
    xf%                     p   d Z ddlZddlZddlZddl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Zddl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Zddlm Z  d Z! G d	 d
      Z" G d d      Z# G d d      Z$ G d d      Z% G d d      Z& G d d      Z'd Z(d Z)d Z* G d d      Z+ G d d      Z,y)z, Test functions for linalg.matfuncs module

    N)arrayidentitydotsqrt)assert_array_almost_equalassert_allcloseassert_assert_array_lessassert_array_equalassert_warns)
funmsignmlogmsqrtmfractional_matrix_powerexpmexpm_frechet	expm_condnorm
khatri_rao)_matfuncs_inv_ssq)minimizec                  T    t        j                  g dg dg dg dgt              } | S )aW  
    Return the test matrix from Experiment (1) of [1]_.

    References
    ----------
    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2012)
           "Improved Inverse Scaling and Squaring Algorithms
           for the Matrix Logarithm."
           SIAM Journal on Scientific Computing, 34 (4). C152-C169.
           ISSN 1095-7197

    )g3d?     L@r   r   )r   gRal!A?r   r   )r   r   gQI?r   )r   r   r   g^?dtype)npr   float)As    B/usr/lib/python3/dist-packages/scipy/linalg/tests/test_matfuncs.py%_get_al_mohy_higham_2012_experiment_1r!      s/     	" 	 &+		,A
 H    c                   $    e Zd Zd Zd Zd Zd Zy)	TestSignMc                     t        g dg dg dg dg dg      }t        g dg dg dg d	g d
g      }t        |      }t        ||       y )Ng333333=@g3333338g     `Q@gfffffH@g      @gffffff"g@      2g0       g      $g      @g      4r(   r)   g333333#g333333#@g     9g.r)   g#@g333333g      2@g3333332@       @)g'@'Rqgy.@ge@5@r.   )g@ȽUЛ'?g9\g+%r/   )gRQQ?gGzgffffffr0   )gר#w?î?gk#egC,Nr1   )g@42
gF(@gcs@@r2   )r   r   r   )selfacrrs       r    	test_nilszTestSignM.test_nils0   sW    00.1-	/ 0
 QO0ON	P Q
 !H!!B'r"   c                 L    t        g dg dg dg dg      }t        |d       y )N)           r   r   )r:   r   r:   r   r   r   r   r:   )r   r   r:   r   Fdispr   r   r3   r4   s     r    test_defective1zTestSignM.test_defective1>   s    ;y9=>aer"   c                 R    t        g dg dg dg dg df      }t        |d       y )Nr&   r'   r*   r+   r,   Fr<   r>   r?   s     r    test_defective2zTestSignM.test_defective2C   s,    &'('$& ' 	aer"   c           
      ^    t        g dg dg dg dg dg dg dg      }t        |d	       y )
Nr)         9@r9   r9   r9   r9   r9   r9               $@      @rI   rI   r9   r9   r9   r-         .@rI   rI   r9   r9   r9   r9   r9   rK   rI   r9   r9   r9   r9   r9   rI   rH   r9   r9   r9   r9   r9   r9   r)   rE   r9   r9   r9   r9   r9   r9   rG   Fr<   r>   r?   s     r    test_defective3zTestSignM.test_defective3M   s2    11000102 3 	aer"   N)__name__
__module____qualname__r7   r@   rB   rP    r"   r    r$   r$   .   s    (
r"   r$   c                   N    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y)TestLogMc           
          t        g dg dg dg dg dg dg dg      }t        d      d	z  d
z   |z
  }t        |d       y )NrD   rF   rJ   rL   rM   rN   rO      g@y                Fr<   )r   r   r   )r3   r4   ms      r    r7   zTestLogM.test_nils[   sI    11000102 3 a[_R"QUr"   c                 l    t               }t        |d      \  }}t        |      }t        ||dd       y )NFr<   g-C6
?+=rtolatol)r!   r   r   r   )r3   r   A_logminfoA_round_trips        r    *test_al_mohy_higham_2012_experiment_1_logmz3TestLogM.test_al_mohy_higham_2012_experiment_1_logmg   s3     23AE*F|ad?r"   c                     t               }t        |t        j                  d      \  }}t	        |      }t        t        j                  ||dd              y )NFr<   h㈵>r[   r\   )r!   r   r   logr   r	   allclose)r3   r   
A_funm_logr`   ra   s        r    .test_al_mohy_higham_2012_experiment_1_funm_logz7TestLogM.test_al_mohy_higham_2012_experiment_1_funm_logo   sG     232666
DJ'BKKadGGHr"   c                    t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      }t        j
                  ddd      D ]  }||z  }t         j                  j                  |      }d| d| }t        |d	
      \  }}|j                  |      }	t        |	|       t        |d	
      \  }
}t        |
      }t        |||         y )N  r:         	   zM:z eivals:Fr<   )err_msg)r   randomseedrangerandnlogspacelinalgeigvalsr   r   r   r   r   )r3   n
M_unscaledscaleMWro   M_sqrtmr`   M_sqrtm_round_tripM_logmM_logm_round_trips               r    test_round_trip_random_floatz%TestLogM.test_round_trip_random_floatw   s    
		tq! 	GAA.JRA. G& II%%a(qc!- !&ae 4%,[[%9" 2A6  $AE2$(L! 11gFG	Gr"   c                 |   t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        j
                  ddd      D ].  }||z  }t        |d	      \  }}t        |      }t        ||       0  y 
Nrj   r:   rk                 ?rl   rm   rn   Fr<   )	r   rp   rq   rr   rs   rt   r   r   r   )r3   rw   rx   ry   rz   r~   r`   M_round_trips           r    test_round_trip_random_complexz'TestLogM.test_round_trip_random_complex   s    
		tq! 	1AA.biiooa6K1KKJRA. 1&#AE2#F|a0	1	1r"   c                    d}ddgddggddgddggddgddggddgddggfD ]#  }t         j                  j                  |      }t        t	        d |D                      t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v       t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v        t        j                  |t               }t        |d	      \  }}t        |j                  j                  |v        & y )
NFDGr:   r         c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   Nimagreal.0ws     r    	<genexpr>zFTestLogM.test_logm_type_preservation_and_conversion.<locals>.<genexpr>   $     <QAFF0affqj0<   ')r   Fr<   )scipyru   rv   r	   anyr   r   r   r   r   charcomplex)r3   complex_dtype_charsmatrix_as_listr{   r   r_   r`   s          r    *test_logm_type_preservation_and_conversionz3TestLogM.test_logm_type_preservation_and_conversion   s8    .Q!Q Q!Q Q!Q Q!Q 	" 	>N $$^4A<!<<<= u5A.LFDFLL%%-@@A w7A.LFDFLL%%)<<= .66A.LFDFLL%%)<<=/	>r"   c                    g dg dg dg}t         t        fD ]  }t        j                  ||      }t        j
                  j                  |      }t        dt        j                  |j                        j                         k         t        |d      \  }}t        t        j                  |j                  t        j                               t        t!        |      |        y )N)r:   r:   r   )r   r:   r:   )r:   r   r:   r   {Gz?Fr<   )r   r   r   r   r   ru   rv   r	   absoluter   sumr   
issubdtyper   inexactr   r   )r3   rz   dtXr   Yr`   s          r    test_complex_spectrum_real_logmz(TestLogM.test_complex_spectrum_real_logm   s     	9-. 	(B"%A$$Q'AD2;;qvv.2244515)GAtBMM!''2::67DGQ'	(r"   c                    ddgddggddgddggfD ]q  }t         t        fD ]`  }t        j                  ||      }t	        |d      \  }}t        t        j                  |j                  t        j                               b s y )Nr:   r   r   Fr<   )	r   r   r   r   r   r	   r   r   complexfloating)r3   rz   r   r   r_   r`   s         r    test_real_mixed_sign_spectrumz&TestLogM.test_real_mixed_sign_spectrum   s     Q!R!Q!Q " 	IA Wn IHHQb)#AE2fllB4F4FGHI	Ir"   c                 ,   t        j                  ddgddgg      }t        j                  ddgddgg      }||j                  ||j                  fD ]A  }t        j
                  }t        |t        |d      \  }}t        |      }t        ||d       C y )Nr   r   r:   Fr<   r[   r^   )
r   r   asarrayTr   LogmExactlySingularWarningr   r   r   r   )r3   r   Brz   expected_warningLr`   Es           r    test_exactly_singularzTestLogM.test_exactly_singular   s    HHq!fr2h'(JJAA'(ACCACC 	.A0KK"#3T15IGAtQAAqu-		.r"   c                     t        j                  dgg      }t        j                  }t	        |t
        |d      \  }}t        |      }t        ||d       y )Ng0.++Fr<   r[   r   )r   r   r   LogmNearlySingularWarningr   r   r   r   )r3   rz   r   r   r`   r   s         r    test_nearly_singularzTestLogM.test_nearly_singular   sJ    HHvhZ ,FF/quE4G15)r"   c                    ddgddgg}dt         j                  dz  gt         j                   dz  dgg}t        t        |      |d       t        t	        |      |d       ddgdd	gg}dt         j                  z  dz  d
t         j                  z  gdd	t         j                  z  dz  gg}t        t        |      |d       t        t	        |      |d       ddgdd	gg}dt         j                  z  dz  dgdd	t         j                  z  dz  gg}t        t        |      |d       t        t	        |      |d       y )Nr   r:   r         ?r[   r   r   rm   y             r   )r   pir   r   r   )r3   r   r   s      r    &test_opposite_sign_complex_eigenvaluesz/TestLogM.test_opposite_sign_complex_eigenvalues   s   Vb!Ws^ruufSj!_-Q/Q/!Wq#hhslAbeeG$q#bee)C-&89Q/Q/!Wq#hhslACIcM 23Q/Q/r"   N)rQ   rR   rS   r7   rb   rh   r   r   r   r   r   r   r   r   rT   r"   r    rV   rV   Y   s=    	@IG*1><
(	I.*0r"   rV   c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zy)	TestSqrtMc                 @   t         j                  j                  d       t        dd      D ]p  }t         j                  j	                  ||      }t        j
                  ddd      D ]4  }||z  }t        |d      \  }}|j                  |      }t        ||       6 r y )	Nrj   r:   rk   rl   rm   rn   Fr<   	r   rp   rq   rr   rs   rt   r   r   r   r3   rw   rx   ry   rz   r|   r`   r}   s           r    r   z&TestSqrtM.test_round_trip_random_float   s    
		tq! 	7AA.JRA. 7& %ae 4%,[[%9" 2A6	7	7r"   c                    t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        j
                  ddd      D ]4  }||z  }t        |d	      \  }}|j                  |      }t        ||       6  y r   r   r   s           r    r   z(TestSqrtM.test_round_trip_random_complex   s    
		tq! 	7AA.biiooa6K1KKJRA. 7& %ae 4%,[[%9" 2A6	7	7r"   c                 p   d}t        |      }t        g dd|ddgdd|dgg dg      }t        g dd|ddgdd|dgg dg      }|j                  d   }t        t	        ||      |       t        |d|      d   }t        t	        ||      |       t        |dd      d   }t        t	        ||      |       y )	Ng      ?)      ?r   r   r:   r   r;   )r:   r   r   r   Fr=   	blocksizer   )r   r   shaper   r   r   )r3   eser4   sarw   esas          r    test_badzTestSqrtM.test_bad   s    !W;a!9a!9  Kr!AJqAJ   GGAJ!#b*Q/AEQ/2!#c#,q1AEQ/2!#c#,q1r"   c                    d}ddgddggddgddggddgddggddgddggddgddggfD ]#  }t         j                  j                  |      }t        t	        d |D                      t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v       t        j                  |t              }t        |d	      \  }}t        |j                  j                  |v        t        j                  |t               }t        |d	      \  }}t        |j                  j                  |v        & y )
Nr   r:   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r    r   zHTestSqrtM.test_sqrtm_type_preservation_and_conversion.<locals>.<genexpr>#  r   r   r   Fr<   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r3   r   r   r{   r   A_sqrtmr`   s          r    +test_sqrtm_type_preservation_and_conversionz5TestSqrtM.test_sqrtm_type_preservation_and_conversion  sH    .Q!Q Q!Q Q!Q Q!Q Q!Q " 	?N $$^4A<!<<<= u5A!!%0MGTGMM&&.AAB w7A!!%0MGTGMM&&*==> .66A!!%0MGTGMM&&*==>1	?r"   c                    d}ddgddggddgddggg dg dg dgfD ]  }t         j                  j                  |      }t        t	        d |D                     t        j                  |t        	      }t        |d
      \  }}t        |j                  j                  |v        t        j                  |t        	      }t        |d
      \  }}t        |j                  j                  |v         y )Nr   r:   r   r   r   r:   r   r   r   r:   r:   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r    r   zVTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>=  $     8,!&&1*,8r   r   Fr<   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r   s          r    9test_sqrtm_type_conversion_mixed_sign_or_complex_spectrumzCTestSqrtM.test_sqrtm_type_conversion_mixed_sign_or_complex_spectrum4  s    -Q!R!Q!Q Iy13 	?N $$^4AC8a889 w7A!!%0MGTGMM&&*==> u5A!!%0MGTGMM&&*==>#	?r"   c                    t         j                  j                  d       t        dd      D ]  }t         j                  j	                  ||      dt         j                  j                  ||      z  z   }t        |d|      \  }}t        |t         j                  j                  |d             t        dd      D ]  }t        |d|      \  }}t        ||       !  y )	Nrj   r:      r   Fr   r   
   )
r   rp   rq   rr   randrs   r   r   ru   matrix_power)r3   rw   r   A_sqrtm_defaultr`   r   A_sqrtm_news          r    test_blocksizeszTestSqrtM.test_blocksizesI  s    
		tq! 	>A		q!$r"))//!Q*?'??A$)!%1$E!OTAryy55oqIJ"1b\ >	$)!%9$M!T=>		>r"   c                     t               }t        |d      \  }}|j                  |      }t        ||d       t        t	        j
                  |      t	        j
                  |             y )NFr<   rd   r]   )r!   r   r   r   r   tril)r3   r   r   r`   ra   s        r    %test_al_mohy_higham_2012_experiment_1z/TestSqrtM.test_al_mohy_higham_2012_experiment_1T  sO    13ae,{{7+ad3-rwwqz:r"   c                     t         t        fD ]a  }t        j                  g dg dg dg dg|      }t	        |d      \  }}t        t        j                  |      j                                c y )N)r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r   Fr<   )intr   r   r   r   r	   isnanall)r3   r   r   r   r`   s        r    test_strict_upper_triangularz&TestSqrtM.test_strict_upper_triangular\  se    u* 	-B	 &(	)A
 "!%0MGTBHHW%))+,	-r"   c                 T   t         t        fD ]  }t        j                  g dg dg dg|      }t        j                  g dg dg dg|      }t	        ||j                  |             t        |d      \  }}t        t        j                  |      j                                 y )Nr   r   r   r   r   r   Fr<   )
r   r   r   r   r   r   r   r	   r   r   )r3   r   r   r   B_sqrtmr`   s         r    test_weird_matrixzTestSqrtM.test_weird_matrixg  s    u* 	-B #%&A  #%&A q!%%(+ "!%0MGTBHHW%))+,	-r"   c                     t         j                  j                  d       t         j                  j                  dd      }t	        |d      }t        |j                  |      |       y )Nrj   r   Tr<   )r   rp   rq   r   r   r   r   )r3   r   r   s      r    	test_dispzTestSqrtM.test_dispx  sD    
		tIINN1a !$a!$r"   c                     ddgddgg}ddgddgg}t        t        j                  ||      |d	       t        t        |      |d	       y )
N               @rm   r                       ?      ?r         ?      r[   r   )r   r   r   r   r3   rz   Rs      r    r   z0TestSqrtM.test_opposite_sign_complex_eigenvalues  sL    !Wq#hAYD	"q!ae4a!%0r"   c                 J   t        j                  g dg dg dg dg      }t        j                  t        d      ddt        d      gg dg dt        d      ddt        d      gg      }t        t        j                  ||      |d       t        t        |      |d       y )N)r:   r   r   r:   r   r   r   r[   r   )r   r   r   r   r   r   r   s      r    test_gh4866zTestSqrtM.test_gh4866  s    HHl"""$ % HHtCy!QS	2""Cy!QS	24 5 	q!ae4a!%0r"   c                     t        j                  g d      }t        j                  t        d      ddg      }t        t        j                  ||      |d       t        t        |      |d       y )N)r   r:   r   r   r:   r   r[   r   )r   diagr   r   r   r   r   s      r    test_gh5336zTestSqrtM.test_gh5336  sN    GGIGGT!WaO$q!ae4a!%0r"   c                     t        j                  d      }t        j                  d      }t        t        j                  ||      |d       t        t	        |      |d       y )N)r   r   r[   r   )r   zerosr   r   r   r   s      r    test_gh7839zTestSqrtM.test_gh7839  sD    HHVHHVq!ae4a!%0r"   c                 l   t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ y Nr   r   r   )r   r   uint8r   r   float16uint16uint32float32uint64float64r3   rz   s     r    -test_data_size_preservation_uint_in_float_outz7TestSqrtM.test_data_size_preservation_uint_in_float_out  s    HHXRXX.Qx~~+++HHXRYY/Qx~~+++HHXRYY/Qx~~+++HHXRYY/Qx~~+++r"   c                 l   t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ y r  )r   r   int8r   r   r  int16int32r  int64r
  r  s     r    ,test_data_size_preservation_int_in_float_outz6TestSqrtM.test_data_size_preservation_int_in_float_out  s    HHXRWW-Qx~~+++HHXRXX.Qx~~+++HHXRXX.Qx~~+++HHXRXX.Qx~~+++r"   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ y )Nr   rm   r   r   )
r   r   r  r   r   	complex64r  r  r  
complex128r  s     r    +test_data_size_preservation_int_in_comp_outz5TestSqrtM.test_data_size_preservation_int_in_comp_out  s    HHq!fq"g&bgg6Qx~~---HHq!fq"g&bhh7Qx~~---HHq!fq"g&bhh7Qx~~---HHq!fq"g&bhh7Qx~~...r"   c                    t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ t        j                  dt         j
                        }t        |      j                  t         j
                  k(  sJ t        j                  dt         j                        }t        |      j                  t         j                  k(  sJ t        t         d      rNt        j                  dt         j                        }t        |      j                  t         j                  k(  sJ y y )Nr  r   float128)	r   r   r  r   r   r  r
  hasattrr  r  s     r    .test_data_size_preservation_float_in_float_outz8TestSqrtM.test_data_size_preservation_float_in_float_out  s    HHXRZZ0Qx~~+++HHXRZZ0Qx~~+++HHXRZZ0Qx~~+++2z"5A8>>R[[000 #r"   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ t        t         d      ret        t         d      rTt        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ y y y )Nr   rm   r   r  r   r  
complex256)r   r   r  r   r   r  r  r
  r  r  r  r  r  s     r    -test_data_size_preservation_float_in_comp_outz7TestSqrtM.test_data_size_preservation_float_in_comp_out  s
   HHq!fq"g&bjj9Qx~~---HHq!fq"g&bjj9Qx~~---HHq!fq"g&bjj9Qx~~...2z"wr<'@1a&1b'*"++>A8>>R]]222 (A"r"   c                    t        j                  ddgddggt         j                        }t        |      j                  t         j
                  k(  sJ t        t         d      rt        j                  ddgddggt         j
                        }t        |      j                  t         j                  k(  sJ t        j                  ddgddggt         j                        }t        |      j                  t         j                  k(  sJ y y )Nr   rm   r   r   r   r  )r   r   r  r   r   r  r  r  r  s     r    ,test_data_size_preservation_comp_in_comp_outz6TestSqrtM.test_data_size_preservation_comp_in_comp_out  s    HHr1g3x(=Qx~~...2|$2q'As8,BMMBA8>>R]]2222q'As8,BMMBA8>>R]]222	 %r"   N)rQ   rR   rS   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r   rT   r"   r    r   r      sf    772*?>?*	>;	--"%1
111	,	,
/	1
33r"   r   c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
ej                  j                  d	
      d        Zd Zy)TestFractionalMatrixPowerc                    t         j                  j                  d       t        dd      D ]  }t        dd      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        j
                  ddd      D ]B  }||z  }t        |d|z        }t         j                  j                  ||      }t        ||       D   y )Nrj   r:      r   rl   rm   rn   
r   rp   rq   rr   rs   rt   r   ru   r   r   r3   prw   rx   ry   rz   M_rootr   s           r    r   z8TestFractionalMatrixPower.test_round_trip_random_complex  s    
		tq! 	5A1a[ 5YY__Q2R"))//!Q:O5OO
[[Q2 5E"U*A4Q!<F#%99#9#9&!#DL#L!4	55	5r"   c                 ~   t         j                  j                  d       t        dd      D ]  }t        dd      D ]~  }t         j                  j	                  ||      }t        j
                  ddd      D ]B  }||z  }t        |d|z        }t         j                  j                  ||      }t        ||       D   y )Nrj   r:   r$  rl   rm   rn   r%  r&  s           r    r   z6TestFractionalMatrixPower.test_round_trip_random_float  s    
 			tq! 	5A1a[ 5YY__Q2
[[Q2 5E"U*A4Q!<F#%99#9#9&!#DL#L!4	55	5r"   c                 J   t         j                  j                  d       dD ]  }t        d      D ]  }t         j                  j	                  ||      dt         j                  j	                  ||      z  z   }t        |d      }t         j                  j                  |d      }t        ||       t        |d      }t         j                  j                  |d      }t        ||       t        |d	      }t         j                  j                  |d
      }t        ||         y )Nrj   )r   r   r$  r   r   皙?r$  gigffffff@   )	r   rp   rq   rr   rs   r   ru   r   r   )r3   rw   irz   M_one_fifthr   r   r   s           r    (test_larger_abs_fractional_matrix_powerszBTestFractionalMatrixPower.test_larger_abs_fractional_matrix_powers  s    
		t 	&A2Y &IIOOAq)BA1F,FF5a=!yy55k1E<0+At4II**;<1%+As3II**;;1%&	&r"   c                 L   t         j                  j                  d       d}t        |      D ]  }t        j                  dd      }t         j                  j                         }t        j                  t        j                  dd            }t         j                  j                  ||      }t        j                  d      r&|dt         j                  j                  ||      z  z   }||z  }t        ||      }t        |d	      \  }}	t        ||z        }
t        ||
        y )
Nrj      r:   r$  rl   )TFr   Fr<   )r   rp   rq   rr   	randrangers   expchoicer   r   r   r   )r3   nsamplesr-  rw   r'  matrix_scaler   A_powerr_   r`   A_power_expm_logms              r    test_random_matrices_and_powersz9TestFractionalMatrixPower.test_random_matrices_and_powers  s     			tx 	8A  A&A		!A 66&"2"22q"9:L		1%A}}]+RYY__Q222L A
 .a3G.LFD $VaZ 0G%67%	8r"   c                    t               }t        |t        j                  d      \  }}t	        |d      \  }}t        j                  |d      }t        |d      }t        ||d       t        ||       t        ||       dD ]_  }t        ||      }t        |d|z        }t        ||d       t        t        j                  |d      t        j                  |d             a y )	NFr<   r   g|=r   )r   g?r:   r   )
r!   r   r   r   r   r   _remainder_matrix_powerr   r   r   )	r3   r   A_funm_sqrtr`   r   A_rem_powerr7  r'  ra   s	            r    r   z?TestFractionalMatrixPower.test_al_mohy_higham_2012_experiment_1&  s    13 !BGG%8Tae,'??3G)!S1W59)-  	EA-a3G27AaC@LL!$7BGGL!4bggamD		Er"   c                 l   t         j                  j                  d       t         j                  j                  d      dt         j                  j                  d      z  z   D ]P  }t	        d      D ]@  }t        j                  ||      }|t        j                  |       z  dz
  }t        ||       B R y )Nrj   r   r   r$  r:   )	r   rp   rq   rs   rr   r   _briggs_helper_functionexp2r   )r3   r4   k
x_observed
x_expecteds        r    test_briggs_helper_functionz5TestFractionalMatrixPower.test_briggs_helper_function:  s    
		t$rBIIOOB,?'?? 	8A1X 8.FFq!L
"''1"+-1

J78	8r"   c                    d}ddgddggddgddggddgddggddgddggfD ]  }t         j                  j                  |      }t        t	        d |D                      dD ]  }t        j                  |t              }t        ||      }t        |j                  j                  |v       t        j                  |t              }t        ||      }t        |j                  j                  |v        t        j                  |t               }t        ||      }t        |j                  j                  |v         ! y )	Nr   r:   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r    r   zRTestFractionalMatrixPower.test_type_preservation_and_conversion.<locals>.<genexpr>P  r   r   333333r+  gffffff
@r   )r   ru   rv   r	   r   r   r   r   r   r   r   r   r3   r   r   r{   r'  r   r7  s          r    %test_type_preservation_and_conversionz?TestFractionalMatrixPower.test_type_preservation_and_conversionB  sA   
 .Q!Q Q!Q Q!Q Q!Q 	" 	CN $$^4A<!<<<= , C HH^591!Q7**2EEF HH^7;1!Q7**.AAB XXnE::1!Q7**.AABC	Cr"   c                    d}ddgddggddgddggg dg dg dgfD ]  }t         j                  j                  |      }t        t	        d |D                     d	D ]  }t        j                  |t        
      }t        ||      }t        |j                  j                  |v        t        j                  |t        
      }t        ||      }t        |j                  j                  |v          y )Nr   r:   r   r   r   r   r   c              3   V   K   | ]!  }|j                   xs |j                  d k   # ywr   r   r   s     r    r   z`TestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrum.<locals>.<genexpr>n  r   r   rG  r   )r   ru   rv   r	   r   r   r   r   r   r   r   r   rJ  s          r    3test_type_conversion_mixed_sign_or_complex_spectrumzMTestFractionalMatrixPower.test_type_conversion_mixed_sign_or_complex_spectrume  s    -Q!R!Q!Q Iy13 	CN $$^4AC8a889 , 
C HH^7;1!Q7**.AAB HH^591!Q7**.AAB
C	Cr"   zToo unstable across LAPACKs.reasonc                 z   ddgddggddgddggddgddggg dg dg dgfD ]  }t         t        fD ]  }t        j                  ||	      }d
D ]:  }t	        ||      }t        t        j                  |      j                                < dD ])  }t	        ||      }t	        |d|z        }t        ||       +   y )Nr   r:   r   r   rk   r   )r   r:   r:   )r   r   r:   r   )gffffffrI  rH  g)r+  gzG?)	r   r   r   r   r   r	   r   r   r   )r3   r   newtyper   r'  r7  ra   s          r    test_singularz'TestFractionalMatrixPower.test_singular~  s     Q!Q Q!Q Q!Q Iz2	4 	5N "7+ 5HH^7;1 5A5a;GBHHW-11345 % 5A5a;G#:7AaC#HL#L!455	5r"   c                     ddgddgg}ddgddgg}t        t        j                  ||      |d	       t        t        |d
      |d	       y )Nr   rm   r   r   r   r   r   r[   r   r   )r   r   r   r   r   s      r    r   z@TestFractionalMatrixPower.test_opposite_sign_complex_eigenvalues  sP    !Wq#hAYD	"q!ae4/37Gr"   N)rQ   rR   rS   r   r   r/  r9  r   rD  rK  rN  pytestmarkxfailrS  r   rT   r"   r    r"  r"    s[    	55&$82E(8!CFC2 [[<=5 >5&Hr"   r"  c                   *    e Zd Zd Zd Zd Zd Zd Zy)TestExpMc                 \    t        ddgddgg      }t        t        |      ddgddgg       y )Nr9   r   r:   )r   r   r   r?   s     r    	test_zerozTestExpM.test_zero  s2    Bq61Q%.!!$q'Aa5!A-8r"   c                 x    t        d      }t        |t        j                  t        j                  gg             y )Nr:   )r   r   r   r   r   )r3   elts     r    test_single_eltzTestExpM.test_single_elt  s&    1gRXXvh/0r"   c                 f    t        j                  d      }t        |      }|j                  dk(  sJ y )Nr   r   r   )r   r   r   size)r3   r   results      r    test_empty_matrix_inputz TestExpM.test_empty_matrix_input  s+    HHVa{{ar"   c                    t         j                  }t        ddgddgg      }|dz  dz   d|z  z  }|dz  dz
  |z  }t        t	        |      t        ||g|dz  |gg             t	        |j                  t         j                              j                  j                  dk(  sJ t	        |j                  t         j                              j                  j                  dk(  sJ y )Nr:   rm   r   r   f)
r   r   r   r   r   astyper  r   r   r  )r3   r   r4   aabbs        r    test_2x2_inputzTestExpM.test_2x2_input  s    DDAq6Aq6"#dQh1dQh\QR2a4*'=!>?AHHR\\*+1166#===AHHRZZ()//44;;;r"   c                    t         j                  }t        j                  ddgddggddgddggddgddggddgddggddgddgggd	      }t        j                  |dz  dz   d
|z  z  |dz  dz
  |z  g|dz  dz
  dz  |z  |dz  dz   d
|z  z  ggdd|d
z  z  z  d|d
z  z  dz  z   d|d
z  z  dz  dd|d
z  z  z  z
  g|d
z  dz  dd|d
z  z  z  z
  dd|d
z  z  z  |d
z  dz  z   ggdd|z  z  |dz  dz  z   dd|z  z  d|dz  z  dz  z   gdd
|z  z  |dz  d
z  z   dd|z  z  d|dz  z  dz  z   ggdd|d
z  z  z  d|dz  z  dz  z   dd|d
z  z  z  d|dz  z  dz  z   gdd|d
z  z  z  d|dz  z  dz  z   dd|d
z  z  z  d|dz  z  dz  z   ggdd
|z  z  d|z  d
z  z   dd
|z  z  d|z  d
z  z   gdd
|z  z  d|z  d
z  z
  dd
|z  z  d|z  d
z  z
  ggg      }t        t	        |      |       y )Nr:   rm   r   r   r$  rl   r   )orderr   rX   r   rk   )r   r   r   r   r   )r3   r   r4   a_ress       r    test_nx2x2_inputzTestExpM.test_nx2x2_input  s   DDHH1v1v&1v2w'1v1v&1v1v&1vBx(	* 25	6 T!VacNQT!VQJ7T!VQJqL1a46AaC.9;qAvJ!Q$z1AadFA:a1a4j3HIqDF1a1f:-q!AqD&z!Q$q&/@ACqsGAqDFNB!Ha1faZ,?@!HQT!VOQ!Wa1faZ-?@BqAvJ!Q$z12qAv;!Q$z3IJ!Q$K1a4
2AqAvJ!Q$z4IJL!Hac1W,b!A#h!Qw.>?qsGQqS!GOQ!Wac1W_=?  	Q'r"   N)rQ   rR   rS   r[  r^  rc  ri  ro  rT   r"   r    rY  rY    s    91 <(r"   rY  c                       e Zd Zd Zd Zd Zd Zej                  j                  ej                  j                  d      d               Zy)	TestExpmFrechetc                    t        j                  g dg dg dg dgt              }t        j                  ddgdd	ggt              }t        j                  d
dgddggt              }t        j                  j                  |      }t        j                  j                  |      d ddd f   }i ddiddifD ]*  }t        ||fi |\  }}t        ||       t        ||       , y )Nr:   r   r   rm   r$  rk   rX   r   r   r   r:   r   r   r   r$  rk   r   r:   r   r$  rk   r   rm   rX   r   methodSPSblockEnlarge)r   r   r   r   ru   r   r   r   )	r3   rz   r   r   expected_expmexpected_frechetkwargsobserved_expmobserved_frechets	            r    test_expm_frechetz!TestExpmFrechet.test_expm_frechet  s    HH	
  HHFF  HHFF  ))!, <<,,Q/AB7HU+h~-FG 	@F.:1a.J6.J+M+M=9,.>?	@r"   c                    t        j                  g dg dg dg dgt              }t        j                  ddgdd	ggt              }t        j                  d
dgddggt              }t        j                  j                  |d      }g d}t        |d d |dd        }|D ]  \  }}t        j                  j                  j                  |   }	t        j                  j                  j                  |   }
d|	|
z   z  }||z  }||z  }||z  }||z  }t        j                  j                  |      }t        j                  j                  |      d ddd f   }t        ||      \  }}t        ||       t        ||        y )Nrs  rt  ru  rv  r   r:   r   r$  rk   r   rm   rX   r   )r:   r   r$  rX   rn            r   r   )r   r   r   r   ru   r   zip_expm_frechetell_table_61r   r   r   )r3   
M_original
A_original
E_originalA_original_norm_1selected_m_listm_neighbor_pairsmambell_aell_btarget_norm_1ry   rz   r   r   rz  r{  r}  r~  s                       r    test_small_norm_expm_frechetz,TestExpmFrechet.test_small_norm_expm_frechet  s   XX	
 
 XXFF 
 XXFF 
 "LL--j!<5s3_QR5HI& 	@FBLL..;;B?ELL..;;B?E55=1M!$55E
"A
"A
"A!LL--a0M$||003BQBF;.:1a.@+M+M=9,.>?	@r"   c           	         t         j                  j                  t         j                  j                  t         j                  j                  t         j                  j
                  f}d}t        |      D ]N  }t        j                  |      }t        j                  d      }t        j                  dd      } |||f      } |||f      }t        j                  j                  |d      }	||	z  }
|
|z  }|
|z  }t        j                  t        j                  ||g      t        j                  t        j                  |      |g      g      }t        j                  j!                  |      }t        j                  j!                  |      d ||d f   }t#        ||      \  }}t%        ||d       t%        ||d	       Q y )
Nd   r   r      ra  r:   gHj>r   gHz>)r   rp   uniformnormalstandard_cauchyexponentialrr   r4  expovariater2  r   ru   r   vstackhstack
zeros_liker   r   r   )r3   rfuncsntestsr-  rfuncr  rw   r  r  r  ry   r   r   rz   rz  r{  r}  r~  s                     r    	test_fuzzzTestExpmFrechet.test_fuzz  s    		!!		  		))		%%	'
 v 	KAMM&)E"..s3M  B'AQqE*JQqE*J % 1 1*a @!$55E
"A
"A				1a&!		2==+Q/02 3A "LL--a0M$||003BQBF;.:1a.@+M+M=tD,.>TJ#	Kr"   c                 <   t        j                  ddgddggt              }t        j                  ddgdd	ggt              }t        j                  j                  |d
       t        ||d      \  }}t        ||d      \  }}t        ||       t        ||       y )Ng]؉??gvP?g^?guÝ?r   gS,?g| @gJt?g~3?r:   rx  rw  ry  )r   r   r   r   ru   r   r   r   )r3   r   r   sps_expmsps_frechetblockEnlarge_expmblockEnlarge_frechets          r    test_problematic_matrixz'TestExpmFrechet.test_problematic_matrix  s    HHZ(Z(   HHZ(Z(   	!Q ,1U!$+2>1^3-//"34%9:r"   zthis test is deliberately slowrO  c                    d}t         j                  j                  ||f      }t         j                  j                  ||f      }t        ||d      \  }}t        ||d      \  }}t	        ||       t	        ||       y )Ni  r  rx  r  ry  )r   rp   r  r   r   )r3   rw   r   r   r  r  r  r  s           r    test_medium_matrixz"TestExpmFrechet.test_medium_matrix0  s     II!!1v!.II!!1v!. ,1U!$+2>1^3-//"34%9:r"   N)rQ   rR   rS   r  r  r  r  rU  rV  slowskipr  rT   r"   r    rq  rq    sS    @.@BK6;$ [[[[=>
; ? 
;r"   rq  c                     t        j                  || j                        }t        |      }||z  ||z  z  }t	        | |z         }t        ||z
        ||z  z  }	|	 S N)r   reshaper   r   r   )
r   A_normr   X_normepsr'  p_normperturbationX_primescaled_relative_errors
             r    _help_expm_cond_searchr  ?  sa    


1aggA!WF7fvo.L1|#$G 1-#>!!!r"   c                     | t         j                  j                  |      t         j                  j                  |       z  z  S r  )r   ru   r   )r   r   s     r    _normalized_liker  H  s0    !!!$u||'8'8';;<<r"   c                 \     | |      } | ||z         }t        ||z
        t        |      z  S r  )r   )re  r   r  r   r  s        r    _relative_errorr  L  s2    	!AL !G!tAw&&r"   c                   V    e Zd Zd Zd Zd Zej                  j                  d        Z	y)TestExpmConditionNumberc                     t         j                  j                  d       t        dd      D ]9  }t         j                  j	                  ||      }t        |      }t        d|       ; y )Nrj   r:   rm   r   )r   rp   rq   rr   rs   r   r
   )r3   rw   r   kappas       r    test_expm_cond_smokez,TestExpmConditionNumber.test_expm_cond_smokeS  sN    
		tq! 	(A		1%AaLEa'	(r"   c                 t    t        j                  g dg dg dg dg      }t        |      }t        d|       y )N)g(gٙBgx@g  =g ZdB)r   gzNV7g@g  2p)r   r   gᙥT g?W[E@)r   r   r   gT!g yhG)r   r   r   r
   )r3   r   r  s      r    test_expm_bad_condition_numberz6TestExpmConditionNumber.test_expm_bad_condition_numberZ  s6    HHI</#	  !$&r"   c                 @   t         j                  j                  d       t        j                  ddd      D ]7  }t        j                  |gg      }t        t        |      t        |             9 t        j                  ddd      D ]7  }t        j                  |gg      }t        t        |      t        |             9 t        d      D ]M  }t         j                  j                  d	d	      }t        t        |      t        j                  |      d
          O y )N90  rm  r$  r  )numr  r   r   r:   r`  )r   rp   rq   linspacer   r   r   absrt   rr   rs   r   )r3   xr   r-  s       r    test_univariatez'TestExpmConditionNumber.test_univariated  s    
		uR+ 	2A1#AIaL#a&1	2 R+ 	2A1#AIaL#a&1	2 r 	@A		1%AIaL"++a.*>?	@r"   c           	         t         j                  j                  d       d}d}t        |      D ]  }t         j                  j	                  dd      }t         j                  j                  ||      }t        j                  j                  |      }t        |      }t        j                  j                  |      }t        |      }	t        j                  t        |||||      }
t        j                  ||z        }t        |
|d      }|j                   } |
|      }|t#        t        j$                  ||j&                        |      z  }t)        t        ||      }t+        || |z         t        d      D ]p  }|t#        t        j                  j
                  |j&                   |      z  }t+        t        |      t        |             t)        t        ||      }t-        ||       r t-        |dd|z  z   |z  |	z          y )	Nr  rd   r   r   r$  zL-BFGS-Br  r:   )r   rp   rq   rr   randintrs   r   ru   r   r   r   	functoolspartialr  onesr   r  r  r  r   r  r   r
   )r3   r  r5  r-  rw   r   r  r   r  r  re  guessoutxoptyoptp_bestp_best_relerrjp_randp_rand_relerrs                       r    test_expm_cond_fuzzz+TestExpmConditionNumber.test_expm_cond_fuzzp  s   
		ux 	HA		!!!Q'A		1%A\\&&q)FQA\\&&q)FaLE !!"8vq&#/AGGAaCLE1eJ7C55DT7D+BJJtQWW,EqIIF+D!V<MMD53;7 1X @/		0I1MMVd6l; /a @!-?	@ ma!C%i3->-FG?	Hr"   N)
rQ   rR   rS   r  r  r  rU  rV  r  r  rT   r"   r    r  r  R  s2    ('
@ [[#H #Hr"   r  c                   $    e Zd Zd Zd Zd Zd Zy)TestKhatriRaoc           
      2   t        t        ddgddgg      t        ddgddgg            }t        |t        dd	gdd
gddgddgg             t        t        j                  ddg      t        j                  ddg            }t        |j
                  d       y )Nr:   r   r   rm   r$  rk   rX   r      r  r            )rm   r   )r   r   r   r   emptyr   r3   r4   bs      r    
test_basiczTestKhatriRao.test_basic  s    uq!fq!f-.q!fq!f-.0 	1eaW&'W&("X&("X%/ 0 	1
 rxxA'1a&)9:177F+r"   c                     t        j                  t              5  t        g dg dg      }t        ddgddgg      }t	        ||       d d d        y # 1 sw Y   y xY w)Nr:   r   r   rm   r$  rk   r:   r   r   rm   rU  raises
ValueErrorr   r   r  s      r    test_number_of_columns_equalityz-TestKhatriRao.test_number_of_columns_equality  s]    ]]:& 	y " #A1v1v  Aq!	 	 	s   /AAc                    t        j                  t              5  t        g d      }t        g d      }t	        ||       d d d        t        j                  t              5  t        g d      }t        g dg dg      }t	        ||       d d d        t        j                  t              5  t        g dg dg      }t        g d      }t	        ||       d d d        y # 1 sw Y   xY w# 1 sw Y   bxY w# 1 sw Y   y xY w)Nr  r  )rX   r   rn   r  r  s      r    test_to_assure_2d_arrayz%TestKhatriRao.test_to_assure_2d_array  s    ]]:& 	i Ai Aq!		 ]]:& 	i A A q!	 ]]:& 	 A i Aq!	 		 		 		 	s#   'C""+C..+C:"C+.C7:Dc                 L   t        ddgddgg      }t        ddgddgg      }t        ||      }t        j                  t	        |j
                  d         D cg c]&  }t        j                  |d d |f   |d d |f         ( c}      j                  }t        ||       y c c}w )	Nr:   r   r   rm   r$  rk   rX   r   )	r   r   r   r  rr   r   kronr   r   )r3   r4   r  res1rA  res2s         r    test_equality_of_two_equationsz,TestKhatriRao.test_equality_of_two_equations  s    Aq6Aq6"#Aq6Aq6"#!Qyy#(#46 ''!AqD'1QT73 6 778q 	 	4&6s   +B!N)rQ   rR   rS   r  r  r  r  rT   r"   r    r  r    s    
,2'r"   r  )-__doc__rp   r  numpyr   r   r   r   r   numpy.testingr   r   r	   r
   r   r   rU  scipy.linalgr   r   r   r   r   r   r   r   r   r   r   r   scipy.linalg._expm_frechetscipy.optimizer   r!   r$   rV   r   r"  rY  rq  r  r  r  r  r  rT   r"   r    <module>r     s       , ,P P  K K K * ! #*' 'VO0 O0dr3 r3jvH vHr-( -(`s; s;l"='BH BHJ7' 7'r"   