
    -iir                       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mZmZmZmZmZ d dl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l(m)Z) d dl*m+Z+m,Z, d dl-m.Z. d d	l/m0Z0 ej        ej1        ej2        fZ3ej4        ej5        ej6        fZ7e3e7z   Z8ej9        :                    d
ddiddii g          Z;d Z< G d d          Z= G d d          Z> G d d          Z? G d d          Z@ G d d          ZA G d d          ZBd0dZC G d d          ZD G d d          ZE G d  d!          ZFej9        :                    d"d#          ej9        :                    d$eef          d%                         ZG G d& d'          ZH G d( d)          ZI G d* d+          ZJ G d, d-          ZK G d. d/          ZLdS )1    N)arangearraydotzerosidentity	conjugate	transposefloat32)assert_equalassert_almost_equalassert_assert_array_almost_equalassert_allcloseassert_array_equal)raises)solveinvdetlstsqpinvpinvhnormsolve_bandedsolveh_bandedsolve_triangularsolve_circulant	circulantLinAlgError
block_diagmatrix_balanceqrLinAlgWarningassert_no_overwrite)check_free_memoryIS_MUSL)	HAS_ILP64)skip_xp_invalid_argoverwrite_kwoverwrite_aTFc                     | }|t           j        k    rt           j        }n|t           j        k    rt           j        }t          j        |          j        S )z;Get the epsilon for dtype, possibly downcast to BLAS types.)np
longdoublefloat64clongdouble
complex128finfoeps)dtypdts     c/var/www/html/bet.cuttalo.com/ml/venv/lib/python3.11/site-packages/scipy/linalg/tests/test_basic.py	_eps_castr6   "   sB    	B	R]Z	r~		]8B<<    c            	          e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                            d	eeej        eej        g          ej                            d
eeej        eej        g          d                         ZdS )TestSolveBandedc                    t          g dg dg dg dg          }t          g dg dg dg dg          }d	\  }}t          g d
          }|                    dd          }t          ddgddgddgddgg          }t          g dg dg dg dg          }||||fD ]3}	t          ||f||	          }
t          t	          ||
          |	           4d S )N      ?   r   r         r         r=   rC   r                 r=   rA   rC   rD   r@   r=   rH   r?   rD   rG   r   rC   rF   r   r   rC   rD         $@rJ          @g      ,@rF   rD   rC   r?   r@      rD   r   r   r   r   r   r   rD   r   rD   r   r   r   reshaper   r   r   selfaablub4b4by1b4by2b4by4bxs              r5   	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 	4r7   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>   )               @rD   r=   rf   rE   rJ   r=   rA   rf   rK   rL   )rf   rF   r   r   rN   rP   rJ   rQ   y              ,@rF   rD   rC   r?   r@   rR   rS   )r   r   r                 ?rU   rV   rX   s              r5   test_complexzTestSolveBanded.test_complexF   sK   ???!>>"??!>># $ $ $$$"NN"NN"NN$ % % 1***++

2q!!1vQx1v1v     |||$}}#||#||% & & eUE* 	4 	4AaVR++A%c!Qii3333	4 	4r7   c                    t          g dg dg dg          }t          j        |ddd f         d          t          j        |dd d f         d          z   t          j        |dd df         d          z   }t          g d          }|                    dd          }t          ddgd	d
gddgddgg          }t          g dg dg dg dg          }||||fD ]1}t	          d||          }t          t          ||          |           2d S )NrI   rK   rL   r   rD   rC   rF   rO   r?   r@   rR   rS   rT   rU   rD   rD   r   r,   diagrW   r   r   r   	rY   r[   rZ   r^   r_   r`   ra   rb   rc   s	            r5   test_tridiag_realz!TestSolveBanded.test_tridiag_real^   sd   OOO!>>!>># $ $ 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 	4r7   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 )Nrg   rK   rL   r   rD   rC   rF   rh   r?   r@   rR   rS   rT   rU   rl   rm   ro   s	            r5   test_tridiag_complexz$TestSolveBanded.test_tridiag_complexr   sg   $$$!>>!>># $ $ 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 	4r7   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>   rB   rE   rI   rK   rL   rM   rN   rO   Fcheck_finite)r   r   r   r   )rY   rZ   r[   r\   r]   r^   rc   s          r5   test_check_finitez!TestSolveBanded.test_check_finite   s    ???!>> ==!>># $ $ OOO"NN"NN!MM# $ $ 1)))**!QRe<<<!#a))R00000r7   c                 N   t          g dg dg dg dg          }d\  }}t          g d                              dd          }t          t          t          ||f||           t          t          t          ||f|d	d
g           t          t          t          d|d	d
g           d S )NrI   rK   rL   rM   rN   )r<   rQ         @      @rF   r@   r<   rQ   rl   )r   rW   assert_raises
ValueErrorr   )rY   r[   r\   r]   bads        r5   test_bad_shapezTestSolveBanded.test_bad_shape   s    OOO"NN"NN!MM# $ $ 1((())11"a88j,AC@@@j,AS#JGGG 	j,S#JGGGGGr7   c                 ^   t          g dg          }t          g dg          }t          ddgg|          }t          ||d           t          ddgdgdgg|          }t          ||d           t          |j        t          j        d	                     t          |g dg           d S )
Nr<   rQ   rx   )      ?r<   g      ?r   r   rC   V瞯<rtolrl   r   f8)r   r   r   r   dtyper,   r   )rY   rb   refrc   s       r5   test_1x1zTestSolveBanded.test_1x1   s    
 <<<.!!___%&&1#**3U++++ 1#sQC!443U++++QWbhtnn---1/00000r7   c                     g dg dg dg dg}g dg dg dg dg}d	\  }}g d
}t          ||f||          }t          t          ||          |           d S )Nr;   r>   rB   rE   rI   rK   rL   rM   rN   rO   )r   r   r   )rY   rZ   r[   r\   r]   rb   rc   s          r5   test_native_list_argumentsz*TestSolveBanded.test_native_list_arguments   s    __^^]]^^ oonnnnmm 1"""!QQ''!#a))Q/////r7   dt_abdt_bc                 $   t          j        g g|          }t          j        g |          }t          d||          }|j        dk    sJ |j        t          t          j        d|          t          j        d|                    j        k    sJ t          j        d|          }t          d||          }|j        dk    sJ |j        t          t          j        d|          t          j        d|                    j        k    sJ d S )Nr   r   r   rD   )	r,   r   r   shaper   r   eyeonesemptyrY   r   r   r[   rb   rc   s         r5   
test_emptyzTestSolveBanded.test_empty   s    Xrd%(((HRt$$$Q''w$w%q 6 6 68N8N8NOOUUUUUHV4(((Q''w&    w%q 6 6 68N8N8NOOUUUUUUUr7   N)__name__
__module____qualname__rd   rj   rp   rr   rv   r}   r   r   pytestmarkparametrizeintfloatr,   r
   complex	complex64r    r7   r5   r9   r9   ,   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 [WsE2:w&UVV[Vc5"*gr|%TUUV V VU WVV V Vr7   r9   c            	       X   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ej                            deeej        e ej!        g          ej                            deeej        e ej!        g          d                         Z"dS )TestSolveHBandedc                     t          g dg dg dg          }t          g d          }t          ||          }t          |g d           d S NrJ   rJ   rQ   rQ   r<   r<   r<   ry   ry   ry   ry   r<   ry   r<   rQ   rJ   r<   rJ   rJ   r   r   r   rY   r[   rb   rc   s       r5   test_01_upperzTestSolveHBanded.test_01_upper   su     (((((((((* + + &&&''"a  !!%9%9%9:::::r7   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<         @ry   rQ   rJ   r   rY   r[   rb   rc   expecteds        r5   test_02_upperzTestSolveHBanded.test_02_upper   s     (((((((((* + + C::::     "a  3****& ' ' 	"!X.....r7   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   rF   rD   r   r   rW   r   r   r   s       r5   test_03_upperzTestSolveHBanded.test_03_upper   s     (((((((((* + + &&&''//A66"a  !!U+;+;+;%<%<%D%DR%K%KLLLLLr7   c                     t          g dg dg dg          }t          g d          }t          ||d          }t          |g d           d S )Nr   r<   r<   r<   r   rQ   rQ   rJ   rJ   r   Tlowerr   r   r   s       r5   test_01_lowerzTestSolveHBanded.test_01_lower  sz     (((((((((* + + &&&''"at,,,!!%9%9%9:::::r7   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   ry   rQ   Tr   rJ   r   r   s        r5   test_02_lowerzTestSolveHBanded.test_02_lower  s     (((((((((* + + C::::     "at,,,3****& ' ' 	"!X.....r7   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       r5   test_01_float32z TestSolveHBanded.test_01_float32(  s     (((((((((*18: : : &&&g666"a  !!%9%9%9:::::r7   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   ry   rQ   rJ   r   r   s        r5   test_02_float32z TestSolveHBanded.test_02_float326  s     (((((((((*18: : : C:::: './ / / "a  3****& ' ' 	"!X.....r7   c                     t          g dg dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r                r   r   r   )       @            @            @      ?       @      ?)rJ   r<   r<   rJ   r   r   s       r5   test_01_complexz TestSolveHBanded.test_01_complexK  su     (((...(((* + + ...//"a  !!%9%9%9:::::r7   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   ri   rJ   r<   r   r   s        r5   test_02_complexz TestSolveHBanded.test_02_complexY  s     (((...(((* + + D$<E?D>":     "a  3+***& ' ' 	"!X.....r7   c                     t          g dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r<   r<   ry   ry   ry   r<   ry   r<   rJ   r<   rJ   r   r   s       r5   test_tridiag_01_upperz&TestSolveHBanded.test_tridiag_01_uppern  sX     OOO___566///"""a  !!___55555r7   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<   ry   rQ   rJ   r   r   s        r5   test_tridiag_02_upperz&TestSolveHBanded.test_tridiag_02_uppery  s     OOO#OO% & &C:::     "a  3***& ' ' 	"!X.....r7   c                     t          g dg dg          }t          g d                              dd          }t          ||          }t          |t          g d                              dd                     d S )Nr   r   r   rF   rD   r   r   r   s       r5   test_tridiag_03_upperz&TestSolveHBanded.test_tridiag_03_upper  s     OOO___566///""**2q11"a  !!U???%;%;%C%CB%J%JKKKKKr7   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       r5   test_tridiag_01_lowerz&TestSolveHBanded.test_tridiag_01_lower  sd     OOO#OO% & &///"""at,,,!!___55555r7   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<   ry   rQ   Tr   rJ   r   r   s        r5   test_tridiag_02_lowerz&TestSolveHBanded.test_tridiag_02_lower  s     OOO#OO% & &C:::     "at,,,3***& ' ' 	"!X.....r7   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       r5   test_tridiag_01_float32z(TestSolveHBanded.test_tridiag_01_float32  sb     OOO___5WEEE///111"a  !!___55555r7   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<   ry   rQ   rJ   r   r   s        r5   test_tridiag_02_float32z(TestSolveHBanded.test_tridiag_02_float32  s     OOO#OO%,35 5 5C:::&-/ / / "a  3***& ' ' 	"!X.....r7   c                     t          g dg dg          }t          g d          }t          ||          }t          |g d           d S )Nr   r   r   r   )r   r   r   )rJ   r<   r<   r   r   s       r5   test_tridiag_01_complexz(TestSolveHBanded.test_tridiag_01_complex  s^     '''9::'''(("a  !!___55555r7   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   ry   rJ   ri   r<   r   r   s        r5   test_tridiag_02_complexz(TestSolveHBanded.test_tridiag_02_complex  s     '''#OO% & &C;G$C=" # # "a  3+**& ' ' 	"!X.....r7   c                     t          g dg dg          }t          g d          }t          ||d          }t          |g d           d S )Nr   r   r   Frt   r   r   r   s       r5   rv   z"TestSolveHBanded.test_check_finite  s]     OOO___566///"""ae444!!___55555r7   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<   ry   rQ   )r   rz   r{   r   )rY   r[   rb   s      r5   test_bad_shapesz TestSolveHBanded.test_bad_shapes  s    OOO#OO% & &C::    j-Q777j-c3Z@@@j-cU;;;;;r7   c                     t          dggg dg          }t          |g dg           t          |j        t	          j        d                     d S )NrD   rD   rC   rR   r   r   )r   r   r   r   r,   )rY   rc   s     r5   r   zTestSolveHBanded.test_1x1  sR    A3%)))--1/000QWbhtnn-----r7   c                 h    g dg dg dg}g d}t          ||          }t          |g d           d S r   )r   r   r   s       r5   r   z+TestSolveHBanded.test_native_list_arguments  s]    """""""""$ !  "a  !!%9%9%9:::::r7   r   r   c                     t          j        g g|          }t          j        g |          }t          ||          }|j        dk    sJ |j        t          t          j        d|          t          j        d|                    j        k    sJ t          j        d|          }t          ||          }|j        dk    sJ |j        t          t          j        d|          t          j        d|                    j        k    sJ d S )Nr   r   rD   r   )	r,   r   r   r   r   r   r   r   r   r   s         r5   r   zTestSolveHBanded.test_empty  s    Xrd%(((HRt$$$"a  w$w%q 6 6 68N8N8NOOUUUUUHV4((("a  w&    w%q 6 6 68N8N8NOOUUUUUUUr7   N)#r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rv   r   r   r   r   r   r   r   r   r,   r
   r   r   r   r   r7   r5   r   r      s       ; ; ;/ / /*M M M; ; ;/ / /*; ; ;/ / /*; ; ;/ / /*	6 	6 	6/ / /"	L 	L 	L
6 
6 
6/ / /"	6 	6 	6/ / /"	6 	6 	6/ / /"	6 	6 	6< < <. . .
; ; ; [WsE2:w&UVV[Vc5"*gr|%TUUV V VU WVV V Vr7   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ej                            dddg          d             Zd Zd Zej                            dd          d             Zej                            dd          d             Zd Zd  Zej                             d!"          d#             Z!d$ Z"d% Z#d& Z$ej                            d'd(d)g          ej                            dg d*          ej                            d+e%j&        e%j'        e%j(        e%j)        g          d,                                     Z*ej                            d-e+e,e%j&        e-e%j(        g          ej                            d.e+e,e%j&        e-e%j(        g          d/                         Z.d0 Z/ej                            d+e%j'        e%j)        g          ej                            dg d1          ej                            d2d3d4g          ej                            d5d6d7g          ej                            d8d6d7g          ej                            d9d6d7g          d:                                                                         Z0ej        1                    e%j2        d;k     d<"          ej                            dg d=          d>                         Z3d? Z4d@ Z5e6dA             Z7e6dB             Z8e6dC             Z9e6dD             Z:e6dE             Z;dF Z<dG Z=dH Z>dIS )J	TestSolvec                     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 )NrD   r<   r                   333333?r   r   r   )rY   rZ   x0rb   s       r5   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5r7   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 )NrD   r=   r?   r@   r   rC   r   rY   rZ   rb   rc   s       r5   test_simplezTestSolve.test_simple*  s    WsAhq6Aq6"a&q6C8$ 	4 	4A aA%c!Qii3333	4 	4r7   c                     t          ddgddggd          }ddgddgddggdd	gt          ddgd          fD ]0}t          ||          }t          t          ||          |           1d S )
N   rC   rf   r@   Dri   r   rD   r   )r   r   r   r   r   s       r5   test_simple_complexzTestSolve.test_simple_complex3  s    Aq6B7#S))q'8aV$b'A$$ 	4 	4A
 aA%c!Qii3333	4 	4r7   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 )	NrC   rR   r   r   rD   rD   r   posassume_ar   r   rY   rZ   r   rb   rc   s        r5   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 	8r7   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   rC   r@   ri   r   r   r  r   r   s       r5   test_simple_pos_complexbz"TestSolve.test_simple_pos_complexbF  sw    VaVq'8aV$ 	4 	4A aU+++A%c!Qii3333		4 	4r7   c                     ddgddgg}dD ]B}ddgddggddgfD ]3}t          ||d|          }t          t          ||          |           4Cd S )	NrC   rR   r   rD   r   symr  r   r  s        r5   test_simple_symzTestSolve.test_simple_symN  s    VaW 	8 	8E1v1v&!f 8 8 !Qe<<<)#a))Q7777	8	8 	8r7   c                     ddgddgg}ddgddgddggfD ]2}t          ||d          }t          t          ||          |           3d S )Nr   rC   ri   r   r
  r  r   r   s       r5   test_simple_sym_complexbz"TestSolve.test_simple_sym_complexbW  sw    VaWq'8aV$ 	4 	4A aU+++A%c!Qii3333		4 	4r7   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  ri   r   rD   rC   r
  r  r   r   s       r5   test_simple_sym_complexz!TestSolve.test_simple_sym_complex_  ~    Yr
#q'a&8aV$ 	4 	4A aU+++A%c!Qii3333	4 	4r7   c                     ddgddgg}dD ]E}ddgddggddgddgfD ]3}t          ||d|	          }t          t          ||          |           4Fd S )
NrC   rR   r	  r   rD   r   ri   herr  r   r  s        r5   test_simple_her_actuallysymz%TestSolve.test_simple_her_actuallysymh  s    VaW 	8 	8E1v1v&!f1g 8 8 !Qe<<<)#a))Q77778	8 	8r7   c                     ddgddgg}ddgddgddgddggfD ]2}t          ||d	
          }t          t          ||          |           3d S )Nr   r   r   r  ri   r   rD   rC   r  r  r   r   s       r5   test_simple_herzTestSolve.test_simple_herr  r  r7   c                    t           j                            d          }d}|                    ||g          |                    ||g          dz  z   }t          ||fd          }t	          |          }t          |          t          |          dz  z   }t          d|          D ]%}|d d |f         }t          ||          |d d |f<   &t          ||           d S )N  rC   ri   r   r   r   )	r,   randomdefault_rngr   r   r   r   r   r   )	rY   rngnAXAinvRirs	            r5   test_nils_20Feb04zTestSolve.test_nils_20Feb04{  s    i##D))JJ1vszz1a&11"441a&#1vvQKKB&1 	" 	"A!!!Q$AAqkkAaaadGG!!T*****r7   c                 r   t           j                            d          }d}|                    ||g          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]G}|                    |dg          }t	          ||          }t          t          ||          |           Hd S )Nr  r=   皙?r@   rR   r,   r  r  ranger   r   r   rY   r  r  rZ   r!  rb   rc   s          r5   test_randomzTestSolve.test_random  s    i##D))JJ1vq 	& 	&A"Qq!tW*oAadGGq 	4 	4A

Aq6""AaA%c!Qii3333	4 	4r7   c                    t           j                            d          }d}|                    ||g          d|                    ||g          z  z   }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]G}|                    |dg          }t	          ||          }t          t          ||          |           Hd S )Nr  r=   ri   r%  rC   rR   r&  r(  s          r5   test_random_complexzTestSolve.test_random_complex  s    i##D))JJ1vcjj!Q&8&8!88q 	& 	&A"Qq!tW*oAadGGq 	4 	4A

Aq6""AaA%c!Qii3333	4 	4r7   c                    t           j                            d          }d}|                    ||g          }t          |          D ]E}t	          dd|||f         z   z            |||f<   t          |          D ]}|||f         |||f<   Ft          d          D ]H}|                    |g          }t          ||d          }t          t          ||          |           Id S )Nr  r=   r%  r@   r   r  )r,   r  r  r'  absr   r   r   rY   r  r  rZ   r!  jrb   rc   s           r5   test_random_symzTestSolve.test_random_sym  s    i##D))JJ1vq 	" 	"A"b1a4j/**AadG1XX " "AqD'!Q$"q 	4 	4A

A3AaU+++A%c!Qii3333	4 	4r7   c                 X   t           j                            d          }d}|                    ||g          }|d|                    ||g          z  z   }t          |          D ]R}t	          dd|||f         z   z            |||f<   t          |          D ]}t          |||f                   |||f<   S|                    |g          d|                    |g          z  z   }t          d          D ]2}t          ||d          }t          t          ||          |           3d S )	Nr  r=   ri   r%  rf   rC   r   r  )	r,   r  r  r'  r-  r   r   r   r   r.  s           r5   test_random_sym_complexz!TestSolve.test_random_sym_complex  s8   i##D))JJ1v3::q!f%%%%q 	- 	-A"b1a4j/**AadG1XX - -#AadG,,!Q$-JJsOOBszz1#..q 	4 	4AaU+++A%c!Qii3333	4 	4r7   c                     ddgddgg}ddgddggddgddgddggfD ]2}t          ||d          }t          t          ||          |           3d S )	NrD   r=   r?   r@   r   rC   Frt   r   r   s       r5   rv   zTestSolve.test_check_finite  s    WsAhq6Aq6"QFq6C8$& 	4 	4Aa///A%c!Qii3333	4 	4r7   c                     d}g d}t          ||          }t          |                                |           t          |j        dk    d           d S )NrD   r   rR   z'Scalar_a_1D_b test returned wrong shape)r   r   ravelr   r   r   s       r5   test_scalar_a_and_1D_bz TestSolve.test_scalar_a_and_1D_b  sR    II!QKK!!''))Q///4!JKKKKKr7   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<   rF   rR   r	  )rR   rC   r@   rD   )r,   r   r   r   Tr   s       r5   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r7   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       r5   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> &? &? 	@ 	@ 	@ 	@ 	@r7   r  r  r
  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          }|dk    r|j        n|                                j        }||z   }t          j        |          |t          j        d          t          j        d          f<   t          ||d          }t          |||          }t          ||           t          |||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
  r@   generalr  Tr  )r,   r   r:  conjrn   r   r   r   )rY   r  rZ   rb   a2a3r   rc   s           r5   test_symmetric_hermitianz"TestSolve.test_symmetric_hermitian  s,    HBBB999///&&&( ) ) H{L1"L1#[1!=13 4 4
 %%QSS16688:V)+29Q<<1%&BI...!Q***!!S))) "a($777!!S)))))r7   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 )	NrD   
   rR   	   r   r  )      "@r9  r<   r
  r,   r   rW   r   trilr   r   rY   r  rc   s      r5   test_pos_and_symzTestSolve.test_pos_and_sym  s    Ia$$Q**"'!**Q,

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

U;;;!!]]]33333r7   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)	rD   r   r   r   r   r   rD   r   rD   )	rD   rD   rD   r   r   r   rD   r   rD   )	r   rD   rD   r   r   r   rD   r   rD   )	rD   r   rD   rD   rD   rD   r   r   r   )	rD   rD   rD   rD   rD   rD   rD   rD   rD   rG  )r,   r   r   rz   r   r   rY   rZ   rb   s      r5   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/////r7   	structure)
diagonaltridiagonallower triangularupper triangular	symmetric	hermitianpositive definiter@  bandedNc                 X   t           j                            d          }d}t          j        dd|          }t          j        |          }|                    |          }d}t          j        t          |          5  t          |||           d d d            d S # 1 swxY w Y   d S )	Nl   Ej] rF  r   2   sizez2(Ill-conditioned matrix|An ill-conditioned matrix)matchr  )	r,   r  r  logspacern   r   warnsr"   r   )rY   rP  r  r  dr  rb   messages           r5   test_ill_condition_warningz$TestSolve.test_ill_condition_warning  s    
 i##L11K2q!!GAJJJJAJF\-w777 	, 	,!Q++++	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	,s   ?BB#&B#)	rQ  rR  rS  rT  rU  rV  rW  r@  Nc                 D   d}t          j        ||f          }t          j        |          }t          j        t
          d          5  t          j        d          5  t          |||           d d d            n# 1 swxY w Y   d d d            d S # 1 swxY w Y   d S )NrF  singularr]  ignore)allr  )r,   r   r   r   r   r   errstater   )rY   rP  r  r  rb   s        r5   test_exactly_singular_gh22263z'TestSolve.test_exactly_singular_gh22263   s   
 HaVGAJJmKz::: 	, 	,BKH<U<U<U 	, 	,!Q++++	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	, 	,s6   BA=1B=B	BB	BBBc                     t          j        d          }t           j                            d          }|                    d          }t	          ||          }t          ||           d S )NrC   r  )rC      )r,   r   r  r  r   r   )rY   rZ   r  rb   rc   s        r5   test_multiple_rhszTestSolve.test_multiple_rhs+  sX    F1IIi##D))JJw!QKK!!Q'''''r7   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 )	NrG  rR   rD   T
transposed)r   g?rD   F)rG  gg333333rI  rK  s      r5   test_transposed_keywordz!TestSolve.test_transposed_keyword2  s    IaLL  A&&*"'!**Q,

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

u===!!___55555r7   z*1. why? 2. deprecate the kwarg altogether?reasonc                     t          j        d                              t                    }t	          t
                    5  t          ||d           d d d            d S # 1 swxY w Y   d S )NrR   Trn  )r,   r   astyper   rz   NotImplementedErrorr   rY   rZ   s     r5   test_transposed_notimplementedz(TestSolve.test_transposed_notimplemented9  s    F1IIW%%.// 	) 	)!Q4((((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)s   A!!A%(A%c                 B    t          t          t          ddgd           d S )NrD   rC   rz   r{   r   rY   s    r5   test_nonsquare_azTestSolve.test_nonsquare_a?  s     j%!Q33333r7   c                 .   t          t          t          j        d          t          j        d                    t          j        d                     t          t          t          t          j        d          t          j        d                     d S )NrR   r@   )r   r   r,   r   r   rz   r{   rz  s    r5   test_size_mismatch_with_1D_bz&TestSolve.test_size_mismatch_with_1D_bB  s^    !%q		271::">">

KKKj%BGAJJ?????r7   c                 B    t          t          t          ddd           d S )NrD   zxcvr  ry  rz  s    r5   test_assume_a_keywordzTestSolve.test_assume_a_keywordF  s!    j%A??????r7   r\  rF  d   )genr
  r   r  rR  r   c                    t           j                            d          }|t           j        t           j        fv }|                    ||f                              |          }|                    |                              |          }|r0|d|                    ||f          z                      |          z  }|dk    r||j        z   }n|dk    r||j                                        z   }n|dk    r5|j                                        |z  dt          j	        |          z  z   }n~|dk    rxt          j
        t          j
        |                    t          j
        t          j
        |d          d          z   t          j
        t          j
        |d	          d	          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  ||z             |dk    r3|s3t          |||d          }	t          ||	z  |||z  ||z             d S d S d S )Nr  ri   r
  r  r   r%  rR  rD   rF   -q=gư>)r  r
  r  rF  r  atolr   T)r  ro  )r,   r  r  r   r0   standard_normalrt  r:  rA  r   rn   r.   r
   r   r   )
rY   r\  r   r  r  
is_complexrZ   rb   tolrc   s
             r5   'test_all_type_size_routine_combinationsz1TestSolve.test_all_type_size_routine_combinationsI  sO    i##D))r|R];;
t--44U;;%%,,U33 	F"S(($666>>uEEEAuACAAACHHJJAA

QRVD\\!11AA&&$$A**+B,,-A
 R] ;;;ee,,, R\222r	!Q***AqsTzd
CCCCuZaX$???AAE13:C$JGGGGGG r7   dt_ar   c                 8   t          j        d|          }t          j        d|          }t          ||          }|j        dk    sJ t          t          j        d|          t          j        d|                    j        }|j        |k    sJ |j        t           j                            ||          j        k    sJ t          j        d|          }t          j        d|          }t          ||          }|j        dk    sJ |j        |k    sJ d S )Nr   r   r   rC   rR   r   rC   rC   rC   r@   )rR   r   rC   r@   )	r,   r   r   r\  r   r   r   r   linalgrY   r  r   rZ   rb   rc   dt_nonemptys          r5   r   zTestSolve.test_emptyr  s    HV4(((HQd###!QKKv{{{{BF1D111271D3I3I3IJJPw+%%%%w")//!Q//55555GL---GF$'''!QKKw,&&&&w+%%%%%%r7   c                     t          j        d          }g g g}t          ||          }t          |j        dk    d           t          |j        dk    d           d S NrC   r   zReturned array is not empty)rC   r   z#Returned empty array shape is wrong)r,   r   r   r   r\  r   r   s       r5   test_empty_rhszTestSolve.test_empty_rhs  sZ    F1IIH!QKK!:;;;6!#HIIIIIr7   )rQ  rR  rX  rS  rT  r   rW  rU  rV  rX  r@  r
  r  r  nrhsr   )r   ro  TF	overwritefortranc                    t           j                            d          }|dk    sdnd}|                    |f|z             }	|                    ||f          }
t          j        |t           j                  r>|	|                    |f|z             dz  z   }	|
|                    ||f          dz  z   }
|dk    r(t          j        t          j        |
                    }
n5|dk    rt          j        |
          }
n|d	k    rt          j        |
          }
n|d
k    ryt          j        t          j        |
                    t          j        t          j        |
d          d          z   t          j        t          j        |
d          d          z   }
n|dk    r)t          j        t          j        |
d          d          }
nP|dv r|
|
j        z   }
nA|dv r|
|
	                                j        z   }
n |dv r|
|
j        	                                z  }
|rt          j
        |
          }
|
                    d          }|	                                }t          j        |t           j                  rM|rKd}t          j        t          |          5  t          |
|	|||           d d d            n# 1 swxY w Y   d S t          |
|	||||          }t           j                            |r|j        n||          }t#          ||           |dk    r"t#          t          |||          |d           |s"t%          |
|           t%          |	|           d S d S )Nl   q~u rX  r   r=   r[  ri   rQ  rS  rT  rR  rF   rD   rC   >   r
  rU  >   r  rV  >   r   rW  r  orderz#scipy.linalg.solve can currently...r]  )r*   overwrite_bro  )r*   r  ro  r  rn  r   r  )r,   r  r  
issubdtypecomplexfloatingrn   rJ  triur:  rA  asfortranarraycopyr   r   ru  r   r  r   r   )rY   r   r  r  ro  r  r  r  r  rb   r  A_copyb_copyrb  resr   s                   r5   test_structure_detectionz"TestSolve.test_structure_detection  s    i##O44))AArJJQD4KJ((JJQFJ##= 233 	1CJJQD4KJ00255ACJJQFJ++b00Az!!

##AA+++

AA+++

AA&&$$7271b>>2../7271a==!,,-AA !!1r**AA---ACAA---AFFHHJAA555ACHHJJA 	%!!$$Ac""= 233 	
 	;G2'BBB - -a	y!+- - - -- - - - - - - - - - - - - - - FAqiY)H> > > ioo*@fhh&&IIS!!! xff<<<c   
  	$F###F#####	$ 	$s   J;;J?J?2z(solve chokes on b.ndim == 1 in numpy < 2)NrQ  r@  rT  rS  r   c                 z   t          j        d          }t          j        dd                              d          |z  }t          j        d          }t          t          |||          t           j                            ||                     t          j        d          }t          t          |||          t           j                            ||                     t          j        d          ddgz  }t          t          |||          t           j                            ||                     d S )NrC   rD      )r@   rR   rC   rD   rD   r  rN   rC   rC   )r,   r   r   rW   r   r   r   r  )rY   r  erZ   rb   s        r5   test_vs_np_solvezTestSolve.test_vs_np_solve  s     F1IIIa##++O<<q@GAJJaX666	18M8MNNNGFOOaX666	18M8MNNNGFOOq!f$aX666	18M8MNNNNNr7   c                 X   t           j                            d          }|                    d          }t          j        t          j        |t          j        |j                                      }|                    d          }t          ||dd          }||j        z   t          j	        t          j	        |                    z
  }t           j
                            ||          }t          ||d	           t          |j        |dd
          }t          ||d	           d S )Nr   r@   r@   r[  r@   rC   r   Tr  r   r  F)r,   r  r  normalrJ  matmulrA  r:  r   rn   r  r   )rY   r  rZ   rb   outaa	result_nps          r5   test_pos_lowerzTestSolve.test_pos_lower  s     i##A&&JJFJ##GBIa..//JJFJ##Aq5555Wrwrwqzz***IOOB**	YU3333 ACU%888YU333333r7   c                     t          j        d          }d|j        _        t          j        d          }t          ||          }t          ||d           d S NrR   F+=r  )r,   r   flags	writeabler   r   r   r   s       r5   test_readonlyzTestSolve.test_readonly  sN    F1II!GAJJ!QKK15))))))r7   c                    t          j        d                              dddd          }|d d d d dd d d d f         }t          j        d          }t	          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd           t          j        d	          d d d d df         }t	          ||fi |}|j        |j        d d         |j        d         fz   k    sJ t          ||z  |z
  dd           d S 
N   rC   rR   rF   .Nr   r  r  r  r,   r   rW   r   r   r   r   rY   r)   rZ   rb   rc   s        r5   test_batch_negative_stridez$TestSolve.test_batch_negative_stride  s1   IcNN""1aA..aaa2qqq!!!mGAJJ!Q'',''w!'#2#,&&&&AiL(1,ae<<<< GFOOAAAtttG$!Q'',''w!'#2#,!'"+77777A	15111111r7   c                    t          j        d                              dddd          }|d d d d d d dd d f         }t          j        d          }t	          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd           t          j        d	          d d dd d f         }t	          ||fi |}|j        |j        d d         |j        d         fz   k    sJ t          ||z  |z
  dd           d S r  r  r  s        r5   test_core_negative_stridez#TestSolve.test_core_negative_stride  s1   IcNN""1aA..aaaDDbD!!!mGAJJ!Q'',''w!'#2#,&&&&AiL(1,ae<<<< GFOODDbD!!!G$!Q'',''w!'#2#,!'"+77777A	15111111r7   c                    t          j        d                              dddd          }|dd d df         }t          j        d          }t	          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd	
           t          j        d          d d d         }t	          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd	
           d S )N0   rC   rR   r@   .rF   r  r   r  r  r  r  s        r5   test_core_non_contiguousz"TestSolve.test_core_non_contiguous   s   Ie$$Q1a00c33Q3hKGAJJ!Q'',''w!'#2#,&&&&AiL(1,ae<<<< GAJJsssO!Q'',''w!'#2#,&&&&AiL(1,ae<<<<<<r7   c                    t          j        d                              dddd          }|d d d d ddf         }t          j        d          }t	          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd	           t          j        d
          d d d d df         }t	          ||fi |}|j        |j        d d         |j        d         fz   k    sJ t          ||z  |z
  dd	           d S )Nr  rC   rA   .rF   r  r   r  r  rC   rA   r  r  s        r5   test_batch_non_contiguousz#TestSolve.test_batch_non_contiguous/  s(   Ie$$Q1a00aaa1ckNGAJJ!Q'',''w!'#2#,&&&&AiL(1,ae<<<< GFOOAAAsssF#!Q'',''w!'#2#,!'"+77777A	15111111r7   c                 B   t          j        d                              ddddd          }|                    ddddd          }t          j        d          }t          ||fi |}|j        |j        d d         k    sJ t          ||d         z  |z
  dd	
           d S )Nr  rC   rR   rD   r@   r   rF   r  r  r  )r,   r   rW   r	   r   r   r   r   r  s        r5   test_batch_weird_stridesz"TestSolve.test_batch_weird_strides>  s    Ie$$Q1a33KK1aA&&GAJJ!Q'',''w!'#2#,&&&&AiL(1,ae<<<<<<r7   c                    t          j        d                              dd          }||j        z   t          j        d          z   }t          j        d          }t          ||          }t          ||z  |d           t          t                    5  t          ||d           d d d            d S # 1 swxY w Y   d S )NrG  rR   r  r  r   r  )
r,   r   rW   r:  r   r   r   r   rz   r   )rY   rZ   r  rb   r   s        r5   test_posdef_not_posdefz TestSolve.test_posdef_not_posdefH  s    IaLL  A&&GbfQiiGAJJ 1a[[B.... ;'' 	( 	(!Q''''	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	(s   B55B9<B9c           	      .   t          j        t          j        t          j        d                    t          j        t          j        dd                    g          }t          j        d          }t          ||          }t          |d         dt          j        dd          z  d           t          j        dd	gd	dgg          }t          j        d
          }t          j
        t                    5  t          ||d           d d d            n# 1 swxY w Y   t          j        d	d	gd	dgg          }t          j        d
          }t          j        t                    5  t          ||d           d d d            d S # 1 swxY w Y   d S )NrR   rR   rD   r@   rR   rD   .r  r  ꌠ9Y>)Fr   rC   rQ  r  )r,   stackr  r   rn   r   r   r   asarrayr   r`  r"   r   r   r   s       r5   test_diagonalzTestSolve.test_diagonalV  s   Hbgbgfoo..	!Q0H0HIJJGAJJ!QKK 	&	1ryA#6UCCCC Jq	Aq6*++GAJJ\-(( 	- 	-!Q,,,,	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- JAA'((GAJJ];'' 	- 	-!Q,,,,	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	- 	-s$   9DDD*F

FFc                 @   d}dt          j        t          j        |                    z  t          j        t          j        d          d          z   t          j        t          j        d          d          z   }t          j        t          j        t          j        ||f                    |g          }t          j        d          }t          ||          }t          |d         t          j        g d          d	           d
|d<   t          j	        t                    5  t          ||d           d d d            n# 1 swxY w Y   dx|d<   |d<   t          j        t                    5  t          ||d           d d d            d S # 1 swxY w Y   d S )Nr@   rR   rD   rF   r  )             r  r  r   r  @xD)rD   r   r   rR  r  r   )rD   r   rD   )r,   rn   r   r  r  r   r   r  r   r`  r"   r   r   )rY   r  rZ   rb   rc   s        r5   test_tridiagonalzTestSolve.test_tridiagonalj  s   rwrwqzz"""RWRWQZZ%;%;;bgbgajjRT>U>UUHbgbgq!foo..233GAJJ!QKK 	&	2:.B.B.B#C#C%PPPP '
\-(( 	0 	0!Q////	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 #$#'
QwZ];'' 	0 	0!Q////	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0s$   &EE	E	3FFFN)?r   r   r   r   r   r   r  r  r  r  r  r  r  r#  r)  r+  r0  r2  rv   r7  r;  r>  r   r   r   rD  rL  rO  rc  ri  rl  rp  skiprw  r{  r}  r  r,   r
   r.   r   r0   r  r   r   r   r   r  r  skipif__version__r  r  r  parametrize_overwrite_argr  r  r  r  r  r  r  r  r   r7   r5   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@ @ @" [Z%88* * 98*.4 4 40 0 0 [[NO O, ,	O O, [[DE E, ,	E E,( ( (6 6 6 [IJJ) ) KJ)
4 4 4@ @ @@ @ @ [Vb#Y//[Z)T)T)TUU["*bj",F "H "H  VU 0/
"HH [Vc5"*gr|%TUU[Vc5"*gr|%TUU& & VU VU& J J J [Wrz2=&ABB[Z *J *J *J K K
 [Vb$Z00[\D%=99[[4-88[Yu66<$ <$ 76 98 :9 10K K CB<$| [
%O    [	
 	
 	
 O O  O4 4 4"* * * 2 2 2 2 2 2 = = = 2 2 2 = = =( ( (- - -(0 0 0 0 0r7   r   c            	           e Zd Zd Zd Zd Zej                            de	e
ej        eej        g          ej                            de	e
ej        eej        g          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.
        rD   r   rC   Tr   Fr   r   transr<         N)r   r   r   r:  r   rY   r  rb   sols       r5   r   zTestSolveTriangular.test_simple  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'<=====r7   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
        r=  r   ri   rC   TrD   r  y      ?      y      п      пr         ?       @y             y      ?      ?y      ?      y            пFr  N)r   r   r   r   r,   rn   r:  r  s       r5   r   z'TestSolveTriangular.test_simple_complex  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Ar7   c                     t          ddgddgg          }ddg}t          ||dd          }t          |ddg           dS )r  rD   r   rC   TF)r   ru   N)r   r   r   r  s       r5   rv   z%TestSolveTriangular.test_check_finite  sW     Aq6Aq6"##Fq!4eDDD!#1v.....r7   r  r   c                 ,   t          j        d|          }t          j        d|          }t          ||          }|j        dk    sJ t          t          j        d|          t          j        d|                    j        }|j        |k    sJ d S Nr   r   r   rC   )r,   r   r   r\  r   r   r   r  s          r5   r   zTestSolveTriangular.test_empty  s     HV4(((HQd###Q""v{{{{&F1D!!!271D#9#9#9
 

 	 w+%%%%%%r7   c                     t          j        d          }g g g}t          ||          }t          |j        dk    d           t          |j        dk    d           d S r  )r,   r   r   r   r\  r   r   s       r5   r  z"TestSolveTriangular.test_empty_rhs  s\    F1IIHQ""!:;;;6!#HIIIIIr7   N)r   r   r   r   r   rv   r   r   r   r   r   r,   r
   r   r   r   r  r   r7   r5   r  r    s        > > >*B B B:/ / / [Vc5"*gr|%TUU[Vc5"*gr|%TUU	& 	& VU VU	&J J J J Jr7   r  c                      e Zd Zd Zd Zd Zd Zd Zej	        
                    deeej        eej        g          d             Zej	                            d	          d
             Zd Zej	        
                    deeej        eej        g          d             Zed             Zed             Zed             Zed             Zed             Zed             Zd Zd Zd Zej	        
                    dddg          d             Z ej	        
                    dddg          ej	        
                    dddg          d                         Z!d Z"d Z#d  Z$d!S )"TestInvc                 (   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 )NrD   rC   rR   r@   r   r@   r   rA   rG      rF  )r   r   r   r,   r   rY   rZ   a_invs      r5   r   zTestInv.test_simple  s    VaVA!#a--;;;YY			:::.A!#a--;;;;;r7   c                 \   t           j                            d          }d}t          d          D ]z}|                    ||g          }t          |          D ]}dd|||f         z   z  |||f<   t	          |          }t          t          ||          t          |                     {d S )Nr  r=   r@   r%  r,   r  r  r'  r   r   r   r   rY   r  r  r!  rZ   r  s         r5   r)  zTestInv.test_random  s    i##D))q 	3 	3A

Aq6""A1XX * *b1a4j/!Q$FFE%c!Umm&.qkk3 3 3 3	3 	3r7   c                 |    ddgddgg}t          |          }t          t          ||          ddgddgg           d S )NrD   rC   rR   r   r   r   r   r   r  s      r5   r   zTestInv.test_simple_complex  sJ    VaWA!#a--1a&1a&1ABBBBBr7   c                    t           j                            d          }d}t          d          D ]}|                    ||g          d|                    ||g          z  z   }t          |          D ]}dd|||f         z   z  |||f<   t	          |          }t          t          ||          t          |                     d S )Nr  r=   r@   rf   r%  r  r  s         r5   r+  zTestInv.test_random_complex  s    i##D))q 	3 	3A

Aq6""2cjj!Q&8&8#88A1XX * *b1a4j/!Q$FFE%c!Umm&.qkk3 3 3 3	3 	3r7   c                     ddgddgg}t          |d          }t          t          ||          ddgddgg           d S )NrD   rC   rR   r@   Frt   r   r  r  s      r5   rv   zTestInv.test_check_finite  sQ    VaVAE***!#a--1a&1a&1ABBBBBr7   r4   c                    t          j        d|          }t          |          }|j        dk    sJ |j        t          t          j        d|                    j        k    sJ t          j        d|          }t          |          }|j        dk    sJ t          j        d|          }t          |          }|j        dk    sJ d S )Nr   r   r   rC   r  )rR   rD   r   r   )r,   r   r   r\  r   r   r   r   rY   r4   rZ   r  s       r5   r   zTestInv.test_empty  s    HV2&&&AzQ{c"&""5"5"566<<<<<GL+++A{l****GL+++A{l******r7   zTODO: re-enable overwrite_arq  c                    t          j        dd                              dd          }t          |d          }t	          ||z  t          j        d          d           t          j        ||          rJ |                    t                    	                    d	          }t          |d          }t          j        ||          sJ d S )
NrD   r   rC   Tr*   r  r  Fr  )
r,   r   rW   r   r   r   shares_memoryrt  r   r  r  s      r5   test_overwrite_azTestInv.test_overwrite_a	  s    IaOO##Aq))A4(((	26!9959999#Au----- HHUOO  s ++A4(((5)))))))r7   c                     t          j        d          }d|j        _        t	          |          }t          ||d           d S r  )r,   r   r  r  r   r   r  s      r5   r  zTestInv.test_readonly  s?    F1II!Aqu------r7   c                     t          j        d|                              dddd          dz   }t          |          }|j        |j        k    sJ t          ||z  d           d S )NrA   r   rR   rC   rD   r<   )r,   r   rW   r   r   r   r  s       r5   test_batch_core_1x1zTestInv.test_batch_core_1x1  si    Ic$$$,,Q1a881<A{ag%%%%E	2&&&&&r7   c                    t          j        dt                                        ddd          }|d         }t	          |fi |}|j        |j        k    sJ t          ||z  t          j        t          j        d          |j                  d           |d d d df         }t	          |fi |}|j        |j        k    sJ t          ||z  t          j        t          j        d          |j                  d           d S )	Nrk  r   rR   rC   )N.g+=r  .)	r,   r   r   rW   r   r   r   broadcast_tor   )rY   r)   rZ   r  r  s        r5   test_batch_zero_stridezTestInv.test_batch_zero_stride#  s    Ie5)))11!Q::y\B'',''{bh&&&&U
BOBF1IIrx$H$HuUUUUqqq$|_B'',''{bh&&&&U
BOBF1IIrx$H$HuUUUUUUr7   c                 @   t          j        d                              dddd          }|d d d d dd d d d f         }t          |fi |}|j        |j        k    sJ t          ||z  t          j        t          j        d          |j                  d           d S Nr  rC   rR   rF   vIh%,=r  r,   r   rW   r   r   r   r  r   rY   r)   rZ   r  s       r5   r  z"TestInv.test_batch_negative_stride0  s    IcNN""1aA..aaa2qqq!!!mA&&&&{ag%%%%E	2?26!99ag#F#FUSSSSSSr7   c                 @   t          j        d                              dddd          }|d d d d d d dd d f         }t          |fi |}|j        |j        k    sJ t          ||z  t          j        t          j        d          |j                  d           d S r  r  r  s       r5   r  z!TestInv.test_core_negative_stride8  s    IcNN""1aA..aaaDDbD!!!mA&&&&{ag%%%%E	2?26!99ag#F#FUSSSSSSr7   c                 &   t          j        d                              dddd          }|dd d df         }t          |fi |}|j        dk    sJ t          ||z  t          j        t          j        d          |j                  d           d S )	Nr  rC   rR   r@   .rC   rR   rC   rC   r  r  r  r  s       r5   r  z TestInv.test_core_non_contiguous@  s    Ie$$Q1a00c33Q3hKA&&&&{l****E	2?26!99ag#F#FUSSSSSSr7   c                 ,   t          j        d                              dddd          }|d d d d ddf         }t          |fi |}|j        dk    sJ t          ||z  t          j        t          j        d          |j                  d           d S )Nr  rC   rA   .r  gvIh%L=r  r  r  s       r5   r  z!TestInv.test_batch_non_contiguousH  s    Ie$$Q1a00aaa1ckNA&&&&{l****E	2?26!99ag#F#FUSSSSSSr7   c                 \   t          t                    5  t          t          j        d                     d d d            n# 1 swxY w Y   t          t                    5  t          t          j        d                     d d d            n# 1 swxY w Y   t          j        t          j        dt                    t          j        d                              dd          f          }t          t                    5  t          |           d d d            d S # 1 swxY w Y   d S )Nr  )rR   rC   rC   r   r@   rC   )	rz   r   r   r,   r   r  r   r   rW   )rY   r)   rZ   s      r5   test_singularzTestInv.test_singularP  s    ;'' 	! 	!   	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! ;'' 	$ 	$	""###	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ HbgfG444bill6J6J1a6P6PQRR;'' 	 	FFF	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s5   "AA
A""BBBD!!D%(D%c                    t          j        ddg          }t          j        t                    5  t          |           d d d            n# 1 swxY w Y   t          j        t          j        ddg          t          j        ddg          t          j        ddg          g          }t          j        t                    5  t          |           d d d            d S # 1 swxY w Y   d S )Nr<   #B;rD   )r,   rn   r   r`  r"   r   r  )rY   rZ   rB  s      r5   test_ill_condzTestInv.test_ill_condi  sD   GRK  \-(( 	 	FFF	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 XrwE{++RWaV__bgq%j>Q>QRSS\-(( 	 	GGG	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s#   AAAC  C$'C$c                     t          t                    5  t          t          j        d          d           d d d            d S # 1 swxY w Y   d S )NrC   kaboomr  )rz   KeyErrorr   r,   r   rz  s    r5   test_wrong_assume_azTestInv.test_wrong_assume_ar  s    8$$ 	. 	.q		H----	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	.s   $AA
A
c                 4   t          j        dt                                        dd          }||j        z   }|dt          j        d          z  z  }t          |          }t          |d          }t          ||d           t          j        d	t          j	        g |j
        d
R  z
  dk    t           j        d	          }t          ||z  ddd          }t          ||d           t          ||j        z  ddd          }t          ||d           d S )Nr  r   r      r   r  r   r  rD   rF   r   Fru   r  r   T)r,   r   r   rW   r:  r   r   r   wheretrir   nan)rY   rc   yy_inv0y_inv1masky_inv2y_inv3s           r5   test_posdefzTestInv.test_posdefv  s   Ib&&&..q!44G	Rq		\QQ'''U3333 xBF0AG0R0000A5rvqAAQtV%%uMMMU3333 QtvXEENNNU333333r7   complex_FTc                    t          j        d                              dd          }||j        z   t          j        d          z   }|r|d|z  z   }t          |          }t          ||z  t          j        d          d           t          t                    5  t          |d           d d d            n# 1 swxY w Y   |rt          j        d                              dd          }|d|z  z   }||j        	                                z   t          j        d          z   }t          t          |          |z  t          j        d          d           d S d S )NrG  rR   ri   g [n<r  r   r  )
r,   r   rW   r:  r   r   r   rz   r   rA  )rY   r)  rZ   rb   b_inv0s        r5   r  zTestInv.test_posdef_not_posdef  s    IaLL  A&&GbfQii 	BqDA Q
BF1IIE:::: ;'' 	# 	#E""""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#  	?	!$$Q**ABqDAACHHJJ*ACFFQJq		>>>>>>		? 	?s   B::B>B>sym_hermr
  r  c                    t          j        d                              dd          }|r|d|z  z   }|dk    r||j        z   }n||j                                        z   }|t          j        d          z   }t           j                            |          }t          ||z  t          j        d          d           t          ||          }t          ||d           t          j	        d	t          j
        g |j        d
R  z
  dk    t           j        d	          }t          ||z  d|d          }t          ||d           t          ||j        z  d|d          }	t          |	|d           d S )NrG  rR   ri   r
  r  r  r  r   rD   rF   r   Fr  T)r,   r   rW   r:  rA  r   r  r   r   r  r   r   r!  )
rY   r)  r,  rZ   rb   r+  b_inv1r%  b_inv2b_inv3s
             r5   test_sym_herzTestInv.test_sym_her  sm    IaLL  A&& 	BqDAuACAAACHHJJAq		Mq!!
BF1IIE::::Q***U3333 xBF0AG0R0000A5rvqAAQtV%(%PPPU3333 QtvXEHDQQQU333333r7   c                    t          j        dt                                        dd          }||j        z   }|dt          j        d          z  z  }t          |d          }t          |d          }t          j        ||          rJ d S )Nr  r   r   r  rT  r  r   )r,   r   r   rW   r:  r   r   allclose)rY   rc   r"  r#  y_inv_posdefs        r5   test_triangular_1zTestInv.test_triangular_1  s    Ib&&&..q!44G	Rq		\Q!3444 1u---;v|4444444r7   c                 *   t          j        dt                                        dd          }t	          t          j        |                    }t          |t          j        |          z  t          j        d          d           t	          |d          }t          |t          j        |          z  t          j        d          d           t          j        dt          j	        g |j
        d	R  z
  d
k    t           j        d          }t	          ||z  dd          }t          |t          j        |          z  t          j        d          d           t	          t          j        |                    }t          |t          j        |          z  t          j        d          d           t	          |d          }t          |t          j        |          z  t          j        d          d           t          j        dt          j	        g |j
        d	R  z
  d
k    t           j        d          }t	          ||j        z  dd          }t          |t          j        |          z  t          j        d          d           d S )Nr  r   r   r   r  rT  r  rD   rF   r   F)ru   r  rS  )r,   r   r   rW   r   r  r   r   r  r   r   r!  rJ  r:  )	rY   r"  	y_inv_0_u	y_inv_1_ur%  	y_inv_2_u	y_inv_0_l	y_inv_1_l	y_inv_2_ls	            r5   test_triangular_2zTestInv.test_triangular_2  s   GBe$$$,,Q22

OO		BGAJJ.q		FFFF$6777		BGAJJ.q		FFFF xBF0AG0R0000A5rvqAA$U=OPPP		BGAJJ.q		FFFF 

OO		BGAJJ.q		FFFF$6777		BGAJJ.q		FFFF xBF0AG0R0000A5rvqAA$&u?QRRR		BGAJJ.q		FFFFFFr7   c           
         t          j        t          j        t          j        d                    t          j        t          j        dd                    g          }t          |          }t          |d         t          j        dt          j        dd          z            d           t          j        ddgddgg          }t          j
        t                    5  t          |d	           d d d            n# 1 swxY w Y   t          j        ddgddgg          }t          j        t                    5  t          |d	           d d d            d S # 1 swxY w Y   d S )
Nr  rD   r@   r  r  r  r   rQ  r  )r,   r  r  r   rn   r   r   r   r  r   r`  r"   r   r   )rY   rZ   inv_as      r5   r  zTestInv.test_diagonal  s   Hbgbgfoo..	!Q0H0HIJJA 	a"'!bi1oo*=">">UKKKK Jq	Aq6*++\-(( 	( 	(J''''	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( JAA'((];'' 	( 	(J''''	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	( 	(s$   "D  DD>EE!$E!N)%r   r   r   r   r)  r   r+  rv   r   r   r   r   r   r,   r
   r   r   r   xfailr  r  r  r  r	  r  r  r  r  r  r  r  r(  r  r1  r5  r=  r  r   r7   r5   r  r    s       < < <	3 	3 	3C C C
	3 	3 	3C C C
 [TC
GR\#RSS+ + TS+ [;<<	* 	* =<	*. . . [TC
GR\#RSS' ' TS' 
V 
V 
V T T T T T T T T T T T T   0  . . .4 4 4& [Z%77? ? 87?, [Z%77[Z%884 4 98 87485 5 5G G G4( ( ( ( (r7   r  c                      e Zd Zd Zd Zej                            dddgddgg dg          d             Zd Z	ej                            d	d
 e
j        d         dd         D                       d             Zd Zd Zej                            deee
j        ee
j        g          d             Zd Zd Zd ZdS )TestDetc                 (   t          j        dgg          }t          |          }|j        j        dk    sJ t          j        |          sJ |dk    sJ t          j        dggggd          }t          |          }|j        j        dk    sJ |j        dk    sJ t          |dgg           t          j        dgggt           j                  }t          |          }|j        j        dk    sJ |j        d	k    sJ t          |dg           d S )
NrD   ra  r<   fr   rl   y      ?      @r   )rD   )	r,   r   r   r   charisscalarr   r   r   )rY   rZ   detas      r5   test_1x1_all_singleton_dimsz#TestDet.test_1x1_all_singleton_dims  s    HqcUOO1vvz#%%%%{4     rzzzzHugYc***1vvz#%%%%zV####TSE7###Hyk]",7771vvz#%%%%zT!!!!TF8$$$$$r7   c                 :   t           j                            d          }|                    g dt           j                  }t	          |          }|j        j        dk    sJ |j        dk    sJ t          |t          j	        |                     |                    g dt           j                  t          j
        d          z  }t	          |          }|j        j        dk    sJ |j        dk    sJ t          |t          j	        |                     d S )N   *n`/ )r@   r   rD   rD   r   ra  r@   r   ri   r   )r,   r  r  r
   r   r   rE  r   r   squeezer   )rY   r  rZ   rG  s       r5   test_1by1_stacked_input_outputz&TestDet.test_1by1_stacked_input_output  s    i##$455JJ|||2:J661vvz#%%%%zV####bjmm,,,JJ|||2:J66r|C7H7HH1vvz#%%%%zV####bjmm,,,,,r7   r   rC   r=   )rR   rC   r=   r=   c                    t           j                            d          }|                    dd|          }t	          |          t           j                            |          }}t          ||           |                    dd|          dz  }||                    dd|          z  }t	          |          t           j                            |          }}t          ||           d S )NrJ        r<   r[  ri   r  r   )r,   r  r  uniformr   r  r   )	rY   r   r  rZ   d1d2rb   d3d4s	            r5   #test_simple_det_shapes_real_complexz+TestDet.test_simple_det_shapes_real_complex  s    i##$455KKReK,,Qq))BBKKReK,,R/	S[[s[///Qq))BBr7   c                 H   t          j        g dg dg dg dg dg dg dg dg          }t          t          |          d	           t          t          t          j        d
                              dd                    d           t          j        g dg dg dg dgt           j                  }t          t          |          d           t          j        g dg dg dg dg dg dg dg dg          dz  }t          t          |          d           d S )N)rD   rD   rD   rD   rD   rD   rD   rD   )rD   rF   rD   rF   rD   rF   rD   rF   )rD   rD   rF   rF   rD   rD   rF   rF   )rD   rF   rF   rD   rD   rF   rF   rD   )rD   rD   rD   rD   rF   rF   rF   rF   )rD   rF   rD   rF   rF   rD   rF   rD   )rD   rD   rF   rF   rF   rF   rD   rD   )rD   rF   rF   rD   rF   rD   rD   rF   g      @r  r   rJ   )r   r                 y      ?      )r   r         ?        rW  )ri   r=  r   r   )rX  ri   r   r   r   y      @        )r  r  r<   rJ   rJ   rJ   rJ   rJ   )r<   rJ   rJ   rJ   rJ   rJ   rJ   rJ   )rJ   g      rJ   g      r<   rJ   rJ   rJ   )rJ   r<   rJ   rJ   rJ   rJ   rJ   rJ   )rJ   rJ   rJ   g      rJ   g      r<   rJ   )rJ   rJ   rJ   r<   rJ   rJ   rJ   rJ   )rJ   rJ   rJ   rJ   rJ   g       rJ   g      ")rJ   rJ   rJ   rJ   rJ   r<   rJ   rJ   ri   rH  )r,   r   r   r   r   rW   r   rv  s     r5   test_for_known_det_valuesz!TestDet.test_for_known_det_values   s   H...2222222222222222222224 5 5 	A&&& 	BIbMM11!Q7788"===
 H6666666666668 @B|M M M 	A''' H8886668886668886668886668 9 9 :== 	A#####r7   typc                     g | ]}|d v|	S )gGr   ).0rc   s     r5   
<listcomp>zTestDet.<listcomp>E  s(     %7 %7 %71() &'(5r7   AllNc                    t           j                            d          }d}|                    ||g                              |          }t	          t          |          t           j        t           j        z            sJ d S )NrJ  r@   )r,   r  r  rt  
isinstancer   r.   r0   )rY   rZ  r  r  rZ   s        r5   "test_sample_compatible_dtype_inputz*TestDet.test_sample_compatible_dtype_inputE  sm     i##$455JJ1v%%c**#a&&2:#=???????r7   c                    d}t          dg d          D ]\\  }}t          t          |          5  t          t	          j        ddggdz  |                     d d d            n# 1 swxY w Y   ]t          t          |          5  t          t	          j        d	d
ggdz  d                     d d d            n# 1 swxY w Y   t          t          |          5  t          t	          j        ddggdz  d                     d d d            n# 1 swxY w Y   t          t          |          5  t          t	          j        ddggdz  d                     d d d            d S # 1 swxY w Y   d S )Nz!cannot be cast to float\(32, 64\)SUO)bytes8str32objectr]  rZ   rb   rC   r      a   bVr     zdatetime64[s]ztimedelta64[s])ziprz   	TypeErrorr   r,   r   )rY   msgcts       r5   test_incompatible_dtype_inputz%TestDet.test_incompatible_dtype_inputM  s   3<<<== 	7 	7DAqy444 7 7BHsCj\!^15556667 7 7 7 7 7 7 7 7 7 7 7 7 7 79C000 	7 	74,)555666	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	79C000 	A 	A3*a???@@@	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A9C000 	B 	B3*a/?@@@AAA	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	BsG   *A&&A*	-A*	*B>>CC*DDD6*E--E14E1c                    t          t          t          j        ddg                    d           t          t          t          j        g d                    t          j        g                      t          t          t          j        g d                    t          j        g d                     t          t          d          5  t          t          j        g d                     d d d            n# 1 swxY w Y   t          t          d	          5  t          t          j        g                      d d d            n# 1 swxY w Y   t          t          d          5  t          t          j        g g                     d d d            n# 1 swxY w Y   t          t          d          5  t          t          j        g gg                     d d d            d S # 1 swxY w Y   d S )
Nr   r<   )r   r   r   rR   r   r   r<   r<   r<   zLast 2 dimensionsr]  )r   r   rR   zat least two-dimensional)r   r   r,   r   r   rz   r{   rz  s    r5   test_empty_edge_caseszTestDet.test_empty_edge_cases[  s   BHaV,,--r222BHYYY//00"(2,,???BHYYY//00"(<<<2H2HIII:-@AAA 	% 	%##$$$	% 	% 	% 	% 	% 	% 	% 	% 	% 	% 	% 	% 	% 	% 	%:-GHHH 	 		 	 	 	 	 	 	 	 	 	 	 	 	 	 	:-@AAA 	  	 "	  	  	  	  	  	  	  	  	  	  	  	  	  	  	 :-@AAA 	" 	"2$  !!!	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	" 	"sH   $D  DD!"EEE0#FF#&F# $G11G58G5r4   c                    t          j        d|          }t          |          }|j        dk    sJ |j        t          t          j        d|                    j        k    sJ t          j        d|          }t          |          }|j        dk    sJ |j        t          t          j        d|                    j        k    sJ d S )Nr   r   r   rC   rs  r5  )rR   rD   rD   )r,   r   r   r   r   r   r   )rY   r4   rZ   ra  s       r5   test_empty_dtypezTestDet.test_empty_dtypeh  s    HV2&&&FFw"}}}}w#bfQb1112288888HYb)))FFw$w#bhy;;;<<BBBBBBBr7   c                 .   t          j        d                              dd                              t           j                  }|                                }t          |d          }t          |d           ||k                                    rJ d S )NrG  rR   Tr   rJ   )	r,   r   rW   rt  r
   r  r   r   rg  )rY   rZ   acrG  s       r5   r  zTestDet.test_overwrite_at  s~    
 IaLL  A&&--bj99VVXX24(((b!!!G==??"""""r7   c                     t          j        g dg dg dg          }|                    d           t          t	          |d          d           d S )	N)rQ   rJ   r<   )      @rx   rO  rt  F)writeTr   rP   )r,   r   setflagsr   r   rv  s     r5   test_readonly_arrayzTestDet.test_readonly_array  s[    HlllMMM<<<@AA	


A4000#66666r7   c                     ddgdt           j        gg}t          t          d          5  t	          |           d d d            d S # 1 swxY w Y   d S )NrD   rC   rR   zarray must not containr]  )r,   infrz   r{   r   rv  s     r5   test_simple_check_finitez TestDet.test_simple_check_finite  s    Va[!:-EFFF 	 	FFF	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s   AA
A
)r   r   r   rH  rM  r   r   r   rU  rY  r,   	typecodesrb  rq  ru  r   r   r
   r   r   rw  r  r~  r  r   r7   r5   rB  rB    ss       % % %"- - - [W1vBx&HII	  	  JI	 "$ "$ "$J [U %7 %7U0CCRC0H %7 %7 %7 8 8@ @8 8@B B B" " " [TC
GR\#RSS	C 	C TS	C	# 	# 	#7 7 7    r7   rB  c                     t          |           }|rt          |          }t          ||           }t          ||          }t          ||          S )N)r	   r   r   r   )rZ   rb   cmplxata1b1s         r5   direct_lstsqr    sH    	1B r]]	RB	RBR==r7   c            	       h   e Zd ZdZd Zd Zd Zd Zej	        
                    de          ej	        
                    dd          ej	        
                    d	e          ej	        
                    d
d          d                                                 Zej	                            ed          ej	        
                    de          ej	        
                    dd          ej	        
                    d	e          ej	        
                    d
d          d                                                             Zd Zd Zd Zd Zej	        
                    deeej        eej        g          ej	        
                    deeej        eej        g          d                         ZdS )	TestLstsq)gelsdgelssgelsyNc                    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|            t          t          ||
          |dt          |j                  z  dt          |j                  z  d|            ˌЌՐd S )NrD   r=   r?   r@   r   TF)rD   r   r   r  )rN   r?   r@   lapack_driverr*   r  r   rC   expected efficient rank 2, got r  driver: )r  r   err_msg)REAL_DTYPESr,   r   r  lapack_driversr  r   r   r   r   r6   r   )rY   r   rZ   r  r  btr  rb   r  r  rc   r"  s               r5   test_simple_exactzTestLstsq.test_simple_exact  sq     	L 	LE1b'C8,E:::A!*!9 L L!. L LI3 L L VVXXHRu555VVXX#B2?0909; ; ;  FFQ E! E EG G G'Aq		1-/)BH2E2E-E-/)BH2E2E-E0J=0J0JL L L L LLLL	L 	Lr7   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|            t          t          t          ||	          |z
  dz                                d
          |
dt          |j                  z  dt          |j                  z  d|            t          |	ddt          |j                  z  dt          |j                  z  d|            [bd S )NrD   rC   r@   r   rR   r   r   r  r  r   r  r  axisr  r  r   r  r  )gm۶mۿgm۶m?)r  r,   r   r  r  r  r   sumr   r   r   r-  r6   r   )rY   r   rZ   rb   r  r  r  r  r  rc   	residualsr"  s               r5   test_simple_overdetzTestLstsq.test_simple_overdet  s     	H 	HE1a&1a&1a&1???A%000A!*!9 H H!. H HIBBBm,5,57 7 7C AA$//$&FAaL1+<$=$=		$'F	AAAF$Ia$I$IJJJ#CQQ(:$;$;$?$?Q$?$G$G$-)+i.A.A)A)+i.A.A)A,F},F,F	H H H H
 $A'M)+i.A.A)A)+i.A.A)A,F},F,FH H H H H'HH	H 	Hr7   c                    t           D ]}t          j        ddgddgddgg|          }t          j        g d|          }t          j        D ]t}dD ]m}|                                }|                                }t          |||||	          }|d
         }	|dk    rB||                    |	          z
  }
t          j        |
|
	                                z            }n|d         }|d         }t          |dk    d|            t          t          t          ||	          |z
  dz                                d
          |dt          |j                  z  dt          |j                  z  d|            t          |	ddt          |j                  z  dt          |j                  z  d|            ovd S )Nr  rC   r@   r   rR   r   )rD   r   rR   r  r  r   r  rD   r  r  r  r  r  )yu{޿E(B?yӽu{?(YJV?)COMPLEX_DTYPESr,   r   r  r  r  r   r   r  rA  r   r   r-  r6   r   )rY   r   rZ   rb   r  r  r  r  r  rc   r  r  r"  s                r5   test_simple_overdet_complexz%TestLstsq.test_simple_overdet_complex  s   # 	D 	DE4)aVaV4EBBBAU333A!*!9 D D!. D DIBBBm,5,57 7 7C AA$//!%%((l$&F3+;$<$<		$'F	AAAF$Ia$I$IJJJ#CQQ(:$;$;$?$?Q$?$G$G$-)+i.A.A)A)+i.A.A)A,F},F,F	H H H H
 $ ! $L%')BH*=*=%=%')BH*=*=%=(B=(B(BD D D D D+DD	D 	Dr7   c                    t           D ]}t          j        g dg dg|          }t          j        ddg|          }t          j        D ]}dD ]}|                                }|                                }t          |||||          }|d         }	|d         }
t          |
dk    d	|
            t          |	d
dt          |j
                  z  dt          |j
                  z  d|            d S )Nr   r  r   rD   rC   r  r  r   r  )gqqgqq?gdq?r  r  r  )r  r,   r   r  r  r  r   r   r   r6   r   )rY   r   rZ   rb   r  r  r  r  r  rc   r"  s              r5   test_simple_underdetzTestLstsq.test_simple_underdet  sK     	H 	HE)))YYY/u===A!Qu---A!*!9 H H!. H HIBBBm,5,57 7 7C AAAAAF$Ia$I$IJJJ#A (;)+i.A.A)A)+i.A.A)A,F},F,F	H H H H HHH	H 	Hr7   r   r  )r=   rk  r  r  r  c           
         t           j                            d          }t          j        |                    ||g          |          }t	          |          D ]}dd|||f         z   z  |||f<   t	          d          D ]A}t          j        |                    |dg          |          }|                                }	|                                }
t          |	|
|||          }|d         }|d	         }t          ||k    d
| d|            |t           j        u rPt          t          ||          |dt          |	j                  z  dt          |	j                  z  d|            t          t          ||          |dt          |	j                  z  dt          |	j                  z  d|            Cd S )Nr  r   r=   r%  r@   rR   r  r   rC   expected efficient rank , got i  r  r    )r,   r  RandomStater  r'  r  r   r   r
   r   r   r6   r   rY   r   r  r  r  r  rZ   r!  rb   r  r  r  rc   r"  s                 r5   test_random_exactzTestLstsq.test_random_exact  s   
 i##D))Jszz1a&))777q 	+ 	+AC!AqD'M*AadGGq 	> 	>A
3::q!f--U;;;ABBB&3$-$-/ / /C AAAAAF q         
""a))Q"Yrx%8%88"Yrx%8%88"<]"<"<	> > > > >  a))Q#i&9&99#i&9&99"<]"<"<	> > > > >)	> 	>r7   z$may segfault on Alpine, see gh-17630rq  c           
         t           j                            d          }t          j        |                    ||g          d|                    ||g          z  z   |          }t	          |          D ]}dd|||f         z   z  |||f<   t	          d          D ]A}t          j        |                    |dg          |          }|                                }	|                                }
t          |	|
|||          }|d	         }|d         }t          ||k    d
| d|            |t           j        u rPt          t          ||          |dt          |	j                  z  dt          |	j                  z  d|            t          t          ||          |dt          |	j                  z  dt          |	j                  z  d|            Cd S )Nr  ri   r   r=   r%  rC   rR   r  r   r  r  i  r  r  r  )r,   r  r  r  r'  r  r   r   r   r   r   r6   r   r  s                 r5   test_random_complex_exactz#TestLstsq.test_random_complex_exact(  s    i##D))Jszz1a&))Bszz1a&/A/A,AA"$ $ $q 	+ 	+AC!AqD'M*AadGGq 	> 	>A
3::q!f--U;;;ABBBm$-$-/ / /C AAAAAF q         $$a))Q"Yrx%8%88"Yrx%8%88"<]"<"<	> > > > >  a))Q#i&9&99#i&9&99"<]"<"<	> > > > >'	> 	>r7   c                 ,   t           j                            d          }t          D ]k}dD ]d\  }}t          j        D ]P}dD ]I}t          j        |                    ||g          |          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]}t          j        |                    |dg          |          }	|                                }
|	                                }t          |
||||	          }|d
         }|d         }t          ||k    d| d|            t          |t          ||	d
          dt          |
j                  z  dt          |
j                  z  d|            KRfmd S )Nr  )r=      )rk  rC   r  r   r=   r%  r@   rR   r  r   rC   r  r  r  r  r  r  )r,   r  r  r  r  r  r  r'  r  r   r   r   r  r6   r   rY   r  r   r  mr  r  rZ   r!  rb   r  r  r  rc   r"  s                  r5   test_random_overdetzTestLstsq.test_random_overdetM  s   i##D))  	N 	NE. N NA%.%= N NM%2 N N	Jszz1a&'9'9GGG!&q ; ;A&(C!AqD'M&:AadGG!&q N NA "
3::q!f+=+=U K K KA!"B!"B"'B6C4=4=#? #? #?C !$AA #AA#AF -/q -/ -/+,-/ -/ 0 0 0+*+\!Qa-H-H-H/1Ibh4G4G/G/1Ibh4G4G/G2L]2L2L	N N N N NN	NNN	N 	Nr7   c                 b   t           j                            d          }t          D ]}dD ]\  }}t          j        D ]k}dD ]d}t          j        |                    ||g          d|                    ||g          z  z   |          }t          |          D ]}dd|||f         z   z  |||f<   t          d          D ]}t          j        |                    |d	g          |          }	|                                }
|	                                }t          |
||||
          }|d         }|d         }t          ||k    d| d|            t          |t          ||	d          dt          |
j                  z  dt          |
j                  z  d|            fmd S )Nr  r  r  ri   r   r=   r%  rC   rR   r  r   r  r  rD   r  r  r  r  )r,   r  r  r  r  r  r  r'  r  r   r   r   r  r6   r   r  s                  r5   test_random_complex_overdetz%TestLstsq.test_random_complex_overdeti  s&   i##D))# 	J 	JE. J JA%.%= J JM%2 J J	Jszz1a&'9'9Bszz1a&?Q?Q<Q'Q-24 4 4!&q ; ;A&(C!AqD'M&:AadGG!&q J JA "
3::q!f+=+=U K K KA "#B!"B"'B6C4=4=#? #? #?C !$AA #AA#AF -/q -/ -/+,-/ -/ 0 0 0+&'a!)D)D)D+-	"(0C0C+C+-	"(0C0C+C.H.H.H	J J J J JJJJJ	J 	Jr7   c           
         t          j                    5  t          j        ddt                     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
|            t          t!          ||          |dt#          |j                  z  dt#          |j                  z  d|            d S )Nrf  zIinternal gelsd driver lwork query error,.*Falling back to 'gelss' driver.))rD   r=   r  r  r  r   )r  ru   r*   r  r   rC   r  r  r  r  )warningscatch_warningsfilterwarningsRuntimeWarningr,   r   	itertoolsproductr  r  r  rt  r  r   r   r   r   r6   r   )rY   r  r   r  r  r  ru   rZ   rb   r  r  r  rc   r"  s                 r5   rv   zTestLstsq.test_check_finite  s   $&& 	W 	W#H%FGUW W W	W 	W 	W 	W 	W 	W 	W 	W 	W 	W 	W 	W 	W 	W 	W X)**kL'6++	- -	@ 	@=E2}i 		%  A5)))A BBBm%1y$-/ / /C AAAAAFAaAABBBC1IIq!#i&8&8!8!#i&8&8!8$>}$>$>@ @ @ @ @'	@ 	@s   <A A 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   rC   r   ))r   r@   r  )r@   r   )r@   )r  r  rD   r   r   r  rC   zexpected rank 0)	r,   r   r   r   r   r   r  r   r   )	rY   a_shapeb_shaperb   rc   residuesranksresidues_should_bes	            r5   r   zTestLstsq.test_empty  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++++	, 	,r7   r  r   c                 B   t          j        d|          }t          j        d|          }t          ||          \  }}}}|j        dk    sJ t          t          j        d|          t          j        d|                    d         j        }	|j        |	k    sJ d S r  )r,   r   r   r\  r   r   r   )
rY   r  r   rZ   rb   rc   r  r  r  r  s
             r5   rw  zTestLstsq.test_empty_dtype  s     HV4(((HQd###$Q{{8T1v{{{{BF1D111271D3I3I3IJJ1MSw+%%%%%%r7   N)r   r   r   r  r  r  r  r  r   r   r   r  r  r  r&   r  r  r  r  rv   r   r   r   r,   r
   r   r   rw  r   r7   r5   r  r    sA       6NL L L2H H H:D D DBH H H, [Wk22[S),,[_n==[[-88> > 98 >= -, 32>@ [(NOO[Wn55[S),,[_n==[[-88> > 98 >= -, 65 PO
>@N N N8J J J<@ @ @@, , , [Vc5"*gr|%TUU[Vc5"*gr|%TUU& & VU VU& & &r7   r  c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                            d	eej        eej        g          d
             ZdS )TestPinvc                     t          g dg dg dgt                    }t          |          }t          t	          ||          t          j        d                     d S Nr   r  r  r   rR   r   r   r   r   r   r,   r   rY   rZ   a_pinvs      r5   test_simple_realzTestPinv.test_simple_real  sX    999iii4EBBBa!#a.."&))<<<<<r7   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   ri   )rF  r  rG   )rA   r   r@   )rR   rC   rD   rR   r  r  s      r5   r   zTestPinv.test_simple_complex  s    IIIyyy***5  


IIIyyy'I-2"4 "4 "4 44 a!#a.."&))<<<<<r7   c                     t          g dg dg dgt                    }t          |          }t          g dg dg dg          }t          ||           d S )Nr   r  rG   r  rG  r   g|qgԕVUUſgc8?gqg^0<gq?g9?gԕVUU?g:87ȿr   r   r   r   rY   rZ   r  r   s       r5   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3r7   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       r5   test_simple_colszTestPinv.test_simple_cols  so    999iii(666a;
3&
3%{35 6 6 	"&(33333r7   c                     t          ddgddgddggt                    }t          |          }t          g dg d	g          }t          ||           d S )
NrD   rC   rR   r@   r   rA   r   )gDpTUUgQUUտgvWUU?)gDpTUU?gQUU?g&>ڿr  r  s       r5   test_simple_rowszTestPinv.test_simple_rows  sq    Aq6Aq6Aq6*%888a@@@???A B B!&(33333r7   c                     t          g dg dg dg          }t          |d          }t          t          ||          t	          j        d                     d S )Nr   )r@   r   r   r  Frt   rR   )r   r   r   r   r,   r   r  s      r5   rv   zTestPinv.test_check_finite  sZ    999jjj***566ae,,,!#a.."&))<<<<<r7   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       r5   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3r7   c                 8   t           j                            d          }d}t          |                    ||f                    \  }}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 )Nr  rk  g     A@rG   r   gMbP?r   h㈵>g?rJ   r  gMb@?r  r  g;O@{Gz?r   )r,   r  r  r!   r   rW   r  r   r   r  r   )rY   r  r  q_a_mrZ   r  r   a_padiff1adiff2s               r5   test_atol_rtolzTestPinv.test_atol_rtol  s   i##D))#**aV$$%%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Ar7   r4   c                     t          j        d|          }t          |          }|j        dk    sJ |j        t          t          j        d|                    j        k    sJ d S r  )r,   r   r   r\  r   r   rY   r4   rZ   r  s       r5   r   zTestPinv.test_empty  sg    HV2&&&a{a|tBF1B$7$7$788>>>>>>>r7   N)r   r   r   r  r   r  r  r  rv   r  r  r   r   r   r   r,   r
   r   r   r   r   r7   r5   r  r    s        = = =
= = =4 4 44 4 44 4 4= = =
4 4 4B B B8 [TE2:w#MNN? ? ON? ? ?r7   r  c                       e Zd Zd Zd Zd Zd Zd Zd Ze	j
                            deej        eej        g          d             Zd	S )
TestPinvSymmetricc                     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   r   r  s      r5   r  z"TestPinvSymmetric.test_simple_real  sm    999iii4EBBBF1acNNq!"&F"3"3RVAYY?????r7   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   rF   )
r   r   r,   r   r:  r  svdr   r   r   )rY   rZ   r]   r  vtr  a_pinvhs          r5   test_nonpositivez"TestPinvSymmetric.test_nonpositive  s    999iii35AAAF1acNN9==##1b	!
F1q5"a((!&'22222r7   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   rA  r:  r   r   r   r  s      r5   r   z%TestPinvSymmetric.test_simple_complex'  s    IIIyyy***5  


IIIyyy'I-2"4 "4 "4 44 F1affhhj!!q!"&F"3"3RVAYY?????r7   c                 $   t          g dg dg dgt                    }t          j        ||j                  }t          |                                          }t          t          j        ||          t          j        d                     d S r  )	r   r   r,   r   r:  r   tolistr   r   r  s      r5   r  z+TestPinvSymmetric.test_native_list_argument/  sw    999iii4EBBBF1acNNqxxzz""!"&F"3"3RVAYY?????r7   c                     t          j        g dg dg dg          }t          |          }t          ||z  |z  |d           t          ||z  |z  |d           d S )N)rD   rF   r   )rF   rC   rF   )r   rF   rD   r   r  )r,   r   r   r   )rY   rZ   ps      r5   test_zero_eigenvaluez&TestPinvSymmetric.test_zero_eigenvalue5  sq     Hjjj+++zzz:;;!HHA	151111A	15111111r7   c                    t           j                            d          }d}t          |                    ||f                    \  }}t          j        g ddg|dz
  z  z             }|j        |z  |z  }t          j        g ddg|dz
  z  z             }|j        |z  |z  }d}d	}t          ||d
          }	||	z  |z  |z
  }
||	z  |z  |z
  }t          t          |
          |d           t          t          |          dd           t          |||
          }	||	z  |z  |z
  }
||	z  |z  |z
  }t          t          |
          dd           t          t          |          dd           d S )Nr  rk  )r@   rR   rC   rD   vk?gﭣ>gu>rA   )r@   rR   rC   rD   r  rJ   rJ   r  g1?r  r%  r   r  gdy=r  -C6?)	r,   r  r  r!   rn   r:  r   r   r   )rY   r  r  r  r  rZ   r  r  r   r  r  r  s               r5   r  z TestPinvSymmetric.test_atol_rtol=  s   i##D))#**aV$$%%1G222gY!_DEEC!GaKg///2$!*<==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5r7   r4   c                     t          j        d|          }t          |          }|j        dk    sJ |j        t          t          j        d|                    j        k    sJ d S r  )r,   r   r   r\  r   r   r   r  s       r5   r   zTestPinvSymmetric.test_emptyY  sg    HV2&&&q{a|tBF1B$7$7$788>>>>>>>r7   N)r   r   r   r  r  r   r  r  r  r   r   r   r   r,   r
   r   r   r   r   r7   r5   r  r    s        @ @ @3 3 3@ @ @@ @ @2 2 26 6 68 [TE2:w#MNN? ? ON? ? ?r7   r  scale)r  r<   r  pinv_c                     t          j        ddgddgg          | z  }t          j        dt          j        |          z            } ||          }t          ||           d S )NrD   r   g|=r<   )r,   r   rn   r   )r  r  rc   r   x_invs        r5   test_auto_rcondr  a  sc     	1a&1e*%&&.AwrBGAJJ''HE!HHEE8$$$$$r7   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   r   r=   rH   r   rC   Complex)ri   rf   y              @)
r,   r  r   maxr1   r2   realr   r   sqrt)rY   r   rc   r  s       r5   
test_typeszTestVectorNorms.test_typesl  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#>>>>>		? 	?r7   c                 n    t          dgt                    }t          t          |          |           d S )Nr  r   )r   r
   r   r   rv  s     r5   test_overflowzTestVectorNorms.test_overflowy  s4     4&(((DGGQ'''''r7   c                     t          dgdgdz  z   t                    }	 t          t          |          dz
  dd           d S # t          $ r( d}t          t          |          dz
  d	|
           Y d S w xY w)N     @rD   i'  r   r   r  r  zO: Result should equal either 0.0 or 0.5 (depending on implementation of snrm2).rJ   )r  )r   r
   r   r   AssertionErrorr   )rY   rZ   rn  s      r5   test_stablezTestVectorNorms.test_stable  s    3%1#e)#7333	A DGGcM3T:::::: 	A 	A 	A.CQ#sC@@@@@@@		As   "A .A65A6c                     t          t          g dd          d           t          t          g dd          d           d S )N)rD   r   rR   r   rC   r   rR   )r   r   rz  s    r5   test_zero_normzTestVectorNorms.test_zero_norm  sD    T)))Q''+++T)))Q''+++++r7   c                     t          j        ddgddgggdz  d          }t          t          |d          ddggdz             t          t          |dd          d	gdz  gdz             d S )
NrC   rD   rR   r@   ra  r  5D+@6f~@r{  )r,   r   r   r   rv  s     r5   test_axis_kwdzTestVectorNorms.test_axis_kwd  s    H1v1v&'!+S11QQ:z*B)Ca)GHHHQ***bTAXJN;;;;;r7   c                    t          j        ddgddgggdz  d          }t          |dd          }t          |dd	gggdz             t	          |j        d
k               t          t          |ddd          dgdgggdz             d S )NrC   rD   rR   r@   ra  T)r  keepdimsr  r  )rC   rD   rC   rx   g      @)r,   r   r   r   r   r   rN  s      r5   test_keepdims_kwdz!TestVectorNorms.test_keepdims_kwd  s    H1v1v&'!+S11T***j*567!;<<<9$%%%QD999bTB4L>A;MNNNNNr7   z64-bit BLAS requiredrq  c                     t          d           t          j        dgt          j                  }d|d<   t	          |          }~t          |d           d S )NihB  )free_mbl        r   rD   rF   r<   )r%   r,   r   r.   r   r   )rY   rc   r  s      r5   test_large_vectorz!TestVectorNorms.test_large_vector  sX    %((((HeWBJ///"1ggS!!!!!r7   N)r   r   r   r  r  r  r  r  r  r   r   r  r'   r!  r   r7   r5   r  r  j  s        ? ? ?( ( (A A A, , ,< < <
O O O [I.DEE" " FE" " "r7   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestMatrixNormsc           
      <   t           j                            d          }dD ]x\  }}t           j        t           j        t           j        t           j        t           j        fD ]7}d|                    ||f          	                    |          z  }t          j
        |j        t           j                  r*|d|                    ||f          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#          ||	           9zd S )Nr  )rl   )rD   rR   )rR   rD   r  rK  )r   r@   rF  y              $@frorD   rF   rC   r  )ord)r,   r  r  r
   r.   r   r0   int64r  rt  r  r   r  r  r   r  r3  r   )
rY   r  r  r  rp  r  t_highr  actualdesireds
             r5   test_matrix_normsz!TestMatrixNorms.test_matrix_norms  so   i##D))B 	9 	9DAqZR\2="(R 9 9,,aV44;;A>>>="*<== (s22Aq6::::A]FFZF"E1b!R"&I 9 9E!!///F innQEn::G ;vw77 9"$)..&1A1Au."M"M'88899	9 	9r7   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 )
NrC   rD   rR   r@   ra  r  )r&  r  r   r   )r,   r   r   r  swapaxesr   r   r   )rY   rZ   rb   ro  ra  s        r5   r  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----.....r7   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   ra  r   rC   rR   r@   r   r  T)r&  r  r  rD   r   )r,   r   rW   r   r  r   r   r   )rY   rZ   rb   ro  s       r5   r  z!TestMatrixNorms.test_keepdims_kwd  s    Ic%%%--aAq99Vd;;;666117"#####r7   c                 R   t          j        d          }t          t          |          d           t          t          |d          t          j        d                     t          t          |d          t          j        d                     t          j        d	          }t          t          |          d           t          t          |d          t          j        d
                     t          t          |d          t          j        d                     d S )Nr   rJ   r   r  r   T)r  rl   )r   rR   r5  )r,   r   r   r   r   rv  s     r5   r   zTestMatrixNorms.test_empty  s    HVQ$$$QQ$888Q...0@0@AAAHVQ$$$QQ$888Q...0@0@AAAAAr7   N)r   r   r   r+  r  r  r   r   r7   r5   r#  r#    sU        9 9 9(/ / /"$ $ $	B 	B 	B 	B 	Br7   r#  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestOverwritec                 4    t          t          ddg           d S Nr  r5  )r$   r   rz  s    r5   
test_solvezTestOverwrite.test_solve      EFD>22222r7   c                 4    t          t          ddg           d S r4  )r$   r   rz  s    r5   test_solve_triangularz#TestOverwrite.test_solve_triangular  s    ,vtn=====r7   c                 ,    t          d ddg           d S )Nc                 $    t          d| |          S )NrN   )r   )r[   rb   s     r5   <lambda>z1TestOverwrite.test_solve_banded.<locals>.<lambda>  s    ,vr1*E*E r7   )r@   rA   rA   r#   rz  s    r5   test_solve_bandedzTestOverwrite.test_solve_banded  s+    EE#TN	, 	, 	, 	, 	,r7   c                 4    t          t          ddg           d S )Nr  r<  )r$   r   rz  s    r5   test_solveh_bandedz TestOverwrite.test_solveh_banded  s    MFD>:::::r7   c                 2    t          t          dg           d S Nr  )r$   r   rz  s    r5   test_invzTestOverwrite.test_inv      C&*****r7   c                 2    t          t          dg           d S rA  )r$   r   rz  s    r5   test_detzTestOverwrite.test_det  rC  r7   c                 4    t          t          ddg           d S )N)rR   rC   r5  )r$   r   rz  s    r5   
test_lstsqzTestOverwrite.test_lstsq  r6  r7   c                 2    t          t          dg           d S rA  )r$   r   rz  s    r5   	test_pinvzTestOverwrite.test_pinv  s    D6(+++++r7   c                 2    t          t          dg           d S rA  )r$   r   rz  s    r5   
test_pinvhzTestOverwrite.test_pinvh  s    EF8,,,,,r7   N)r   r   r   r5  r8  r=  r?  rB  rE  rG  rI  rK  r   r7   r5   r2  r2    s        3 3 3> > >, , ,; ; ;+ + ++ + +3 3 3, , ,- - - - -r7   r2  c            	          e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                            d	eeej        eej        g          ej                            d
eeej        eej        g          d                         ZdS )TestSolveCirculantc                     t          j        g d          }t          j        g d          }t          ||          }t          t	          |          |          }t          ||           d S N)rD   rC   rR   r   )rD   rF   rD   r   )r,   r   r   r   r   r   rY   ro  rb   rc   r"  s        r5   test_basic1zTestSolveCirculant.test_basic1 	  sb    H\\\""H]]]##Aq!!)A,,""1r7   c                     t          j        g d          }t          j        d                              dd          }t	          ||          }t          t          |          |          }t          ||           d S )NrD   rC   r	  rk  r@   rR   r,   r   r   rW   r   r   r   r   rP  s        r5   test_basic2zTestSolveCirculant.test_basic2	  sl    H^^^$$IbMM!!!Q''Aq!!)A,,""1r7   c                 V   t          j        g d          }t          j        d                              ddd          }t	          ||          }t          t          |          |                    dd                                        |j                  }t          ||           d S )NrS  r  r@   rR   rC   rF   )	r,   r   r   rW   r   r   r   r   r   rP  s        r5   test_basic3zTestSolveCirculant.test_basic3	  s    H^^^$$IbMM!!!Q**Aq!!)A,,		!R 0 01199!'BB1r7   c                    t          j        g d          }t          j        d                              dd          dz   }t	          ||          }t          t          |          |          }t          ||           d S )N)r  rT  r   r   r  r@   rC   y              ?rU  rP  s        r5   rj   zTestSolveCirculant.test_complex	  st    H&&&''IaLL  A&&-Aq!!)A,,""1r7   c                    t           j                            d          }|                    d          }|                    d          }t	          ||          }t          t          |          |          }t          ||           d S )Ni1  rZ  )r,   r  r  r  r   r   r   r   )rY   r  ro  rb   rc   r"  s         r5   test_random_b_and_cz&TestSolveCirculant.test_random_b_and_c	  sw    i##E**####Aq!!)A,,""1r7   c                    t          j        g d          }t          j        g d          }t          ||d          }t          t	          |          |          \  }}}}t          ||           t          t          t          ||           d S )NrD   rD   r   r   )rD   rC   rR   r@   r   )re  )r,   r   r   r   r   r   rz   r   )rY   ro  rb   rc   r"  r  rnkr  s           r5   r  z TestSolveCirculant.test_singular(	  s    H\\\""H\\\""Aq7333y||Q//3Q1k?Aq99999r7   c                 V   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)rF   g      @rR   g      @)rD   rA   rA   g      @)r   r   rD   rD   r]  )rD   rF   r   r   rD   )baxis)r@   rC   rR   r   rF   )r`  outaxis)rC   rR   r@   rC   )caxis)r,   r   r   r   r   
empty_liker   r   r6  r:  r   moveaxisr-  )rY   ro  rb   rc   r   s        r5   test_axis_argsz!TestSolveCirculant.test_axis_args1	  s    H((()NNN+;<== HlllLLL---@AAAq***QWi(((=##!)AaDJJLL"9"913??Aqqq!)AaDJJLL"9"913??Aqqq8$$$Aq2666QWi(((Ar1--x888 BK1a00!#Q???QWi(((8$$$$$r7   c                     g d}g d}t          ||          }t          t          |          |          }t          ||           d S rO  )r   r   r   r   rP  s        r5   r   z-TestSolveCirculant.test_native_list_argumentsJ	  sN    LLMMAq!!)A,,""1r7   dt_cr   c                    t          j        g |          }t          j        g |          }t          ||          }|j        dk    sJ |j        t          t          j        d|          t          j        d|                    j        k    sJ t          j        d|          }t          ||          }|j        dk    sJ |j        |j        k    sJ d S )Nr   r   rR   r   )r,   r   r   r   r   r   r   r   )rY   rg  r   ro  rb   rc   x1s          r5   r   zTestSolveCirculant.test_emptyR	  s     HRt$$$HRt$$$Aq!!w$w/")AT*B*B*B*,'!4*@*@*@B BBGH H H H HV4(((Q""x6!!!!x17""""""r7   N)r   r   r   rQ  rV  rX  rj   r[  r  re  r   r   r   r   r   r   r,   r
   r   r   r   r   r7   r5   rM  rM    s                  : : :% % %2   [Vc5"*gr|%TUU[Vc5"*gr|%TUU# # VU VU# # #r7   rM  c                       e Zd Zed             Zd Zd Zd Zd Zd Z	d Z
ej                            deeej        eej        g          d	             Zd
S )TestMatrix_Balancec                 <    t          t          t          d           d S )NzSome string for fail)rz   r{   r    rz  s    r5   test_string_argz"TestMatrix_Balance.test_string_argc	  s    j.2HIIIIIr7   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 )NrD   rC   rR   )rz   r{   r    r,   r   r  r!  rz  s    r5   test_infnan_argz"TestMatrix_Balance.test_infnan_argg	  sp    j.hABF455	7 	7 	7j.hABF455	7 	7 	7 	7 	7r7   c           	          t          t          j        ddgddgg                    \  }}t          t          j        t          j        t          j        |                              dg           d S )Nr  rD   r   r   )r    r,   r   r   difflog2rn   )rY   r  r"  s      r5   test_scalingzTestMatrix_Balance.test_scalingm	  s`    bhq	D!9'=>>??1 	

 3 344qc:::::r7   c                     t          j        g dg dg dg          }t          |          \  }}t          t	          ||                              |          |           d S )N)rD   r   r   )rD   rD   r  )r  g      Y@rD   )r,   r   r    r   r   r   )rY   r  rc   r"  s       r5   test_scaling_orderz%TestMatrix_Balance.test_scaling_ordert	  s_    HlllLLL---@AAa  1a**A.....r7   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  rD   r   separater   rC   )r    r,   r   r   rq  rr  r   r   )rY   r  r"  zs       r5   test_separatez TestMatrix_Balance.test_separatey	  s|    "28dAYq	,B#C#C,-/ / /	6AqRWRWQZZ((1#...29Q<<(((((r7   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 )Nr  r  rD   rw  )r   rD   rA   r   r@   rR   rC   )r   r,   r   rJ  r    r   	ones_liker   )rY   r  rc   r"  ry  s        r5   test_permutationz#TestMatrix_Balance.test_permutation	  s    rwv(@(@wv( ("1q111	6Aq2<??+++28$9$9$9::;;;;;r7   c           	      L   t          j        g dg dg dg dg dg          t          j        g dg dg dg dg          t          j        g d	g d
g dg dg          f}|D ]}t          |          \  }}t          |d          \  }\  }}t          j        |          }t          j        |j        d                   ||<   t          |t          j        |          |d d f                    t          t          ||          	                    |          |           d S )N)rJ   rJ   rJ   rJ   >)rJ   rJ   rJ   rJ   rJ   )rQ   rQ   rJ   rJ   rJ   )rJ   rJ   r  rJ   rJ   )r  rJ   rJ   rJ   )rJ   rO  rJ   rJ   )r<   rJ   r  rJ   )rJ   r<   rJ   rO  )r  rJ   r<   rJ   )rO  rO         r<   )r  r  r  rJ   )rO  r  r<   rO  rD   rw  r   )
r,   r   r    rc  r   r   r   rn   r   r   )rY   casesr  rc   r"  r  r  ips           r5   test_perm_and_scalingz(TestMatrix_Balance.test_perm_and_scaling	  sz    555/////////555	7 8 8 ---,,,---,,,. / /
 ,,,.........0 1 1$  	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 	3r7   r4   c                 4   t          j        d|          }t          |          \  }}|j        dk    sJ |j        dk    sJ t          t          j        d|                    \  }}|j        |j        k    sJ |j        |j        k    sJ t          |d          \  }\  }}|j        dk    sJ |j        dk    sJ |j        dk    sJ t          |d          \  }\  }	}
|j        |j        k    sJ |j        |	j        k    sJ |j        |
j        k    sJ d S )Nr   r   r   rC   Trw  )r,   r   r    r\  r   r   )rY   r4   rZ   rb   rp  b_nt_nr  permscale_nperm_ns              r5   r   zTestMatrix_Balance.test_empty	  s8   HV2&&&a  1v{{{{v{{{{!"&""5"5"566Sw#)####w#)####)!d;;;=E4v{{{{zQyA~~~~!/D!A!A!Agvw#)####{gm++++zV\))))))r7   N)r   r   r   r(   rm  ro  rs  ru  rz  r}  r  r   r   r   r   r   r,   r
   r   r   r   r   r7   r5   rk  rk  b	  s        J J J7 7 7; ; ;/ / /
) ) )< < <3 3 38 [TC
GR\#RSS* * TS* * *r7   rk  r   )Mr  r  numpyr,   r   r   r   r   r   r   r	   r
   numpy.testingr   r   r   r   r   r   r   r   rz   scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   scipy.linalg._testutilsr$   scipy._lib._testutilsr%   r&   scipy.linalg.blasr'   scipy.conftestr(   r.   r-   r  r   r0   r/   r  DTYPESr   r   r  r6   r9   r   r   r  r  rB  r  r  r  r  r  r  r#  r2  rM  rk  r   r7   r5   <module>r     s                              / / / / / / / / / / / / / / / /  * * * * * *= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
 8 7 7 7 7 7 < < < < < < < < ' ' ' ' ' ' . . . . . .z2:r}5,r~>	~	% #K33mT*]E,BBG  
  cV cV cV cV cV cV cV cVLIV IV IV IV IV IV IV IVX
^	0 ^	0 ^	0 ^	0 ^	0 ^	0 ^	0 ^	0BOJ OJ OJ OJ OJ OJ OJ OJd`( `( `( `( `( `( `( `(F	T T T T T T T Tn   j& j& j& j& j& j& j& j&Z	R? R? R? R? R? R? R? R?jH? H? H? H? H? H? H? H?V "3444-00% % 10 54%9" 9" 9" 9" 9" 9" 9" 9"x7B 7B 7B 7B 7B 7B 7B 7Bt- - - - - - - -<a# a# a# a# a# a# a# a#HT* T* T* T* T* T* T* T* T* T*r7   