o
    ?Hh}                    @   s  d dl mZ d dl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 e3y   dZ2Y nw zd dlm4Z5 W n e3y   dZ5Y nw 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(ZMe
jGHde?e
jGHd)g d*e
jGHd+d,d-ge
jGHd.d/d,ge
jGHd0d1d2gd3d4 ZNd5d6 ZOd7d8 ZPd9d: ZQd;d< ZRG d=d> d>ZSG d?d@ d@ZTdAdB ZUdCdD ZVdEdF ZWdGdH ZXdIdJ ZYdKdL ZZdMdN Z[dOdP Z\dQdR Z]dSdT Z^dUdV Z_dWdX Z`dYdZ Zad[d\ ZbG d]d^ d^Zcd_d` Zddadb Zedcdd Zfdedf Zge
jGjhdgdhdidjdk Zidldm Zje
jGHdndodpge
jGHde;e
jGHdqekdre
jGHdsekdte
jGHduekdte
jGHdvd dwge
jGHdxd dwgddydzZle
jGHde;d{d| Zme
jGHd}dqd~idsd~idud~idvd~idd~idxd~ifdd Zne
jGHdeog dg dg dg dg dg dgeog deog dg dg dg dg dg dgeog dg dg dg dgfgdd Zpe
jGHde?dd Zqe
jGHdeog deog deog deog deog deog deog deoddgddgddgddgddggeoddgddgd1dgddgddwggf	eog deog deog deog deog deog deog deoddgddgddgddgddggeoddgddgddgddgddggf	gddɄ Zre
jGHde?e
jGHd)g dʢe
jGHd0d1d2gdd̄ Zse
jGHde?e
jGHdg d͢ddτ Zte
jGHdeue;e; e?dd҄ Zve
jGHdeue;e; e?ddԄ Zwe
jGHdeue;e; e?ddք Zxe
jGHdeog dآeog d٢eog dڢeog dۢeodrd2gd~dtgdd~gddgddggeoddgddgdwdgddrgd1dggfeog deog deog deog deoddgddgddgddggeoddgddgddgddggfgdd Zydd Zze
jGHdeue?e;e; e
jGHdekd1dd Z{e
jGHdeue?e;e; e
jGHdekd1dd Z|e
jGHdeue?e;e; e
jGHdekd1dd Z}e
jGHdeue?e;e; e
jGHdekd1dd Z~e
jGHddeog d eog deog deog dg dg dg dgfgdd Ze
jGHde?e
jGHd	g d
dd Zdd Ze
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"dgge
jGHd#d$d/gd%d& Ze
jGHde?e
jGHd!d dwge
jGHd#d$d/gd'd( Ze
jGHde?d e
jGHd!d"dgge
jGHd#d$d/gd)d* Ze
jGHd+eog deog deog deoddgddgddgddgddggeoddgddgd1dgddgddwggfeog deog deog deoddgddgddgddgddggeoddgddgddgddgddggfgd,d- Ze
jGHdeue?e;e; e
jGHd.d$d/d0 fd/d1d0 fgd2d3 Ze
jGHdeue?e;e; e
jGHd.d$d4d0 fd/d5d0 fgd6d7 Ze
jGHdeue?e;e; e
jGHd.d$d8d0 fd/d9d0 fgd:d; Ze
jGHd<eog dآeog d٢eodrd2gd~dtgdd~gddgddggeoddgddgdwdgddrgd1dggfeog deog deoddgddgddgddggeoddgddgddgddggfgd=d> Ze
jGHd?d"dgge
jGHde?d@dA Ze
jGHde?dBdC Ze
jGHdDeog dEg dFg dGg dHgeog dIg dJg dKg dHgddwfeog dLg dMg dNg dOgeog dPg dQg dRg dSgdwdtfgdTdU Ze
jGHde?dVdW Ze
jGHde?dXdY Ze
jGHdZeog d[g d\g d]g d^geog d_g d`g dag dbgeog dcg ddg deg dfgeog dgdhdifeog djg dkg dlg dmgeog dng dog dpg dqgeog drg dsg dtg dugeog dgdvdwfgdxdy Ze
jGHde?dzd{ Ze
jGHd|eog d}g d~g dg dgeog dg d~g dg dgeog dg dg dg dgeog dg dg dg dgeog dg dg dg dgeog dg dg dg dgeog dg dg dg dgeog 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 Ze
jGHdddge
jGHde?e
jGHd?ddd Ze
jGHd)ede
jGHdg de
jGHd.d/d,ge
jGHde?dd ZdS (      )reduceN)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 Dependenciesblasnameversionc                 C   s6   |t v r|j|  |j|  d  |S |j|  |S )N              ?)COMPLEX_DTYPESr   astype)shapedtyperng r1   ^/home/air/sanwanet/gpt-api/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>   np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   



rI   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)         )         )      	   )rL   r   r   ga2U0*3?)rO   r   r   gMb`?)rR   rL   r   r   )r   rL   r   r   sdzcgebalr   rL   )permutescale)	getattrr6   r   reprr   r   lenr4   r   )
selfaa1pfbalohipivscaleinfor1   r1   r2   
test_gebalR   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)rY   r6   r   rZ   )r\   r]   r_   r`   httaure   r1   r1   r2   
test_gehrdg   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 )NrL   rM   r   rO   rP   rQ   rS   rT   
         TfdFD)trsylr+   C)tranatranbdecimal)isgn)	r4   arrayr-   r&   isupperr   dot	conjugaters   )r\   r]   bctransr/   r^   b1c1ru   xrX   re   r1   r1   r2   
test_trsylr   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 )Nrg   rh   rj   rt   Mm1OoIiFfEer   r   r+   )langeFfEeFfrN   rR   Mm1Oor   axisIirL   )r4   r}   r-   r~   r&   sqrtsumsquareabsr   maxr   )	r\   r]   r/   norm_strr^   r   valuerz   refr1   r1   r2   
test_lange   s6   

zTestFlapackSimple.test_langeN)__name__
__module____qualname__rf   ro   r   r   r1   r1   r1   r2   rK   P   s
    rK   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)hasattrr6   r\   r1   r1   r2   test_flapack      
zTestLapack.test_flapackc                 C   r   r   )r   r5   r   r1   r1   r2   test_clapack   r   zTestLapack.test_clapackN)r   r   r   r   r   r1   r1   r1   r2   r      s    r   c                   @   rJ   )
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  rp      rL   )gels
gels_lworkr/   lworkr   TTCCr   r         ?       @      @      @      @       @      0@g      1@g      4@)r   r   geqrfrM   r{   祪,-@   rtol      ?      @      @      ?      @            @              @ffffff?r   y      1@       @y      4@      R ?\j,? W?)r   	enumerateDTYPESr   r-   r&   r!   r   REAL_DTYPESr4   r}   r.   r[   r   finfoepsr   r,   )r\   indr/   mnnrhsr^   r   glsglslwr   r<   re   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_lworkrM   rL   r{   Fr   r   r   r   YN))1)@*@.?r   r   r   r   r   r   r   r   U.*@_Y@r   r4   r}   r&   r.   r[   intrealr   r   r   r,   )r\   r/   r^   r   r   r   r   r   r   workiworkre   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_lworkrM   rL   r{   Fr   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   re   r   vr   r   r   r1   r1   r2   
test_gelss?  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   rM   rL   rp   Fr{   r   r   r   r   r   r   r   r   r   r   r   r   )r   r4   r}   r&   r.   r[   r   r   r   r   r   int32r   r,   )r\   r/   r^   r   r   gelsy_lworkr   r   r   r   re   r   jptvr   r   jr   r1   r1   r2   
test_gelsyx  st   



z"TestLeastSquaresSolvers.test_gelsyN)r   r   r   r   r   r   r   r1   r1   r1   r2   r      s
    D<9r   r/   r.   )rN   rO   )rP   rM      r   c                 C   2   t d| d}|\}}|||d\}}t|d d S )Ngeqrf_lworkr   r   r   r   r&   r   )r/   r.   r   r   r   r   re   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,  rM   r   gerqfrM   r   orgrqrL   ungrq)r   r4   r   r&   assert_raises	Exceptionr   r,   )
r\   r/   r]   r   rqrn   r   re   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*   )rN   rN   size)potrfpotri)cleanr   )r4   randomr   normalr   rs   r&   r   r   r   r   )
r\   lowerr	  r   r]   dpotrfdpotrir   re   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   r{   rL   F)full_matrices
compute_uvoverwrite_acheck_finiter   lasd4rN   zcLAPACK root finding dlasd4 failed to find                                     the singular value %izThere are NaN rootsd   atolr   )r4   r}   hstackvstackdiagr   r[   newaxisr   concatenater   r&   rangerE   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   r1  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 )	TestTbtrsr/   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=
ף0r3  g(\+gףp=
0g333333*@g(\gHzG,gQ#rO   rL   r{   rN   rM   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   r4   r}   r,   
ValueErrorr&   r   r   )r\   r/   r8  r   x_outr5  r   re   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 ))Nrs   rv   rv   )r   ).0r/   r   r1   r1   r2   
<listcomp>3  s    zTestTbtrs.<listcomp>r9  Ur6  r   r?  c                    s  t jdd\}}td d}|dk}|| }	||	 }
t|	|
 d d}fdd	|D } fd
d	|D }|dkrFt j d||	< tj||dd}t |d f }t	|D ]\}}|
|||t|dt| f< q\t|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  )rO   rN   rM   r5  r   rB  rL   r{   c                    s   g | ]} t | qS r1   )r   r@  r   r   r1   r2   rA  H      z2TestTbtrs.test_random_matrices.<locals>.<listcomp>c                    s   g | ]	}t |f qS r1   )r3   )r@  widthr/   r0   r1   r2   rA  I  s    dia)formatr   )r8  r   r9  r   r   r?  g-C6
?r   rs   rv   zInvalid trans argument)r4   r
  RandomStater&   r#  r   spsdiagsr   r   diagonalr   minr3   r   r   rs   r   r<  )r\   r/   r   r9  r   r   kdr5  is_upperkuklband_offsetsband_widthsbandsr]   r8  rowkr   r   re   r1   )r/   r   r0   r2   test_random_matrices2  s6   
(
zTestTbtrs.test_random_matriceszuplo,trans,diag)rB  r?  Invalid)rB  rY  r?  )rY  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 exceptionsr5  r   rO   rM   N)r&   r4   r&  r   r   r   )r\   r9  r   r   r5  r8  r   r1   r1   r2   &test_invalid_argument_raises_exceptionf  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   rO   r5  r   )r{   rN   rB  r7  N)r4   r   floatr&   r   )r\   r8  r   r5  r<   re   r1   r1   r2   test_zero_element_in_diagonals  s   z'TestTbtrs.test_zero_element_in_diagonalzldab,n,ldb,nrhs)rP   rP   r   rP   )rP   rP   rN   rP   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   r5  Nr4   r   r[  r&   r   r   )r\   ldabr   ldbr   r8  r   r5  r1   r1   r2   test_invalid_matrix_shapes  s   z$TestTbtrs.test_invalid_matrix_shapesN)r   r   r   r>   markparametrizer   r>  rX  rZ  r\  r`  r1   r1   r1   r2   r2    s0    
-.
	r2  r   )I1Or9  rB  r6  r   r?  r   rN   rp   c              	   C   s  t |  | | | |  tj t dd}|j ||fd|j ||fdd  }|td|dd|}||7 }t| tj	rG|j
n|}|dkrRt|nt|}|dkri|t|d d tjf  }|| }td|f}|||||d\}	}
|d	krtjj|tjd
}tjjtj|tjd
}d||  }n#t|jdd }td|f\}}||\}}}||||d\}}
d}t|	||d d S )Nr   l   a$r  r+   rp   rB  trcon)r   r9  r   rc  )ordrL   r   gecongetrfr   r   )r
  r   r4   default_rngr   permutedlogspaceintegers
issubdtypefloatingr   r   r   r   r!  r-   r&   linalgr   infr   r   r   r   r   )r/   r   r9  r   r   r0   Aoffsetrf  r0  r<   norm_A
norm_inv_Ar   anormri  rj  luipvtre   r   r1   r1   r2   
test_trcon  s,   $
r{  c                  C   s   dD ]M} t d| d}td| }td| }t|r|d9 }|||\}}}t|d t|d t|rJt|d	 tt|t tt|t qt|d
 qd S )Nrt   lartgr   rN   rO   r+   333333?r   y       皙?)	r&   r4   r}   iscomplexobjr   r   
isinstancecomplexr[  )r/   r|  r`   gcs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 )Nrt   r}  r~  rO   rN   rp   rL   fdrotr   y             r+   y              @)rP   rP   rP   rP   )r   r   r   r   r  rM   rD  )rP   rP   rN   rN   r   )offxoffy)rN   rN   rP   rP   )incxr  r   )rP   rN   rP   rN   )r  incyr   )r  r  r  r  r   )rN   rN   rP   rN   r   )r  r  r   )overwrite_xoverwrite_y)r4   fullr   	precisionr'   r&   r   r   )
r/   r   r   ur   r  r  r`   r]   r   r1   r1   r2   test_rot  sX   

r  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   )rO   rO   r+   rt   larfglarfr   FDr   rL   rL   r   rM   r   r   Rsider:  r  )r4   r
  r   rs   r   conjr&   copyr.   r   r   r   r   )a0a0jr/   r  r  r]   alphar   rn   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r/   ilp64iA%  T)r  r  i`DiD)r&   r4   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 )		TestSytrdr/   c                 C   *   t jd|d}td|f}tt|| d S )Nr   r   sytrdr4   r   r&   r   r<  )r\   r/   rt  r  r1   r1   r2   test_sytrd_with_zero_dim_array@     z(TestSytrd.test_sytrd_with_zero_dim_arrayr   rL   rN   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_lworkrL   rM   r   r  r   rP   r   r          r   r{   )r4   r   r&   arangetriu_indices_fromr   r   r   r   r   r   r.   r
   r#  outerr   r   rs   )r\   r/   r   rt  r  r  r   re   datark   ern   rs   rW  k2Qr/  r   Hi_lowerQTAQr1   r1   r2   
test_sytrdG  s@   





$ zTestSytrd.test_sytrdN)	r   r   r   r>   ra  rb  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  rt  r  r1   r1   r2   test_hetrd_with_zero_dim_array  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_lworkrL   rM   r+   r   rL   r  r   r  rP   r   r  r  r   r{   rp   )r4   r   r&   r  r  fill_diagonalr   r   r   r!   r   r   r   r   r.   r   r
   r#  r  r  r   r   rs   )r\   r   
real_dtyper  rt  r  r  r   r<   re   r   r  rk   r  rn   rs   rW  r  r  r/  r   r  r  QHAQr1   r1   r2   
test_hetrd  sR   
"





zTestHetrd.test_hetrdN)r   r   r   r>   ra  rb  r,   r  zipr   r  r1   r1   r1   r2   r    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   rQ   rO   rM   )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?$_Kdy^gŵ翸F@y!f?}dy61ŵe_@ry   )r   r   r&   r!   r4   r}   r   r   )r   r/   func
func_lworkr   r]   r   rk   r   r<   resultr  r1   r1   r2   
test_gglse  sN   


r  c                  C   s  t d ttt D ]\} }d}| dk r+td|d}td|d\}}t|||}ntd|d}td|d\}}t||t||d	  |}|| j d
 d
t	j
||d  }t|d}t||}|||dd\}	}
}||	|
|dd\}}ttd| t	jj|dd | dk  q
d S )Nr   rp   rO   sytrf_lworkr   )syconsytrfhetrf_lwork)heconhetrfr+   rM   rL   )r   r  )r]   ipivrx  r  r_   )r   r   r   r,   r&   r   r-   r  rs   r4   r
   r   r!   r   r   rr  cond)r   r/   r   r  funconfunctrfrt  rx  r   ldur  r<   rcondr1   r1   r2   test_sycon_hecon  s"   $

*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   rp   )r  sygstsyevdsygvdr   rM   r   giUMu?r   )r   r   r   r&   r   r-   rs   r4   r
   r   r   )r   r/   r   r  r  r  r  rt  Beig_gvdr<   re   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   rp   )r  hegstheevdhegvdr   r+   rM   r   -C6?r   )r   r   r,   r&   r   r-   r  rs   r4   r
   r   r   )r   r/   r   r  r  r  r  rt  r  r  r<   re   r   r]   r  r1   r1   r2   
test_hegst=  s(   $$$r  c               	      sv  t jd} d\}}ttD ]\}}td|d\}}t|||}|dk r0t| ||	|}n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   rp      tzrzftzrzf_lworkr   rM   r+   r   r   Nc              
      D   g | ]} | |gd d f j |gd d f    qS Nrs   r   r  rC  IdVrn   r1   r2   rA  x     D ztest_tzrzf.<locals>.<listcomp>rp   r   r  r  )r4   r
  rJ  r   r   r&   r!   r   r   r-   r   r   rs   r   r  r   r
   r#  r   r   r   r   spacingr   )r0   r   r   r   r/   r  tzrzf_lwr   rt  rzre   r  r   Zr1   r  r2   
test_tzrzf\  s,   
&0(r  c               	   C   s  t jd} ttD ]\}}d}|dkr.t| ||| ||d  t| |}d}nt| ||t| |}d}t	d|d\}}}||\}	}
| |d	|}|d
|	|}t
|t| ||d	 dkrld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 | 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   rL   r+   rv   rs   )trttftfttrtfsmr   rM   r{   r   rO   rQ   ry   r   r   rB  )r   r   rN   r  )r   r   r  N)r4   r
  rJ  r   r   r   r   r
   r-   r&   r   r   r  rs   r  )r0   r   r/   r   rt  r   r  r  r  Afpr<   r  solnB2r1   r1   r2   	test_tfsm~  s@   .r  c               	      s  t jd} d\}}}ttD ]3\}}td|d\}}t|||}|dk rCt| ||	|}	| ||	|}
td|d\}}n+t| ||| ||d  	|}	| ||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 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   )rp   r  r  r  r   rM   )ormrzormrz_lworkr+   )unmrzunmrz_lworkr   Nc              
      r  r  r  rC  r  r1   r2   rA    r   z$test_ormrz_unmrz.<locals>.<listcomp>rs   rv   rp   r   r   r  r  r   r  )r  r   )r  r   r   )r4   r
  rJ  r   r   r&   r!   r   r   r-   r  r
   r#  r   r   r  r   r   r   r   r  rs   )r0   qmqncnr   r/   r  r  lwork_rzrt  rv   orun_mrzorun_mrz_lw	lwork_mrzr  re   r   r  r   tolcqr1   r  r2   test_ormrz_unmrz  sV   

& 
(r  c               	   C   s
  t jd} ttD ]w\}}d}|dkr)| ||| ||d  |}d}n| |||}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 Rectangular Full Packed (RFP) format
    and Standard Triangular Array (TR)
    r   r   rL   r+   rv   rs   )r  r  r   r   r6  r9  rB  )transrr9  rM   Nr{   F)order)r4   r
  rJ  r   r   r   r-   r&   r   r   r   r  rs   r   r   reshape)r0   r   r/   r   A_fullr  r  r  A_tf_Ure   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   s|  t jd} ttD ]\}}d}|dkr&| ||| ||d  |}n	| |||}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   rL   r+   )trttptpttrr   r   r6  r  rM   N)r4   r
  rJ  r   r   r   r-   r&   r   r   r   r   rs   r   r   r   )r0   r   r/   r   r"  r.  r/  A_tp_Ure   A_tp_LindsA_tp_U_mA_tp_L_mr)  r*  r1   r1   r2   test_tpttr_trttp  s4   $

r5  c                  C   s   t jd} ttD ]i\}}d}|dkr3| ||| ||d  |}|| j |t	|  }n| |||}||j |t	|  }t
d|d\}}}||\}}	|||\}
}	t|	dk |||
\}}t|}t|| q
dS )	zk
    Test Cholesky factorization of a positive definite Rectangular Full
    Packed (RFP) format array
    r   r   rL   r+   )pftrfr  r  r   r   N)r4   r
  rJ  r   r   r   r-   r  rs   r
   r&   r   r   r   )r0   r   r/   r   rt  r6  r  r  r
  re   	Achol_rfpA_chol_rr<   Acholr1   r1   r2   
test_pftrfD  s$   "r:  c                  C   s  t jd} ttD ]}\}}d}|dkr3| ||| ||d  |}|| j |t	|  }n| |||}||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 Rectangular Full
    Packed (RFP) format array to find its inverse
    r   r   rL   r+   )pftrir6  r  r  r   r   rM   rO   rQ   ry   N)r4   r
  rJ  r   r   r   r-   r  rs   r
   r&   r   r   r   r   )r0   r   r/   r   rt  r;  r6  r  r  r
  re   
A_chol_rfp	A_inv_rfpA_inv_rr<   Ainvr1   r1   r2   
test_pftri_  s*   "
r@  c                  C   sf  t jd} ttD ]\}}d}|dkr3| ||| ||d  |}|| j |t	|  }n| |||}||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 Rectangular Full
    Packed (RFP) format array and solve a linear system
    r   r   rL   r+   rN   r   rM   )pftrsr6  r  r  r   rO   rQ   ry   N)r4   r
  rJ  r   r   r   r-   r  rs   r
   r   r&   r   r   r   r   r   )r0   r   r/   r   rt  r  Bf1Bf2rA  r6  r  r  r
  re   r<  r  r1   r1   r2   
test_pftrs  s2   "rD  c                  C   s8  t jd} ttD ]\}}d}|dkr3| ||| ||d  |}|| j |t	|  }n| |||}||j |t	|  }|dk rMdnd}t
dd	| d
f|d\}}}||\}	}
| |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   rL   r+   rM   r   hr  r  frkr   r{   r   rO   rQ   ry   N)r4   r
  rJ  r   r   r   r-   r  rs   r
   r&   r   r   r   )r0   r   r/   r   rt  prefixr  r  shfrkr
  r<   rv   Afp_outA_outr1   r1   r2   test_sfrk_hfrk  s(   " rK  c                  C   s  t jd} ttD ]\}}d}|dkr3| dd||f| dd||fd  |}|| j }n| 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   rp   rL   i   r+   r  r   )syconvr  r  r   r  F)r  	hermitianr  r{   Nr  r  r   )r4   r
  rJ  r   r   r   r-   r  rs   r
   r  r   r&   r!   r   r   r   r   )r0   r   r/   r   rt  r  rM  trf	trf_lworklwr6  Dpermr  r  re   r]   r  rB  r1   r1   r2   test_syconv  s6   (*rT  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   sB  t jd}ttD ]\}}d}|dkr'||||||d  |}n	||||}dt |dj }t	d|d\}}|||\}	}
}|d	ksPJ t 
|	d
t j||d }t j||d||
 |j   }t |	}t|j | t j||d|dd t|| ||dd |dkr||||||d  |}d}n||||}d}dD ]V}d|fD ]O}||	|
|||d\}}|d	ksJ ||kr|j }n|}|dkr|| }n|| }t|||dd ||fdkr||	|
|\}}|d	ksJ t|| qqtt||	|
|dd tt||	|
|dd q
d S )Nr   r   rL   r+   r  r   )geqrtgemqrtr   r   r{   r  r  rv   rs   r6  r  r?  r  r   r6  r6  r?  rt  r  r	  )r4   r
  rJ  r   r   r   r-   r  r   r&   r   r
   rs   r  r   r   r   r   r   )r\   r0   r   r/   r   rt  r  rV  rW  r]   tre   r   r  r  rv   	transposer  r   r   qqC	c_defaultr1   r1   r2   test_geqrt_gemqrt  sT   $ 
"

zTestBlockedQR.test_geqrt_gemqrtc           !      C   s  t jd}ttD ]\}}d}|dkr8||||||d  |}||||||d  |}n||||}||||}dt |dj }t	d|d\}}	d	|d
 |fD ]z}
||
|||\}}}}|d	kswJ t
t |dt |d t
t ||
| d t ||
| d  t ||
| t ||
| }}t t j||d|f}t jd
| |d|| |j   }t t |t |f}t|j | t jd
| |d|dd t|| t t ||f|dd |dkr%||||||d  |}||||||d  |}d}n||||}||||}d}dD ]}d|fD ]}|	|
||||||d\}}}|d	ksXJ ||krc|j }n|}|dkrt j||fd	d}t j||fd	d}|| }nt j||fdd}t j||fdd}|| }t|||dd ||fdkr|	|
||||\}} }|d	ksJ t
|| t
| | qAq;tt|	|
||||dd tt|	|
||||dd qcq
d S )Nr   r   rL   r+   r  r   )tpqrttpmqrtr   r   rM   r{   r  r  rv   rs   rX  r?  rY  r6  r   rZ  rt  r  r	  )r4   r
  rJ  r   r   r   r-   r  r   r&   r   r   r   r"  r
   rs   r  r   r   r   r   )!r\   r0   r   r/   r   rt  r  r  ra  rb  lr]   r   r[  re   B_pentb_pentr   r  r  rv   rR  r\  r  r   r   rk   r]  cdCDqCDr_  	d_defaultr1   r1   r2   test_tpqrt_tpmqrt%  sx   "$*"$
""




zTestBlockedQR.test_tpqrt_tpmqrtN)r   r   r   r=   r`  rj  r1   r1   r1   r2   rU    s    >rU  c                  C     t jd} ttD ]\}}d}d}td|d}|dkr<| ||| |d| ||| |  }|| j	 }n| ||| |}||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   rp   rM   pstrfr   rL   r+   r    r   rM   r;  r  r4   r
  rJ  r   r   r&   r   r-   r  rs   r   r   r   r  r   r&  r   r   )r0   r   r/   r   r  rl  rt  r   pivr_cre   rB  single_atoldouble_atolr  r6  r1   r1   r2   
test_pstrfy  6   0

2
4rt  c                  C   rk  )Nr   rp   rM   pstf2r   rL   r+   r  rm  rn  r;  r  ro  )r0   r   r/   r   r  rv  rt  r   rp  rq  re   rB  rr  rs  r  r6  r1   r1   r2   
test_pstf2  ru  rw  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ſFxrM   )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;  )r4   r}   r   r   r-   r&   r   )desired_realdesired_cplxr   r/   rt  ry  r  r   rowcndcolcndamaxre   r1   r1   r2   
test_geequ  sP   





  r  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   r{   r{   r   r4  rp   r   rM   r   r+   c                    s   g | ]} d |  qS )r   r1   rC  r  r1   r2   rA    rE  ztest_syequb.<locals>.<listcomp>rP   syequb)r4   r}   r   r   r
   r#  rot90r   r&   r   log2r-   r   )
desired_log2sr   r/   rt  rk   r  r   scondr~  re   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 )NrM   rP   i  rT   rL   )rW  r+   r   r  r  r  rQ                   i   rP   rP   y              0@)rP   r   r  )r   r{   r{   r   r   r  r   r{   r{   r   r   )r4   r   r   r   zheequbr   r   r  r   r  cheequbr-   	complex64)rt  r   r  r~  re   r1   r1   r2   test_heequb  s   2
( 
r  c                  C   s.  t jd} d}| |}| || |d  }ttD ]w\}}|dk r:| ||}||}|| }||}n| ||| ||d  }||}|| }||}td|d}td|d}	||dd	\}
}}}|	|
|||dd
\}}|dk rt|||| dd qt|||| dd qd S )Nr  rp   r+   rM   getc2r   gesc2r   r  )overwrite_rhsrO   ry   )	r4   r
  rJ  r   r   r   r-   r&   r   )r0   r   rz  r{  r   r/   rt  r   r  r  ry  r  jpivre   r   rX   r1   r1   r2   test_getc2_gesc2  s4   





r  r  )rQ   rP   r  jobarQ   joburO   jobvjobrrL   jobpc              
   C   s  t jd}| \}	}
dt |j }t| ||}td|d}|dk }|dk }|dko-|	|
k}t |}|dko<| o<| }|dkoG|oD| oG|}|dkoR|oO| oR|}|rXd}n	|s\|r_d}nd	}|dkrw|dkrwt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   rM   rL   r   r4  r   )r  r  r  r  jobtr  NF)r  r  )r4   r
  rJ  r   r   r3   r&   r  r   r   r   r   r   r   r  rs   identityrr  matrix_rankcount_nonzero)r  r/   r  r  r  r  r  r  r0   r   r   r  rt  r  lsvecrsvecl2tran
is_complexinvalid_real_jobvinvalid_cplx_jobuinvalid_cplx_jobvexit_statussvar  r   r   r   re   sigmar1   r1   r2   test_gejsv_general8  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   rL   rL   rL   r  r  rp   rt  N)r&   r   r.   r4   r}   r   sinr  r!  r-   asfortranarrayrs   r  r   )r/   r  r  r  r   r   r   re   rt  Acr<   r1   r1   r2   test_gejsv_edge_arguments  s.   



r  kwargsrT   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)rM   rM   r   r  Nr]  )r  rt  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$g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ?g_vO?)g}?5^Iؿg58EGr?gi o?g7[ Ac                 C   sT   d}t d| jd}|| \}}}}	}
}t|||d t|||d t|||d dS )z~
    This test implements the example found in the NAG manual, f08khf.
    An example was not found for the complex case.
    r  r  r   r  N)r&   r/   r   )rt  
sva_expectu_expectv_expectr  r  r  r  r   r   r   re   r1   r1   r2   test_gejsv_NAG  s   r  c           "   	   C   s  t jd}d}dt | j }t|d f| |d}t|f| |d}t|d f| |d}| | | g}t |t |d t |d }t j|}	||	 }
t	d| d\}}||||\}}}}}}t
||d	  t
||d  t
||d
  t |d	t |d t |d
 }t j|| d}t|D ]2\}}|| d }|d d ||gf |d d ||gf< |d d |f  |d d |d f | 7  < qd|d d }}|d d ||gf |d d ||gf< t||| |d |
 }|||||||
\}}t
|
| t|	||d | tv rd}|j|	 }n	d}| j|	 }||||||||d\}}t|	||d tt ||d d || W d    n	1 sNw   Y  tt |||d d | W d    n	1 smw   Y  tt ||||d d  W d    n	1 sw   Y  tt ||d	 |d d |d	  W d    n	1 sw   Y  d	|d	< d	|d	< ||||\}}}}} }!t j||d  d	kd||d   d d S )Nr  rp   r  rL   rG  r{   gttrfgttrsr   r   rM   r  rs   rv   r	  z?gttrf: _d[info-1] is , not the illegal value :0.)r4   r
  rJ  r   r   r3   r  r   r   r&   r   r
   r   r   r   rs   r  r   r<  testingr   )"r/   r0   r   r  durk   dldiag_cpyrt  r   r   r  r  _dl_d_dudu2r  re   rB  r6  r/  r   rp  b_cpyx_gttrsr   b_trans__dl__d__du_du2_ipiv_infor1   r1   r2   test_gttrf_gttrs  sf   "$$.$





.r  z1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g @r  ffffff?r   )r  r        ffffff@)333333@@r         )r  r  r  r  )r  r  rR   gC>)r{   r  rS   )rM   rN   rO   rP   rP   g@gffffff@      g%@g@g	r}  gffffff&g3@r  rP   rR   r4  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  rk   r  du_expd_expdu2_expipiv_expr   r   r  r  r  r  r  r  r  re   r  r1   r1   r2   0test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csfU  s   2


r  )rd  rc  re  c              	   C   s  t jd}||||d  }||d ||d d  }||d ||d d  }t |t |d t |d }t | t jrX|j|j|j|jf\}}}}|| || || || f\}}}}t |j	dd
 }td|f\}	}
|	|||\}}}}}}|
|||||||d\}}td	|f\}}||\}}}||||d\}}t | jd
 }t|||d d S )NiTfr+   rL   r{   r   r   )r  gtconrk  rh  g      ?r   )r4   r
  rl  r   rp  rq  r   r-   r   r   r   r&   r   r   r   )r/   r   r   r0   rk   r  r  rt  rx  r  r  r  r  re   r0  r<   ri  rj  ry  rz  r   r   r1   r1   r2   
test_gtcon  s"     ",r  ))rN   rR   )rR   rN   r   c                 C   r   )Ngeqrfp_lworkr   r   r   r   )r/   r.   r  r   r   r   re   r1   r1   r2   test_geqrfp_lwork  r   r  zddtype,dtypec                 C   sj  t j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  rp   rO   rL   r{   pttrfr   r   zpttrf: info = z, should be 0)err_msgr  pttrszpttrs: info = )r4   r
  rJ  r   r   r3   r   r  r  r&   r   r   r   r   r   rs   )ddtyper/   r0   r  r   rk   r  rt  r  r  r  _ere   r6  rR  r   r   r  _xr1   r1   r2   test_pttrf_pttrs  s*   (
r  c                 C   sp   d}t jd}td|d}t|f| |d }t|d f||}tt||d d | tt|||d d  d S )Nrp   r   r  r   rM   rL   r{   )r4   r
  rJ  r&   r3   r   r<  )r  r/   r   r0   r  rk   r  r1   r1   r2   *test_pttrf_pttrs_errors_incompatible_shape  s   r  c           
      C   s   d}t j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 )Nrp   r  r  r   rM   rL   r   z?pttrf: _d[info-1] is r  z2?pttrf should fail with non-spd matrix, but didn't)r4   r
  rJ  r&   r3   r   r   )
r  r/   r   r0   r  rk   r  r  r  re   r1   r1   r2   'test_pttrf_pttrs_errors_singular_nonSPD  s   r  z%d, e, d_expect, e_expect, b, x_expect)rO   rp      r   rP   )r   r  r  rS   )rO   rT   r      rL   )r  gK=Ur}  r  rM      A      g      @r{   r  )r  )   .      )y      0@      0@y      2@      "      ?      )r  rT   rL   rO   )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   r  r  rL   r  )r&   r   r  r/   r,   )rk   r  d_expecte_expectr   x_expectr  r  r  r  re   r  r  r1   r1   r2   test_pttrf_pttrs_NAG	  s   
r  c                 C   s4  t jd}|dkr^t||f| |}|t t |d|   }|| j d }t|d }t|f||d }t|d f||}t |t |d t |d }	||	 | j }
|}n6t|f||}t|d f||}|d }t |t |d t |d }
t |t |d t |d }|||
|fS )Nr  rL   rO   rM   r{   )	r4   r
  rJ  r3   r   r   r  rs   r   )r/   realtyper   	compute_zr0   A_eigvrrk   r  trirt  zr1   r1   r2   pteqr_get_d_e_A_z6	  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  rm  pteqrr   rp   rk   r  r  r  r   zinfo = z, should be 0.r  N)r   r4   r   r   r&   r  r   r   sortr   r  rs   r  r   )r/   r  r  r  r	  r   rk   r  rt  r  d_pteqre_pteqrz_pteqrre   r1   r1   r2   
test_pteqrV	  s    
"
r  c                 C   sZ   t d td| d}d}t| |||\}}}}||d |||d\}	}
}}|dks+J d S )Nr  r	  r   rp   rO   r  r  r   r   r&   r  r/   r  r  r	  r   rk   r  rt  r  r  r  r  re   r1   r1   r2   test_pteqr_error_non_spdw	  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   rp   r{   r  )r   r&   r  r   r<  )	r/   r  r  r	  r   rk   r  rt  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   rp   r   r  r  r  r1   r1   r2   test_pteqr_error_singular	  s   r  zcompute_z,d,e,d_expect,z_expect)gp=
ף@rx  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   rL   r{   r
  r  N)r&   r/   r4   r   r   r   )r  rk   r  r  z_expectr  r	  r  r  r  _zre   r1   r1   r2   test_pteqr_NAG_f08jgf	  s   "r  matrix_size)r   )rR   rQ   rQ   rQ   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   orgqrrG  )rn   r   r   r   r;  r{   )r4   r
  rJ  r   r   r&   r3   r   r   r   r
   r.   r  rs   r   allr   r[   r   r$  )r/   r  r0   r   r  r  gqrr   r   rt  qr_Arn   re   r  qqrr]  
A_negativer_rq_negq_rq_negrq_A_negtau_neginfo_negr1   r1   r2   test_geqrfp	  s6   
"(r(  c                  C   s(   t g } td| jd}tt||  d S )Nr  r   )r4   r}   r&   r/   r   r   )A_emptyr  r1   r1   r2   #test_geqrfp_errors_with_empty_array	  s   
r*  driver)evevdevrevxpfxsyhec              
   C   s   d}| dkrt nt}t| | d |d d}t| | d |d d}zt||dd t||dd W d S  tyR } zt| |  d|  W Y d }~d S d }~ww )	N  r1  _lworkr   r   rL   r  $_lwork raised unexpected exception: r   r,   r&   r!   r   r>   failr0  r+  r   r/   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yR } zt| |  d	|  W Y d }~d S d }~ww )
Nr3  r1  r4  r   r   rL   r6  r  r5  r6  r8  r1   r1   r2   test_generalized_eigh_lworks
  s   &r>  dtype_r   )rL   rp   r  rm  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   rC  r1   r1   r2   rA  .
  s    z*test_orcsd_uncsd_lwork.<locals>.<listcomp>)r   r   r   r&   r!   r  )r?  r   r_   r]  r0  dlwrQ  lwvalr1   r1   r2   test_orcsd_uncsd_lwork#
  s   
rE  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@  rA  csdrB  r   r   lrworkr   r   r  g     @r;  )r   r"   rvsr#   r&   r!   dictr  r   rN  r4   r   r#  cosr  r   r   r   )r?  r   r_   r]  r0  XdrvrC  rD  lwvalscs11cs12cs21cs22thetau1u2v1tv2tre   rB  VHr  n11n12n21n22Soner/  Xcr1   r1   r2   test_orcsd_uncsd1
  sJ   
T

,$*,& ra  
trans_boolFfactr  c           !      C   s$  t j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}|rX| tv rVd
ndnd}|ra|	 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  d|jd   t|jd |jd kd|jd  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   rp   rL   rG  r{   rM   rs   rv   r?  r  NrQ   rc  r   dlfdfdufr  r  r   z?gtsvx info = z, should be zerorN   r  __len__Trcond should be scalar but is ferr.shape is z but should be berr.shape is )r4   r
  rJ  r   r   r&   r3   r   r   r  rs   r  r   r   r   r   r.   )!r/   rb  rc  r0   r  re  r  r   r  rk   r  rt  r   r   r   
inputs_cpydlf_df_duf_du2f_ipiv_info_	gtsvx_outrg  rh  ri  du2fr  x_solnr  ferrberrre   r1   r1   r2   
test_gtsvx`
  sB   """rz  c                 C   s  t j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 rLd	nd
}|rU|
 jn|
| }|dkrc||||	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  rd  r   rp   rL   rG  r{   rM   rs   rv   r  rQ   rf  r?  r   z&info should be > 0 for singular matrix)rc  rg  rh  ri  r  r  )	r4   r
  rJ  r&   r3   r   r   r  rs   )r/   rb  rc  r0   re  r  r   r  rk   r  rt  r   r   r   ro  rp  rq  rr  rs  rt  ru  rg  rh  ri  rv  r  rw  r  rx  ry  re   r1   r1   r2   test_gtsvx_error_singular
  sB   "
r{  c                 C   s<  t j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 rLd	nd
}|rU|
 jn|
| }|dkrc||||	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  rd  r   rp   rL   rG  r{   rM   rs   rv   r  rQ   r?  rf  )r4   r
  rJ  r&   r3   r   r   r  rs   r   r<  r   )r/   rb  rc  r0   re  r  r   r  rk   r  rt  r   r   r   ro  rp  rq  rr  rs  rt  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 )Nre  r   r&   r/   r   )r  rk   r  r   r   re  ru  rg  rh  ri  rv  r  rw  r  rx  ry  re   r1   r1   r2   test_gtsvx_NAG  s   r~  zfact,df_de_lambdac                 C      t d|jd| |S Nr  r   r&   r/   rk   r  r1   r1   r2   <lambda>&  
    r  c                 C      dS N)NNNr1   r  r1   r1   r2   r  (      c                 C   s  t j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 d t|jdkd|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   rP   rO   rL   r{   rM   rG  rc  rh  efr   zinfo should be 0 but is .r  rj  rk  )rM   rl  z# but should be ({x_soln.shape[1]},)rm  N)r4   r
  rJ  r   r   r&   r3   r   r  r  r   r   r   r   r   rs   r   r.   )r/   r  rc  df_de_lambdar0   r  r  r   rk   r  rt  rw  r   rh  r  re   r  r   r  rx  ry  r6  rR  r1   r1   r2   
test_ptsvx"  s6   (


r  c                 C   r  r  r  r  r1   r1   r2   r  a  r  c                 C   r  r  r1   r  r1   r1   r2   r  c  r  c              
   C   s   t j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   rP   rO   rL   r{   rM   rG  r  )
r4   r
  rJ  r&   r3   r   r  r   r<  r   )r/   r  rc  r  r0   r  r   rk   r  rt  rw  r   rh  r  re   r1   r1   r2   test_ptsvx_error_raise_errors]  s   (  $r  c                 C   r  r  r  r  r1   r1   r2   r  |  r  c                 C   r  r  r1   r  r1   r1   r2   r  ~  r  c                 C   sr  t j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rn||kspJ t|f||}||||\}}}}}}}|dkr||ksJ d S |||\}}}d|d< d|d< |||||||d\}}}}}}}|dksJ d S )Nr  r  r   rP   rO   rL   r{   rM   rG  r?  r   rN   r  )r4   r
  rJ  r&   r3   r   r  )r/   r  rc  r  r0   r  r   rk   r  rt  rw  r   rh  r  re   r   r  rx  ry  r1   r1   r2   test_ptsvx_non_SPD_singularx  s0   (
r  zd,e,b,xc                 C   s6   t d|jd}|| ||\}}}}}	}
}t|| d S )Nr  r   r}  )rk   r  r   r   r  rh  r  x_ptsvxr  rx  ry  re   r1   r1   r2   test_ptsvx_NAG  s   r  r  c                    s   t jd}t | jd }d\ }t  g| |d}t |g| |d}| j| t j | d| d  }|rO 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  )rp   rO   rG  r   r   c                    s    g | ]}t | D ]}|q	qS r1   r#  r@  yr   rD  r1   r2   rA         z5test_pptrs_pptri_pptrf_ppsv_ppcon.<locals>.<listcomp>c                    s    g | ]}t | D ]}|q	qS r1   r  r  rD  r1   r2   rA    r  c                 S   s   g | ]}t |D ]}|qqS r1   r  r  r1   r1   r2   rA    s    rL   c                 S   s"   g | ]}t |D ]}|d  qqS r  r  r  r1   r1   r2   rA    s   " )ppsvpptrfpptrspptrippconr  r  r  r   r;  )rx  r  r  )r4   r
  rJ  r   r   r3   r  rs   r
   r#  r&   r   r   r   r   r   rr  r   r   r   r  )r/   r  r0   r  r   r]   r   r2  apr  r  r  r  r  ulre   aululiaulir   bxxvrx  r  r1   rD  r2   !test_pptrs_pptri_pptrf_ppsv_ppcon  sL   $





,r  c                 C   s6  t jd}t | jd }d}t||g| |d}td| d\}}|dd |d	d
}t|d d |d }|d }	|d }
| tv rLt	|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  rp   rG  )geestrexcr   c                 S      d S r  r1   r   r1   r1   r2   r    r  z!test_gees_trexc.<locals>.<lambda>Fr  r{   r   r4  r  r;  rR   rL   r   r   r4   r
  rJ  r   r   r3   r&   r   r,   r   r   r  rs   )r/   r0   r  r   r]   r  r  r  r[  r  d2r1   r1   r2   test_gees_trexc  s*   r  zt, expect, ifst, ilst)r~  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  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   )wantqr{   r  N)r&   r/   r   r   )r[  ifstilstexpectr  r  r  r1   r1   r2   test_trexc_NAG  s   r  c                 C   s  t j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 rvt	|	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 )Nr   r  rp   rG  )ggestgexcr   c                 S   r  r  r1   r  r1   r1   r2   r  J  r  z!test_gges_tgexc.<locals>.<lambda>Fr  overwrite_br{   r   rL   r  r4  r   r  r;  rR   rM   rN   r  r  )r/   r0   r  r   r]   r   r  r  r  r   r[  r]  r  d1r  r1   r1   r2   test_gges_tgexc?  s@    r  c                 C   sx  t jd}t | jd }d}t||g| |d}td| d\}}}|dd |d	d
}t|d d |d }	|d }
|	d }| tv rMt	|	t 
|	d|d t	|
|	 |
 j |d|d t |}d|d< t|||	}| tv rx|||	|
|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  rp   rG  )r  trsentrsen_lworkr   c                 S   r  r  r1   r  r1   r1   r2   r  z  r  z!test_gees_trsen.<locals>.<lambda>Fr  r{   r   r4  r  r;  rL   rQ   r   r   liworkr   r4   r
  rJ  r   r   r3   r&   r   r,   r   r   r  rs   r   r!   )r/   r0   r  r   r]   r  r  r  r  r[  r  r  selectr   r1   r1   r2   test_gees_trseno  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)\(?)rL   r   r   rL   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 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   rL   r  r{   r   rO   rP   rQ   r  N)r&   r/   r!   r,   r   r   r  rs   )r[  r]  r  r  expect_s
expect_sepr  atol2r  r  r   r  r   sepr1   r1   r2   test_trsen_NAG  s(   0



r  c                 C   sL  t j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 rwt	|
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  rp   rG  )r  tgsentgsen_lworkr   c                 S   r  r  r1   r  r1   r1   r2   r    r  z!test_gges_tgsen.<locals>.<lambda>Fr  r{   r   rL   r  r4  r   r  r;  rQ   r   ir  r  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  sL   
 r  za, b, c, d, e, f, rans, lans)r   r   r   r   )r  r  r   r   )r  r   r  r   )r  r  r  g      @)r   r   r   r   )r  r  r  r   )      r   r   g      (@)g      "r          r  )r  r   r  r   )      r   r  g      3@)r   r   r   r  )r  r   r   r   )r  r  r   r   )r  r  r  r   )r   r   r   r   )r  r   r   r   )r  r  r  r   )r  r   r  r   )r  r   g       r  )r  r         r   )r  r   r  r   )r  r   r  r  )r  r   r  r   )r  r   r  r   )r   r  r   r  )r   r  r  r   )r  r   r   r  )r   r  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  r  zDIF must be nearly 0zSolution for R is incorrect)r  r  zSolution for L is incorrect)r&   r   r   r4   r   r   )r]   r   r   rk   r  r`   ranslansr/   r  r  routloutrX   difre   r1   r1   r2   test_tgsyl_NAG!  s    $

r  r   )r?  rs   ijob)r   rL   rM   rN   rO   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sJ d|dksJ d|dkrt|ddt 	| j
d dd n|dksJ d|d
kr
|dkr|| ||
  }|| }|| ||  }|| }n*|dkrt || t ||  }|| }|t |
 |t |  }d| | }t|||ddd t|||ddd d S d S )NgMbP?g|=l   OElt/ r  irp   r   )outputr   rM   r  r   )r   r  r   zINFO is non-zeror  zSCALE must be non-negativer  zDIF must be 0 for ijob =0r  zDIF must be non-negativer?  rs   r  zlhs1 and rhs1 do not match)r  r   r  zlhs2 and rhs2 do not match)r4   r  r
  rl  r    uniformr-   r&   r   r   r   r\  )r/   r   r  r  r0   r   r   r]   rk   r<   r   r  r   r`   r  r  r  rX   r  re   lhs1rhs1lhs2rhs2r1   r1   r2   
test_tgsylU  sT   




r  mtyper  c                 C   sN  | dkr|t v rtd tjd}d\}}|tv r1|j||fd|j||fdd  |}n|j||fd|}| dkrE||j	 n||
 j	 }|j||fd|}|  d|  d	|  d
f}t||d\}	}
}|
||d}|	||d\}}}|dksJ ||||d\}}|dksJ t|j}t|| |d| | d d S )Nr2  zhetrs not for real dtypes.l   *M/t|0 )r   rP   r  r+   r1  rO  rP  trsr   r  r   r   )r]   r  r   r  r  )r   r>   r?   r4   r
  rl  r,   r  r-   rs   r  r&   r   r   r   )r  r/   r  r0   r   r   rt  r   rF   rO  rP  r  r   r  r  re   r   r   r1   r1   r2   test_sy_hetrs  s$   
, r  r   z
uplo, m, n))rB  rP   rp   )rB  rp   rp   )r6  rp   rP   )r6  rp   rp   c                 C   s   t jd}|j||fd|}td|f\}}	|| |||d}
|dkr*t |nt |}|dkrAt t||}d|||f< |	| |}t	|
|dd d S )	Nl   8#q9
r  )lantrr   )r9  r   rB  rL   g>r   )
r4   r
  rl  r-   r&   r   r   r  rN  r   )r   r9  r   r   r   r/   r0   rt  r  r   r0  r/  r   r1   r1   r2   
test_lantr  s   
r  r  )	functoolsr   r
  numpy.testingr   r   r   r   r   r   r>   r	   r   numpyr4   r
   r   r   r   r   r   r   r   numpy.randomr   r   r   scipy.linalgr   r6   r   r   r   r   r   r   r   r   r   r   r    scipy.linalg.lapackr!   scipy.statsr"   r#   scipy.sparsesparserK  scipy.__config__r$   ImportErrorr%   r5   r&   scipy.linalg.blasr'   r  r&  r   r  
complex128r,   r   blas_providerblas_versionr3   rI   rK   r   r   ra  rb  r   r   r  r  r2  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r-  r5  r:  r@  rD  rK  rT  rU  rt  rw  r  r  skipifr  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>  rE  ra  rz  r{  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rB   r  r1   r1   r1   r2   <module>   s   (8` t  #**DO1")::) %# ((-
e
#





[




+
/

	
 
@.:0
0


4




%

.$	/-*!8"0