
     h                     |   d dl Z d dlZd dlZd dlZd dlmZmZmZmZm	Z	m
Z
mZmZ d dlmZ d dlmZ d dlmZmZmZmZmZmZmZ d dlZd dlmZ d dlmZ d dlmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/ d dl0m1Z1 d d	l2m3Z3 d d
l4m5Z5 ej        ej6        ej7        fZ8ej9        ej:        ej;        fZ<e8e<z   Z=d Z> G d d          Z? G d d          Z@ G d d          ZA G d d          ZB G d d          ZC G d d          ZDd-dZE G d d          ZF G d d          ZG G d d          ZHejI        J                    dd           ejI        J                    d!e#e$f          d"                         ZK G d# d$          ZL G d% d&          ZM G d' d(          ZN G d) d*          ZO G d+ d,          ZPdS ).    N)arangearraydotzerosidentity	conjugate	transposefloat32)random)assert_equalassert_almost_equalassert_assert_array_almost_equalassert_allcloseassert_array_equalsuppress_warnings)raises)_pep440)solveinvdetlstsqpinvpinvhnormsolve_bandedsolveh_bandedsolve_triangularsolve_circulant	circulantLinAlgError
block_diagmatrix_balanceqrLinAlgWarningassert_no_overwrite)check_free_memory)	HAS_ILP64c                     | }|t           j        k    rt           j        }n|t           j        k    rt           j        }t          j        |          j        S )z;Get the epsilon for dtype, possibly downcast to BLAS types.)np
longdoublefloat64clongdouble
complex128finfoeps)dtypdts     Y/var/www/html/Sam_Eipo/venv/lib/python3.11/site-packages/scipy/linalg/tests/test_basic.py	_eps_castr5       sB    	B	R]Z	r~		]8B<<    c                   >    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	S )
TestSolveBandedc                    t          g dg dg dg dg          }t          g dg dg dg dg          }d	\  }}t          g d
          }|                    dd          }t          ddgddgddgddgg          }t          g dg dg dg dg          }||||fD ]3}	t          ||f||	          }
t          t	          ||
          |	           4d S )N      ?   r   r         r         r<   rB   r                 r<   r@   rB   rC   r?   r<   rG   r>   rC   rF   r   rB   rE   r   r   rB   rC         $@rI          @g      ,@rE   rC   rB   r>   r?      rC   r   r   r   r   r   r   rC   r   rC   r   r   r   reshaper   r   r   selfaablub4b4by1b4by2b4by4bxs              r4   	test_realzTestSolveBanded.test_real,   sH   ???!>> ==!>># $ $ OOO"NN"NN!MM# $ $ 1)))**

2q!!1vQx1v1v     |||#||#||#||% & & eUE* 	4 	4AaVR++A%c!Qii3333	4 	4r6   c                    t          g dg dg dg dg          }t          g dg dg dg dg          }d	\  }}t          g d
          }|                    dd          }t          ddgddgddgddgg          }t          g dg dg dg dg          }||||fD ]3}	t          ||f||	          }
t          t	          ||
          |	           4d S )Nr:   r=   )               @rC   r<   re   rD   rI   r<   r@   re   rJ   rK   )re   rE   r   r   rM   rO   rI   rP   y              ,@rE   rC   rB   r>   r?   rQ   rR   )r   r   r                 ?rT   rU   rW   s              r4   test_complexzTestSolveBanded.test_complexD   sK   ???!>>"??!>># $ $ $$$"NN"NN"NN$ % % 1***++

2q!!1vQx1v1v     |||$}}#||#||% & & eUE* 	4 	4AaVR++A%c!Qii3333	4 	4r6   c                    t          g dg dg dg          }t          j        |ddd f         d          t          j        |dd d f         d          z   t          j        |dd df         d          z   }t          g d          }|                    dd          }t          ddgd	d
gddgddgg          }t          g dg dg dg dg          }||||fD ]1}t	          d||          }t          t          ||          |           2d S )NrH   rJ   rK   r   rC   rB   rE   rN   r>   r?   rQ   rR   rS   rT   rC   rC   r   r+   diagrV   r   r   r   	rX   rZ   rY   r]   r^   r_   r`   ra   rb   s	            r4   test_tridiag_realz!TestSolveBanded.test_tridiag_real\   sd   OOO!>>!>># $ $ GBq!""uIq!!BGBq!!!tHa$8$8827@B1crc6
B<P <P P)))**

2q!!1vQx1v1v     |||#||#||#||% & & eUE* 	4 	4AVR++A%c!Qii3333	4 	4r6   c                    t          g dg dg dg          }t          j        |ddd f         d          t          j        |dd d f         d          z   t          j        |dd df         d          z   }t          g d          }|                    dd          }t          ddgd	d
gddgddgg          }t          g dg dg dg dg          }||||fD ]1}t	          d||          }t          t          ||          |           2d S )Nrf   rJ   rK   r   rC   rB   rE   rg   r>   r?   rQ   rR   rS   rT   rk   rl   rn   s	            r4   test_tridiag_complexz$TestSolveBanded.test_tridiag_complexp   sg   $$$!>>!>># $ $ GBq!""uIq!!BGBq!!!tHa$8$8827?A!SbS&z2<O <O O***++

2q!!1vQx1v1v     |||#||#||#||% & & eUE* 	4 	4AVR++A%c!Qii3333	4 	4r6   c                    t          g dg dg dg dg          }t          g dg dg dg dg          }d	\  }}t          g d
          }t          ||f||d          }t          t          ||          |           d S )Nr:   r=   rA   rD   rH   rJ   rK   rL   rM   rN   Fcheck_finite)r   r   r   r   )rX   rY   rZ   r[   r\   r]   rb   s          r4   test_check_finitez!TestSolveBanded.test_check_finite   s    ???!>> ==!>># $ $ OOO"NN"NN!MM# $ $ 1)))**!QRe<<<!#a))R00000r6   c                 N   t          g dg dg dg dg          }d\  }}t          g d                              dd          }t          t          t          ||f||           t          t          t          ||f|d	d
g           t          t          t          d|d	d
g           d S )NrH   rJ   rK   rL   rM   )r;   rP         @      @rE   r?   r;   rP   rk   )r   rV   assert_raises
ValueErrorr   )rX   rZ   r[   r\   bads        r4   test_bad_shapezTestSolveBanded.test_bad_shape   s    OOO"NN"NN!MM# $ $ 1((())11"a88j,AC@@@j,AS#JGGG 	j,S#JGGGGGr6   c                     t          g dg          }t          ddgdgdgg|          }t          |g dg           t          |j        t          j        d                     t          |g dg           d S )Nr;   rP   rw   rk   r   rB   )      ?r;   g      ?f8)r   r   r   r   dtyper+   )rX   ra   rb   s      r4   test_1x1zTestSolveBanded.test_1x1   s    <<<.!!1#sQC!441/000QWbhtnn---1/00000r6   c                     g dg dg dg dg}g dg dg dg dg}d	\  }}g d
}t          ||f||          }t          t          ||          |           d S )Nr:   r=   rA   rD   rH   rJ   rK   rL   rM   rN   )r   r   r   )rX   rY   rZ   r[   r\   ra   rb   s          r4   test_native_list_argumentsz*TestSolveBanded.test_native_list_arguments   s    __^^]]^^ oonnnnmm 1"""!QQ''!#a))Q/////r6   N)__name__
__module____qualname__rc   ri   ro   rq   ru   r|   r   r    r6   r4   r8   r8   *   s        4 4 404 4 404 4 4(4 4 4(1 1 1H H H1 1 10 0 0 0 0r6   r8   c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdS )TestSolveHBandedc                     t          g dg dg dg          }t          g d          }t          ||          }t          |g d           d S NrI   rI   rP   rP   r;   r;   r;   rx   rx   rx   rx   r;   rx   r;   rP   rI   r;   rI   rI   r   r   r   rX   rZ   ra   rb   s       r4   test_01_upperzTestSolveHBanded.test_01_upper   su     (((((((((* + + &&&''"a  !!%9%9%9:::::r6   c                     t          g dg dg dg          }t          ddgddgddgddgg          }t          ||          }t          ddgddgddgddgg          }t          ||           d S )	Nr   r   r   r;         @rx   rP   rI   r   rX   rZ   ra   rb   expecteds        r4   test_02_upperzTestSolveHBanded.test_02_upper   s     (((((((((* + + C::::     "a  3****& ' ' 	"!X.....r6   c                    t          g dg dg dg          }t          g d                              dd          }t          ||          }t          |t          g d                              dd                     d S )Nr   r   r   r   rE   rC   r   r   rV   r   r   r   s       r4   test_03_upperzTestSolveHBanded.test_03_upper   s     (((((((((* + + &&&''//A66"a  !!U+;+;+;%<%<%D%DR%K%KLLLLLr6   c                     t          g dg dg dg          }t          g d          }t          ||d          }t          |g d           d S )Nr   r;   r;   r;   r   rP   rP   rI   rI   r   Tlowerr   r   r   s       r4   test_01_lowerzTestSolveHBanded.test_01_lower   sz     (((((((((* + + &&&''"at,,,!!%9%9%9:::::r6   c                     t          g dg dg dg          }t          ddgddgddgddgg          }t          ||d	          }t          d
dgdd
gd
dgd
d
gg          }t          ||           d S )Nr   r   r   r;   r   rx   rP   Tr   rI   r   r   s        r4   test_02_lowerzTestSolveHBanded.test_02_lower   s     (((((((((* + + C::::     "at,,,3****& ' ' 	"!X.....r6   c                     t          g dg dg dgt                    }t          g dt                    }t          ||          }t          |g d           d S )Nr   r   r   r   r   r   r   r
   r   r   r   s       r4   test_01_float32z TestSolveHBanded.test_01_float32  s     (((((((((*18: : : &&&g666"a  !!%9%9%9:::::r6   c                     t          g dg dg dgt                    }t          ddgddgddgddggt                    }t          ||          }t          d	dgdd	gd	dgd	d	gg          }t          ||           d S )
Nr   r   r   r   r;   r   rx   rP   rI   r   r   s        r4   test_02_float32z TestSolveHBanded.test_02_float32  s     (((((((((*18: : : C:::: './ / / "a  3****& ' ' 	"!X.....r6   c                     t          g dg dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r                r   r   r   )       @            @            @      ?       @      ?)rI   r;   r;   rI   r   r   s       r4   test_01_complexz TestSolveHBanded.test_01_complex.  su     (((...(((* + + ...//"a  !!%9%9%9:::::r6   c                     t          g dg dg dg          }t          ddgddgdd	gd
dgg          }t          ||          }t          ddgddgddgddgg          }t          ||           d S )Nr   r   r   r          @      @r               r   y      @       @r   rh   rI   r;   r   r   s        r4   test_02_complexz TestSolveHBanded.test_02_complex<  s     (((...(((* + + D$<E?D>":     "a  3+***& ' ' 	"!X.....r6   c                     t          g dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r;   r;   rx   rx   rx   r;   rx   r;   rI   r;   rI   r   r   s       r4   test_tridiag_01_upperz&TestSolveHBanded.test_tridiag_01_upperQ  sX     OOO___566///"""a  !!___55555r6   c                     t          g dg dg          }t          ddgddgddgg          }t          ||          }t          ddgddgddgg          }t          ||           d S )Nr   r   r;   rx   rP   rI   r   r   s        r4   test_tridiag_02_upperz&TestSolveHBanded.test_tridiag_02_upper\  s     OOO#OO% & &C:::     "a  3***& ' ' 	"!X.....r6   c                     t          g dg dg          }t          g d                              dd          }t          ||          }t          |t          g d                              dd                     d S )Nr   r   r   rE   rC   r   r   r   s       r4   test_tridiag_03_upperz&TestSolveHBanded.test_tridiag_03_upperm  s     OOO___566///""**2q11"a  !!U???%;%;%C%CB%J%JKKKKKr6   c                     t          g dg dg          }t          g d          }t          ||d          }t          |g d           d S )Nr   r;   r;   r   r   Tr   r   r   r   s       r4   test_tridiag_01_lowerz&TestSolveHBanded.test_tridiag_01_lowerx  sd     OOO#OO% & &///"""at,,,!!___55555r6   c                     t          g dg dg          }t          ddgddgddgg          }t          ||d          }t          ddgddgddgg          }t          ||           d S )	Nr   r   r;   rx   rP   Tr   rI   r   r   s        r4   test_tridiag_02_lowerz&TestSolveHBanded.test_tridiag_02_lower  s     OOO#OO% & &C:::     "at,,,3***& ' ' 	"!X.....r6   c                     t          g dg dgt                    }t          g dt                    }t          ||          }t          |g d           d S )Nr   r   r   r   r   r   r   s       r4   test_tridiag_01_float32z(TestSolveHBanded.test_tridiag_01_float32  sb     OOO___5WEEE///111"a  !!___55555r6   c                     t          g dg dgt                    }t          ddgddgddggt                    }t          ||          }t          ddgddgddgg          }t          ||           d S )Nr   r   r   r;   rx   rP   rI   r   r   s        r4   test_tridiag_02_float32z(TestSolveHBanded.test_tridiag_02_float32  s     OOO#OO%,35 5 5C:::&-/ / / "a  3***& ' ' 	"!X.....r6   c                     t          g dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r   r   r   )r   r   r   )rI   r;   r;   r   r   s       r4   test_tridiag_01_complexz(TestSolveHBanded.test_tridiag_01_complex  s^     '''9::'''(("a  !!___55555r6   c                     t          g dg dg          }t          ddgddgddgg          }t          ||          }t          d	d
gdd	gddgg          }t          ||           d S )Nr   r   r                 @r   r   r   rx   rI   rh   r;   r   r   s        r4   test_tridiag_02_complexz(TestSolveHBanded.test_tridiag_02_complex  s     '''#OO% & &C;G$C=" # # "a  3+**& ' ' 	"!X.....r6   c                     t          g dg dg          }t          g d          }t          ||d          }t          |g d           d S )Nr   r   r   Frs   r   r   r   s       r4   ru   z"TestSolveHBanded.test_check_finite  s]     OOO___566///"""ae444!!___55555r6   c                    t          g dg dg          }t          ddgddgg          }t          t          t          ||           t          t          t          |ddg           t          t          t          |dg           d S )Nr   r   r;   rx   rP   )r   ry   rz   r   )rX   rZ   ra   s      r4   test_bad_shapesz TestSolveHBanded.test_bad_shapes  s    OOO#OO% & &C::    j-Q777j-c3Z@@@j-cU;;;;;r6   c                     t          dggg dg          }t          |g dg           t          |j        t	          j        d                     d S )NrC   rC   rB   rQ   r~   r   )r   r   r   r   r+   )rX   rb   s     r4   r   zTestSolveHBanded.test_1x1  sR    A3%)))--1/000QWbhtnn-----r6   c                 h    g dg dg dg}g d}t          ||          }t          |g d           d S r   )r   r   r   s       r4   r   z+TestSolveHBanded.test_native_list_arguments  s]    """""""""$ !  "a  !!%9%9%9:::::r6   N)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   ru   r   r   r   r   r6   r4   r   r      sd       ; ; ;/ / /*M M M; ; ;/ / /*; ; ;/ / /*; ; ;/ / /*	6 	6 	6/ / /"	L 	L 	L
6 
6 
6/ / /"	6 	6 	6/ / /"	6 	6 	6/ / /"	6 	6 	6< < <. . .
; ; ; ; ;r6   r   c                      e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Z!d  Z"e#j$        %                    d!"          d#             Z&d$S )%	TestSolvec                 D    t           j                            d           d S N  r+   r   seedrX   s    r4   setup_methodzTestSolve.setup_method      
	tr6   c                     ddgddgg}t          |ddg          }t          t          ||          ddg           ddgddgg}ddg}t          ||          }t          t          ||          ddg           d S )NrC   r;   r                   333333?r   r   r   )rX   rY   x0ra   s       r4   test_20Feb04_bugzTestSolve.test_20Feb04_bug  s    Vc1X1q"g!#a**q!f555 Vc1XG1a[[!#a**q!f55555r6   c                     ddgddgg}ddgddggddgddgddggfD ]0}t          ||          }t          t          ||          |           1d S )NrC   r<   r>   r?   r   rB   r   rX   rY   ra   rb   s       r4   test_simplezTestSolve.test_simple  s    WsAhq6Aq6"a&q6C8$ 	4 	4A aA%c!Qii3333	4 	4r6   c                     t          ddgddggd          }ddgddgddggdd	gt          ddgd          fD ]0}t          ||          }t          t          ||          |           1d S )
N   rB   re   r?   Drh   r   rC   r   )r   r   r   r   r   s       r4   test_simple_complexzTestSolve.test_simple_complex  s    Aq6B7#S))q'8aV$b'A$$ 	4 	4A
 aA%c!Qii3333	4 	4r6   c                     ddgddgg}dD ]B}ddgddggddgfD ]3}t          ||d|          }t          t          ||          |           4Cd S )	NrB   rQ   r   r   rC   rC   r   posassume_ar   r   rX   rY   r   ra   rb   s        r4   test_simple_poszTestSolve.test_simple_pos  s    VaV 	8 	8E1v1v&!f 8 8 !Qe<<<)#a))Q7777	8	8 	8r6   c                     ddgddgg}ddgddgddggfD ]2}t          ||d          }t          t          ||          |           3d S )Nr   rB   r?   rh   r   r   r   r   r   s       r4   test_simple_pos_complexbz"TestSolve.test_simple_pos_complexb  sw    VaVq'8aV$ 	4 	4A aU+++A%c!Qii3333		4 	4r6   c                     ddgddgg}dD ]B}ddgddggddgfD ]3}t          ||d|          }t          t          ||          |           4Cd S )	NrB   rQ   r   rC   r   symr   r   r   s        r4   test_simple_symzTestSolve.test_simple_sym#  s    VaW 	8 	8E1v1v&!f 8 8 !Qe<<<)#a))Q7777	8	8 	8r6   c                     ddgddgg}ddgddgddggfD ]2}t          ||d          }t          t          ||          |           3d S )Nr   rB   rh   r   r   r   r   r   s       r4   test_simple_sym_complexbz"TestSolve.test_simple_sym_complexb,  sw    VaWq'8QF# 	4 	4A aU+++A%c!Qii3333		4 	4r6   c                     ddgddgg}ddgddgddgddggfD ]2}t          ||d	          }t          t          ||          |           3d S )
Nr   r   r   rh   r   rC   rB   r   r   r   r   s       r4   test_simple_sym_complexz!TestSolve.test_simple_sym_complex4  ~    Yr
#q'a&8aV$ 	4 	4A aU+++A%c!Qii3333	4 	4r6   c                     ddgddgg}dD ]E}ddgddggddgddgfD ]3}t          ||d|	          }t          t          ||          |           4Fd S )
NrB   rQ   r   r   rC   r   rh   herr   r   r   s        r4   test_simple_her_actuallysymz%TestSolve.test_simple_her_actuallysym=  s    VaW 	8 	8E1v1v&!f1g 8 8 !Qe<<<)#a))Q77778	8 	8r6   c                     ddgddgg}ddgddgddgddggfD ]2}t          ||d	
          }t          t          ||          |           3d S )Nr   r   r   r   rh   r   rC   rB   r  r   r   r   s       r4   test_simple_herzTestSolve.test_simple_herG  r  r6   c                 h   d}t          ||g          t          ||g          dz  z   }t          ||fd          }t          |          }t          |          t          |          dz  z   }t	          d|          D ]%}|d d |f         }t          ||          |d d |f<   &t          ||           d S )NrB   rh   r   r   r   )r   r   r   r   r   r   r   )rX   nAXAinvRirs           r4   test_nils_20Feb04zTestSolve.test_nils_20Feb04P  s    Aq6NN61a&>>",,1a&#1vvQKKB&1 	" 	"A!!!Q$AAqkkAaaadGG!!T*****r6   c                    d}t          ||g          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]A}t          |dg          }t          ||          }t          t	          ||          |           Bd S )Nr<   皙?r?   rQ   r   ranger   r   r   rX   r  rY   r  ra   rb   s         r4   test_randomzTestSolve.test_random[  s    Aq6NNq 	& 	&A"Qq!tW*oAadGGq 	4 	4A1vAaA%c!Qii3333	4 	4r6   c                 F   d}t          ||g          dt          ||g          z  z   }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]A}t          |dg          }t          ||          }t          t	          ||          |           Bd S )Nr<   rh   r  rB   rQ   r  r  s         r4   test_random_complexzTestSolve.test_random_complexf  s    Aq6NNR&!Q..00q 	& 	&A"Qq!tW*oAadGGq 	4 	4A1vAaA%c!Qii3333	4 	4r6   c                     t          j        t          d          5  t          dggdgd           d d d            d S # 1 swxY w Y   d S )Nz#The 'sym_pos' keyword is deprecated)matchr;   rC   T)sym_pos)pytestwarnsDeprecationWarningr   r   s    r4   test_sym_pos_depzTestSolve.test_sym_pos_depp  s    \";
 
 
 	- 	- B4&1#t,,,,		- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	-s   ?AAc                 z   d}t          ||g          }t          |          D ]E}t          dd|||f         z   z            |||f<   t          |          D ]}|||f         |||f<   Ft          d          D ]B}t          |g          }t          ||d          }t	          t          ||          |           Cd S )Nr<   r  r?   r   r   )r   r  absr   r   r   rX   r  rY   r  jra   rb   s          r4   test_random_symzTestSolve.test_random_symw  s    Aq6NNq 	" 	"A"b1a4j/**AadG1XX " "AqD'!Q$"q 	4 	4AsAaU+++A%c!Qii3333	4 	4r6   c                    d}t          ||g          }|dt          ||g          z  z   }t          |          D ]R}t          dd|||f         z   z            |||f<   t          |          D ]}t          |||f                   |||f<   St          |g          dt          |g          z  z   }t          d          D ]2}t	          ||d          }t          t          ||          |           3d S )Nr<   rh   r  re   rB   r   r   )r   r  r   r   r   r   r   r!  s          r4   test_random_sym_complexz!TestSolve.test_random_sym_complex  s   Aq6NN61a&>>!!q 	- 	-A"b1a4j/**AadG1XX - -#AadG,,!Q$-A3KK61#;;&q 	4 	4AaU+++A%c!Qii3333	4 	4r6   c                     ddgddgg}ddgddggddgddgddggfD ]2}t          ||d          }t          t          ||          |           3d S )	NrC   r<   r>   r?   r   rB   Frs   r   r   s       r4   ru   zTestSolve.test_check_finite  s    WsAhq6Aq6"QFq6C8$& 	4 	4Aa///A%c!Qii3333	4 	4r6   c                     d}g d}t          ||          }t          |                                |           t          |j        dk    d           d S )NrC   r   rQ   z'Scalar_a_1D_b test returned wrong shape)r   r   ravelr   shaper   s       r4   test_scalar_a_and_1D_bz TestSolve.test_scalar_a_and_1D_b  sR    II!QKK!!''))Q///4!JKKKKKr6   c                     t          j        g dg dg dg dg          }t          j        ddgddgd	d
gddgg          }t          ||          }t          |t          j        g dg dg          j                   d S )N)?g
ףp=
@gffffff @g{Gz)g     h@g     prg     Wg     w)gHzG?gQg333333gp=
ף)g(\gQgzGg?g
ףp=
#@gQx2@g     @g      l@gp=
ף?g(\*gzGgףp=
)r;   rE   rQ   r   )rQ   rB   r?   rC   )r+   r   r   r   Tr   s       r4   test_simple2zTestSolve.test_simple2  s    H///8881111113 4 4
 HtUm'Vnen& ' '
 !QKK!!RX/;||/= &> &>>?	A 	A 	A 	A 	Ar6   c           
         t          j        g dg dg dg dg          }t          j        ddgddgd	d
gddgg          }t          ||          }t          |t          j        ddgddgddgddgg                     d S )N)yq=
ףpffffff@yQ?\(\	@y(\y
ףp=
?q=
ףp)y333333333333,y̌@@      y      *@y)@+@)yRQ
Qy(\Gz@yQyQ??)yHzG@(\?yQ῅Q?y(\Gzy\(\q=
ףp?y(\B:@p=
I@yRQ?@y33333P@33333Uy33333c@ffffff,y      (\O9@y333333q=
ף0>@y(\?(\@y{Gz333333@      ?      ?y             y       @      y      @      ?y            y            @y              @)r+   r   r   r   r   s       r4   test_simple_complex2zTestSolve.test_simple_complex2  s    HHHHMMMIIIIIIK L L
 H|[1#]3#\2!;/1 2 2
 !QKK!!RY16170@14e0> &? &? 	@ 	@ 	@ 	@ 	@r6   c                 ~   t          j        g dg dg dg dg          }t          j        ddgddgd	d
gddgg          }t          j        ddgddgddgddgg          }t          ||d          }t          ||           t          |                                j        |dd          }t          ||           d S )N)gq=
ףpy)\(?)\(y{GzzGyHzG@      )r   gQyq=
ףpQ?yGz@zG?)r   r   g=
ףp!yHzG?)r   r   r   g(\yףp=
@\(\$yGz<@RCy)\(#
ףp=
@y
ףp=8 yp=
ף0yQ@zGQy)\(@Q@yRA(\2@r   y             @y      @       y      @       y             @y            @y      ?      y      @      r  r   Tr   )r+   r   r   r   conjr.  )rX   rY   ra   resrb   s        r4   test_hermitianzTestSolve.test_hermitian  s   HBBB999///&&&( ) ) H{L1"L1#[1!=13 4 4 h' ( ( !Q'''!!S)))!&&((*a%t<<<!!S)))))r6   c                    t          j        dd                              dd          }t          t          j        |          dz  t          j        d          d          }t          |g d           t          t          j        |          dz  t          j        d          d          }t          |g d           d S )	NrC   
   rQ   	   r   r   )g      "@r-  r;   r   r+   r   rV   r   trilonesr   rX   r	  rb   s      r4   test_pos_and_symzTestSolve.test_pos_and_sym  s    Ia$$Q**"'!**Q,

U;;;!!]]]333"'!**Q,

U;;;!!]]]33333r6   c                     t          j        g dg dg dg dg dg dg dg dg dg	          }t          j        d          d d d f         }t          t          t
          ||           d S )N)	rC   r   r   r   r   r   rC   r   rC   )	rC   rC   rC   r   r   r   rC   r   rC   )	r   rC   rC   r   r   r   rC   r   rC   )	rC   r   rC   rC   rC   rC   r   r   r   )	rC   rC   rC   rC   rC   rC   rC   rC   rC   r9  )r+   r   r   ry   r!   r   rX   rY   ra   s      r4   test_singularityzTestSolve.test_singularity  s    H1111111111111111111111111113 4 4 IaLLD!k5!Q/////r6   c                    t          j        ddgddgg          }t          j        d          }t          j                    5  t          j        d           t          t          t          ||           d d d            d S # 1 swxY w Y   d S )NrC   r;   g?rB   error)	r+   r   r<  warningscatch_warningssimplefilterry   r%   r   r@  s      r4   test_ill_condition_warningz$TestSolve.test_ill_condition_warning  s    Hq!fw0122GAJJ$&& 	6 	6!'***-1555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   1B  BBc                     t          j        d          }g g g}t          ||          }t          |j        dk    d           t          |j        dk    d           d S )NrB   r   zReturned array is not empty)rB   r   z#Returned empty array shape is wrong)r+   eyer   r   sizer*  r   s       r4   test_empty_rhszTestSolve.test_empty_rhs  sZ    F1IIH!QKK!:;;;6!#HIIIIIr6   c                     t          j        d          }t           j                            ddd          }t	          ||          }t          ||           d S )NrB   rQ   r?   )r+   rI  r   randr   r   r   s       r4   test_multiple_rhszTestSolve.test_multiple_rhs  sI    F1IIINN1a##!QKK!!Q'''''r6   c                    t          j        d                              dd          dz   }t          t          j        |          dz  t          j        d          d          }t          |g d           t          t          j        |          dz  t          j        d          d          }t          |g d           d S )	Nr9  rQ   rC   T
transposed)r   g?rC   F)r9  gg333333r:  r=  s      r4   test_transposed_keywordz!TestSolve.test_transposed_keyword  s    IaLL  A&&*"'!**Q,

t<<<!!]]]333"'!**Q,

u===!!___55555r6   c                     t          j        d                              t                    }t	          t
                    5  t          ||d           d d d            d S # 1 swxY w Y   d S )NrQ   TrP  )r+   rI  astypecomplexry   NotImplementedErrorr   rX   rY   s     r4   test_transposed_notimplementedz(TestSolve.test_transposed_notimplemented  s    F1IIW%%.// 	) 	)!Q4((((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)s   A!!A%(A%c                 B    t          t          t          ddgd           d S )NrC   rB   ry   rz   r   r   s    r4   test_nonsquare_azTestSolve.test_nonsquare_a  s     j%!Q33333r6   c                 .   t          t          t          j        d          t          j        d                    t          j        d                     t          t          t          t          j        d          t          j        d                     d S )NrQ   r?   )r   r   r+   rI  r<  ry   rz   r   s    r4   test_size_mismatch_with_1D_bz&TestSolve.test_size_mismatch_with_1D_b	  s^    !%q		271::">">

KKKj%BGAJJ?????r6   c                 B    t          t          t          ddd           d S )NrC   zxcvr   rZ  r   s    r4   test_assume_a_keywordzTestSolve.test_assume_a_keyword  s!    j%A??????r6   z5Failure on OS X (gh-7500), crash on Windows (gh-8064)reasonc                     ddg}g d}t           j        t           j        t           j        t           j        g}t          j        |||          D ]?\  }}}|t           j        t           j        fv }|dk    r|s*d                    |||          }t           j        	                    ||          
                    |          }	t           j        	                    |          
                    |          }
|r9|	dt           j        	                    ||          z  
                    |          z   }	|dk    r|	|	j        z   }	nm|dk    r|	|	j                                        z   }	nJ|dk    rD|	                                j                            |	          d	t          j        |          z  z   }	|t           j        t           j        fv rd
nd}|dv r|t           j        t           j        fv r|dz  }t          |	|
|          }t!          |	                    |          |
||z  ||z  |           |dk    rZ|t           j        t           j        fvr@t          |	|
|d          }t!          |	                    |          |
||z  ||z  |           Ad S )Nr8  d   )genr   r   r  r  z+Failed for size: {}, assume_a: {},dtype: {}rh   r   r   r  -q=gư>)re  r   r  r   atolrtolerr_msgT)r   rQ  )r+   r
   r-   	complex64r/   	itertoolsproductformatr   randnrT  r.  r4  r   rI  r   r   )rX   sizes	assume_asdtypesrJ  r   r   
is_complexrj  rY   ra   tolrb   s                r4   'test_all_type_size_routine_combinationsz1TestSolve.test_all_type_size_routine_combinations  s    S	000	*bj",F%.%6ui7=&? &? )	1 )	1!D(E2<"??J5   ##)6$%#@#@  	d++22599A	%%,,U33A GBIOOD$777??FFF5  GU""

NU""FFHHJNN1%%BF4LL(88 RZ$???%%TC000 RZ6662ICaX...AAEE!HHa!$t!$t$+- - - -
 5  U2<35=3B &B &B!QdCCCa!%(4Z%(4Z(/1 1 1 1M)	1 )	1r6   N)'r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r#  r%  ru   r+  r/  r2  r6  r>  rA  rG  rK  rN  rR  rX  r[  r]  r`  r  markskipru  r   r6   r4   r   r     s>         	6 	6 	64 4 44 4 48 8 84 4 48 8 84 4 44 4 48 8 84 4 4	+ 	+ 	+	4 	4 	44 4 4- - -
4 
4 
44 4 44 4 4L L LA A A@ @ @"* * *(4 4 40 0 06 6 6J J J( ( (6 6 6) ) )
4 4 4@ @ @@ @ @ [ : ; ;-1 -1; ;-1 -1 -1r6   r   c                        e Zd Zd Zd Zd ZdS )TestSolveTriangularc                    t          ddgddgg          }ddg}t          ||d          }t          |ddg           t          |j        |d          }t          |ddg           t          ||dd          }t          |ddg           t	          d          }t          ||dd          }t          |d	d
gddgg           dS ):
        solve_triangular on a simple 2x2 matrix.
        rC   r   rB   Tr   Fr   r   transr;         N)r   r   r   r.  r   rX   r	  ra   sols       r4   r   zTestSolveTriangular.test_simpleD  s     Aq6Aq6"##Fq!4000!#1v... qsAU333!#Bx000 q!4q999!#Bx000QKKq!4q999!#S	As8'<=====r6   c                    t          ddgddgg          }t          d          }t          ||dd          }t          |dd	gdd
gg           t	          j        ddg          }t          ||dd          }t          |ddgddgg           t          ||dd          }t          |ddgddgg           t          ||dd          }t          |ddgddgg           t          |j        |dd          }t          |ddgddgg           t          |j        |dd          }t          |ddgddgg           t          |j        |dd          }t          |ddgddgg           dS )zA
        solve_triangular on a simple 2x2 complex matrix
        r1  r   rh   rB   TrC   r|  y      ?      y      п      пr         ?       @y             y      ?      ?y      ?      y            пFr~  N)r   r   r   r   r+   rm   r.  r  s       r4   r   z'TestSolveTriangular.test_simple_complexY  s    D!9r1g&''QKKq!4q999!#(;aX'FGGG GT4L!!q!4q999!#A'@AAAq!4q999!#J!V'EFFFq!4q999!#[(9Av;'GHHHqsAU!<<<!#J!V'EFFFqsAU!<<<!#A'@AAAqsAU!<<<!#Q$'@AAAAAr6   c                     t          ddgddgg          }ddg}t          ||dd          }t          |ddg           dS )r{  rC   r   rB   TF)r   rt   N)r   r   r   r  s       r4   ru   z%TestSolveTriangular.test_check_finitev  sW     Aq6Aq6"##Fq!4eDDD!#1v.....r6   N)r   r   r   r   r   ru   r   r6   r4   ry  ry  B  sD        > > >*B B B:/ / / / /r6   ry  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestInvc                 D    t           j                            d           d S r   r   r   s    r4   r   zTestInv.setup_method  r   r6   c                 (   ddgddgg}t          |          }t          t          ||          t          j        d                     g dg dg dg}t          |          }t          t          ||          t          j        d                     d S )NrC   rB   rQ   r?   r   r?   r   r@   rF      r8  )r   r   r   r+   rI  rX   rY   a_invs      r4   r   zTestInv.test_simple  s    VaVA!#a--;;;YY			:::.A!#a--;;;;;r6   c                    d}t          d          D ]t}t          ||g          }t          |          D ]}dd|||f         z   z  |||f<   t          |          }t          t	          ||          t          |                     ud S )Nr<   r?   r  r  r   r   r   r   r   rX   r  r  rY   r  s        r4   r  zTestInv.test_random  s    q 	3 	3A1vA1XX * *b1a4j/!Q$FFE%c!Umm&.qkk3 3 3 3	3 	3r6   c                 |    ddgddgg}t          |          }t          t          ||          ddgddgg           d S )NrC   rB   rQ   r   r   r   r   r   r  s      r4   r   zTestInv.test_simple_complex  sJ    VaWA!#a--1a&1a&1ABBBBBr6   c                 <   d}t          d          D ]}t          ||g          dt          ||g          z  z   }t          |          D ]}dd|||f         z   z  |||f<   t          |          }t          t	          ||          t          |                     d S )Nr<   r?   re   r  r  r  s        r4   r  zTestInv.test_random_complex  s    q 	3 	3A1vr&!Q..00A1XX * *b1a4j/!Q$FFE%c!Umm&.qkk3 3 3 3	3 	3r6   c                     ddgddgg}t          |d          }t          t          ||          ddgddgg           d S )NrC   rB   rQ   r?   Frs   r   r  r  s      r4   ru   zTestInv.test_check_finite  sQ    VaVAE***!#a--1a&1a&1ABBBBBr6   N)	r   r   r   r   r   r  r   r  ru   r   r6   r4   r  r    sv          < < <3 3 3C C C
3 3 3C C C C Cr6   r  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestDetc                 D    t           j                            d           d S r   r   r   s    r4   r   zTestDet.setup_method  r   r6   c                 T    ddgddgg}t          |          }t          |d           d S )NrC   rB   rQ   r?          r   r   rX   rY   a_dets      r4   r   zTestDet.test_simple  s5    VaVAE4(((((r6   c                 T    ddgddgg}t          |          }t          |d           d S )NrC   rB   rQ   r   y            @r  r  s      r4   r   zTestDet.test_simple_complex  s5    VaWAE5)))))r6   c                     t           j        }d}t          d          D ]=}t          ||g          }t          |          } ||          }t	          ||           >d S )Nr<   r?   )linalgr   r  r   r   rX   	basic_detr  r  rY   d1d2s          r4   r  zTestDet.test_random  sg    J	q 	( 	(A1vAQB1BB''''		( 	(r6   c                     t           j        }d}t          d          D ]T}t          ||g          dt          ||g          z  z   }t          |          } ||          }t	          ||d           Ud S )Nr<   r?   re   gvIh%<=ri  )r  r   r  r   r   r  s          r4   r  zTestDet.test_random_complex  s    J	q 	0 	0A1vFAq6NN!22AQB1BB/////		0 	0r6   c                 X    ddgddgg}t          |d          }t          |d           d S )NrC   rB   rQ   r?   Frs   r  r  r  s      r4   ru   zTestDet.test_check_finite  s<    VaVAE***E4(((((r6   N)	r   r   r   r   r   r   r  r  ru   r   r6   r4   r  r    sn          ) ) )
* * *
( ( (0 0 0) ) ) ) )r6   r  c                     t          |           }|rt          |          }t          ||           }t          ||          }t          ||          S )N)r	   r   r   r   )rY   ra   cmplxata1b1s         r4   direct_lstsqr    sH    	1B r]]	RB	RBR==r6   c                   T    e Zd ZdZd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd ZdS )	TestLstsq)gelsdgelssgelsyNc                 D    t           j                            d           d S r   r   r   s    r4   r   zTestLstsq.setup_method  r   r6   c                    t           D ] }t          j        ddgddgg|          }t          j        D ]}dD ]}dD ]}|                                }t          j        ||          }|                                }t          |||||          }	|	d	         }
|	d
         }t          |d
k    d|z             t          t          ||
          |dt          |j                  z  dt          |j                  z  d|z             ˌЌՐd S )NrC   r<   r>   r?   r   TF)rC   r   r   r  )rM   r>   r?   lapack_driveroverwrite_aoverwrite_br   rB   !expected efficient rank 2, got %s   
driver: %srg  )REAL_DTYPESr+   r   r  lapack_driverscopyr   r   r   r   r5   r   )rX   r   rY   r  	overwritebtr  ra   r  outrb   r  s               r4   test_simple_exactzTestLstsq.test_simple_exact  sk     	N 	NE1b'C8,E:::A!*!9 N N!. N NI3 N N VVXXHRu555VVXX#B2?0909; ; ;  FFQ Ca GI I I'Aq		1-/)BH2E2E-E-/)BH2E2E-E0<}0LN N N N NNNN	N 	Nr6   c                 h   t           D ]}t          j        ddgddgddgg|          }t          j        g d|          }t          j        D ]`}dD ]Y}|                                }|                                }t          |||||	          }|d
         }	|dk    r.t          j        ||                    |	          z
  dz            }
n|d         }
|d         }t          |dk    d|z             t          t          t          ||	          |z
  dz                                d
          |
dt          |j                  z  dt          |j                  z  d|z             t          |	ddt          |j                  z  dt          |j                  z  d|z             [bd S )NrC   rB   r?   r   rQ   r   r   r  r  r   r  r  axisr  r  ri  rh  rj  )gm۶mۿgm۶m?)r  r+   r   r  r  r  r   sumr   r   r   r   r5   r   )rX   r   rY   ra   r  r  r  r  r  rb   	residualsr  s               r4   test_simple_overdetzTestLstsq.test_simple_overdet  s     	J 	JE1a&1a&1a&1???A%000A!*!9 J J!. J JIBBBm,5,57 7 7C AA$//$&FAaL1+<$=$=		$'F	AAAF$G!$KLLL#CQQ(:$;$;$?$?Q$?$G$G$-)+i.A.A)A)+i.A.A)A,8=,H	J J J J
 $A'M)+i.A.A)A)+i.A.A)A,8=,HJ J J J J'JJ	J 	Jr6   c                    t           D ]}t          j        ddgddgddgg|          }t          j        g d|          }t          j        D ]t}dD ]m}|                                }|                                }t          |||||	          }|d
         }	|dk    rB||                    |	          z
  }
t          j        |
|
	                                z            }n|d         }|d         }t          |dk    d|z             t          t          t          ||	          |z
  dz                                d
          |dt          |j                  z  dt          |j                  z  d|z             t          |	ddt          |j                  z  dt          |j                  z  d|z             ovd S )Nr  rB   r?   r   rQ   r   )rC   r   rQ   r  r  r   r  rC   r  r  r  r  r  )yu{޿E(B?yӽu{?(YJV?)COMPLEX_DTYPESr+   r   r  r  r  r   r   r  r4  r   r   r   r5   r   )rX   r   rY   ra   r  r  r  r  r  rb   r5  r  r  s                r4   test_simple_overdet_complexz%TestLstsq.test_simple_overdet_complex  s
   # 	F 	FE4)aVaV4EBBBAU333A!*!9 F F!. F FIBBBm,5,57 7 7C AA$//!%%((l$&F3+;$<$<		$'F	AAAF$G!$KLLL#CQQ(:$;$;$?$?Q$?$G$G$-)+i.A.A)A)+i.A.A)A,8=,H	J J J J
 $ ! $L%')BH*=*=%=%')BH*=*=%=(4}(DF F F F F+FF	F 	Fr6   c                    t           D ]}t          j        g dg dg|          }t          j        ddg|          }t          j        D ]}dD ]}|                                }|                                }t          |||||          }|d         }	|d         }
t          |
dk    d	|
z             t          |	d
dt          |j
                  z  dt          |j
                  z  d|z             d S )Nr   r  r   rC   rB   r  r  r   r  )gqqgqq?gdq?r  r  r  )r  r+   r   r  r  r  r   r   r   r5   r   )rX   r   rY   ra   r  r  r  r  r  rb   r  s              r4   test_simple_underdetzTestLstsq.test_simple_underdet8  sE     	J 	JE)))YYY/u===A!Qu---A!*!9 J J!. J JIBBBm,5,57 7 7C AAAAAF$G!$KLLL#A (;)+i.A.A)A)+i.A.A)A,8=,H	J J J J JJJ	J 	Jr6   c                    t           D ]}dD ]}t          j        D ]}dD ]}t          j        t          ||g          |          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ];}t          j        t          |dg          |          }|                                }|                                }	t          ||	|||          }
|
d	         }|
d
         }t          ||k    d|d|           |t          j
        u rPt          t          ||          |dt          |j                  z  dt          |j                  z  d|z             t          t          ||          |dt          |j                  z  dt          |j                  z  d|z             =d S )Nr<      r  r   r<   r  r?   rQ   r  r   rB   expected efficient rank , got i  r  r    )r  r  r  r+   asarrayr   r  r  r   r   r
   r   r   r5   r   )rX   r   r  r  r  rY   r  ra   r  r  r  rb   r  s                r4   test_random_exactzTestLstsq.test_random_exactN  s1     	P 	PE P P%.%= P PM%2 P P	Jvq!f~~UCCC!&q ; ;A&(C!AqD'M&:AadGG!&q P PA "
61a&>> G G GA!"B!"B"'B6C4=4=#? #? #?C !$AA #AA#AFF0111-6 7 7 7$
22 /*-a))Q/2Yrx5H5H/H/2Yrx5H5H/H2>2N	!P !P !P !P !P !0*-a))Q/3i6I6I/I/3i6I6I/I2>2N	!P !P !P !P !P)P	PPP	P 	Pr6   c                    t          j                    dk    rgt          j        t          j                  t          j        d          k    r3t          j                    d         }|dk    rt          j	        d           t          D ]}dD ]}t          j        D ]}dD ]}t	          j        t          ||g          dt          ||g          z  z   |	          }t          |          D ]}d
d|||f         z   z  |||f<   t          d          D ];}t	          j        t          |dg          |	          }|                                }	|                                }
t#          |	|
|||          }|d         }|d         }t%          ||k    d|d|           |t          j        u rPt)          t+          ||          |dt-          |	j                  z  dt-          |	j                  z  d|z             t)          t+          ||          |dt-          |	j                  z  dt-          |	j                  z  d|z             =ʐd S )NWindowsz1.24.0r   glibcz(segfault observed on alpine per gh-17630r  r  rh   r   r<   r  rB   rQ   r  r  r  i  r  r  r  )platformsystemr   parser+   __version__Versionlibc_verr  rw  r  r  r  r  r   r  r  r   r   rk  r   r   r5   r   )rX   libc_flavorr   r  r  r  rY   r  ra   r  r  r  rb   r  s                 r4   test_random_complex_exactz#TestLstsq.test_random_complex_exactp  s   ?	))}R^,,0I0III&/11!4'))K JKKK# 	P 	PE P P%.%= P PM%2 P P	Jvq!f~~61a&>>8I'I-24 4 4!&q ; ;A&(C!AqD'M&:AadGG!&q P PA "
61a&>> G G GA!"B!"B"'Bm4=4=#? #? #?C !$AA #AA#AFF0111-6 7 7 7$44 /*-a))Q/2Yrx5H5H/H/2Yrx5H5H/H2>2N	!P !P !P !P !P !0*-a))Q/3i6I6I/I/3i6I6I/I2>2N	!P !P !P !P !P'PPPP	P 	Pr6   c                    t           D ]_}dD ]X\  }}t          j        D ]D}dD ]=}t          j        t          ||g          |          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]}t          j        t          |dg          |          }|                                }	|                                }
t          |	|
|||          }|d	         }|d
         }t          ||k    d|d|           t          |t          ||d	          dt          |	j                  z  dt          |	j                  z  d|z             ߐ?FZad S )N)r<      )r  rB   r  r   r<   r  r?   rQ   r  r   rB   r  r  r  r  r  r  )r  r  r  r+   r  r   r  r  r   r   r   r  r5   r   rX   r   r  mr  r  rY   r  ra   r  r  r  rb   r  s                 r4   test_random_overdetzTestLstsq.test_random_overdet  s     	P 	PE. P PA%.%= P PM%2 P P	Jvq!f~~UCCC!&q ; ;A&(C!AqD'M&:AadGG!&q P PA "
61a&>> G G GA!"B!"B"'B6C4=4=#? #? #?C !$AA #AA#AFF0111-6 7 7 7+*+\!Qa-H-H-H/1Ibh4G4G/G/1Ibh4G4G/G2>2N	P P P P PP	PPP	P 	Pr6   c                     t           D ]t}dD ]m\  }}t          j        D ]Y}dD ]R}t          j        t          ||g          dt          ||g          z  z   |          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]}t          j        t          |dg          |          }|                                }	|                                }
t          |	|
|||	          }|d
         }|d         }t          ||k    d|d|           t          |t          ||d          dt          |	j                  z  dt          |	j                  z  d|z             ߐT[ovd S )Nr  r  rh   r   r<   r  rB   rQ   r  r   r  r  rC   r  r  r  r  )r  r  r  r+   r  r   r  r  r   r   r   r  r5   r   r  s                 r4   test_random_complex_overdetz%TestLstsq.test_random_complex_overdet  s   # 	L 	LE. L LA%.%= L LM%2 L L	Jvq!f~~61a&>>8I'I-24 4 4!&q ; ;A&(C!AqD'M&:AadGG!&q L LA "
61a&>> G G GA "#B!"B"'B6C4=4=#? #? #?C !$AA #AA#AFF0111-6 7 7 7+&'a!)D)D)D+-	"(0C0C+C+-	"(0C0C+C.:].J	L L L L LLLLL	L 	Lr6   c           
         t                      5 }|                    t          d           d d d            n# 1 swxY w Y   t          j        d          }t          j        t          dt          j	        dd          D ]\  }}}}}|
                    |          }t          j        ||          }	|                                }
|	                                }t          |
|||||          }|d         }|d         }t          |dk    d	|z             t          t          ||          |	d
t!          |j                  z  d
t!          |j                  z  d|z             d S )NzIinternal gelsd driver lwork query error,.*Falling back to 'gelss' driver.))rC   r<   r  r  r  r   )r  rt   r  r  r   rB   r  r  r  r  )r   filterRuntimeWarningr+   r   rl  rm  r  r  r  rT  r  r   r   r   r   r5   r   )rX   supr  r   r  r  r  rt   rY   ra   r  r  r  rb   r  s                  r4   ru   zTestLstsq.test_check_finite  s      	:CJJ~9: : :	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: X)**kL'6++	- -	B 	B=E2}i 		%  A5)))A BBBm%1y$-/ / /C AAAAAF?!CDDDC1IIq!#i&8&8!8!#i&8&8!8$0=$@B B B B B'	B 	Bs   7;;c           
          dD ]\  }}t          j        |          }t          t          j        |          |          \  }}}}t	          |t          j        |d         f|dd          z                        |d         rt          j        d          n#t           j                            |d          dz  }t	          ||           t          |dk    d           t	          |t          j        d                     d S )N))r   rB   r   ))r   r?   r  )r?   r   )r?   )r  )r?   rB   rC   r  r   r  rB   zexpected rank 0)	r+   r<  r   r   r   emptyr  r   r   )	rX   a_shapeb_shapera   rb   residuesranksresidues_should_bes	            r4   test_zero_sizezTestLstsq.test_zero_size  s    !3 	, 	,GW   A#('):):A#>#> AxqBHgaj]WQRR[%@AABBB4;AJ #D"(4...')y~~aa~'@'@!'C #5666DAI0111BHTNN++++	, 	,r6   N)r   r   r   r  r   r  r  r  r  r  r  r  r  ru   r  r   r6   r4   r  r    s        6N  N N N2J J J:F F FBJ J J, P  P  PD%P %P %PNP P P6L L L:B B B@, , , , ,r6   r  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestPinvc                 D    t           j                            d           d S r   r   r   s    r4   r   zTestPinv.setup_method  r   r6   c                     t          g dg dg dgt                    }t          |          }t          t	          ||          t          j        d                     d S Nr   r  r  r   rQ   r   floatr   r   r   r+   rI  rX   rY   a_pinvs      r4   test_simple_realzTestPinv.test_simple_real  sX    999iii4EBBBa!#a.."&))<<<<<r6   c                    t          g dg dg dgt                    dt          g dg dg dgt                    z  z   }t          |          }t          t	          ||          t          j        d	                     d S 
Nr   r  r  r   rh   )r8  r  rF   )r@   r   r?   )rQ   rB   rC   rQ   r  r  s      r4   r   zTestPinv.test_simple_complex  s    IIIyyy***5  


IIIyyy'I-2"4 "4 "4 44 a!#a.."&))<<<<<r6   c                     t          g dg dg dgt                    }t          |          }t          g dg dg dg          }t          ||           d S )Nr   r  rF   r  r9  r   g|qgԕVUUſgc8?gqg^0<gq?g9?gԕVUU?g:87ȿr   r  r   r   rX   rY   r  r   s       r4   test_simple_singularzTestPinv.test_simple_singular  s|    999iii35AAAaLLLKKKKKKM N N 	"&(33333r6   c                     t          g dg dgt                    }t          |          }t          ddgddgdd	gg          }t          ||           d S )
Nr   r  r   g֋8g#q?g#qg#q?gIq?g#q̿r  r  s       r4   test_simple_colszTestPinv.test_simple_cols  so    999iii(666a;
3&
3%{35 6 6 	"&(33333r6   c                     t          ddgddgddggt                    }t          |          }t          g dg d	g          }t          ||           d S )
NrC   rB   rQ   r?   r   r@   r   )gDpTUUgQUUտgvWUU?)gDpTUU?gQUU?g&>ڿr  r  s       r4   test_simple_rowszTestPinv.test_simple_rows  sq    Aq6Aq6Aq6*%888a@@@???A B B!&(33333r6   c                     t          g dg dg dg          }t          |d          }t          t          ||          t	          j        d                     d S )Nr   )r?   r   r   r  Frs   rQ   )r   r   r   r   r+   rI  r  s      r4   ru   zTestPinv.test_check_finite%  sZ    999jjj***566ae,,,!#a.."&))<<<<<r6   c                     g dg dg dg}t          |          }t          g dg dg dg          }t          ||           d S )Nr   r  r
  r  r  r  )r   r   r   r  s       r4   test_native_list_argumentz"TestPinv.test_native_list_argument*  so    YY			999-aLLLKKKKKKM N N 	"&(33333r6   c                    d}t          t          j                            ||                    \  }}t          j        d                              dd          }|                                }d|d<   d}d}t          ||d	
          }||z  |z  |z
  }	||z  |z  |z
  }
t          t          j	        
                    |	          dd           t          t          j	        
                    |
          dd           t          |||
          }||z  |z  |z
  }	||z  |z  |z
  }
t          t          j	        
                    |	          dd           t          t          j	        
                    |
          dd           d S )N   g     A@rF   r   gMbP?)r   r   h㈵>g?rI   rh  ri  gMb@?rh  gvIh%,=g;O@{Gz?r  )r$   r+   r   rM  r   rV   r  r   r   r  r   )rX   r  q_a_mrY   rh  ri  a_padiff1adiff2s              r4   test_atol_rtolzTestPinv.test_atol_rtol2  sk   ")..A&&''1ioo%%a**HHJJ# 3T+++S1qsS3& 		v..5AAAA	v..FCCCC 3T---S1qsS3&	v..DAAAA	v..DAAAAAAr6   N)r   r   r   r   r  r   r  r  r  ru   r  r$  r   r6   r4   r  r    s          = = =
= = =4 4 44 4 44 4 4= = =
4 4 4B B B B Br6   r  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestPinvSymmetricc                 D    t           j                            d           d S r   r   r   s    r4   r   zTestPinvSymmetric.setup_methodP  r   r6   c                     t          g dg dg dgt                    }t          j        ||j                  }t          |          }t          t          j        ||          t          j        d                     d S r  )r   r  r+   r   r.  r   r   rI  r  s      r4   r  z"TestPinvSymmetric.test_simple_realS  sm    999iii4EBBBF1acNNq!"&F"3"3RVAYY?????r6   c                 j   t          g dg dg dgt                    }t          j        ||j                  }t          j                            |          \  }}}|dxx         dz  cc<   t          j        ||z  |          }t          |          }t          |          }t          ||           d S )Nr   r  r
  r   r   rE   )
r   r  r+   r   r.  r  svdr   r   r   )rX   rY   r\   r  vtr  a_pinvhs          r4   test_nonpositivez"TestPinvSymmetric.test_nonpositiveY  s    999iii35AAAF1acNN9==##1b	!
F1q5"a((!&'22222r6   c                 j   t          g dg dg dgt                    dt          g dg dg dgt                    z  z   }t          j        ||                                j                  }t          |          }t          t          j        ||          t          j        d	                     d S r  )	r   r  r+   r   r4  r.  r   r   rI  r  s      r4   r   z%TestPinvSymmetric.test_simple_complexc  s    IIIyyy***5  


IIIyyy'I-2"4 "4 "4 44 F1affhhj!!q!"&F"3"3RVAYY?????r6   c                 $   t          g dg dg dgt                    }t          j        ||j                  }t          |                                          }t          t          j        ||          t          j        d                     d S r  )	r   r  r+   r   r.  r   tolistr   rI  r  s      r4   r  z+TestPinvSymmetric.test_native_list_argumentk  sw    999iii4EBBBF1acNNqxxzz""!"&F"3"3RVAYY?????r6   c                    d}t          t          j                            ||                    \  }}t          j        g ddg|dz
  z  z             }|j        |z  |z  }t          j        g ddg|dz
  z  z             }|j        |z  |z  }d}d}t          ||d	          }||z  |z  |z
  }	||z  |z  |z
  }
t          t          |	          |d
           t          t          |
          dd           t          |||	          }||z  |z  |z
  }	||z  |z  |z
  }
t          t          |	          dd
           t          t          |
          dd
           d S )Nr  )r?   rQ   rB   rC   vk?gﭣ>gu>r@   )r?   rQ   rB   rC   r2  rI   rI   r  g1?r  r  r  rf  gdy=r  -C6?)	r$   r+   r   rM  rm   r.  r   r   r   )rX   r  r  r  rY   r   rh  ri  r!  r"  r#  s              r4   r$  z TestPinvSymmetric.test_atol_rtolq  s~   ")..A&&''1G222gY!_DEEC!GaKg///2$!*<==cCi!m!ADr***S1qsS3& 	Vd5555Ve%8888 ADt,,,S1qsS3&Vd5555Vd555555r6   N)	r   r   r   r   r  r-  r   r  r$  r   r6   r4   r&  r&  N  sw          @ @ @3 3 3@ @ @@ @ @6 6 6 6 6r6   r&  scale)g#B;r;   @xDpinv_c                     t          j        ddgddgg          | z  }t          j        dt          j        |          z            } ||          }t          ||           d S )NrC   r   g|=r;   )r+   r   rm   r   )r4  r6  rb   r   x_invs        r4   test_auto_rcondr9    sc     	1a&1e*%&&.AwrBGAJJ''HE!HHEE8$$$$$r6   c                   ~    e Zd Zd Zd Zd Zd Zd Zd Ze	j
                            e d          d	             Zd
S )TestVectorNormsc                    t           j        d         D ]}t          j        g d|          }t          dt          j        |          j        j        dz            }t          t          |          t          j	        d          |           t          t          |d          t          j	        d          |           t           j        d	         D ]}t          j        g d
|          }t          dt          j        |          j        j        dz            }t          t          |          t          j	        d          |           t          t          |d          t          j	        d          |           d S )NAllFloatr   r   gV瞯<r<   rG   r  rB   Complex)rh   re   y              @)
r+   	typecodesr   maxr0   r1   realr   r   sqrt)rX   r   rb   rt  s       r4   
test_typeszTestVectorNorms.test_types  sB   \*- 	? 	?E%000AeRXe__05:;;CDGGRWR[[s;;;;DAJJ#>>>>>\), 	? 	?EU333AeRXe__05:;;CDGGRWR[[s;;;;DAJJ#>>>>>		? 	?r6   c                 n    t          dgt                    }t          t          |          |           d S )Nr5  r   )r   r
   r   r   rW  s     r4   test_overflowzTestVectorNorms.test_overflow  s4     4&(((DGGQ'''''r6   c                     t          dgdgdz  z   t                    }	 t          t          |          dz
  dd           d S # t          $ r( d}t          t          |          dz
  d	|
           Y d S w xY w)N     @rC   i'  r   r   r  r  zO: Result should equal either 0.0 or 0.5 (depending on implementation of snrm2).rI   )rj  )r   r
   r   r   AssertionErrorr   )rX   rY   msgs      r4   test_stablezTestVectorNorms.test_stable  s    3%1#e)#7333	A DGGcM3T:::::: 	A 	A 	A.CQ#sC@@@@@@@		As   "A .A65A6c                     t          t          g dd          d           t          t          g dd          d           d S )N)rC   r   rQ   r   rB   r   rQ   )r   r   r   s    r4   test_zero_normzTestVectorNorms.test_zero_norm  sD    T)))Q''+++T)))Q''+++++r6   c                     t          j        ddgddgggdz  d          }t          t          |d          ddggdz             t          t          |dd          d	gdz  gdz             d S )
NrB   rC   rQ   r?   dr  5D+@6f~@g      @)r+   r   r   r   rW  s     r4   test_axis_kwdzTestVectorNorms.test_axis_kwd  s    H1v1v&'!+S11QQ:z*B)Ca)GHHHQ***bTAXJN;;;;;r6   c                    t          j        ddgddgggdz  d          }t          |dd          }t          |dd	gggdz             t	          |j        d
k               t          t          |ddd          dgdgggdz             d S )NrB   rC   rQ   r?   rN  T)r  keepdimsrO  rP  )rB   rC   rB   rw   g      @)r+   r   r   r   r   r*  r@  s      r4   test_keepdims_kwdz!TestVectorNorms.test_keepdims_kwd  s    H1v1v&'!+S11T***j*567!;<<<9$%%%QD999bTB4L>A;MNNNNNr6   z64-bit BLAS requiredra  c                     t          d           t          j        dgt          j                  }d|d<   t	          |          }~t          |d           d S )NihB  )free_mbl        r   rC   rE   r;   )r(   r+   r   r-   r   r   )rX   rb   r5  s      r4   test_large_vectorz!TestVectorNorms.test_large_vector  sX    %((((HeWBJ///"1ggS!!!!!r6   N)r   r   r   rC  rE  rJ  rL  rQ  rT  r  rv  skipifr)   rW  r   r6   r4   r;  r;    s        ? ? ?( ( (A A A, , ,< < <
O O O [I.DEE" " FE" " "r6   r;  c                        e Zd Zd Zd Zd ZdS )TestMatrixNormsc           
         t           j                            d           dD ]\  }}t           j        t           j        t           j        t           j        t           j        fD ]\}dt           j                            ||          	                    |          z  }t          j
        |j        t           j                  rF|dt           j                            ||          z  z   	                    |          }t           j        }nt           j        }d ddddd	t           j        t           j         fD ]}t          ||
          }t           j                            ||
          }t          j        ||          sDt           j                            |	                    |          |
          }t#          ||           ^d S )Nr   )rk   )rC   rQ   )rQ   rC   )r?   r?   )r?   r   )r   r?   r8  y              $@frorC   rE   rB   )ord)r+   r   r   singledoublecsinglecdoubleint64ro  rT  
issubdtyper   complexfloatinginfr   r  allcloser   )	rX   r  r  tr	  t_highorderactualdesireds	            r4   test_matrix_normsz!TestMatrixNorms.test_matrix_norms  sx   
	tB 	9 	9DAqY	2:rz28K 9 9A..55a888="*<== 'S29??1a#8#888@@CCAZFFYF"E1b!R"&I 9 9E!!///F innQEn::G ;vw77 9"$)..&1A1Au."M"M'88899	9 	9r6   c                    t          j        ddgddgggdz  d          }t          |t           j        d          }t          t          j        |dd          t           j        d	          }t          |dd	          }t          ||           t          ||           t          ||           t          |j        |j        cxk    o
|j        k    nc            t          |dd          }t          t          j        |dd          dd	          }t          |t           j        d	          }t          ||           t          ||           t          ||           t          |j        |j        cxk    o
|j        k    nc            d S )
NrB   rC   rQ   r?   rN  r  )r^  r  r   r   )r+   r   r   rf  swapaxesr   r   r*  )rX   rY   ra   crN  s        r4   rQ  zTestMatrixNorms.test_axis_kwd  s   H1v1v&'!+S11V,,,Q1%%26???'''11117----ag----...'''Q1%%16:::V,,,11117----ag----.....r6   c                    t          j        dd                              dddd          }t          |t           j        dd	
          }t          |ddd	
          }t          ||           t          |j        |j        k               d S )Nx   rN  r   rB   rQ   r?   r   r  T)r^  r  rS  rC   r   )r+   r   rV   r   rf  r   r   r*  )rX   rY   ra   rp  s       r4   rT  z!TestMatrixNorms.test_keepdims_kwd  s    Ic%%%--aAq99Vd;;;666117"#####r6   N)r   r   r   rm  rQ  rT  r   r6   r4   rZ  rZ    sA        9 9 9(/ / /"$ $ $ $ $r6   rZ  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestOverwritec                 4    t          t          ddg           d S NrQ   rQ   r(  )r'   r   r   s    r4   
test_solvezTestOverwrite.test_solve      EFD>22222r6   c                 4    t          t          ddg           d S rv  )r'   r   r   s    r4   test_solve_triangularz#TestOverwrite.test_solve_triangular  s    ,vtn=====r6   c                 ,    t          d ddg           d S )Nc                 $    t          d| |          S )NrM   )r   )rZ   ra   s     r4   <lambda>z1TestOverwrite.test_solve_banded.<locals>.<lambda>	  s    ,vr1*E*E r6   )r?   r@   r@   r&   r   s    r4   test_solve_bandedzTestOverwrite.test_solve_banded  s+    EE#TN	, 	, 	, 	, 	,r6   c                 4    t          t          ddg           d S )N)rB   r@   r  )r'   r   r   s    r4   test_solveh_bandedz TestOverwrite.test_solveh_banded  s    MFD>:::::r6   c                 2    t          t          dg           d S Nrw  )r'   r   r   s    r4   test_invzTestOverwrite.test_inv      C&*****r6   c                 2    t          t          dg           d S r  )r'   r   r   s    r4   test_detzTestOverwrite.test_det  r  r6   c                 4    t          t          ddg           d S )N)rQ   rB   r(  )r'   r   r   s    r4   
test_lstsqzTestOverwrite.test_lstsq  ry  r6   c                 2    t          t          dg           d S r  )r'   r   r   s    r4   	test_pinvzTestOverwrite.test_pinv  s    D6(+++++r6   c                 2    t          t          dg           d S r  )r'   r   r   s    r4   
test_pinvhzTestOverwrite.test_pinvh  s    EF8,,,,,r6   N)r   r   r   rx  r{  r  r  r  r  r  r  r  r   r6   r4   rt  rt    s        3 3 3> > >, , ,; ; ;+ + ++ + +3 3 3, , ,- - - - -r6   rt  c                   >    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	S )
TestSolveCirculantc                     t          j        g d          }t          j        g d          }t          ||          }t          t	          |          |          }t          ||           d S N)rC   rB   rQ   r   )rC   rE   rC   r   )r+   r   r   r   r    r   rX   rp  ra   rb   ys        r4   test_basic1zTestSolveCirculant.test_basic1!  sb    H\\\""H]]]##Aq!!)A,,""1r6   c                     t          j        g d          }t          j        d                              dd          }t	          ||          }t          t          |          |          }t          ||           d S )NrC   rB   r   r  r?   rQ   r+   r   r   rV   r   r   r    r   r  s        r4   test_basic2zTestSolveCirculant.test_basic2(  sl    H^^^$$IbMM!!!Q''Aq!!)A,,""1r6   c                     t          j        g d          }t          j        d                              ddd          }t	          ||          }t          t          |          |          }t          ||           d S )Nr     r?   rQ   rB   r  r  s        r4   test_basic3zTestSolveCirculant.test_basic30  sn    H^^^$$IbMM!!!Q**Aq!!)A,,""1r6   c                    t          j        g d          }t          j        d                              dd          dz   }t	          ||          }t          t          |          |          }t          ||           d S )N)r  r  r   r   r  r?   rB   y              ?r  r  s        r4   ri   zTestSolveCirculant.test_complex8  st    H&&&''IaLL  A&&-Aq!!)A,,""1r6   c                 :   t           j                            d           t           j                            d          }t           j                            d          }t	          ||          }t          t          |          |          }t          ||           d S )Ni1  2   )r+   r   r   ro  r   r   r    r   r  s        r4   test_random_b_and_cz&TestSolveCirculant.test_random_b_and_c@  sv    
	uIOOBIOOBAq!!)A,,""1r6   c                    t          j        g d          }t          j        g d          }t          ||d          }t          t	          |          |          \  }}}}t          ||           t          t          t          ||           d S )NrC   rC   r   r   )rC   rB   rQ   r?   r   )singular)r+   r   r   r   r    r   ry   r!   )rX   rp  ra   rb   r  r5  rnkr  s           r4   test_singularz TestSolveCirculant.test_singularI  s    H\\\""H\\\""Aq7333y||Q//3Q1k?Aq99999r6   c                    t          j        g dgg dgg          }t          j        g dg dg dg          }t          ||d          }t          |j        d           t          j        |          }t          t          |d	                   |j                  |d d d	d d f<   t          t          |d                   |j                  |d d dd d f<   t          ||           t          ||dd
          }t          |j        d           t          t          j
        |d
d	          |           t          t          j        |dd          |j        d          }t          |j        d           t          ||           d S )N)rE   g      @rQ   g      @)rC   r@   r@   g      @)r   r   rC   rC   r  )rC   rE   r   r   rC   )baxis)r?   rB   rQ   r   rE   )r  outaxis)rB   rQ   r?   rB   )caxis)r+   r   r   r   r*  
empty_liker   r    r.  r   moveaxisro  )rX   rp  ra   rb   r   s        r4   test_axis_argsz!TestSolveCirculant.test_axis_argsR  s    H((()NNN+;<== HlllLLL---@AAAq***QWi(((=##!)AaD//1377Aqqq!)AaD//1377Aqqq8$$$Aq2666QWi(((Ar1--x888 BK1a00!#Q???QWi(((8$$$$$r6   c                     g d}g d}t          ||          }t          t          |          |          }t          ||           d S r  )r   r   r    r   r  s        r4   r   z-TestSolveCirculant.test_native_list_argumentsk  sN    LLMMAq!!)A,,""1r6   N)r   r   r   r  r  r  ri   r  r  r  r   r   r6   r4   r  r    s                  : : :% % %2    r6   r  c                   8    e Zd Zd Zd Zd Zd Zd Zd Zd Z	dS )	TestMatrix_Balancec                 <    t          t          t          d           d S )NzSome string for fail)ry   rz   r#   r   s    r4   test_string_argz"TestMatrix_Balance.test_string_argv  s    j.2HIIIIIr6   c           	          t          t          t          t          j        ddgdt          j        gg                     t          t          t          t          j        ddgdt          j        gg                     d S )NrC   rB   rQ   )ry   rz   r#   r+   r   rf  nanr   s    r4   test_infnan_argz"TestMatrix_Balance.test_infnan_argy  sp    j.hABF455	7 	7 	7j.hABF455	7 	7 	7 	7 	7r6   c           	          t          t          j        ddgddgg                    \  }}t          t          j        t          j        t          j        |                              dg           d S )Nr  rC   r   r   )r#   r+   r   r   difflog2rm   )rX   r  r  s      r4   test_scalingzTestMatrix_Balance.test_scaling  s`    bhq	D!9'=>>??1 	

 3 344qc:::::r6   c                     t          j        g dg dg dg          }t          |          \  }}t          t	          ||                              |          |           d S )N)rC   r   r3  )rC   rC   r  )rG  g      Y@rC   )r+   r   r#   r   r   r   )rX   r	  rb   r  s       r4   test_scaling_orderz%TestMatrix_Balance.test_scaling_order  s_    HlllLLL---@AAa  1a**A.....r6   c                    t          t          j        ddgddgg          d          \  }\  }}t          t          j        t          j        |                    dg           t          |t          j        d                     d S )Nr  rC   r   separater   rB   )r#   r+   r   r   r  r  r   r   )rX   r  r  zs       r4   test_separatez TestMatrix_Balance.test_separate  s|    "28dAYq	,B#C#C,-/ / /	6AqRWRWQZZ((1#...29Q<<(((((r6   c                 r   t          t          j        d          t          j        t          j        d                    t          j        d                    }t	          |d          \  }\  }}t          |t          j        |                     t          |t          j        g d                     d S )N)rB   rB   rw  rC   r  )r   rC   r@   r   r?   rQ   rB   )r"   r+   r<  r;  r#   r   	ones_liker   )rX   r	  rb   r  r  s        r4   test_permutationz#TestMatrix_Balance.test_permutation  s    rwv(@(@wv( ("1q111	6Aq2<??+++28$9$9$9::;;;;;r6   c           	      L   t          j        g dg dg dg dg dg          t          j        g dg dg dg dg          t          j        g d	g d
g dg dg          f}|D ]}t          |          \  }}t          |d          \  }\  }}t          j        |          }t          j        |j        d                   ||<   t          |t          j        |          |d d f                    t          t          ||          	                    |          |           d S )N)rI   rI   rI   rI   >)rI   rI   rI   rI   rI   )rP   rP   rI   rI   rI   )rI   rI   r  rI   rI   )r~  rI   rI   rI   )rI         rI   rI   )r;   rI   r~  rI   )rI   r;   rI   r  )      rI   r;   rI   )r  r         r;   )r  r  r  rI   )r  r  r;   r  rC   r  r   )
r+   r   r#   r  r   r*  r   rm   r   r   )rX   casesr	  rb   r  r  pips           r4   test_perm_and_scalingz(TestMatrix_Balance.test_perm_and_scaling  sz    555/////////555	7 8 8 ---,,,---,,,. / /
 ,,,.........0 1 1$  	3 	3A!!$$DAq&q1555IAv1q!!BIagaj))BqEArwqzz"aaa%0111E!QKKOOA..2222	3 	3r6   N)
r   r   r   r  r  r  r  r  r  r  r   r6   r4   r  r  t  s        J J J7 7 7; ; ;/ / /
) ) )< < <3 3 3 3 3r6   r  r  )Qr  rl  rD  numpyr+   r   r   r   r   r   r   r	   r
   numpy.linalgr  numpy.randomr   numpy.testingr   r   r   r   r   r   r   r  r   ry   
scipy._libr   scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   scipy.linalg._testutilsr'   scipy._lib._testutilsr(   scipy.linalg.blasr)   r-   r,   r  rk  r/   r.   r  DTYPESr5   r8   r   r   ry  r  r  r  r  r  r&  rv  parametrizer9  r;  rZ  rt  r  r  r   r6   r4   <module>r     so                                           B B B B B B B B B B B B B B B B B B  * * * * * *      = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
 8 7 7 7 7 7 3 3 3 3 3 3 ' ' ' ' ' 'z2:r}5,r~>	~	%  H0 H0 H0 H0 H0 H0 H0 H0Vx; x; x; x; x; x; x; x;v	O1 O1 O1 O1 O1 O1 O1 O1d
;/ ;/ ;/ ;/ ;/ ;/ ;/ ;/|(C (C (C (C (C (C (C (CV#) #) #) #) #) #) #) #)L   a, a, a, a, a, a, a, a,H	MB MB MB MB MB MB MB MB`<6 <6 <6 <6 <6 <6 <6 <6~ "3444-00% % 10 54%9" 9" 9" 9" 9" 9" 9" 9"x,$ ,$ ,$ ,$ ,$ ,$ ,$ ,$^- - - - - - - -<R R R R R R R Rj>3 >3 >3 >3 >3 >3 >3 >3 >3 >3r6   