
    bir                       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jb                  ejd                  fZ3ejh                  ejj                  ejl                  fZ7e3e7z   Z8ejr                  ju                  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jr                  ju                  d"d#      ejr                  ju                  d$eef      d%               ZG G d& d'      ZH G d( d)      ZI G d* d+      ZJ G d, d-      ZK G d. d/      ZLy)1    N)arangearraydotzerosidentity	conjugate	transposefloat32)assert_equalassert_almost_equalassert_assert_array_almost_equalassert_allcloseassert_array_equal)raises)solveinvdetlstsqpinvpinvhnormsolve_bandedsolveh_bandedsolve_triangularsolve_circulant	circulantLinAlgError
block_diagmatrix_balanceqrLinAlgWarningassert_no_overwrite)check_free_memoryIS_MUSL)	HAS_ILP64)skip_xp_invalid_argoverwrite_kwoverwrite_aTFc                     | }|t         j                  k(  rt         j                  }n#|t         j                  k(  rt         j                  }t        j
                  |      j                  S )z;Get the epsilon for dtype, possibly downcast to BLAS types.)np
longdoublefloat64clongdouble
complex128finfoeps)dtypdts     X/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/scipy/linalg/tests/test_basic.py	_eps_castr6   "   sE    	B	R]]ZZ	r~~	]]88B<    c            	       "   e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	eeej"                  eej&                  g      ej                  j                  d
eeej"                  eej&                  g      d               Zy)TestSolveBandedc                 d   t        g dg dg dg dg      }t        g dg dg dg dg      }d	\  }}t        g d
      }|j                  dd      }t        ddgddgddgddgg      }t        g dg dg dg dg      }||||fD ]'  }	t        ||f||	      }
t        t	        ||
      |	       ) y )N      ?   r   r         r         r=   rC   r                 r=   rA   rC   rD   r@   r=   rH   r?   rD   rG   r   rC   rF   r   r   rC   rD         $@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.   s    ?! !# $ O""!# $ 1)*

2q!1vQx1v1v   |###% & eUE* 	4AaVR+A%c!Qi3	4r7   c                 d   t        g dg dg dg dg      }t        g dg dg dg dg      }d	\  }}t        g d
      }|j                  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 ]'  }	t        ||f||	      }
t        t	        ||
      |	       ) y )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   s    ?!"!# $ $"""$ % 1*+

2q!1vQx1v1v   |$##% & eUE* 	4AaVR+A%c!Qi3	4r7   c                    t        g dg dg dg      }t        j                  |ddd f   d      t        j                  |dd d f   d      z   t        j                  |dd df   d      z   }t        g d      }|j                  dd      }t        ddgd	d
gddgddgg      }t        g dg dg dg dg      }||||fD ]%  }t	        d||      }t        t        ||      |       ' y )NrI   rK   rL   r   rD   rC   rF   rO   r?   r@   rR   rS   rT   rU   rD   rD   r   r,   diagrW   r   r   r   	rY   r[   rZ   r^   r_   r`   ra   rb   rc   s	            r5   test_tridiag_realz!TestSolveBanded.test_tridiag_real^   s	   O!!# $ GGBq!"uIq!BGGBq!tHa$88277@B1crc6
B<P P)*

2q!1vQx1v1v   |###% & eUE* 	4AVR+A%c!Qi3	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      }|j                  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 ]%  }t	        d||      }t        t        ||      |       ' y )Nrg   rK   rL   r   rD   rC   rF   rh   r?   r@   rR   rS   rT   rU   rl   rm   ro   s	            r5   test_tridiag_complexz$TestSolveBanded.test_tridiag_complexr   s
   $!!# $ GGBq!"uIq!BGGBq!tHa$88277?A!SbS&z2<O O*+

2q!1vQx1v1v   |###% & eUE* 	4AVR+A%c!Qi3	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        ||      |       y )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   sr    ?! !# $ O""!# $ 1)*!QRe<!#a)R0r7   c                    t        g dg dg dg dg      }d\  }}t        g d      j                  dd      }t        t        t        ||f||       t        t        t        ||f|d	d
g       t        t        t        d|d	d
g       y )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    O""!# $ 1()11"a8j,AC@j,AS#JG 	j,S#J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       y )
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3U+QWWbhhtn-1/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        ||      |       y )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\      1"!QQ'!#a)Q/r7   dt_abdt_bc                 D   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 y )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     XXrd%(HHRt$Q'ww$ww%q 68NOUUUUUHHV4(Q'ww&   ww%q 68NO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    40404(4(1H1"0 [[WsE2::w&UV[[Vc5"**gr||%TUV V WVr7   r9   c            	       v   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j4                  j7                  deeej>                  e ejB                  g      ej4                  j7                  deeej>                  e ejB                  g      d               Z"y)TestSolveHBandedc                 z    t        g dg dg dg      }t        g d      }t        ||      }t        |g d       y 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   s@     (((* + &'"a !!%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        ||       y )	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      j                  dd      }t        ||      }t        |t        g d      j                  dd             y )Nr   r   r   r   rF   rD   r   r   rW   r   r   r   s       r5   test_03_upperzTestSolveHBanded.test_03_upper   s_     (((* + &'//A6"a !!U+;%<%D%DR%KLr7   c                 ~    t        g dg dg dg      }t        g d      }t        ||d      }t        |g d       y )Nr   r<   r<   r<   r   rQ   rQ   rJ   rJ   r   Tlowerr   r   r   s       r5   test_01_lowerzTestSolveHBanded.test_01_lower  sB     (((* + &'"at,!!%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        ||       y )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       y )Nr   r   r   r   r   r   r   r
   r   r   r   s       r5   test_01_float32z TestSolveHBanded.test_01_float32(  sE     (((*18: &g6"a !!%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        ||       y )
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                 z    t        g dg dg dg      }t        g d      }t        ||      }t        |g d       y )Nr   r                r   r   r   )       @            @            @      ?       @      ?)rJ   r<   r<   rJ   r   r   s       r5   test_01_complexz TestSolveHBanded.test_01_complexK  s@     (.(* + ./"a !!%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        ||       y )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    t        g dg dg      }t        g d      }t        ||      }t        |g d       y )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  s3     O_56/""a !!_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        ||       y )Nr   r   r<   ry   rQ   rJ   r   r   s        r5   test_tridiag_02_upperz&TestSolveHBanded.test_tridiag_02_uppery  sx     O#% &C:::   "a 3***& ' 	"!X.r7   c                     t        g dg dg      }t        g d      j                  dd      }t        ||      }t        |t        g d      j                  dd             y )Nr   r   r   rF   rD   r   r   r   s       r5   test_tridiag_03_upperz&TestSolveHBanded.test_tridiag_03_upper  sR     O_56/"**2q1"a !!U?%;%C%CB%JKr7   c                 x    t        g dg dg      }t        g d      }t        ||d      }t        |g d       y )Nr   r<   r<   r   r   Tr   r   r   r   s       r5   test_tridiag_01_lowerz&TestSolveHBanded.test_tridiag_01_lower  s:     O#% &/""at,!!_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        ||       y )	Nr   r   r<   ry   rQ   Tr   rJ   r   r   s        r5   test_tridiag_02_lowerz&TestSolveHBanded.test_tridiag_02_lower  sz     O#% &C:::   "at,3***& ' 	"!X.r7   c                     t        g dg dgt              }t        g dt              }t        ||      }t        |g d       y )Nr   r   r   r   r   r   r   s       r5   test_tridiag_01_float32z(TestSolveHBanded.test_tridiag_01_float32  s7     O_5WE/1"a !!_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        ||       y )Nr   r   r   r<   ry   rQ   rJ   r   r   s        r5   test_tridiag_02_float32z(TestSolveHBanded.test_tridiag_02_float32  s~     O#%,35C:::&-/ "a 3***& ' 	"!X.r7   c                 t    t        g dg dg      }t        g d      }t        ||      }t        |g d       y )Nr   r   r   r   )r   r   r   )rJ   r<   r<   r   r   s       r5   test_tridiag_01_complexz(TestSolveHBanded.test_tridiag_01_complex  s5     '9:'("a !!_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        ||       y )Nr   r   r                 @r   r   r   ry   rJ   ri   r<   r   r   s        r5   test_tridiag_02_complexz(TestSolveHBanded.test_tridiag_02_complex  sz     '#% &C;G$C=" # "a 3+**& ' 	"!X.r7   c                 x    t        g dg dg      }t        g d      }t        ||d      }t        |g d       y )Nr   r   r   Frt   r   r   r   s       r5   rv   z"TestSolveHBanded.test_check_finite  s5     O_56/""ae4!!_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       y )Nr   r   r<   ry   rQ   )r   rz   r{   r   )rY   r[   rb   s      r5   test_bad_shapesz TestSolveHBanded.test_bad_shapes  sb    O#% &C::  j-Q7j-c3Z@j-cU;r7   c                     t        dggg dg      }t        |g dg       t        |j                  t	        j                  d             y )NrD   rD   rC   rR   r   r   )r   r   r   r   r,   )rY   rc   s     r5   r   zTestSolveHBanded.test_1x1  s7    A3%)-1/0QWWbhhtn-r7   c                 V    g dg dg dg}g d}t        ||      }t        |g d       y r   )r   r   r   s       r5   r   z+TestSolveHBanded.test_native_list_arguments  s0    """$ !"a !!%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 y )Nr   r   rD   r   )	r,   r   r   r   r   r   r   r   r   r   s         r5   r   zTestSolveHBanded.test_empty  s     XXrd%(HHRt$"a ww$ww%q 68NOUUUUUHHV4("a ww&   ww%q 68NO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;/*;/*;/*	6/"	L
6/"	6/"	6/"	6<.
; [[WsE2::w&UV[[Vc5"**gr||%TUV V W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.                  j1                  dddg      d        Zd Zd Zej.                  j1                  dd      d        Zej.                  j1                  dd      d        Zd Zd  Zej.                  jA                  d!"      d#        Z!d$ Z"d% Z#d& Z$ej.                  j1                  d'd(d)g      ej.                  j1                  dg d*      ej.                  j1                  d+e%jL                  e%jN                  e%jP                  e%jR                  g      d,                      Z*ej.                  j1                  d-e+e,e%jL                  e-e%jP                  g      ej.                  j1                  d.e+e,e%jL                  e-e%jP                  g      d/               Z.d0 Z/ej.                  j1                  d+e%jN                  e%jR                  g      ej.                  j1                  dg d1      ej.                  j1                  d2d3d4g      ej.                  j1                  d5d6d7g      ej.                  j1                  d8d6d7g      ej.                  j1                  d9d6d7g      d:                                           Z0ej.                  jc                  e%jd                  d;k  d<"      ej.                  j1                  dg d=      d>               Z3d? Z4d@ Z5e6dA        Z7e6dB        Z8e6dC        Z9e6dD        Z:e6dE        Z;dF Z<dG Z=dH Z>yI)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       y )NrD   r<   r                   333333?r   r   r   )rY   rZ   x0rb   s       r5   test_20Feb04_bugzTestSolve.test_20Feb04_bug  st    Vc1X1q"g!#a*q!f5 Vc1XG1a[!#a*q!f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 ]$  }t        ||      }t        t        ||      |       & y )NrD   r=   r?   r@   r   rC   r   rY   rZ   rb   rc   s       r5   test_simplezTestSolve.test_simple*  si    WsAhq6Aq6"a&q6C8$ 	4A aA%c!Qi3	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 ]$  }t        ||      }t        t        ||      |       & y )
N   rC   rf   r@   Dri   r   rD   r   )r   r   r   r   r   s       r5   test_simple_complexzTestSolve.test_simple_complex3  su    Aq6B7#S)q'8aV$b'A$ 	4A
 aA%c!Qi3	4r7   c                     ddgddgg}dD ]8  }ddgddggddgfD ]'  }t        ||d|      }t        t        ||      |       ) : y )	NrC   rR   r   r   rD   rD   r   posassume_ar   r   rY   rZ   r   rb   rc   s        r5   test_simple_poszTestSolve.test_simple_pos=  sm    VaV 	8E1v1v&!f 8 !Qe<)#a)Q7	8	8r7   c                 ~    ddgddgg}ddgddgddggfD ]&  }t        ||d      }t        t        ||      |       ( y )Nr   rC   r@   ri   r   r   r  r   r   s       r5   test_simple_pos_complexbz"TestSolve.test_simple_pos_complexbF  s\    VaVq'8aV$ 	4A aU+A%c!Qi3		4r7   c                     ddgddgg}dD ]8  }ddgddggddgfD ]'  }t        ||d|      }t        t        ||      |       ) : y )	NrC   rR   r   rD   r   symr  r   r  s        r5   test_simple_symzTestSolve.test_simple_symN  sm    VaW 	8E1v1v&!f 8 !Qe<)#a)Q7	8	8r7   c                 ~    ddgddgg}ddgddgddggfD ]&  }t        ||d      }t        t        ||      |       ( y )Nr   rC   ri   r   r
  r  r   r   s       r5   test_simple_sym_complexbz"TestSolve.test_simple_sym_complexbW  s\    VaWq'8aV$ 	4A aU+A%c!Qi3		4r7   c                     ddgddgg}ddgddgddgddggfD ]&  }t        ||d	      }t        t        ||      |       ( y )
Nr   r   r  ri   r   rD   rC   r
  r  r   r   s       r5   test_simple_sym_complexz!TestSolve.test_simple_sym_complex_  c    Yr
#q'a&8aV$ 	4A aU+A%c!Qi3	4r7   c                     ddgddgg}dD ];  }ddgddggddgddgfD ]'  }t        ||d|	      }t        t        ||      |       ) = y )
NrC   rR   r	  r   rD   r   ri   herr  r   r  s        r5   test_simple_her_actuallysymz%TestSolve.test_simple_her_actuallysymh  st    VaW 	8E1v1v&!f1g 8 !Qe<)#a)Q7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 ]&  }t        ||d	
      }t        t        ||      |       ( y )Nr   r   r   r  ri   r   rD   rC   r  r  r   r   s       r5   test_simple_herzTestSolve.test_simple_herr  r  r7   c                 r   t         j                  j                  d      }d}|j                  ||g      |j                  ||g      dz  z   }t        ||fd      }t	        |      }t        |      t        |      dz  z   }t        d|      D ]  }|d d |f   }t        ||      |d d |f<     t        ||       y )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    ii##D)JJ1vszz1a&1"441a&#1vQKB&1 	"A!Q$AAqkAadG	" 	"!T*r7   c                 :   t         j                  j                  d      }d}|j                  ||g      }t        |      D ]  }dd|||f   z   z  |||f<    t        d      D ]7  }|j                  |dg      }t	        ||      }t        t        ||      |       9 y )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    ii##D)JJ1vq 	&A"Qq!tW*oAadG	&q 	4A

Aq6"AaA%c!Qi3	4r7   c                 h   t         j                  j                  d      }d}|j                  ||g      d|j                  ||g      z  z   }t        |      D ]  }dd|||f   z   z  |||f<    t        d      D ]7  }|j                  |dg      }t	        ||      }t        t        ||      |       9 y )Nr  r=   ri   r%  rC   rR   r&  r(  s          r5   test_random_complexzTestSolve.test_random_complex  s    ii##D)JJ1vcjj!Q&8!88q 	&A"Qq!tW*oAadG	&q 	4A

Aq6"AaA%c!Qi3	4r7   c                    t         j                  j                  d      }d}|j                  ||g      }t        |      D ]9  }t	        dd|||f   z   z        |||f<   t        |      D ]  }|||f   |||f<    ; t        d      D ]8  }|j                  |g      }t        ||d      }t        t        ||      |       : y )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    ii##D)JJ1vq 	"A"b1a4j/*AadG1X "AqD'!Q$"	" q 	4A

A3AaU+A%c!Qi3	4r7   c                    t         j                  j                  d      }d}|j                  ||g      }|d|j                  ||g      z  z   }t        |      D ]B  }t	        dd|||f   z   z        |||f<   t        |      D ]  }t        |||f         |||f<    D |j                  |g      d|j                  |g      z  z   }t        d      D ]&  }t        ||d      }t        t        ||      |       ( y )	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  s   ii##D)JJ1v3::q!f%%%q 	-A"b1a4j/*AadG1X -#AadG,!Q$-	- JJsOBszz1#..q 	4AaU+A%c!Qi3	4r7   c                     ddgddgg}ddgddggddgddgddggfD ]&  }t        ||d      }t        t        ||      |       ( y )	NrD   r=   r?   r@   r   rC   Frt   r   r   s       r5   rv   zTestSolve.test_check_finite  si    WsAhq6Aq6"QFq6C8$& 	4Aa/A%c!Qi3	4r7   c                     d}g d}t        ||      }t        |j                         |       t        |j                  dk(  d       y )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  s:    !QK!!'')Q/4!J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                         y )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    HH/8113 4
 HHtUm'Vnen& '
 !QK!!RXX/;/= &>>?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             y )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    HHHMIIK L
 HH|[1#]3#\2!;/1 2
 !QK!!RYY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                         j                  }||z   }t        j                  |      |t        j
                  d      t        j
                  d      f<   t        ||d      }t        |||      }t        ||       t        |||d      }t        ||       y )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     HHB9/&( ) HH{L1"L1#[1!=13 4
 %QSS1668::V)+299Q<1%&BI.!Q*!!S) "a($7!!S)r7   c                 d   t        j                  dd      j                  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       y )	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  sw    IIa$$Q*"''!*Q,
U;!!]3"''!*Q,
U;!!]3r7   c                     t        j                  g dg dg dg dg dg dg dg dg dg	      }t        j                  d      d d d f   }t        t        t
        ||       y )N)	rD   r   r   r   r   r   rD   r   rD   )	rD   rD   rD   r   r   r   rD   r   rD   )	r   rD   rD   r   r   r   rD   r   rD   )	rD   r   rD   rD   rD   rD   r   r   r   )	rD   rD   rD   rD   rD   rD   rD   rD   rD   rG  )r,   r   r   rz   r   r   rY   rZ   rb   s      r5   test_singularityzTestSolve.test_singularity  sV    HH1111111113 4 IIaLD!k5!Q/r7   	structure)
diagonaltridiagonallower triangularupper triangular	symmetric	hermitianpositive definiter@  bandedNc                 B   t         j                  j                  d      }d}t        j                  dd|      }t        j                  |      }|j                  |      }d}t        j                  t        |      5  t        |||       d d d        y # 1 sw Y   y xY w)	Nl   Ej] rF  r   2   sizez2(Ill-conditioned matrix|An ill-conditioned matrix)matchr  )	r,   r  r  logspacern   r   warnsr"   r   )rY   rP  r  r  dr  rb   messages           r5   test_ill_condition_warningz$TestSolve.test_ill_condition_warning  s    
 ii##L1KK2q!GGAJJJAJF\\-w7 	,!Q+	, 	, 	,s   =BB)	rQ  rR  rS  rT  rU  rV  rW  r@  Nc                 2   d}t        j                  ||f      }t        j                  |      }t        j                  t
        d      5  t        j                  d      5  t        |||       d d d        d d d        y # 1 sw Y   xY w# 1 sw Y   y xY w)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   sw    
 HHaVGGAJmmKz: 	,BKKH<U 	,!Q+	, 	, 	, 	, 	, 	,s$   
B!B0BB
	BBc                     t        j                  d      }t         j                  j                  d      }|j                  d      }t	        ||      }t        ||       y )NrC   r  )rC      )r,   r   r  r  r   r   )rY   rZ   r  rb   rc   s        r5   test_multiple_rhszTestSolve.test_multiple_rhs+  sF    FF1Iii##D)JJw!QK!!Q'r7   c                 h   t        j                  d      j                  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       y )	NrG  rR   rD   T
transposed)r   g?rD   F)rG  gg333333rI  rK  s      r5   test_transposed_keywordz!TestSolve.test_transposed_keyword2  sy    IIaL  A&*"''!*Q,
t<!!]3"''!*Q,
u=!!_5r7   z*1. why? 2. deprecate the kwarg altogether?reasonc                     t        j                  d      j                  t              }t	        t
              5  t        ||d       d d d        y # 1 sw Y   y xY w)NrR   Trn  )r,   r   astyper   rz   NotImplementedErrorr   rY   rZ   s     r5   test_transposed_notimplementedz(TestSolve.test_transposed_notimplemented9  sD    FF1IW%./ 	)!Q4(	) 	) 	)s   AAc                 4    t        t        t        ddgd       y )NrD   rC   rz   r{   r   rY   s    r5   test_nonsquare_azTestSolve.test_nonsquare_a?  s    j%!Q3r7   c                    t        t        t        j                  d      t        j                  d            t        j                  d             t        t        t        t        j                  d      t        j                  d             y )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  sI    !%q	2771:">
Kj%BGGAJ?r7   c                 4    t        t        t        ddd       y )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                  j                  d      }|t         j                  t         j                  fv }|j                  ||f      j                  |      }|j                  |      j                  |      }|r(|d|j                  ||f      z  j                  |      z  }|dk(  r||j                  z   }n|dk(  r||j                  j                         z   }n|dk(  r7|j                  j                         |z  dt        j                  |      z  z   }n|dk(  r~t        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(  r+|s(t        |||d      }	t        ||	z  |||z  ||z         y y y )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  s    ii##D)r||R]];;
t-44U;%,,U3"S(($66>>uEEAuACCAACCHHJA
QRVVD\!11A&$A*+B,-A
 R]] ;;e,, R\\22r	!Q*AqsTzd
CuZaX$?AAE13:C$JG &0r7   dt_ar   c                 f   t        j                  d|      }t        j                  d|      }t        ||      }|j                  dk(  sJ t        t        j                  d|      t        j
                  d|            j                  }|j                  |k(  sJ |j                  t         j                  j                  ||      j                  k(  sJ t        j
                  d|      }t        j
                  d|      }t        ||      }|j                  dk(  sJ |j                  |k(  sJ y )Nr   r   r   rC   rR   r   rC   rC   rC   r@   )rR   r   rC   r@   )	r,   r   r   r\  r   r   r   r   linalgrY   r  r   rZ   rb   rc   dt_nonemptys          r5   r   zTestSolve.test_emptyr  s     HHV4(HHQd#!QKvv{{BFF1D12771D3IJPPww+%%%ww"))//!Q/55555GGL-GGF$'!QKww,&&&ww+%%%r7   c                     t        j                  d      }g g g}t        ||      }t        |j                  dk(  d       t        |j
                  dk(  d       y 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  sJ    FF1IH!QK!:;6!#HIr7   )rQ  rR  rX  rS  rT  r   rW  rU  rV  rX  r@  r
  r  r  nrhsr   )r   ro  TF	overwritefortranc                    t         j                  j                  d      }|dk(  sdnd}|j                  |f|z         }	|j                  ||f      }
t        j                  |t         j                        r6|	|j                  |f|z         dz  z   }	|
|j                  ||f      dz  z   }
|dk(  r*t        j
                  t        j
                  |
            }
nC|dk(  rt        j                  |
      }
n'|d	k(  rt        j                  |
      }
n|d
k(  rt        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      }
nW|dv r|
|
j                  z   }
nC|dv r|
|
j                         j                  z   }
n!|dv r|
|
j                  j                         z  }
|rt        j                  |
      }
|
j                  d      }|	j                         }t        j                  |t         j                        r9|r7d}t        j                  t        |      5  t        |
|	|||       d d d        y t        |
|	||||      }t         j                   j                  |r|j                  n||      }t#        ||       |dk7  rt#        t        |||      |d       |st%        |
|       t%        |	|       y y # 1 sw Y   y xY w)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    ii##O4)ArJJQD4KJ(JJQFJ#== 2 23CJJQD4KJ0255ACJJQFJ+b00Az!
#A++
A++
A&$772771b>2./772771a=!,-A !1r*A--ACCA--AFFHJJA55ACCHHJA!!!$Ac"== 2 23
;G2'B -a	y!+-- AqiY)H> iioo*fhh&&IS! xff<c
 F#F# )- s   L;;M2z(solve chokes on b.ndim == 1 in numpy < 2)NrQ  r@  rT  rS  r   c                 J   t        j                  d      }t        j                  dd      j                  d      |z  }t        j                  d      }t        t        |||      t         j                  j                  ||             t        j                  d      }t        t        |||      t         j                  j                  ||             t        j                  d      ddgz  }t        t        |||      t         j                  j                  ||             y )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     FF1IIIa#++O<q@GGAJaX6		18MNGGFOaX6		18MNGGFOq!f$aX6		18MNr7   c                 N   t         j                  j                  d      }|j                  d      }t        j                  t        j
                  |t        j                  |j                                    }|j                  d      }t        ||dd      }||j                  z   t        j                  t        j                  |            z
  }t         j                  j                  ||      }t        ||d	       t        |j                  |dd
      }t        ||d	       y )Nr   r@   r@   r[  r@   rC   r   Tr  r   r  F)r,   r  r  normalrJ  matmulrA  r:  r   rn   r  r   )rY   r  rZ   rb   outaa	result_nps          r5   test_pos_lowerzTestSolve.test_pos_lower  s     ii##A&JJFJ#GGBIIa./JJFJ#Aq55Wrwwrwwqz**IIOOB*	YU3 ACCU%8YU3r7   c                     t        j                  d      }d|j                  _        t        j                  d      }t        ||      }t        ||d       y NrR   F+=r  )r,   r   flags	writeabler   r   r   r   s       r5   test_readonlyzTestSolve.test_readonly  s?    FF1I!GGAJ!QK15)r7   c                    t        j                  d      j                  dddd      }|d d d d dd d d d f   }t        j                  d      }t	        ||fi |}|j
                  |j
                  d d k(  sJ t        ||d   z  |z
  dd       t        j                  d	      d d d d df   }t	        ||fi |}|j
                  |j
                  d d |j
                  d   fz   k(  sJ t        ||z  |z
  dd       y 
N   rC   rR   rF   .Nr   r  r  r  r,   r   rW   r   r   r   r   rY   r)   rZ   rb   rc   s        r5   test_batch_negative_stridez$TestSolve.test_batch_negative_stride  s    IIcN""1aA.a2q!mGGAJ!Q','ww!''#2,&&&AiL(1,ae< GGFOAttG$!Q','ww!''#2,!''"+7777A	151r7   c                    t        j                  d      j                  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       y r  r  r  s        r5   test_core_negative_stridez#TestSolve.test_core_negative_stride  s    IIcN""1aA.aDbD!mGGAJ!Q','ww!''#2,&&&AiL(1,ae< GGFODbD!G$!Q','ww!''#2,!''"+7777A	151r7   c                    t        j                  d      j                  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	
       y )N0   rC   rR   r@   .rF   r  r   r  r  r  r  s        r5   test_core_non_contiguousz"TestSolve.test_core_non_contiguous   s    IIe$$Q1a0c3Q3hKGGAJ!Q','ww!''#2,&&&AiL(1,ae< GGAJssO!Q','ww!''#2,&&&AiL(1,ae<r7   c                    t        j                  d      j                  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	       y )Nr  rC   rA   .rF   r  r   r  r  rC   rA   r  r  s        r5   test_batch_non_contiguousz#TestSolve.test_batch_non_contiguous/  s    IIe$$Q1a0a1ckNGGAJ!Q','ww!''#2,&&&AiL(1,ae< GGFOAssF#!Q','ww!''#2,!''"+7777A	151r7   c                 ,   t        j                  d      j                  ddddd      }|j                  ddddd      }t        j                  d      }t        ||fi |}|j                  |j                  d d k(  sJ t        ||d   z  |z
  dd	
       y )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    IIe$$Q1a3KK1aA&GGAJ!Q','ww!''#2,&&&AiL(1,ae<r7   c                 `   t        j                  d      j                  dd      }||j                  z   t        j                  d      z   }t        j
                  d      }t        ||      }t        ||z  |d       t        t              5  t        ||d       d d d        y # 1 sw Y   y xY w)NrG  rR   r  r  r   r  )
r,   r   rW   r:  r   r   r   r   rz   r   )rY   rZ   r  rb   r   s        r5   test_posdef_not_posdefz TestSolve.test_posdef_not_posdefH  s    IIaL  A&GbffQiGGAJ 1a[B. ;' 	(!Q'	( 	( 	(s   B$$B-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        t        j                  d	d	gd	dgg      }t        j                  d
      }t        j                  t              5  t        ||d       d d d        y # 1 sw Y   jxY w# 1 sw Y   y xY w)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%   HHbggbggfo.		!Q0HIJGGAJ!QK 	&	1ryyA#6UC JJq	Aq6*+GGAJ\\-( 	-!Q,	- JJAA'(GGAJ]];' 	-!Q,	- 	-	- 	-	- 	-s   7E/E;/E8;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        dx|d<   |d<   t        j                  t              5  t        ||d       d d d        y # 1 sw Y   DxY w# 1 sw Y   y xY w)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-   rwwrwwqz""RWWRWWQZ%;;bggbggajRT>UUHHbggbggq!fo.23GGAJ!QK 	&	2::.B#C%P '
\\-( 	0!Q/	0 #$#'
QwZ]];' 	0!Q/	0 	0	0 	0
	0 	0s   &E8 F8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448484484
+	4	4444LA@" [[Z%8* 9*.40 [[[NO,	O, [[[DE,	E,(6 [[IJ) K)
4@@ [[Vb#Y/[[Z)TU[["**bjj",,F"H V 0
"HH [[Vc5"**gr||%TU[[Vc5"**gr||%TU& V V& J [[Wrzz2==&AB[[Z *J K
 [[Vb$Z0[[\D%=9[[[4-8[[Yu6<$ 7 9 : 1K C<$| [[
%O   [[	
OO4"* 2 2 2 2 = = 2 2 = =(-(0r7   r   c            	       
   e Zd Zd Zd Zd Zej                  j                  de	e
ej                  eej                  g      ej                  j                  de	e
ej                  eej                  g      d               Zd Zy)	TestSolveTriangularc                 D   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       y):
        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!#1v. qssAU3!#Bx0 q!4q9!#Bx0QKq!4q9!#S	As8'<=r7   c                 t   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       y)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  sW    D!9r1g&'QKq!4q9!#(;aX'FG GGT4L!q!4q9!#A'@Aq!4q9!#J!V'EFq!4q9!#[(9Av;'GHqssAU!<!#J!V'EFqssAU!<!#A'@AqssAU!<!#Q$'@Ar7   c                 h    t        ddgddgg      }ddg}t        ||dd      }t        |ddg       y)r  rD   r   rC   TF)r   ru   N)r   r   r   r  s       r5   rv   z%TestSolveTriangular.test_check_finite  sB     Aq6Aq6"#Fq!4e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 y Nr   r   r   rC   )r,   r   r   r\  r   r   r   r  s          r5   r   zTestSolveTriangular.test_empty  s     HHV4(HHQd#Q"vv{{&FF1D!2771D#9

% 	 ww+%%%r7   c                     t        j                  d      }g g g}t        ||      }t        |j                  dk(  d       t        |j
                  dk(  d       y r  )r,   r   r   r   r\  r   r   s       r5   r  z"TestSolveTriangular.test_empty_rhs  sK    FF1IHQ"!:;6!#H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:/ [[Vc5"**gr||%TU[[Vc5"**gr||%TU	& V V	&Jr7   r  c                      e Zd Zd Zd Zd Zd Zd Zej                  j                  deeej                  eej                   g      d        Zej                  j%                  d	      d
        Zd Zej                  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                  j                  dddg      d        Z ej                  j                  dddg      ej                  j                  dddg      d               Z!d Z"d Z#d  Z$y!)"TestInvc                     ddgddgg}t        |      }t        t        ||      t        j                  d             g dg dg dg}t        |      }t        t        ||      t        j                  d             y )NrD   rC   rR   r@   r   r@   r   rA   rG      rF  )r   r   r   r,   r   rY   rZ   a_invs      r5   r   zTestInv.test_simple  sb    VaVA!#a-;	:.A!#a-;r7   c                 $   t         j                  j                  d      }d}t        d      D ]a  }|j                  ||g      }t        |      D ]  }dd|||f   z   z  |||f<    t	        |      }t        t        ||      t        |             c y )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    ii##D)q 	3A

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

Aq6"2cjj!Q&8#88A1X *b1a4j/!Q$*FE%c!Um&.qk3	3r7   c                 f    ddgddgg}t        |d      }t        t        ||      ddgddgg       y )NrD   rC   rR   r@   Frt   r   r  r  s      r5   rv   zTestInv.test_check_finite  s=    VaVAE*!#a-1a&1a&1A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 y )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    HHV2&AzzQ{{c"&&""56<<<<<GGL+A{{l***GGL+A{{l***r7   zTODO: re-enable overwrite_arq  c                 v   t        j                  dd      j                  dd      }t        |d      }t	        ||z  t        j
                  d      d       t        j                  ||      rJ |j                  t              j                  d	      }t        |d      }t        j                  ||      sJ y )
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    IIaO##Aq)A4(	266!959##Au--- HHUO  s +A4(5)))r7   c                     t        j                  d      }d|j                  _        t	        |      }t        ||d       y r  )r,   r   r  r  r   r   r  s      r5   r  zTestInv.test_readonly  s0    FF1I!Aqu-r7   c                     t        j                  d|      j                  dddd      dz   }t        |      }|j                  |j                  k(  sJ t        ||z  d       y )NrA   r   rR   rC   rD   r<   )r,   r   rW   r   r   r   r  s       r5   test_batch_core_1x1zTestInv.test_batch_core_1x1  sU    IIc$,,Q1a81<A{{agg%%%E	2&r7   c                    t        j                  dt              j                  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       y )	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    IIe5)11!Q:y\B','{{bhh&&&U
BOOBFF1Irxx$HuUq$|_B','{{bhh&&&U
BOOBFF1Irxx$HuUr7   c                 H   t        j                  d      j                  dddd      }|d d d d dd d d d f   }t        |fi |}|j                  |j                  k(  sJ t        ||z  t        j                  t        j                  d      |j                        d       y Nr  rC   rR   rF   vIh%,=r  r,   r   rW   r   r   r   r  r   rY   r)   rZ   r  s       r5   r  z"TestInv.test_batch_negative_stride0  s    IIcN""1aA.a2q!mA&&{{agg%%%E	2??266!9agg#FUSr7   c                 H   t        j                  d      j                  dddd      }|d d d d d d dd d f   }t        |fi |}|j                  |j                  k(  sJ t        ||z  t        j                  t        j                  d      |j                        d       y r  r  r  s       r5   r  z!TestInv.test_core_negative_stride8  s    IIcN""1aA.aDbD!mA&&{{agg%%%E	2??266!9agg#FUSr7   c                 $   t        j                  d      j                  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       y )	Nr  rC   rR   r@   .rC   rR   rC   rC   r  r  r  r  s       r5   r  z TestInv.test_core_non_contiguous@  sz    IIe$$Q1a0c3Q3hKA&&{{l***E	2??266!9agg#FUSr7   c                 *   t        j                  d      j                  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       y )Nr  rC   rA   .r  gvIh%L=r  r  r  s       r5   r  z!TestInv.test_batch_non_contiguousH  s|    IIe$$Q1a0a1ckNA&&{{l***E	2??266!9agg#FUSr7   c                    t        t              5  t        t        j                  d             d d d        t        t              5  t        t        j                  d             d d d        t        j
                  t        j                  dt              t        j                  d      j                  dd      f      }t        t              5  t        |       d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   y xY w)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     ;' 	! 	! ;' 	$	"#	$ HHbggfG4biil6J6J1a6PQR;' 	F	 		! 	!	$ 	$	 	s#   C$C0C<$C-0C9<Dc                    t        j                  ddg      }t        j                  t              5  t        |       d d d        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        y # 1 sw Y   xY w# 1 sw Y   y xY w)Nr<   #B;rD   )r,   rn   r   r`  r"   r   r  )rY   rZ   rB  s      r5   test_ill_condzTestInv.test_ill_condi  s    GGRK \\-( 	F	 XXrwwE{+RWWaV_bggq%j>QRS\\-( 	G	 			 		 	s   C
5C
CCc                     t        t              5  t        t        j                  d      d       d d d        y # 1 sw Y   y xY w)NrC   kaboomr  )rz   KeyErrorr   r,   r   rz  s    r5   test_wrong_assume_azTestInv.test_wrong_assume_ar  s1    8$ 	.q	H-	. 	. 	.s	   !:Ac                 "   t        j                  dt              j                  dd      }||j                  z   }|dt        j
                  d      z  z  }t        |      }t        |d      }t        ||d       t        j                  d	t        j                  g |j                  d
 z
  dk(  t         j                  d	      }t        ||z  ddd      }t        ||d       t        ||j                  z  ddd      }t        ||d       y )Nr  r   r      r   r  r   r  rD   rF   r   Fru   r  r   T)r,   r   r   rW   r:  r   r   r   wheretrir   nan)rY   rc   yy_inv0y_inv1masky_inv2y_inv3s           r5   test_posdefzTestInv.test_posdefv  s    IIb&..q!4G	Rq	\QQ'U3 xxBFF0AGG0R00A5rvvqAQtV%%uMU3 QtvvXEENU3r7   complex_FTc                    t        j                  d      j                  dd      }||j                  z   t        j                  d      z   }|r|d|z  z   }t        |      }t        ||z  t        j                  d      d       t        t              5  t        |d       d d d        |rt        j                  d      j                  dd      }|d|z  z   }||j                  j                         z   t        j                  d      z   }t        t        |      |z  t        j                  d      d       y y # 1 sw Y   xY w)NrG  rR   ri   g [n<r  r   r  )
r,   r   rW   r:  r   r   r   rz   r   rA  )rY   r)  rZ   rb   b_inv0s        r5   r  zTestInv.test_posdef_not_posdef  s    IIaL  A&GbffQiBqDA Q
BFF1IE: ;' 	#E"	# 		!$$Q*ABqDAACCHHJ*ACFQJq	>	 		# 	#s   D::Esym_hermr
  r  c                    t        j                  d      j                  dd      }|r|d|z  z   }|dk(  r||j                  z   }n||j                  j	                         z   }|t        j
                  d      z   }t         j                  j                  |      }t        ||z  t        j
                  d      d       t        ||      }t        ||d       t        j                  d	t        j                  g |j                  d
 z
  dk(  t         j                  d	      }t        ||z  d|d      }t        ||d       t        ||j                  z  d|d      }	t        |	|d       y )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  s&    IIaL  A&BqDAuACCAACCHHJAq	Mq!
BFF1IE:Q*U3 xxBFF0AGG0R00A5rvvqAQtV%(%PU3 QtvvXEHDQU3r7   c                    t        j                  dt              j                  dd      }||j                  z   }|dt        j
                  d      z  z  }t        |d      }t        |d      }t        j                  ||      rJ y )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  st    IIb&..q!4G	Rq	\Q!34 1u-;;v|4444r7   c                    t        j                  d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	 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	 z
  d
k(  t         j                  d      }t	        ||j                  z  dd      }t        |t        j                  |      z  t        j                  d      d       y )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   GGBe$,,Q2
O		BGGAJ.q	F$67		BGGAJ.q	F xxBFF0AGG0R00A5rvvqA$U=OP		BGGAJ.q	F 
O		BGGAJ.q	F$67		BGGAJ.q	F xxBFF0AGG0R00A5rvvqA$&&u?QR		BGGAJ.q	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        t        j                  ddgddgg      }t        j                  t              5  t        |d	       d d d        y # 1 sw Y   TxY w# 1 sw Y   y xY w)
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   HHbggbggfo.		!Q0HIJA 	a"''!bii1o*=">UK JJq	Aq6*+\\-( 	(J'	( JJAA'(]];' 	(J'	( 	(	( 	(
	( 	(s   E )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C
	3C
 [[TC

GR\\#RS+ T+ [[;<	* =	*. [[TC

GR\\#RS' T' 
V 
V T T T T T T T T  0.4& [[Z%7? 8?, [[Z%7[[Z%84 9 8485G4(r7   r  c            	          e Zd Zd Zd Zej                  j                  dddgddgg dg      d        Zd Z	ej                  j                  d	e
j                  d
   dd D  cg c]  }|dvr|
 c}}       d        Zd Zd Zej                  j                  deee
j"                  ee
j&                  g      d        Zd Zd Zd Zyc c}} w )TestDetc                 R   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       y )
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    HHqcUO1vzz#%%%{{4   rzzHHugYc*1vzz#%%%zzV###TSE7#HHyk]",,71vzz#%%%zzT!!!TF8$r7   c                 R   t         j                  j                  d      }|j                  g dt         j                        }t	        |      }|j
                  j                  dk(  sJ |j                  dk(  sJ t        |t        j                  |             |j                  g dt         j                        t        j                  d      z  }t	        |      }|j
                  j                  dk(  sJ |j                  dk(  sJ t        |t        j                  |             y )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    ii##$45JJ|2::J61vzz#%%%zzV###bjjm,JJ|2::J6r||C7HH1vzz#%%%zzV###bjjm,r7   r   rC   r=   )rR   rC   r=   r=   c                    t         j                  j                  d      }|j                  dd|      }t	        |      t         j
                  j	                  |      }}t        ||       |j                  dd|      dz  }||j                  dd|      z  }t	        |      t         j
                  j	                  |      }}t        ||       y )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    ii##$45KKReK,Qq)BBKKReK,R/	S[[s[//Qq)BBr7   c                    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
      j                  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       y )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    HH.22222224 5 	A& 	BIIbM11!Q78"=
 HH66668 @B||M 	A' HH868686868 9 :== 	A#r7   typAllNgGc                     t         j                  j                  d      }d}|j                  ||g      j                  |      }t	        t        |      t         j                  t         j                  z        sJ y )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  s\     ii##$45JJ1v%%c*#a&2::#=???r7   c                    d}t        dg d      D ]E  \  }}t        t        |      5  t        t	        j
                  ddggdz  |             d d d        G t        t        |      5  t        t	        j
                  d	d
ggdz  d             d d d        t        t        |      5  t        t	        j
                  ddggdz  d             d d d        t        t        |      5  t        t	        j
                  ddggdz  d             d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   cxY w# 1 sw Y   y xY w)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<= 	7DAqy4 7BHHsCj\!^1567 7	7 9C0 	74,)56	79C0 	A3*a?@	A9C0 	B3*a/?@A	B 	B7 7	7 	7	A 	A	B 	Bs/   'D*'D'*'D3*'D?D$	'D03D<?Ec                 z   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        t        t        d	      5  t        t        j                  g              d d d        t        t        d      5  t        t        j                  g g             d d d        t        t        d      5  t        t        j                  g gg             d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   \xY w# 1 sw Y   y xY w)
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,   BHHaV,-r2BHHY/0"((2,?BHHY/0"((<2HI:-@A 	%#$	%:-GH 		:-@A 	 "	 :-@A 	"2$ !	" 	"	% 	%	 		  	 	" 	"s0   8!F2F* F%#!F1FF"%F.1F: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 y )Nr   r   r   rC   rp  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    HHV2&Fww"}}ww#bffQb1288888HHYb)Fww$ww#bhhy;<BBBBBr7   c                    t        j                  d      j                  dd      j                  t         j                        }|j                         }t        |d      }t        |d       ||k(  j                         rJ y )NrG  rR   Tr   rJ   )	r,   r   rW   rt  r
   r  r   r   rg  )rY   rZ   acrG  s       r5   r  zTestDet.test_overwrite_at  sc    
 IIaL  A&--bjj9VVX24(b!G==?""?r7   c                     t        j                  g dg dg dg      }|j                  d       t        t	        |d      d       y )	N)rQ   rJ   r<   )      @rx   rO  rq  F)writeTr   rP   )r,   r   setflagsr   r   rv  s     r5   test_readonly_arrayzTestDet.test_readonly_array  s6    HHlM<@A	


A40#6r7   c                     ddgdt         j                  gg}t        t        d      5  t	        |       d d d        y # 1 sw Y   y xY w)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	 	 	s	   =A)r   r   r   rH  rM  r   r   r   rU  rY  r,   	typecodesr_  rn  rr  r   r   r
   r   r   rt  r  r{  r~  ).0rc   s   00r5   rB  rB    s    %"- [[W1vBx&HI	  J	 "$J [[UU0CCR0H %71() &' %7 8@8@B" [[TC

GR\\#RS	C T	C	#7A%7s   $C
rB  c                 z    t        |       }|rt        |      }t        ||       }t        ||      }t        ||      S )N)r	   r   r   r   )rZ   rb   cmplxata1b1s         r5   direct_lstsqr    s9    	1Br]	RB	RBR=r7   c            	       b   e Zd ZdZd Zd Zd Zd Zej                  j                  de      ej                  j                  dd      ej                  j                  d	e      ej                  j                  d
d      d                             Zej                  j                  ed      ej                  j                  de      ej                  j                  dd      ej                  j                  d	e      ej                  j                  d
d      d                                    Zd Zd Zd Zd Zej                  j                  deeej0                  eej4                  g      ej                  j                  deeej0                  eej4                  g      d               Zy)	TestLstsq)gelsdgelssgelsyNc                    t         D ]  }t        j                  ddgddgg|      }t        j                  D ]  }dD ]  }dD ]  }|j                         }t        j                  ||      }|j                         }t        |||||      }	|	d	   }
|	d
   }t        |d
k(  d|        t        t        ||
      |dt        |j                        z  dt        |j                        z  d|            y )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  s     	LE1b'C8,E:A!*!9!9 L!. LI3 L VVXHHRu5VVX#B2?0909;  FFQ"A! EG'Aq	1-/)BHH2E-E-/)BHH2E-E2:=/0JLLLL	Lr7   c                     t         D ]  }t        j                  ddgddgddgg|      }t        j                  g d|      }t        j                  D ]4  }dD ]+  }|j                         }|j                         }t        |||||	      }|d
   }	|dk(  r+t        j                  ||j                  |	      z
  dz        }
n|d   }
|d   }t        |dk(  d|        t        t        t        ||	      |z
  dz        j                  d
      |
dt        |j                        z  dt        |j                        z  d|        t        |	ddt        |j                        z  dt        |j                        z  d|        . 7  y )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E1a&1a&1a&1?A%0A!*!9!9 H!. HIBBBm,5,57C AA$/$&FFAaL1+<$=	$'F	AAAF&EaS$IJ#CQQ(:$;$?$?Q$?$G$-)+i.A)A)+i.A)A.6}o,F	H
 $A'M)+i.A)A)+i.A)A.6}o,FH'HH	Hr7   c                 @   t         D ]  }t        j                  ddgddgddgg|      }t        j                  g d|      }t        j                  D ]D  }dD ];  }|j                         }|j                         }t        |||||	      }|d
   }	|dk(  r;||j                  |	      z
  }
t        j                  |
|
j                         z        }n|d   }|d   }t        |dk(  d|        t        t        t        ||	      |z
  dz        j                  d
      |dt        |j                        z  dt        |j                        z  d|        t        |	ddt        |j                        z  dt        |j                        z  d|        > G  y )Nr  rC   r@   r   rR   r   )rD   r   rR   r  r  r   r  rD   r  r  r  r  r  )yu{޿E(B?yӽu{?(YJV?)COMPLEX_DTYPESr,   r   r  r  r  r   r   r  rA  r   r   r-  r6   r   )rY   r   rZ   rb   r  r  r  r  r  rc   r  r  r"  s                r5   test_simple_overdet_complexz%TestLstsq.test_simple_overdet_complex  s   # 	DE4)aVaV4EBAU3A!*!9!9 D!. DIBBBm,5,57C AA$/!%%(l$&FF3+;$<	$'F	AAAF&EaS$IJ#CQQ(:$;$?$?Q$?$G$-)+i.A)A)+i.A)A.6}o,F	H
 $ ! $L%')BHH*=%=%')BHH*=%=*2=/(BD+DD	Dr7   c                    t         D ]  }t        j                  g dg dg|      }t        j                  ddg|      }t        j                  D ]  }dD ]  }|j                         }|j                         }t        |||||      }|d   }	|d   }
t        |
dk(  d	|
        t        |	d
dt        |j                        z  dt        |j                        z  d|           y )Nr   r  r   rD   rC   r  r  r   r  )gqqgqq?gdq?r  r  r  )r  r,   r   r  r  r  r   r   r   r6   r   )rY   r   rZ   rb   r  r  r  r  r  rc   r"  s              r5   test_simple_underdetzTestLstsq.test_simple_underdet  s      	HE)Y/u=A!Qu-A!*!9!9 H!. HIBBBm,5,57C AAAAAF&EaS$IJ#A (;)+i.A)A)+i.A)A.6}o,F	HHH	Hr7   r   r  )r=   rh  r  r  r  c           
      2   t         j                  j                  d      }t        j                  |j                  ||g      |      }t	        |      D ]  }dd|||f   z   z  |||f<    t	        d      D ]  }t        j                  |j                  |dg      |      }|j                         }	|j                         }
t        |	|
|||      }|d   }|d	   }t        ||k(  d
| d|        |t         j                  u rJt        t        ||      |dt        |	j                        z  dt        |	j                        z  d|        t        t        ||      |dt        |	j                        z  dt        |	j                        z  d|        " y )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   
 ii##D)JJszz1a&)7q 	+AC!AqD'M*AadG	+q 	>A

3::q!f-U;ABBB&3$-$-/C AAAAAF6qc :#  

"a)Q"Yrxx%88"Yrxx%88$,]O"<	>  a)Q#i&99#i&99$,]O"<	>)	>r7   z$may segfault on Alpine, see gh-17630rq  c           
      `   t         j                  j                  d      }t        j                  |j                  ||g      d|j                  ||g      z  z   |      }t	        |      D ]  }dd|||f   z   z  |||f<    t	        d      D ]  }t        j                  |j                  |dg      |      }|j                         }	|j                         }
t        |	|
|||      }|d	   }|d   }t        ||k(  d
| d|        |t         j                  u rJt        t        ||      |dt        |	j                        z  dt        |	j                        z  d|        t        t        ||      |dt        |	j                        z  dt        |	j                        z  d|        " y )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    ii##D)JJszz1a&)Bszz1a&/A,AA"$q 	+AC!AqD'M*AadG	+q 	>A

3::q!f-U;ABBBm$-$-/C AAAAAF6qc :#  $a)Q"Yrxx%88"Yrxx%88$,]O"<	>  a)Q#i&99#i&99$,]O"<	>'	>r7   c                    t         j                  j                  d      }t        D ]K  }dD ]B  \  }}t        j
                  D ](  }dD ]  }t        j                  |j                  ||g      |      }t        |      D ]  }dd|||f   z   z  |||f<    t        d      D ]  }t        j                  |j                  |dg      |      }	|j                         }
|	j                         }t        |
||||	      }|d
   }|d   }t        ||k(  d| d|        t        |t        ||	d
      dt        |
j                        z  dt        |
j                        z  d|         " + E N y )Nr  )r=      )rh  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   ii##D)  	NE. NA%.%=%= NM%2 N	JJszz1a&'9G!&q ;A&(C!AqD'M&:AadG;!&q NA "

3::q!f+=U KA!"B!"B"'B6C4=4=#?C !$AA #AA#AF.Fqc J++,#-/ 0+*+\!Qa-H/1Ibhh4G/G/1Ibhh4G/G4<]O2L	NN	NNN	Nr7   c                    t         j                  j                  d      }t        D ]b  }dD ]Y  \  }}t        j
                  D ]?  }dD ]6  }t        j                  |j                  ||g      d|j                  ||g      z  z   |      }t        |      D ]  }dd|||f   z   z  |||f<    t        d      D ]  }t        j                  |j                  |d	g      |      }	|j                         }
|	j                         }t        |
||||
      }|d   }|d   }t        ||k(  d| d|        t        |t        ||	d      dt        |
j                        z  dt        |
j                        z  d|         9 B \ e y )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   ii##D)# 	JE. JA%.%=%= JM%2 J	JJszz1a&'9Bszz1a&?Q<Q'Q-24!&q ;A&(C!AqD'M&:AadG;!&q JA "

3::q!f+=U KA "#B!"B"'B6C4=4=#?C !$AA #AA#AF.Fqc J++,#-/ 0+&'a!)D+-	"((0C+C+-	"((0C+C08.H	JJJJJ	Jr7   c           
         t        j                         5  t        j                  ddt               d d d        t	        j
                  d      }t        j                  t        dt        j                  dd      D ]  \  }}}}}|j                  |      }t	        j
                  ||      }|j                         }	|j                         }
t        |	|
||||      }|d   }|d	   }t        |d	k(  d
|        t        t!        ||      |dt#        |j$                        z  dt#        |j$                        z  d|         y # 1 sw Y   xY w)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  sF   $$& 	W##H%FGUW	W XX)*kL'66++	-	@=E2}i 		% A5)A BBBm%1y$-/C AAAAAF=aSABC1Iq!#i&8!8!#i&8!8&.}o$>@'	@	W 	Ws   EEc           
         dD ]  \  }}t        j                  |      }t        t        j                  |      |      \  }}}}t	        |t        j                  |d   f|dd  z                |d   rt        j
                  d      n#t         j                  j                  |d      dz  }t	        ||       t        |dk(  d       t	        |t        j
                  d              y )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BHHgaj]WQR[%@AB4;AJ"((4.')yy~~aa~'@!'C #56DAI01BHHTN+	,r7   r  r   c                 L   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 y r  )r,   r   r   r\  r   r   r   )
rY   r  r   rZ   rb   rc   r  r  r  r  s
             r5   rt  zTestLstsq.test_empty_dtype  s     HHV4(HHQd#$Q{8T1vv{{BFF1D12771D3IJ1MSSww+%%%r7   N)r   r   r   r  r  r  r  r  r   r   r   r  r  r  r&   r  r  r  r  rv   r   r   r   r,   r
   r   r   rt  r   r7   r5   r  r    s   6NL2H:DBH, [[Wk2[[S),[[_n=[[[-8> 9 > - 3>@ [[(NO[[Wn5[[S),[[_n=[[[-8> 9 > - 6 P
>@N8J<@@, [[Vc5"**gr||%TU[[Vc5"**gr||%TU& V V&r7   r  c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	eej                   eej$                  g      d
        Zy)TestPinvc                     t        g dg dg dgt              }t        |      }t        t	        ||      t        j                  d             y Nr   r  r  r   rR   r   r   r   r   r   r,   r   rY   rZ   a_pinvs      r5   test_simple_realzTestPinv.test_simple_real  s6    9i4E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	             y 
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[    Iy*5
Iy'I-2"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        ||       y )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  sD    9i35AaLKKM N 	"&(3r7   c                     t        g dg dgt              }t        |      }t        ddgddgdd	gg      }t        ||       y )
Nr   r  r   g֋8g#q?g#qg#q?gIq?g#q̿r  r  s       r5   test_simple_colszTestPinv.test_simple_cols  sN    9i(6a;
3&
3%{35 6 	"&(3r7   c                     t        ddgddgddggt              }t        |      }t        g dg d	g      }t        ||       y )
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  sK    Aq6Aq6Aq6*%8a@?A B!&(3r7   c                     t        g dg dg dg      }t        |d      }t        t        ||      t	        j
                  d             y )Nr   )r@   r   r   r  Frt   rR   )r   r   r   r   r,   r   r  s      r5   rv   zTestPinv.test_check_finite  s7    9j*56ae,!#a."&&)<r7   c                 p    g dg dg dg}t        |      }t        g dg dg dg      }t        ||       y )Nr   r  r  r  r  r  )r   r   r   r  s       r5   test_native_list_argumentz"TestPinv.test_native_list_argument  s=    	9-aLKKM N 	"&(3r7   c                    t         j                  j                  d      }d}t        |j                  ||f            \  }}t        j                  d      j                  dd      }|j                         }d|d<   d}d	}t        ||d
      }	||	z  |z  |z
  }
||	z  |z  |z
  }t        t         j                  j                  |
      dd       t        t         j                  j                  |      dd       t        |||      }	||	z  |z  |z
  }
||	z  |z  |z
  }t        t         j                  j                  |
      dd       t        t         j                  j                  |      dd       y )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:   ii##D)#**aV$%1iio%%a+HHJ$ 3T+S1qsS3& 			v.5A		v.FC 3T-S1qsS3&		v.DA		v.DAr7   r4   c                     t        j                  d|      }t        |      }|j                  dk(  sJ |j                  t        t        j
                  d|            j                  k(  sJ y r  )r,   r   r   r\  r   r   rY   r4   rZ   r  s       r5   r   zTestPinv.test_empty  sU    HHV2&a{{a||tBFF1B$7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    sb    =
=444=
4B8 [[TE2::w#MN? O?r7   r  c                       e Zd Zd Zd Zd Zd Zd Zd Ze	j                  j                  deej                  eej                   g      d        Zy	)
TestPinvSymmetricc                     t        g dg dg dgt              }t        j                  ||j                        }t        |      }t        t        j                  ||      t        j                  d             y r  )r   r   r,   r   r:  r   r   r   r  s      r5   r  z"TestPinvSymmetric.test_simple_real  sN    9i4EBFF1accNq!"&&F"3RVVAY?r7   c                 N   t        g dg dg dgt              }t        j                  ||j                        }t        j
                  j                  |      \  }}}|dxx   dz  cc<   t        j                  ||z  |      }t        |      }t        |      }t        ||       y )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}    9i35AFF1accN99==#1b	!
FF1q5"a(!&'2r7   c                 L   t        g dg dg dgt              dt        g dg dg dgt              z  z   }t        j                  ||j	                         j
                        }t        |      }t        t        j                  ||      t        j                  d	             y r  )	r   r   r,   r   rA  r:  r   r   r   r  s      r5   r   z%TestPinvSymmetric.test_simple_complex'  sz    Iy*5
Iy'I-2"4 44 FF1affhjj!q!"&&F"3RVVAY?r7   c                    t        g dg dg dgt              }t        j                  ||j                        }t        |j                               }t        t        j                  ||      t        j                  d             y r  )	r   r   r,   r   r:  r   tolistr   r   r  s      r5   r  z+TestPinvSymmetric.test_native_list_argument/  sU    9i4EBFF1accNqxxz"!"&&F"3RVVAY?r7   c                     t        j                  g dg dg dg      }t        |      }t        ||z  |z  |d       t        ||z  |z  |d       y )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  sJ     HHj+z:;!HA	151A	151r7   c                    t         j                  j                  d      }d}t        |j                  ||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       y )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=  sD   ii##D)#**aV$%1GG2gY!_DECC!GaKgg/2$!*<=ccCi!m!ADr*S1qsS3& 	Vd5Ve%8 ADt,S1qsS3&Vd5Vd5r7   r4   c                     t        j                  d|      }t        |      }|j                  dk(  sJ |j                  t        t        j                  d|            j                  k(  sJ y r  )r,   r   r   r\  r   r   r   r  s       r5   r   zTestPinvSymmetric.test_emptyY  sU    HHV2&q{{a||tBFF1B$78>>>>>r7   N)r   r   r   r  r  r   r  r  r  r   r   r   r   r,   r
   r   r   r   r   r7   r5   r  r    sZ    @3@@268 [[TE2::w#MN? O?r7   r  scale)r  r<   r  pinv_c                     t        j                  ddgddgg      | z  }t        j                  dt        j                  |      z        } ||      }t        ||       y )NrD   r   g|=r<   )r,   r   rn   r   )r   r  rc   r   x_invs        r5   test_auto_rcondr  a  sQ     	1a&1e*%&.AwwrBGGAJ'H!HEE8$r7   c                   x    e Zd Zd Zd Zd Zd Zd Zd Ze	j                  j                  e d      d	        Zy
)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      |        y )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  s   \\*- 	?E%0AeRXXe_0055:;CDGRWWR[s;DAJ#>		? \\), 	?EU3AeRXXe_0055:;CDGRWWR[s;DAJ#>		?r7   c                 R    t        dgt              }t        t        |      |       y )Nr  r   )r   r
   r   r   rv  s     r5   test_overflowzTestVectorNorms.test_overflowy  s      4&(DGQ'r7   c                     t        dgdgdz  z   t              }	 t        t        |      dz
  dd       y # t        $ r d}t        t        |      dz
  d	|
       Y y w xY w)N     @rD   i'  r   r   r  r  zO: Result should equal either 0.0 or 0.5 (depending on implementation of snrm2).rJ   )r  )r   r
   r   r   AssertionErrorr   )rY   rZ   rk  s      r5   test_stablezTestVectorNorms.test_stable  sc    3%1#e)#73	A DGcM3T: 	A.CQ#sC@		As   6 %AAc                 d    t        t        g dd      d       t        t        g dd      d       y )N)rD   r   rR   r   rC   r   rR   )r   r   rz  s    r5   test_zero_normzTestVectorNorms.test_zero_norm  s$    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         y )
NrC   rD   rR   r@   ra  r  5D+@6f~@rx  )r,   r   r   r   rv  s     r5   test_axis_kwdzTestVectorNorms.test_axis_kwd  sc    HH1v1v&'!+S1QQ:z*B)Ca)G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         y )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    HH1v1v&'!+S1T*j*567!;<9$%QD9bTB4L>A;MNr7   z64-bit BLAS requiredrq  c                     t        d       t        j                  dgt        j                        }d|d<   t	        |      }~t        |d       y )NihB  )free_mbl        r   rD   rF   r<   )r%   r,   r   r.   r   r   )rY   rc   r  s      r5   test_large_vectorz!TestVectorNorms.test_large_vector  s?    %(HHeWBJJ/"1gS!r7   N)r   r   r   r  r  r  r  r  r  r   r   r  r'   r  r   r7   r5   r  r  j  sN    ?(A,<
O [[I.DE" F"r7   r  c                   $    e Zd Zd Zd Zd Zd Zy)TestMatrixNormsc           
      v   t         j                  j                  d      }dD ]  \  }}t         j                  t         j                  t         j
                  t         j                  t         j                  fD ]=  }d|j                  ||f      j                  |      z  }t        j                  |j                  t         j                        r*|d|j                  ||f      z  z  }t         j                  }nt         j                  }d ddddd	t         j                  t         j                   fD ]  }t        ||
      }t         j                  j                  ||
      }	t        j                   ||	      rHt         j                  j                  |j                  |      |
      }	t#        ||	        @  y )Nr  )rl   )rD   rR   )rR   rD   r  rK  )r   r@   rF  y              $@frorD   rF   rC   r  )ord)r,   r  r  r
   r.   r   r0   int64r  rt  r  r   r  r}  r   r  r3  r   )
rY   r  r  r  rm  r  t_highr  actualdesireds
             r5   test_matrix_normsz!TestMatrixNorms.test_matrix_norms  sH   ii##D)B 	9DAqZZR\\2=="((R 9,,aV4;;A>>=="*<*<=s22Aq6:::A]]FZZF"E1b!R"&&I 9E!!/F iinnQEn:G ;;vw7"$))..&1Au."M'8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(  xr |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(  xr |j                  k(         y c        y )
NrC   rD   rR   r@   ra  r  )r$  r  r   r   )r,   r   r   r}  swapaxesr   r   r   )rY   rZ   rb   rl  ra  s        r5   r  zTestMatrixNorms.test_axis_kwd  s   HH1v1v&'!+S1V,Q1%266?'111177-agg-.'Q1%16:V,111177-agg-.-.r7   c                 
   t        j                  dd      j                  dddd      }t        |t         j                  dd	
      }t        |ddd	
      }t        ||       t        |j                  |j                  k(         y )Nx   ra  r   rC   rR   r@   r   r  T)r$  r  r  rD   r   )r,   r   rW   r   r}  r   r   r   )rY   rZ   rb   rl  s       r5   r  z!TestMatrixNorms.test_keepdims_kwd  sf    IIc%--aAq9Vd;61177"#r7   c                    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             y )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    HHVQ$QQ$8Q.0@AHHVQ$QQ$8Q.0@Ar7   N)r   r   r   r)  r  r  r   r   r7   r5   r!  r!    s    9(/"$	Br7   r!  c                   B    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zy
)TestOverwritec                 (    t        t        ddg       y Nr  r5  )r$   r   rz  s    r5   
test_solvezTestOverwrite.test_solve      EFD>2r7   c                 (    t        t        ddg       y r2  )r$   r   rz  s    r5   test_solve_triangularz#TestOverwrite.test_solve_triangular  s    ,vtn=r7   c                 "    t        d ddg       y )Nc                     t        d| |      S )NrN   )r   )r[   rb   s     r5   <lambda>z1TestOverwrite.test_solve_banded.<locals>.<lambda>  s    ,vr1*E r7   )r@   rA   rA   r#   rz  s    r5   test_solve_bandedzTestOverwrite.test_solve_banded  s    E#TN	,r7   c                 (    t        t        ddg       y )Nr  r:  )r$   r   rz  s    r5   test_solveh_bandedz TestOverwrite.test_solveh_banded  s    MFD>:r7   c                 &    t        t        dg       y Nr  )r$   r   rz  s    r5   test_invzTestOverwrite.test_inv      C&*r7   c                 &    t        t        dg       y r?  )r$   r   rz  s    r5   test_detzTestOverwrite.test_det  rA  r7   c                 (    t        t        ddg       y )N)rR   rC   r5  )r$   r   rz  s    r5   
test_lstsqzTestOverwrite.test_lstsq  r4  r7   c                 &    t        t        dg       y r?  )r$   r   rz  s    r5   	test_pinvzTestOverwrite.test_pinv  s    D6(+r7   c                 &    t        t        dg       y r?  )r$   r   rz  s    r5   
test_pinvhzTestOverwrite.test_pinvh  s    EF8,r7   N)r   r   r   r3  r6  r;  r=  r@  rC  rE  rG  rI  r   r7   r5   r0  r0    s/    3>,;++3,-r7   r0  c            	       "   e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	eeej"                  eej&                  g      ej                  j                  d
eeej"                  eej&                  g      d               Zy)TestSolveCirculantc                     t        j                  g d      }t        j                  g d      }t        ||      }t        t	        |      |      }t        ||       y N)rD   rC   rR   r   )rD   rF   rD   r   )r,   r   r   r   r   r   rY   rl  rb   rc   r"  s        r5   test_basic1zTestSolveCirculant.test_basic1 	  sD    HH\"HH]#Aq!)A,"1r7   c                     t        j                  g d      }t        j                  d      j                  dd      }t	        ||      }t        t        |      |      }t        ||       y )NrD   rC   r	  rk  r@   rR   r,   r   r   rW   r   r   r   r   rN  s        r5   test_basic2zTestSolveCirculant.test_basic2	  sP    HH^$IIbM!!!Q'Aq!)A,"1r7   c                 *   t        j                  g d      }t        j                  d      j                  ddd      }t	        ||      }t        t        |      |j                  dd            j                  |j                        }t        ||       y )NrQ  r  r@   rR   rC   rF   )	r,   r   r   rW   r   r   r   r   r   rN  s        r5   test_basic3zTestSolveCirculant.test_basic3	  sl    HH^$IIbM!!!Q*Aq!)A,		!R 0199!''B1r7   c                     t        j                  g d      }t        j                  d      j                  dd      dz   }t	        ||      }t        t        |      |      }t        ||       y )N)r  rR  r   r   r  r@   rC   y              ?rS  rN  s        r5   rj   zTestSolveCirculant.test_complex	  sV    HH&'IIaL  A&-Aq!)A,"1r7   c                     t         j                  j                  d      }|j                  d      }|j                  d      }t	        ||      }t        t        |      |      }t        ||       y )Ni1  rZ  )r,   r  r  r  r   r   r   r   )rY   r  rl  rb   rc   r"  s         r5   test_random_b_and_cz&TestSolveCirculant.test_random_b_and_c	  s\    ii##E*##Aq!)A,"1r7   c                     t        j                  g d      }t        j                  g d      }t        ||d      }t        t	        |      |      \  }}}}t        ||       t        t        t        ||       y )NrD   rD   r   r   )rD   rC   rR   r@   r   )re  )r,   r   r   r   r   r   rz   r   )rY   rl  rb   rc   r"  r  rnkr  s           r5   r  z TestSolveCirculant.test_singular(	  s\    HH\"HH\"Aq73y|Q/3Q1k?Aq9r7   c                    t        j                  g dgg dgg      }t        j                  g dg dg dg      }t        ||d      }t        |j                  d       t        j
                  |      }t        t        |d	   j                               |j                        |d d d	d d f<   t        t        |d   j                               |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        ||       y )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   rl  rb   rc   r   s        r5   test_axis_argsz!TestSolveCirculant.test_axis_args1	  s+    HH()N+;<= HHlL-@AAq*QWWi(==#!)AaDJJL"9133?Aq!)AaDJJL"9133?Aq8$Aq26QWWi(Ar1-x8 BKK1a0!##Q?QWWi(8$r7   c                 n    g d}g d}t        ||      }t        t        |      |      }t        ||       y rM  )r   r   r   r   rN  s        r5   r   z-TestSolveCirculant.test_native_list_argumentsJ	  s2    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 y )Nr   r   rR   r   )r,   r   r   r   r   r   r   r   )rY   re  r   rl  rb   rc   x1s          r5   r   zTestSolveCirculant.test_emptyR	  s     HHRt$HHRt$Aq!ww$ww/"))AT*B*,''!4*@BBG%H 	H H HHV4(Q"xx6!!!xx177"""r7   N)r   r   r   rO  rT  rV  rj   rY  r  rc  r   r   r   r   r   r   r,   r
   r   r   r   r   r7   r5   rK  rK    s    :%2 [[Vc5"**gr||%TU[[Vc5"**gr||%TU# V V#r7   rK  c                       e Zd Zed        Zd Zd Zd Zd Zd Z	d Z
ej                  j                  deeej"                  eej&                  g      d	        Zy
)TestMatrix_Balancec                 .    t        t        t        d       y )NzSome string for fail)rz   r{   r    rz  s    r5   test_string_argz"TestMatrix_Balance.test_string_argc	  s    j.2H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             y )NrD   rC   rR   )rz   r{   r    r,   r   r}  r!  rz  s    r5   test_infnan_argz"TestMatrix_Balance.test_infnan_argg	  sT    j.hhABFF45	7j.hhABFF45	7r7   c           	          t        t        j                  ddgddgg            \  }}t        t        j                  t        j
                  t        j                  |                  dg       y )Nr  rD   r   r   )r    r,   r   r   difflog2rn   )rY   r  r"  s      r5   test_scalingzTestMatrix_Balance.test_scalingm	  sN    bhhq	D!9'=>?1 	
 34qc:r7   c                     t        j                  g dg dg dg      }t        |      \  }}t        t	        ||      j                  |      |       y )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>    HHlL-@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             y )Nr  rD   r   separater   rC   )r    r,   r   r   ro  rp  r   r   )rY   r  r"  zs       r5   test_separatez TestMatrix_Balance.test_separatey	  s^    "288dAYq	,B#C,-/	6AqRWWRWWQZ(1#.299Q<(r7   c                 \   t        t        j                  d      t        j                  t        j                  d            t        j                  d            }t	        |d      \  }\  }}t        |t        j                  |             t        |t        j                  g d             y )Nr  r  rD   ru  )r   rD   rA   r   r@   rR   rC   )r   r,   r   rJ  r    r   	ones_liker   )rY   r  rc   r"  rw  s        r5   test_permutationz#TestMatrix_Balance.test_permutation	  sn    rwwv(@wwv("1q1	6Aq2<<?+288$9:;r7   c           	      (   t        j                  g dg dg dg dg dg      t        j                  g dg dg dg dg      t        j                  g d	g d
g dg dg      f}|D ]  }t        |      \  }}t        |d      \  }\  }}t        j                  |      }t        j                  |j
                  d         ||<   t        |t        j                  |      |d d f          t        t        ||      j                  |      |        y )N)rJ   rJ   rJ   rJ   >)rJ   rJ   rJ   rJ   rJ   )rQ   rQ   rJ   rJ   rJ   )rJ   rJ   r}  rJ   rJ   )r  rJ   rJ   rJ   )rJ   rO  rJ   rJ   )r<   rJ   r  rJ   )rJ   r<   rJ   rO  )r  rJ   r<   rJ   )rO  rO         r<   )r  r~  r~  rJ   )rO  r~  r<   rO  rD   ru  r   )
r,   r   r    ra  r   r   r   rn   r   r   )rY   casesr  rc   r"  r  r  ips           r5   test_perm_and_scalingz(TestMatrix_Balance.test_perm_and_scaling	  s     5///5	7 8 -,-,. /
 ,...0 1$  	3A!!$DAq&q15IAv1q!BIIaggaj)BqEArwwqz"a%01E!QKOOA.2	3r7   r4   c                    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 y )Nr   r   r   rC   Tru  )r,   r   r    r\  r   r   )rY   r4   rZ   rb   rm  b_nt_nr   permscale_nperm_ns              r5   r   zTestMatrix_Balance.test_empty	  s"   HHV2&a 1vv{{vv{{!"&&""56Sww#))###ww#))###)!d;=E4vv{{zzQyyA~~!/D!Agvww#))###{{gmm+++zzV\\)))r7   N)r   r   r   r(   rk  rm  rq  rs  rx  r{  r  r   r   r   r   r   r,   r
   r   r   r   r   r7   r5   ri  ri  b	  sm    J J7;/
)<38 [[TC

GR\\#RS* T*r7   ri  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!  r0  rK  ri  r   r7   r5   <module>r     s       / /  *= = = = =
 8 < ' .zz2::r}}5,,r~~>	~	% #KK33mT*]E,BBG 
cV cVLIV IVX
^	0 ^	0BOJ OJd`( `(F	T Tnj& j&Z	R? R?jH? H?V "344-0% 1 5%9" 9"x7B 7Bt- -<a# a#HT* T*r7   