZ   intrealr   r   r   r+   )r[   r0   r]   r   r   r   r   r   r   workiworkrd   r   
iwork_sizer   srankrwork
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r8|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 qd S )Nr   r   r   r   r   r   r   r   )gelssgelss_lworkrL   rK   rz   Fr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r[   r0   r]   r   r   r   r   r   r   r   rd   r   vr   r   r   r1   r1   r2   
test_gelss9  s   





z"TestLeastSquaresSolvers.test_gelssc              	   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r8|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 qd S )Nr   r   r   r   r   r   r   r   )gelsyr   rL   rK   ro   Frz   r   r   r   r   r   r   r   r   r   r   r   r   )r   r,   r|   r%   r/   rZ   r   r   r   r   r   int32r   r+   )r[   r0   r]   r   r   gelsy_lworkr   r   r   r   rd   r   jptvr   r   jr   r1   r1   r2   
test_gelsyr  st   



z"TestLeastSquaresSolvers.test_gelsyN)r   r   r   r   r   r   r   r1   r1   r1   r2   r      s
    D<9r   r0   r/   )rM   rN   )rO   rL      r   c                 C   2   t d| d}|\}}|||d\}}t|d d S )Ngeqrf_lworkr   r   r   r   r%   r   )r0   r/   r   r   r   r   rd   r1   r1   r2   test_geqrf_lwork     r   c                   @      e Zd Zdd ZdS )TestRegressionc           
      C   s   t D ]j}tjd|d}tdg|g\}tt||dd ||\}}}}|tv rHtdg|g\}tt||dd  |dd ||dd  |dd q|tv rltd	g|g\}	tt|	|dd  |dd |	|dd  |dd qd S )
N)i,  rL   r   gerqfrL   r   orgrqrK   ungrq)r   r,   r   r%   assert_raises	Exceptionr   r+   )
r[   r0   r\   r   rqrm   r   rd   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                   @   r   )	TestDpotrc           
      C   s   dD ]O}dD ]J}t jd t jjdd}||j}td|f\}}||||d\}}|||d }	|rCtt |	t t	| qtt 
|	t 
t	| qqd S )N)TF*   )rM   rM   )size)potrfpotri)cleanr   )r,   r-   r   normalr~   rr   r%   r   r   r   r   )
r[   lowerr  r   r\   dpotrfdpotrir   rd   dptr1   r1   r2   test_gh_2691  s   zTestDpotr.test_gh_2691N)r   r   r   r  r1   r1   r1   r2   r        r  c                   @   r   )
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 ]}
||
||}|	|d  t|d
 dkd|
  qlt |	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   rz   rK   F)full_matrices
compute_uvoverwrite_acheck_finiter   lasd4rM   zcLAPACK root finding dlasd4 failed to find                                     the singular value %izThere are NaN rootsd   atolr   )r,   r|   hstackvstackdiagr   rZ   newaxisr   concatenater   r%   rangerD   r   anyisnanr   r   float64r   )r[   sigmasm_vecMSMit_lensgm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    r  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 r8t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}nC|tv rst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=
ף0r0  g(\+gףp=
0g333333*@g(\gHzG,gQ#rN   rK   rz   rM   rL   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abr   uplor   h㈵>r   r  N)r   r,   r|   r+   
ValueErrorr%   r   r   )r[   r0   r5  r   x_outr2  r   rd   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 ))Nrr   ru   ru   )r   ).0r0   r   r1   r1   r2   
<listcomp>-  s    zTestTbtrs.<listcomp>r6  Ur3  r  r<  c                    sv  t d d\}}td d}|dk}|| }	||	 }
t|	|
 d d}fdd	|D } fd
d	|D }|dkrCtj d||	< tj||dd}t|d f }t|D ]\}}|	|||t
|dt| f< qYt|f }||||||d\}}t|d |dkrt|| |dd d S |dkrt|j| |dd d S |dkrt|j| |dd d S td)Ni  )rN   rM   rL   r2  r   r?  rK   rz   c                    s   g | ]} t | qS r1   )r   r=  r   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    dia)formatr   )r5  r   r6  r   r  r<  g-C6
?r   rr   ru   zInvalid trans argument)r   r%   r   r,   r   spsdiagsr   r   diagonalr   minr3   r   r   rr   Hr9  )r[   r0   r   r6  r  r   kdr2  is_upperkuklband_offsetsband_widthsbandsr\   r5  rowkr   r   rd   r1   )r0   r   r2   test_random_matrices,  s6   

(
zTestTbtrs.test_random_matriceszuplo,trans,diag)r?  r<  Invalid)r?  rU  r<  )rU  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 exceptionsr2  r   rN   rL   N)r%   r,   r#  r   r   r   )r[   r6  r   r  r2  r5  r   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   rN   r2  r   )rz   rM   r?  r4  N)r,   r   floatr%   r   )r[   r5  r   r2  r;   rd   r1   r1   r2   test_zero_element_in_diagonall  s   z'TestTbtrs.test_zero_element_in_diagonalzldab,n,ldb,nrhs)rO   rO   r   rO   )rO   rO   rM   rO   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   r2  Nr,   r   rW  r%   r   r   )r[   ldabr   ldbr   r5  r   r2  r1   r1   r2   test_invalid_matrix_shapes|  s   z$TestTbtrs.test_invalid_matrix_shapesN)r   r   r   r=   markparametrizer   r;  rT  rV  rX  r\  r1   r1   r1   r2   r/    s0    
--
	r/  c                  C   s   dD ]O} t d| d}td| }td| }t|r|d9 }|||\}}}t|d t|d t|rLt|d	 tt|tk tt|tk qt|d
 qd S )Nrs   lartgr   rM   rN   r*   333333?r   y       皙?)	r%   r,   r|   iscomplexobjr   r   typecomplexrW  )r0   r_  r_   gcssnrr1   r1   r2   
test_lartg  s   




ri  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 )Nrs   r`  ra  rN   rM   ro   rK   fdrotr   y             r*   y              @)rO   rO   rO   rO   )r   r   r   r   r  rL   rA  )rO   rO   rM   rM   r   )offxoffy)rM   rM   rO   rO   )incxrn  r   )rO   rM   rO   rM   )rm  incyr   )rm  ro  rn  rp  r   )rM   rM   rO   rM   r   )ro  rp  r   )overwrite_xoverwrite_y)r,   fullr   	precisionr&   r%   r   r   )
r0   r   r   ur   r  rk  r_   r\   r   r1   r1   r2   test_rot  sX   

rv  c               	   C   s  t jd t jd} | j| } t jddt jd  }|j |}dD ]}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 q*d S )Nr   )rN   rN   r*   rs   larfglarfr   FDr   rK   rK   r   rL   r   r   Rsider7  rl  )r,   r-   r   rr   r~   conjr%   copyr/   r   r   r   r   )a0a0jr0   rw  rx  r\   alphar   rm   expectedr   r1   r1   r2   test_larfg_larf  s,   
,>>r  c                  C   sB   t dtjdd} d}t| ||ddd}|dks|dksJ d S d S )	Ngesdd_lwork	preferredr0   ilp64iA%  T)r  r  i`DiD)r%   r,   float32r    )sgesdd_lworkr   r   r1   r1   r2    test_sgesdd_lwork_bug_workaround  s   r  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   *   t jd|d}td|f}tt|| d S )Nr   r   sytrdr,   r   r%   r   r9  )r[   r0   Ar  r1   r1   r2   test_sytrd_with_zero_dim_array     z(TestSytrd.test_sytrd_with_zero_dim_arrayr   rK   rM   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 ]3}t j||d}|d ||d f |d |< d||< t j|||d|| t ||  }t ||}qt |d}|j| ||< t |jt ||}t||dt |j dd	 d S )Nr   )r  sytrd_lworkrK   rL   r   r	  r   rO   r   r          r   rz   )r,   r   r%   arangetriu_indices_fromr   r   r   r   r  r   r/   r
   r   outerr~   r   rr   )r[   r0   r   r  r  r  r   rd   datarj   erm   rr   rS  k2Qr,  r   rJ  i_lowerQTAQr1   r1   r2   
test_sytrd  s@   





$ zTestSytrd.test_sytrdN)	r   r   r   r=   r]  r^  r   r  r  r1   r1   r1   r2   r    s    
r  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   r  )Nr   r   hetrdr  )r[   r  r  r  r1   r1   r2   test_hetrd_with_zero_dim_arrayT  r  z(TestHetrd.test_hetrd_with_zero_dim_arrayzreal_dtype,complex_dtyper   r  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 qFt	||}
||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 ]6}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   )r  hetrd_lworkrK   rL   r*   )r   rK   r	  r   r  rO   r   r  r  r   rz   ro   )r,   r   r%   r  r  fill_diagonalr   r  r   r    r   r   r   r   r/   r   r
   r   r  r~  r~   r   rr   )r[   r   
real_dtyper  r  r  r  r   r;   rd   r   r  rj   r  rm   rr   rS  r  r  r,  r   rJ  r  QHAQr1   r1   r2   
test_hetrd[  sR   
"





zTestHetrd.test_hetrdN)r   r   r   r=   r]  r^  r+   r  zipr   r  r1   r1   r1   r2   r  S  s    
r  c               
   C   s^  t tD ]\} }td|d\}}t|dddd}| dk rHt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 rtg d}ntg d}t|
|dd  qd S )!N)gglsegglse_lworkr   rP   rN   rL   )r   r   r^   )g=
ףp=g{Gzg(\ؿ      ?)zGgHzG?gףp=
ӿQ)ffffff@gQ?g?gffffffֿ)r  g{Gz?Qg{Gz?)333333?g333333?r  g
ףp=
)g{Gz{Gz?gzG      ?)g      r  gGz?gHzGgzGg=
ףp=?r  )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   r        r  )r  r   r  r  r   )^"L?\}?r  r  )y!f?$_Kdy^gŵ翸F@y!f?}dy61ŵe_@rx   )r   r   r%   r    r,   r|   r   r   )r   r0   func
func_lworkr   r\   r   rj   r   r;   resultr  r1   r1   r2   
test_gglse  sN   


r  c                  C   s  t d ttt D ]\} }d}| dk r+td|d}td|d\}}t|||}ntd|d}td|d\}}t||t||d	  |}|| j d
 d
t	j
||d  }t|d}t||}|||dd\}	}
}||	|
|dd\}}ttd| t	jj|dd | dk  q
d S )Nr   ro   rN   sytrf_lworkr   )syconsytrfhetrf_lwork)heconhetrfr*   rL   rK   )r   r	  )r\   ipivanormr	  r^   )r   r   r   r+   r%   r   r.   r~  rr   r,   r
   r   r    r   r   linalgcond)r   r0   r   r  funconfunctrfr  r  r   ldur  r;   rcondr1   r1   r2   test_sycon_hecon  s"   $

*r  c                  C   s   t d ttD ]r\} }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   ro   )r  sygstsyevdsygvdr   rL   r   -C6?r   )r   r   r   r%   r   r.   rr   r,   r
   r   r   )r   r0   r   r  r  r  r  r  Beig_gvdr;   rd   r   r\   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   ro   )r  hegstheevdhegvdr   r*   rL   r   r  r   )r   r   r+   r%   r   r.   r~  rr   r,   r
   r   r   )r   r0   r   r  r  r  r  r  r  r  r;   rd   r   r\   r  r1   r1   r2   
test_hegst  s(   $$$r  c               	      sl  t d d\} }ttD ]\}}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   )ro      tzrzftzrzf_lworkr   rL   r*   r   r   Nc              
      D   g | ]} | |gd d f j |gd d f    qS Nrr   r~   r~  r@  IdVrm   r1   r2   r>  H     D ztest_tzrzf.<locals>.<listcomp>ro   r   r  r  )r   r   r   r%   r    r   r   r.   r   r   rr   r   r,   r  r   r
   r   r   r~   r   r   spacingr   )r   r   r   r0   r  tzrzf_lwr   r  rzrd   r{  r   Zr1   r  r2   
test_tzrzf,  s,   
"0(r  c               	   C   s  t d ttD ]\} }d}| dkr*tt||t||d  t| |}d}ntt||t| |}d}td|d\}}}||\}}	t|d	|}
|d
||
}t|t	| |
| d	 dkrfdndd |d
||
|d}t|t	|
 j |
| d	 dkrdndd |d|t|t|f< |d
||
|dd}t|t	|
 j |
| d	 dkrd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   rK   r*   ru   rr   )trttftfttrtfsmr   rL   rz   r   rN   rP   rx   r   r   r?  )r   r  rM   r{  )r   r  r}  N)r   r   r   r   r   r
   r.   r%   r   r   r~  rr   r,   r  )r   r0   r   r  r   r  r  r  Afpr;   r  soln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\}
}n(t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 rd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 matric 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   )ro   r  r  r  r   rL   )ormrzormrz_lworkr*   )unmrzunmrz_lworkr   Nc              
      r  r  r  r@  r  r1   r2   r>    r  z$test_ormrz_unmrz.<locals>.<listcomp>rr   ru   ro   r   r   r  r  r   r{  )r}  r   )r}  r   r   )r   r   r   r%   r    r   r   r.   r,   r  r
   r   r   r~   r  r   r   r   r   r~  rr   )qmqncnr   r0   r  r  lwork_rzr  ru   orun_mrzorun_mrz_lw	lwork_mrzr  rd   r   r  r   tolcqr1   r  r2   test_ormrz_unmrzw  sV   

"
(r  c               	   C   s   t d ttD ]t\} }d}| dkr%t||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   rK   r*   ru   rr   )r  r  r   r   r3  r6  r?  )transrr6  rL   Nrz   F)order)r   r   r   r   r.   r%   r   r   r   r~  rr   r   r   reshape)r   r0   r   A_fullr  r  r  A_tf_Urd   A_tf_LA_tf_U_TA_tf_L_TA_tf_U_mA_tf_L_mA_tr_UA_tr_LA_tr_U_TA_tr_L_Tr1   r1   r2   test_tfttr_trttf  sX   ,F,Br  c                  C   sr  t d ttD ]\} }d}| dkr"t||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   rK   r*   )trttptpttrr   r   r3  r   rL   N)r   r   r   r   r.   r%   r   r   r   r   rr   r   r   r   )r   r0   r   r  r  r  A_tp_Urd   A_tp_LindsA_tp_U_mA_tp_L_mr  r  r1   r1   r2   test_tpttr_trttp  s4    

r  c                  C   s   t d ttD ]f\} }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   rK   r*   )pftrfr  r  r   r   N)r   r   r   r   r.   r~  rr   r
   r%   r   r   r   )r   r0   r   r  r  r  r  r  rd   	Achol_rfpA_chol_rr;   Acholr1   r1   r2   
test_pftrf  s$   r  c                  C   s
  t d ttD ]z\} }d}| dkr/t||t||d  |}|| j |t|  }nt|||}||j |t|  }td|d\}}}}||\}}	|||\}
}	|||
\}}	t	|	dk |||\}}t
|}t|t|| d dkr~d	nd
d qdS )z
    Test Cholesky factorization of a positive definite Rectengular Full
    Packed (RFP) format array to find its inverse
    r   r   rK   r*   )pftrir  r  r  r   r   rL   rN   rP   rx   N)r   r   r   r   r.   r~  rr   r
   r%   r   r   r   r   )r   r0   r   r  r  r  r  r  r  rd   
A_chol_rfp	A_inv_rfpA_inv_rr;   Ainvr1   r1   r2   
test_pftri/  s*   
r#  c                  C   s\  t d ttD ]\} }d}| dkr/t||t||d  |}|| j |t|  }nt|||}||j |t|  }t|df|d}t|d df|d}t|d df|d}t	d|d\}}}	}
|	|\}}|||\}}||||\}}t
|d	k tt|||| ||||\}}t
|d	k tt|||| d d	krd
ndd qdS )z
    Test Cholesky factorization of a positive definite Rectengular Full
    Packed (RFP) format array and solve a linear system
    r   r   rK   r*   rM   r   rL   )pftrsr  r  r  r   rN   rP   rx   N)r   r   r   r   r.   r~  rr   r
   r   r%   r   r   r   r   r   )r   r0   r   r  r  Bf1Bf2r$  r  r  r  r  rd   r  r  r1   r1   r2   
test_pftrsO  s2   r'  c                  C   s0  t d ttD ]\} }d}| dkr/t||t||d  |}|| j |t|  }nt|||}||j |t|  }| dk rHdnd}tdd	d
	|f|d\}}}||\}}	t
j|d|}
||dd|
d|}|||\}}	t|t|
|
 j d|  | d dkrdndd qdS )zT
    Test for performing a symmetric rank-k operation for matrix in RFP format.
    r   r   rK   r*   rL   r   hr  r  z{}frkr   rz   r   rN   rP   rx   N)r   r   r   r   r.   r~  rr   r
   r%   rE  r,   r-   r   r   r~   )r   r0   r   r  prefixr  r  shfrkr  r;   ru   Afp_out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   ro   rK   i   r*   r  r   )syconvr  r  r   r  F)r	  	hermitianr  rz   Nr  r  r   )r   r   r   r   r.   r~  rr   r
   r,   r  r   r%   r    r   r   r   r   )r   r0   r   r  r  r/  trf	trf_lworklwr3  Dpermr  r  rd   r\   r  r?  r1   r1   r2   test_syconv  s6   (*r6  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r#t||t||d  |}nt|||}dt|dj }td|d\}}|||\}}	}
|
d	ksKJ t	|d
tj
||d }tj
||d||	 |j   }t|}t|j | tj
||d|dd t|| ||dd |dkrt||t||d  |}d}n
t|||}d}dD ]T}d|fD ]M}|||	|||d\}}
|
d	ksJ ||kr|j }n|}|dkr|| }n|| }t|||dd ||fdkr|||	|\}}
|
d	ksJ t|| qqtt|||	|dd tt|||	|dd qd S )Nr   r   rK   r*   r  r   )geqrtgemqrtr   r   rz   r  r  ru   rr   r3  r{  r<  r}  r   r3  r3  r<  r  r|  r  )r   r   r   r   r.   r,   r  r   r%   r   r
   rr   r~  r   r   r   r   r   )r[   r   r0   r   r  r  r8  r9  r\   trd   r   r  r{  ru   	transposer}  r   r   qqC	c_defaultr1   r1   r2   test_geqrt_gemqrt  sT     


zTestBlockedQR.test_geqrt_gemqrtc                  C   s  t d ttD ]\}}d}|dkr2t||t||d  |}t||t||d  |}nt|||}t|||}dt|dj }td|d\}}d	|d
 |fD ]t}	||	|||\}
}}}|d	ksoJ 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rt||t||d  |}t||t||d  |}d}nt|||}t|||}d}dD ]}d|fD ]}||	||||||d\}}}|d	ksJJ ||krU|j }n|}|dkrst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r||	||||\}}}|d	ksJ t	|| t	|| q3q-tt||	||||dd tt||	||||dd q[qd S )Nr   r   rK   r*   r  r   )tpqrttpmqrtr   r   rL   rz   r  r  ru   rr   r:  r<  r;  r3  r   r<  r  r|  r  )r   r   r   r   r.   r,   r  r   r%   r   r   r   r  r
   rr   r~  r   r   r   r   ) r[   r   r0   r   r  r  r  rC  rD  lr\   r   r=  rd   B_pentb_pentr   r  r{  ru   r4  r>  r}  r   r   rj   r?  cdCDqCDrA  	d_defaultr1   r1   r2   test_tpqrt_tpmqrt  sx    *"$





zTestBlockedQR.test_tpqrt_tpmqrtN)r   r   r   r<   rB  rL  r1   r1   r1   r2   r7    s    >r7  c                  C     t d ttD ]\} }d}d}td|d}| dkr8t||| |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   ro   rL   pstrfr   rK   r*   r    r   rL   r8  r  r   r   r   r%   r   r.   r~  rr   r   r   r,   r   r  r   r#  r   r   )r   r0   r   rh  rN  r  r   pivr_crd   r?  single_atoldouble_atolr  r3  r1   r1   r2   
test_pstrfJ  6   ,

2
4rV  c                  C   rM  )Nr   ro   rL   pstf2r   rK   r*   r  rO  rP  r8  r  rQ  )r   r0   r   rh  rX  r  r   rR  rS  rd   r?  rT  rU  r  r3  r1   r1   r2   
test_pstf2r  rW  rY  c                  C   sV  t g dg dg dg dg} t g dg dg dg}ttD ]\}}|dk rBt g d	g d
g dg dg}||}n't jg dg dg dg|d}|t g dg dg dgd 7 }||}td|d}||\}}}}	}
}|dk rt| ||d d d f | | ddd q#t|||d d d f | | ddd q#d S )N)g      ?r   g1w-!?gd`TRۿ)r   gsr  r  )gs?r  g2%䃮g,eX)r  gsFg%ug??)y/nҿ&?yDioɴ?Af?y o_[ Acп)ysֿAfҿyPkw?JY8y5;NёCl?)yYڊ?1*?y=yXѿ@a+?yh oſFxrL   )g   ЈBg   tBgffffff @g   ٓ )      @gg#fDgffffff)gHzG?gQg'Vgp=
ף)g(\r  gS7нra  )gq=
ףpg   Ag(\)g333333g   Bg333333ÿ)gZ9=gQgֽr   )gffffff@g   tޅBr  )g(\g   Zgq=
ףp?)gEop=gQ?gZEqҽr*   geequr   r  r8  )r,   r|   r   r   r.   r%   r   )desired_realdesired_cplxr   r0   r  r[  rh  r   rowcndcolcndamaxrd   r1   r1   r2   
test_geequ  sP   





  ra  c            
         s   t g d} ttD ]I\}}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   rz   rz   r   r1  ro   r   rL   r   r*   c                    s   g | ]} d |  qS )r   r1   r@  r  r1   r2   r>    rB  ztest_syequb.<locals>.<listcomp>rO   syequb)r,   r|   r   r   r
   r   rot90r  r%   r   log2r.   r   )
desired_log2sr   r0   r  rj   rd  r   scondr`  rd   r1   rb  r2   test_syequb  s   "ri  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 )NrL   rO   i  rS   rK   )rS  r*   r   r  r  rc  rP                   i   rO   rO   y              0@)rO   r   r  )r   rz   rz   r   r   rc  r   rz   rz   r   r   )r,   r  r   r   zheequbr   r   rf  r   r  cheequbr.   	complex64)r  r   rh  r`  rd   r1   r1   r2   test_heequb  s   2
( 
rq  c                  C   s:  t jd d} t j| }t j| t j| d  }ttD ]z\}}|dk r>t j| | }||}|| }||}nt j| | t j| | d  }||}|| }||}td|d}td|d}||dd	\}	}
}}||	||
|dd
\}}|dk rt|||| dd q t|||| dd q d S )Nr  ro   r*   rL   getc2r   gesc2r   r  )overwrite_rhsrN   rx   )	r,   r-   r   r   r   r   r.   r%   r   )r   r\  r]  r   r0   r  r   rr  rs  lur  jpivrd   r   rW   r1   r1   r2   test_getc2_gesc2  s4   
 



rx  r  )rP   rO   rm  jobarP   joburN   jobvjobrrK   jobpc              
   C   s  t d | \}}	dt|j }
t| |}td|d}|dk }|dk }|dko*||	k}t|}|dko9| o9| }|dkoD|oA| oD|}|dkoO|oL| oO|}|rUd}n	|sY|r\d}nd	}|dkrt|dkrttt||||||||	 dS ||||||||d
\}}}}}}t	|| |s	|d	 |d  |d|	  }t
|t|dd|
d |dkr|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 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   rL   rK   r   r1  r   )ry  rz  r{  r|  jobtr}  NF)r  rl  )r   r,   r   r   r3   r%   rb  r   r   r   r   r   r  r~  rr   identityr  matrix_rankcount_nonzero)r  r0   ry  rz  r{  r|  r}  r  r   r   r  r  r~  lsvecrsvecl2tran
is_complexinvalid_real_jobvinvalid_cplx_jobuinvalid_cplx_jobvexit_statussvaru  r   r   r   rd   sigmar1   r1   r2   test_gejsv_general	  sV   !


	"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   rK   rK   rK   rz  r  ro   r  N)r%   r   r/   r,   r|   r   sinr  r  r.   asfortranarrayrr   r  r   )r0   r~  r  ru  r   r   r   rd   r  Acr;   r1   r1   r2   test_gejsv_edge_argumentsu  s.   



r  kwargsrS   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)rL   rL   r   r~  NrY  )r  r  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(\r  g(\)g cZB#@gI.!v@g?ܵ?r  )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$g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ?g_vO?)g}?5^Iؿg58EGr?gi o?g7[ Ac                 C   sT   d}t d| jd}|| \}}}}	}
}t|||d t|||d t|||d dS )z~
    This test implements the example found in the NAG manual, f08khf.
    An example was not found for the complex case.
    r  r~  r   rl  N)r%   r0   r   )r  
sva_expectu_expectv_expectr  r~  r  ru  r   r   r   rd   r1   r1   r2   test_gejsv_NAG  s   r  c           !   	   C   s  t d d}dt| j }t|d f| d}t|f| d}t|d f| d}| | | g}t|t|d t|d }tj|}|| }	t	d| d\}
}|
|||\}}}}}}t
||d  t
||d  t
||d	  t|dt|d t|d	 }tj|| d}t|D ]2\}}|| d }|d d ||gf |d d ||gf< |d d |f  |d d |d f | 7  < qd|d d }}|d d ||gf |d d ||gf< t||| |d
 |	 }|||||||	\}}t
|	| t|||d
 | tv rd}|j| }n	d}| j| }||||||||d\}}t|||d
 tt |
|d d || W d    n	1 sIw   Y  tt |
||d d | W d    n	1 shw   Y  tt |
|||d d  W d    n	1 sw   Y  tt |
|d |d d |d  W d    n	1 sw   Y  d|d< d|d< |
|||\}}}}}} tj||d  dkd||d   d S )Nr  ro   r  rK   r   rz   gttrfgttrsr   rL   rl  rr   ru   r  z3?gttrf: _d[info-1] is {}, not the illegal value :0.)r   r,   r   r   r3   r  r  r-   r   r%   r   r
   r   r   r   rr   r~  r   r9  r   testingr   rE  )!r0   r   r  durj   dldiag_cpyr  r   r   r  r  _dl_d_dudu2r  rd   r?  r3  r,  r   rR  b_cpyx_gttrsr   b_trans__dl__d__du_du2_ipiv_infor1   r1   r2   test_gttrf_gttrs  sl   "$$.$





r  z1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g @r  ffffff?r   )r  r  g      ffffff@)333333@@r   g      )r  rc  r  r  )r  r  rQ   gC>)rz   r  rR   )rL   rM   rN   rO   rO   g@gffffff@      g%@g@g	r`  gffffff&g3@rk  rO   rQ   rM   r1  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  rl  )r%   r   )r  rj   r  du_expd_expdu2_expipiv_expr   r   r  r  r  r  r  r  r  rd   r  r1   r1   r2   0test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csf'  s   2


r  ))rM   rQ   )rQ   rM   r   c                 C   r   )Ngeqrfp_lworkr   r   r   r   )r0   r/   r  r   r   r   rd   r1   r1   r2   test_geqrfp_lworkf  r   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  ro   rN   rK   rz   pttrfr   r   zpttrf: info = z, should be 0)err_msgrl  pttrszpttrs: info = )r   r,   r   r   r3   r  r~  r  r%   r   r   r   r   r   rr   )ddtyper0   r  r   rj   r  r  r  r  r  _erd   r3  r4  r   r   r  _xr1   r1   r2   test_pttrf_pttrso  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 )Nro   r  r   rL   rK   rz   )r%   r3   r   r9  )r  r0   r   r  rj   r  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   t|f| }|||\}}}t|dkd d S )	Nro   r  r   rL   rK   r   z3?pttrf: _d[info-1] is {}, not the illegal value :0.z2?pttrf should fail with non-spd matrix, but didn't)r%   r3   r   rE  r   )	r  r0   r   r  rj   r  r  r  rd   r1   r1   r2   'test_pttrf_pttrs_errors_singular_nonSPD  s   r  z%d, e, d_expect, e_expect, b, x_expect)rN   ro      r   rO   )r   r  r  rR   )rN   rS   r      rK   )r  gK=Ur`  r  ro   rL      A      g      @rz   rc  )r  )   .      )y      0@      0@y      2@      "      ?      )r  rS   rK   rN   )r  r  r  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 rQ|||	|dd\}}
t|||d d S d S )	Nr  r  r   r   rl  r  rK   r  )r%   r   r~  r0   r+   )rj   r  d_expecte_expectr   x_expectr  r  r  r  rd   r  r  r1   r1   r2   test_pttrf_pttrs_NAG  s   
r  c                 C   s  |dkrUt ||f| }|tt|d|   }|| j d }t|d }t |f|d }t |d f|}t|t|d t|d }|| | j }	|}
n4t |f|}t |d f|}|d }t|t|d t|d }	t|t|d t|d }
|||	|
fS )NrK   rN   rL   rz   )r3   r,   r  r   r~  rr   r   )r0   realtyper   	compute_zA_eigvrrj   r  trir  zr1   r1   r2   pteqr_get_d_e_A_z  s    """r  zdtype,realtyper  c                 C   s   t d dt| j }td| d}d}t| |||\}}}}	||||	|d\}
}}}t|dd| d	 ttt	|d t|
|d
 |rlt|t
|j t||d
 t|t|
 t
|j ||d
 dS 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  rO  pteqrr   ro   rj   r  r  r  r   zinfo = z, should be 0.rl  N)r   r,   r   r   r%   r  r   r   sortr   r~  rr   r  r  )r0   r  r  r  r  r   rj   r  r  r  d_pteqre_pteqrz_pteqrrd   r1   r1   r2   
test_pteqr
	  s    
"
r  c                 C   sZ   t d td| d}d}t| |||\}}}}||d |||d\}	}
}}|dks+J d S )Nr  r  r   ro   rN   r  r  r   r   r%   r  r0   r  r  r  r   rj   r  r  r  r  r  r  rd   r1   r1   r2   test_pteqr_error_non_spd+	  s   r  c           	      C   s   t d td| d}d}t| |||\}}}}tt||d d |||d tt|||d d ||d |rEtt||||d d |d d S d S )Nr  r  r   ro   rz   r  )r   r%   r  r   r9  )	r0   r  r  r  r   rj   r  r  r  r1   r1   r2   "test_pteqr_raise_error_wrong_shape:	  s    r  c                 C   sf   t d td| d}d}t| |||\}}}}d|d< d|d< |||||d\}	}
}}|dks1J d S )Nr  r  r   ro   r   r  r  r  r1   r1   r2   test_pteqr_error_singularI	  s   r  zcompute_z,d,e,d_expect,z_expect)gp=
ף@rZ  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  r  r   rK   rz   r  rl  N)r%   r0   r,   r  r   r   )r  rj   r  r  z_expectr  r  r  r  r  _zrd   r1   r1   r2   test_pteqr_NAG_f08jgfX	  s   "r  matrix_size)r   )rQ   rP   rP   rP   c              
   C   s  t jd dt | j }dt | j }td| d}td| d}|\}}t||f| d}||\}	}
}t |	}||kr[t 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   orgqr)rm   r   r   r   r8  rz   )r,   r-   r   r   r   r%   r3   r   r   r   r
   r/   r~  rr   r   allr  rZ   r   r!  )r0   r  r   r  r  gqrr   r   r  qr_Arm   rd   rh  qqrr?  
A_negativer_rq_negq_rq_negrq_A_negtau_neginfo_negr1   r1   r2   test_geqrfpq	  s6   
"(r  c                  C   s(   t g } td| jd}tt||  d S )Nr  r   )r,   r|   r%   r0   r   r   )A_emptyr  r1   r1   r2   #test_geqrfp_errors_with_empty_array	  s   
r  driver)evevdevr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 d S  tyQ } ztd| | | W Y d }~d S d }~ww )	N  r  _lworkr   r   rK   r  ({}_lwork raised unexpected exception: {}r   r+   r%   r    r   r=   failrE  r  r	  r   r0   sc_dlwdz_dlwr  r1   r1   r2   test_standard_eigh_lworks	  s   r  gv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 d S  tyQ } ztd	| | | W Y d }~d S d }~ww )
Nr  r  r  r   r   rK   r3  r   r  r  r  r1   r1   r2   test_generalized_eigh_lworks	  s   r  dtype_r   )rK   ro   r  rO  c                 C   sx   t d td|}|| }| tv rdnd}|d }t|| d}t||||}|dkr,|n|f}tdd |D s:J d S )	Nr   r   orun	csd_lworkr   c                 S   s   g | ]}|d kqS r  r1   r@  r1   r1   r2   r>  	  s    z*test_orcsd_uncsd_lwork.<locals>.<listcomp>)r   r   r   r%   r    r  )r  r   r^   r?  r  dlwr3  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r8d|inttddg|}	||d |d |f |d ||d f ||d d |f ||d |d f fi |	\
}
}}}}}}}}}|d	ks|J t||}t||}t	t	||t	|| || }t	||| }t	||| | }t	|| || }t	|| || | }t
j||f| d}| d
}t|D ]}||||f< qt|D ]}|||| || f< qt|D ]}| ||| | || | | | | f< qt|D ]}|||| | | || | f< qt|D ]N}t
|| ||| || f< t
|| ||| | || | | f< t
||  ||| || | | | f< t
|| ||| | || f< q|| | }t||ddt
| j d d S )N)r  P      r  r  csdr   r   r   lrworkr   r   r  g     @r8  )r   r!   rvsr"   r%   r    dictr  r   rI  r,   r   r   cosr  r   r   r   )r  r   r^   r?  r  Xdrvr!  r"  lwvalscs11cs12cs21cs22thetau1u2v1tv2trd   r?  VHrh  n11n12n21n22Soner,  Xcr1   r1   r2   test_orcsd_uncsd	  sJ   
T

,$*,& r?  
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}|rR| tv rPd	nd
nd}|r[|
 j	n|
| }|
 |
 |	
 |
 g}|dkrw||||	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   ro   rK   rz   rL   rr   ru   r<  r  NrP   rA  r   dlfdfdufr  r  r   z?gtsvx info = z, should be zerorM   rl  __len__Trcond should be scalar but is z!ferr.shape is {} but shoud be {},z!berr.shape is {} but shoud be {},)r   r,   r   r   r%   r3   r  r   r~  rr   r  r   r   r   r   r/   rE  ) r0   r@  rA  r  rC  r  r   r  rj   r  r  r   r   r   
inputs_cpydlf_df_duf_du2f_ipiv_info_	gtsvx_outrE  rF  rG  du2fr  x_solnr  ferrberrrd   r1   r1   r2   
test_gtsvx
  sB   "rV  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 rFdnd	}|rO|	 jn|	|
 }|d
kr]||||nd gd \}}}}}}||||||||||||d}|\
}}}}}}}}}}|dkrd|d< d|d< |||||}|\
}}}}}}}}}}|dksJ dd S |d
krd|d< d|d< d|d< |||||||||||d
}|\
}}}}}}}}}}|dksJ dd S d S )Nr  rB  r   ro   rK   rz   rL   rr   ru   r  rP   rD  r<  r   z&info should be > 0 for singular matrix)rA  rE  rF  rG  r  r  )r   r%   r3   r,   r  r   r~  rr   )r0   r@  rA  rC  r  r   r  rj   r  r  r   r   r   rK  rL  rM  rN  rO  rP  rQ  rE  rF  rG  rR  r  rS  r  rT  rU  rd   r1   r1   r2   test_gtsvx_error_singularS
  sB   "
rW  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 rFdnd	}|rO|	 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 d S tt	||||||||d d ||||d tt	|||||||||d d |||d tt	||||||||||d d ||d tt	|||||||||||d d |d d S )Nr  rB  r   ro   rK   rz   rL   rr   ru   r  rP   r<  rD  )r   r%   r3   r,   r  r   r~  rr   r   r9  r   )r0   r@  rA  rC  r  r   r  rj   r  r  r   r   r   rK  rL  rM  rN  rO  rP  r1   r1   r2   "test_gtsvx_error_incompatible_size
  sZ   "

rX  zdu,d,dl,b,xc              
   C   sB   t d|jd}|||| |}|\
}}}	}
}}}}}}t|| d S )NrC  r   r%   r0   r   )r  rj   r  r   r   rC  rQ  rE  rF  rG  rR  r  rS  r  rT  rU  rd   r1   r1   r2   test_gtsvx_NAG
  s   rZ  zfact,df_de_lambdac                 C      t d|jd| |S Nr  r   r%   r0   rj   r  r1   r1   r2   <lambda>
  
    r_  c                 C      dS N)NNNr1   r^  r1   r1   r2   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rJ 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   rO   rN   rK   rz   rL   rA  rF  efr   zinfo should be 0 but is .rl  rH  rI  )rL   z#ferr.shape is {} but shoud be ({},)z#berr.shape is {} but shoud be ({},)N)r   r,   r   r   r%   r3   r  r~  r  r   r   r   r   r   rr   r   r/   rE  )r0   r  rA  df_de_lambdar  rd  r   rj   r  r  rS  r   rF  rf  rd   r  r   r  rT  rU  r3  r4  r1   r1   r2   
test_ptsvx
  s>   (


ri  c                 C   r[  r\  r]  r^  r1   r1   r2   r_    r`  c                 C   ra  rb  r1   r^  r1   r1   r2   r_    rc  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  rd  r   rO   rN   rK   rz   rL   re  )	r   r%   r3   r,   r  r~  r   r9  r   )r0   r  rA  rh  rd  r   rj   r  r  rS  r   rF  rf  rd   r1   r1   r2   test_ptsvx_error_raise_errors  s   (  $rj  c                 C   r[  r\  r]  r^  r1   r1   r2   r_  2  r`  c                 C   ra  rb  r1   r^  r1   r1   r2   r_  4  rc  c                 C   sf  t d td| d}d}t|f|d }t|d f| }t|t|d tt|d }t|df| d}	||	 }
|||\}}}|d	krd
|d< |||\}}}||||
\}}}}}}}|d
kri||kskJ t|f|}||||
\}}}}}}}|d
kr||ksJ d S |||\}}}d
|d
< d
|d
< ||||
|||d\}}}}}}}|d
ksJ d S )Nr  rd  r   rO   rN   rK   rz   rL   r<  r   rM   re  )r   r%   r3   r,   r  r~  )r0   r  rA  rh  rd  r   rj   r  r  rS  r   rF  rf  rd   r   r  rT  rU  r1   r1   r2   test_ptsvx_non_SPD_singular.  s0   (
rk  zd,e,b,xc                 C   s6   t d|jd}|| ||\}}}}}	}
}t|| d S )Nrd  r   rY  )rj   r  r   r   rd  rF  rf  x_ptsvxr  rT  rU  rd   r1   r1   r2   test_ptsvx_NAGZ  s   rm  r	  c                    s  t d t| jd }d\ }t  g| d}t |g| d}| j| tj | d| d  }|rK fddt D  fddt D f}nd	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  )ro   rN   r   r   c                    s    g | ]}t | D ]}|q	qS r1   r   r=  yr   rA  r1   r2   r>         z5test_pptrs_pptri_pptrf_ppsv_ppcon.<locals>.<listcomp>c                    s    g | ]}t | D ]}|q	qS r1   rn  ro  rA  r1   r2   r>    rq  c                 S   s   g | ]}t |D ]}|qqS r1   rn  ro  r1   r1   r2   r>    s    rK   c                 S   s"   g | ]}t |D ]}|d  qqS r  rn  ro  r1   r1   r2   r>    s   " )ppsvpptrfpptrspptrippconr  r  r  r   r8  )r  r	  r  )r   r,   r   r   r3   r~  rr   r
   r   r%   r   r   r   r   r   r  r   r   r   r  )r0   r	  r  r   r\   r   r  aprr  rs  rt  ru  rv  ulrd   aululiaulir   bxxvr  r  r1   rA  r2   !test_pptrs_pptri_pptrf_ppsv_ppconx  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 rIt|t	|d|d t|| |
 j |d|d |||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  ro   r   )geestrexcc                 S      d S r  r1   r   r1   r1   r2   r_    rc  z!test_gees_trexc.<locals>.<lambda>Frt  rz   r   r1  r  r8  rQ   rK   r   r   )r   r,   r   r   r3   r%   r   r+   r   r   r~  rr   )
r0   r  r   r\   r  r  r  r=  r  d2r1   r1   r2   test_gees_trexc  s*   r  zt, expect, ifst, ilst)ra  g)\({Gz?gQ?)r  皙r  ffffff?)r  gr  g?)r  r  r  r  )r  lV}gV_?g|?5^?)g?r  gV/?g;On?)r  r  ra  ggj+)            y
ףp=
?
ףp=
׿yRQȿQ?y)\(?      п)rl               @yQ
ףp=
yq=
ףpͿp=
ף?)rl  rl         @      yGz?(\?)rl  rl  rl        @      )r  y1%Ŀq?ys??ܵ|ȿyHzG??ܵ?)rl  r  yV/?ݓ?yjt?vտ)rl  rl  r  yB>٬?=U?)rl  rl  rl  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   )wantqrz   rl  N)r%   r0   r   r   )r=  ifstilstexpectr  r  r  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 rt|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  ro   r   )ggestgexcc                 S   r  r  r1   r  r1   r1   r2   r_    rc  z!test_gges_tgexc.<locals>.<lambda>Fr  overwrite_brz   r   rK   rk  r1  r   r  r8  rQ   rL   rM   r  )r,   r  sysplatformblas_providerblas_versionr=   xfailr   r   r   r3   r%   r   r+   r   r   r~  rr   )r0   r  r   r\   r   r  r  r  r   r=  r?  r  d1r  r1   r1   r2   test_gges_tgexc  sJ   


 r  c                 C   sr  t d t| jd }d}t||g| d}td| d\}}}|dd |dd	}t|d
 d |d }|d }	|d }
| tv rJt|t	|d|d t|	| |	
 j |d|d t|}d|d< t|||}| tv ru||||	|d}n||||	||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  ro   r   )r  trsentrsen_lworkc                 S   r  r  r1   r  r1   r1   r2   r_  8  rc  z!test_gees_trsen.<locals>.<lambda>Frt  rz   r   r1  r  r8  rK   rP   r   r   liworkr   )r   r,   r   r   r3   r%   r   r+   r   r   r~  rr   r   r    )r0   r  r   r\   r  r  r  r  r=  r  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?)r  58EGrgGr?gyX5;?)r  g?߾r  gt?)r  r  r  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)\(?)rK   r   r   rK   g      ?g(\	@)yqh yfc]F?ڊe׿yMbȿ&S?y&1??п)rl  y      ?5^I @yo0*yZd;OͿ~:p?)rl  rl  yx$(@4@y[ A?&?)rl  rl  rl  y?ܵ@St$)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 r!||| ||
d}n||| ||
|
d d}t|d d	 |d	 } |d }| jtv rI|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   rK   r  rz   r   rN   rO   rP   rl  N)r%   r0   r    r+   r   r   r~  rr   )r=  r?  r  r  expect_s
expect_sepr  atol2r  r  r   r  r   sepr1   r1   r2   test_trsen_NAG[  s(   0



r  c                 C   sr  | 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 rt|	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  ro   r   )r  tgsentgsen_lworkc                 S   r  r  r1   r  r1   r1   r2   r_    rc  z!test_gges_tgsen.<locals>.<lambda>Fr  rz   r   rK   rk  r1  r   r  r8  rP   r   ir  r  )r,   r  r  r  r  r  r=   r  r   r   r   r3   r%   r   r+   r   r   r~  rr   r   r    )r0   r  r   r\   r   r  r  r  r  r   r=  r?  r  r  r  r  r   r1   r1   r2   test_gges_tgsen  sV   



 r  r  )r  	functoolsr   numpy.testingr   r   r   r   r   r   r=   r	   r   numpyr,   r
   r   r   r   r   r   r   r   numpy.randomr   r   r   scipy.linalgr   r5   r   r   r   r   r   r   r   r   r   r   scipy.linalg.lapackr    scipy.statsr!   r"   scipy.sparsesparserF  scipy.__config__r#   ImportErrorr$   r4   r%   scipy.linalg.blasr&   r  r#  r   rp  
complex128r+   r   r  r  r3   rH   rJ   r   r   r]  r^  r   r   r  r  r/  ri  rv  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r#  r'  r-  r6  r7  rV  rY  ra  ri  skipifrq  rx  r   r  r  r  r|   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r#  r?  rV  rW  rX  rZ  ri  rj  rk  rm  r~  r  r  r  r  r  r  r1   r1   r1   r2   <module>   sf   (4` t  **DO1")::) %# ((-
e
#





\




+
/


	



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