+
    Y°³j$U  ã                   ó¨   € R t ^ RIt^ RIt^ RIHtHtHt ^ RIH	t	H
t
HtHtHt ^ RIHtHtHtHt RR lt ! R R4      t ! R R	4      t ! R
 R4      tR# )z4
Unit tests for trust-region iterative subproblem.

N)Ú estimate_smallest_singular_valueÚsingular_leading_submatrixÚIterativeSubproblem)ÚsvdÚget_lapack_funcsÚdetÚqrÚnorm)Úassert_allcloseÚassert_array_equalÚassert_equalÚassert_array_almost_equalc                 ót  € \         P                  P                  V4      pVP                  R^W 3R7      p\	        VRR7      w  p pVP                  WV R7      p\         P
                  ! V4      RRR1,          p\         P                  ! W†4      p	\         P                  ! W–P                  4      p
VR8X  dN   \         P                  ! V 4      pVP                  R^V ^,
          R7      VRR% \         P                  ! Wk4      pW«3# VR8X  d   \         P                  ! V 4      pW«3# VP                  R^V R7      pW«3# )é   )ÚlowÚhighÚsizeÚTrue)ÚpivotingNÚhardÚjac_equal_zeroéÿÿÿÿ)
ÚnpÚrandomÚdefault_rngÚuniformr   ÚsortÚmultiplyÚdotÚTÚzeros)ÚnÚmin_eigÚmax_eigÚcaseÚrngÚrandÚQÚ_Ú	eigvaluesÚQauxÚAÚgs   &&&&&       Úl/home/luca/screen-checking/.venv/lib/python3.14/site-packages/scipy/optimize/tests/test_trustregion_exact.pyÚrandom_entryr.      s  € Ü
�)‰)×
Ñ
 Ó
$€Cð �;‰;˜2 A¨Q¨Fˆ;Ó3€Dô � Ô'�G€A€qˆ!ð —‘ ¸A�Ó>€IÜ—’˜	Ó"¡4 R 4Õ(€Iô �;Š;�yÓ$€DÜ
�Šˆt—S‘SÓ€Að ˆv„~Ü�HŠH�Q‹KˆØ—‘ ¨!°!°Aµ#�Ó6ˆˆ#ˆ2ˆÜ�FŠF�1‹Lˆð ˆ4€Kð 
Ð!Ô	!Ü�HŠH�Q‹Kˆð ˆ4€Kð �K‰K˜B Q¨QˆKÓ/ˆàˆ4€Kó    c                   ó&   a € ] tR t^/t o R tRtV tR# )Ú!TestEstimateSmallestSingularValuec                óþ   € \         P                  ! . RO. RO. RO. RO.4      p\        V4      w  r#pVR,          pVR,          p\        V4      w  rx\	        Wu^R7       \	        \        V4      \        V4      ^R7       R# )	r   )ÚdecimalN)r   é   é   é   )é    gš™™™™™©?é<   é   )r7   r7   çš™™™™™é?é	   )r7   r7   r7   é
   r   )r   :NNN)r   Úarrayr   r   r   Úabs)	ÚselfÚCÚUÚsÚVtÚsmin_svdÚzmin_svdÚsminÚzmins	   &        r-   Ú test_for_ill_condiotioned_matrixÚBTestEstimateSmallestSingularValue.test_for_ill_condiotioned_matrix1   ss   € ô �HŠH’lÚ&Ú$Ú#ð%ó &ˆô �q“6‰ˆˆbð �R•5ˆØ�e•9ˆô 6°aÓ8‰
ˆô 	" $¸!Õ<Ü!¤# d£)¬S°«]ÀA×Fr/   © N)Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__rH   Ú__static_attributes__Ú__classdictcell__©Ú__classdict__s   @r-   r1   r1   /   s   ø‡ € ÷Gð Gr/   r1   c                   ó2   a € ] tR t^Ht o R tR tR tRtV tR# )ÚTestSingularLeadingSubmatrixc                ó”  € \         P                  ! . RO. RO. RO.4      p\        RV34      w  pV! VRRRR7      w  r4\        WV4      w  rVW^,
          V^,
          3;;,          V,          uu&   \	        \        VRV1RV13,          4      ^ 4       \         P                  ! V\         P                  ! W4      4      p\	        V^ 4       R# )	r   FT©ÚlowerÚoverwrite_aÚcleanN)r   r4   r5   )r4   r6   é   )r5   rZ   é   ©Úpotrf©r   r=   r   r   r   r   r   ©r?   r+   ÚcholeskyÚcÚkÚdeltaÚvÚquadratic_terms   &       r-   Ú+test_for_already_singular_leading_submatrixÚHTestSingularLeadingSubmatrix.test_for_already_singular_leading_submatrixJ   s¯   € ô �HŠH’iÚÚð!ó "ˆô
 % Z°!°Ó6‰	ˆñ ˜ °EÀÔF‰ˆä-¨a°AÓ6‰ˆà	ˆA�#ˆq��sˆ(��uÕ‹ô 	"¤# a¨¨¨¨B¨Q¨B¨¥i£.°!Ô4ô Ÿš ¤2§6¢6¨!£<Ó0ˆÜ! .°!Ö4r/   c                ó   € \         P                  ! . RO. RO. RO. RO. R	O.4      p\        R
V34      w  pV! VRRRR7      w  r4\        WV4      w  rVW^,
          V^,
          3;;,          V,          uu&   \	        \        VRV1RV13,          4      ^ 4       \         P                  ! V\         P                  ! W4      4      p\	        V^ 4       R# )r   FTrV   N)r   r4   r5   r9   é   )r4   rZ   rZ   r;   r7   )r5   rZ   é   r   r4   )r9   r;   r   r9   rZ   )ri   r7   r4   rZ   ri   r\   )r   Úasarrayr   r   r   r   r   r_   s   &       r-   Ú#test_for_simetric_indefinite_matrixÚ@TestSingularLeadingSubmatrix.test_for_simetric_indefinite_matrixc   sµ   € ô �JŠJšÚ'Ú(Ú'Ú'ð	)ó *ˆô % Z°!°Ó6‰	ˆñ ˜ °EÀÔF‰ˆä-¨a°AÓ6‰ˆà	ˆA�#ˆq��sˆ(��uÕ‹ô 	"¤# a¨¨¨¨B¨Q¨B¨¥i£.°!Ô4ô Ÿš ¤2§6¢6¨!£<Ó0ˆÜ! .°!Ö4r/   c                ó”  € \         P                  ! . RO. RO. RO.4      p\        RV34      w  pV! VRRRR7      w  r4\        WV4      w  rVW^,
          V^,
          3;;,          V,          uu&   \	        \        VRV1RV13,          4      ^ 4       \         P                  ! V\         P                  ! W4      4      p\	        V^ 4       R# )	r7   FTrV   N)r7   r5   rj   )r5   é   rZ   )rj   rZ   r[   r\   r^   r_   s   &       r-   Ú$test_for_first_element_equal_to_zeroÚATestSingularLeadingSubmatrix.test_for_first_element_equal_to_zero~   s¯   € ô �HŠH’jÚ Ú ð"ó #ˆô
 % Z°!°Ó6‰	ˆñ ˜ °EÀÔF‰ˆä-¨a°AÓ6‰ˆà	ˆA�#ˆq��sˆ(��uÕ‹ô 	"¤# a¨¨¨¨B¨Q¨B¨¥i£.°!Ô4ô Ÿš ¤2§6¢6¨!£<Ó0ˆÜ! .°!Ö4r/   rJ   N)	rK   rL   rM   rN   rf   rl   rp   rO   rP   rQ   s   @r-   rT   rT   H   s   ø‡ € ò5ò25÷65ð 5r/   rT   c                   óÊ   a € ] tR t^˜t o R tR tR tR tR tR t	]
P                  P                  RR7      ]
P                  P                  ^
4      R	 4       4       tR
 tRtV tR# )ÚTestIterativeSubproblemc           	     óÀ   aa€ . RO. R	O. R
O. RO.o. ROo^p\        ^ R V3R lV3R lRRR7      pVP                  V4      w  r4\        V. RO4       \        VR4       R# )r<   c                 ó   € ^ # ©r7   rJ   ©Úxs   &r-   Ú<lambda>Ú@TestIterativeSubproblem.test_for_the_easy_case.<locals>.<lambda>©   ó   € ±Ar/   c                 ó0   <€ \         P                  ! S4      # ©N©r   r=   ©rx   r,   s   &€r-   ry   rz   ª   ó   ø€ ´B·H²H¸Q´Kr/   c                 ó0   <€ \         P                  ! S4      # r}   r~   ©rx   ÚHs   &€r-   ry   rz   «   ó   ø€ ´R·X²X¸a´[r/   ç»½×Ùß|Û=©rx   ÚfunÚjacÚhessÚk_easyÚk_hardTN©r<   r4   r5   r6   ©r4   r   r9   r   ©r5   r9   r   r9   ©r6   r   r9   r4   )r   r   r   r   )gë8<Œbp?gøgÌEø®á¿gÎþ vå?gË�ùëÛªß¿©r   Úsolver   )r?   Útrust_radiusÚsubprobÚpÚhits_boundaryrƒ   r,   s   &    @@r-   Útest_for_the_easy_caseÚ.TestIterativeSubproblem.test_for_the_easy_caseš   sp   ù€ ò ÚÚÚðˆò ˆð ˆô &¨Ù*5Ü*?Ü+@Ø-2Ø-2ô4ˆð #Ÿ=™=¨Ó6Ñˆä! !ò &?ô 	@ä! -°Ö6r/   c           	     ó¾   aa€ . RO. RO. R	O. R
O.o. ROoRp^p\        ^ R V3R lV3R lRRR7      pVP                  V4      w  rE\        V) VP                  4       R# )r<   c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   Ú@TestIterativeSubproblem.test_for_the_hard_case.<locals>.<lambda>Ä   r{   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r   s   &€r-   ry   rš   Å   r€   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r‚   s   &€r-   ry   rš   Æ   r„   r/   r…   r†   NrŒ   r�   rŽ   r�   )gASýéð@r   r   r   grv»f(n À)r   r‘   r   Úlambda_current)r?   rB   r’   r“   r”   r•   rƒ   r,   s   &     @@r-   Útest_for_the_hard_caseÚ.TestIterativeSubproblem.test_for_the_hard_case´   sm   ù€ ò ÚÚÚðˆò *ˆØˆð ˆô &¨Ù*5Ü*?Ü+@Ø-2Ø-2ô4ˆð #Ÿ=™=¨Ó6Ñˆä! 1 " g×&<Ñ&<Ö=r/   c           	     óÔ   aa€ ^R
.o^^ .^ ^..o\        \        P                  ! ^4      R V3R lV3R lRRR7      pVP                  R4      w  r#\	        VRR.4       V'       g   Q hR	# )é   c                 ó   € ^ # rv   rJ   )r(   s   &r-   ry   Ú6TestIterativeSubproblem.test_gh20244.<locals>.<lambda>Ñ   s   € Á1r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   )r(   r,   s   &€r-   ry   r£   Ò   r€   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   )r(   rƒ   s   &€r-   ry   r£   Ó   r„   r/   g�íµ ÷Æ°>g•Ö&è.>r†   g      ð?g«Ã<ñ½;ä?NéöÿÿÿgÑœÌª•Êè¿)r   r   r    r‘   r
   ©r?   r“   r”   r•   rƒ   r,   s   &   @@r-   Útest_gh20244Ú$TestIterativeSubproblem.test_gh20244Í   si   ù€ Ø�ˆIˆØ�!ˆW�q˜!�fÐˆä%¬¯ª°«¹Ü*?Ü+@ÈØ-1ô3ˆð #Ÿ=™=¨Ó-Ñˆä˜˜K¨*Ð5Ô6ßÐŠ}r/   c                ó  aa€ . RO. R	O. R
O. RO. RO.o. ROo\        ^ R V3R lV3R lR7      pVP                  R4      w  r#\        V. RO4       \        VR4       \        VP                  ^ 4       \        VP                  ^4       R# )çÛn‚ošþü?c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   ÚGTestIterativeSubproblem.test_for_interior_convergence.<locals>.<lambda>æ   r{   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r   s   &€r-   ry   r­   ç   r€   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r‚   s   &€r-   ry   r­   è   r„   r/   )rx   r‡   rˆ   r‰   çš™™™™™ñ?FN)r«   ç�ž¶¡½uê?ç,wnó)ôË?ç”/ËK¼Ëà¿çÿëš˜GÐ?)r±   gì¼®ÛwO@çÙ¢y¾n*Ô?çr–<8±Ù¿çõ¶Û&ÃŽ¶?)r²   rµ   gÓ6›ª
@çøòÄ½CÔ¿ç8Š¤ÄKƒÑ?)r³   r¶   r¸   gÀc‘‰èù?çò†«>øÚ¿)r´   r·   r¹   rº   gÂ-£Qõ?)g*‹ã<sAè?g³¢¼E�?gM x¾—©Õ?gzý‹˜ÀÊê?gôÒ=€©Þ¿)g8bÒ„òå¿gåO
©‘L¿?g p4OÇFÌ¿g� Ïqå¿g­oš-7Ô?)r   r‘   r   r�   Úniterr§   s   &   @@r-   Útest_for_interior_convergenceÚ5TestIterativeSubproblem.test_for_interior_convergenceÚ   s…   ù€ âHÚJÚIÚLÚJð	Lˆò Jˆô &¨Ù*5Ü*?Ü+@ôBˆð #Ÿ=™=¨Ó-Ñˆä! !ò &?ô 	@ä! -°Ô7Ü! '×"8Ñ"8¸!Ô<Ü! '§-¡-°Ö3r/   c           	     óÂ   aa€ . R	O. R
O. RO. RO. RO.o. ROo\        ^ R V3R lV3R lRRR7      pVP                  R4      w  r#\        V. RO4       \        VR4       R# )çÝVaÐUì?c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   ÚATestIterativeSubproblem.test_for_jac_equal_zero.<locals>.<lambda>ý   r{   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r   s   &€r-   ry   rÁ   þ   r€   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r‚   s   &€r-   ry   rÁ   ÿ   r„   r/   r…   r†   r°   TN©r¿   çø˜›±`A@ç5“ýF€ï?çÔ9Ô)n@é¿ç€îcñÑ¿©rÅ   gµÚ{ú¥§¿ç.<íøÕ?ç~õýÏËê¿çÔ:]³èÅ?©rÆ   rÊ   g@33ôë¿ç �5Ð:²°¿ç¦ä¤IŒâö¿©rÇ   rË   rÎ   gÐ¹ÛõÒTú¿ç¦F¦K°Õ¿©rÈ   rÌ   rÏ   rÑ   g¬¢&—Rùú¿)r7   r7   r7   r7   r7   ©g÷iG7ã°±?glµ$“•W�¿gÀü€ÍZæä¿g-ðOˆ|Î¿g¦mô‚/ë¿r�   r§   s   &   @@r-   Útest_for_jac_equal_zeroÚ/TestIterativeSubproblem.test_for_jac_equal_zeroñ   sl   ù€ âKÚKÚLÚLÚMð	Oˆò ˆô &¨Ù*5Ü*?Ü+@Ø-2Ø-2ô4ˆð #Ÿ=™=¨Ó-Ñˆä! !ò &3ô 	4ô 	" -°Ö6r/   c           	     óÂ   aa€ . R	O. R
O. RO. RO. RO.o. ROo\        ^ R V3R lV3R lRRR7      pVP                  R4      w  r#\        V. RO4       \        VR4       R# )r¿   c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   ÚITestIterativeSubproblem.test_for_jac_very_close_to_zero.<locals>.<lambda>  r{   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r   s   &€r-   ry   rØ     r€   r/   c                 ó0   <€ \         P                  ! S4      # r}   r~   r‚   s   &€r-   ry   rØ     r„   r/   r…   r†   r°   TNrÄ   rÉ   rÍ   rÐ   rÒ   )r7   r7   r7   r7   gVçž¯Ò<rÓ   r�   r§   s   &   @@r-   Útest_for_jac_very_close_to_zeroÚ7TestIterativeSubproblem.test_for_jac_very_close_to_zero	  sl   ù€ âKÚKÚLÚLÚMð	Oˆò  ˆô &¨Ù*5Ü*?Ü+@Ø-2Ø-2ô4ˆð #Ÿ=™=¨Ó-Ñˆä! !ò &3ô 	4ô 	" -°Ö6r/   zfails in parallel)Úreasonc                ó4  aa€ \         P                  P                  ^4      p^pR EFí  p. ROpV EFÞ  w  rV\        W%WcVR7      w  oo. ROpV EF¼  p\	        ^ R V3R lV3R lRRR7      p	V	P                  V4      w  r«R\         P                  ! V
\         P                  ! SV
4      4      ,          \         P                  ! SV
4      ,           p. ROpV EF1  w  rï\        V^,
          ^\         P                  ! V4      ,
          4      p^V,
          p\	        ^ R V3R	 lV3R
 lVVR7      pVP                  V4      w  ppR\         P                  ! V\         P                  ! SV4      4      ,          \         P                  ! SV4      ,           pV'       dC   \        \         P                  ! \        V4      V,
          4      V^,
          V,          8*  R4       M\        \        V4      V8*  R4       \        VWì,          8*  R4       EK4  	  EK¿  	  EKá  	  EKð  	  R# )r   )r%   c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   ÚATestIterativeSubproblem.test_for_random_entries.<locals>.<lambda>?  s   € ¹qr/   c                 ó   <€ S# r}   rJ   r   s   &€r-   ry   rà   @  ó   ø€ ¹qr/   c                 ó   <€ S# r}   rJ   r‚   s   &€r-   ry   rà   A  râ   r/   r…   )rŠ   r‹   ç      à?c                 ó   € ^ # rv   rJ   rw   s   &r-   ry   rà   Z  s   € Ár/   c                 ó   <€ S# r}   rJ   r   s   &€r-   ry   rà   [  ó   ø€ Ár/   c                 ó   <€ S# r}   rJ   r‚   s   &€r-   ry   rà   \  rç   r/   TN)Úeasyr   r   ))iìÿÿÿiñÿÿÿ)r¦   éûÿÿÿ)r¦   r7   )rê   rZ   )r¦   r<   )r7   r<   )rZ   r<   )é   r¡   )	çš™™™™™¹?g333333Ó?g333333ã?r:   r   g333333ó?gffffff
@g      @r<   ))rì   r4   )rä   r°   )gÍÌÌÌÌÌì?g)\�Âõ(ð?)r   r   r   r.   r   r‘   r   ÚminÚsqrtr   r>   r	   r   )r?   r%   r!   r$   Ú
eig_limitsr"   r#   Útrust_radius_listr’   Ú
subprob_acÚp_acÚhits_boundary_acÚJ_acÚstop_criteriaÚk_optÚk_trfrŠ   r‹   r“   r”   r•   ÚJrƒ   r,   s   &                     @@r-   Útest_for_random_entriesÚ/TestIterativeSubproblem.test_for_random_entries!  sÉ  ù€ ô �i‰i×#Ñ# AÓ&ˆð ˆä6ˆDò$ˆJô %/Ñ �ô $ A°À3ÔG‘��1ò %OÐ!ä$5�Lä!4°QÙ5@Ü5@Ü5@Ø<AØ<Aô"C�Jð .8×-=Ñ-=¸lÓ-KÑ*�Dð œrŸvšv d¬B¯FªF°1°d«OÓ<Õ<¼R¿VºVÀAÀt»_ÕL�Dò%2�Mô )6™˜ô "% U¨1¥WØ%&¤r§w¢w¨u£~Õ%5ó"7˜à!" 5¥˜ô #6°aÙ6AÜ6AÜ6AØ=CØ=Cô#E˜ð ,3¯=©=¸Ó+FÑ(˜˜=ð  ¤§¢ q¬"¯&ª&°°A«,Ó 7Õ7¼¿º¸qÀ!»ÕD˜÷ )Ü.¬r¯vªv´d¸1³g¸lÕ6JÓ/KØ05°aµ¸Õ/Eñ0FØGKõMô )¬¨a«°LÑ)@À$ÔGô % Q¨%­*¡_°d×;ô= )6ô% %6ô %/ó 7r/   c                óÆ  aa€ \         P                  ! . RO. R	O. R
O. RO. RO. RO. R	O. RO. RO. RO. RO. RO. RO. RO. RO. RO. RO. RO. RO.4      o\         P                  ! . RO4      oR^
.pV Fm  p\        ^ R V3R lV3R lRRVR7      p^pVP                  V4      w  rVVf$   VP                  \        P
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