+
    LV-j÷`  ã                   óN  € R t ^ RIt^ RIHtHtHtHtHtHtH	t	H
t
HtHtHt ^ RIHtHtHtHtHt ^ RIt^ RIHt ^ RIHtHtHt  ! R R4      t ! R R	4      t ! R
 R]4      t ! R R]4      t ! R R4      t ! R R4      t  ! R R4      t! ! R R]!4      t" ! R R]!4      t# ! R R]!4      t$ ! R R]!4      t%]"]#]$]%.t&R t'R t(R t)R t*R  t+R! t,R" t-R# t. ! R$ R%4      t/ ! R& R']/4      t0 ! R( R)]/4      t1 ! R* R+]/4      t2 ! R, R-]/4      t3 ! R. R/]/4      t4R0 t5R1 t6R2 t7R3 t8R4 t9R# )5z"
Tests for numerical integration.
N)ÚarangeÚzerosÚarrayÚdotÚsqrtÚcosÚsinÚeyeÚpiÚexpÚallclose)Úassert_Úassert_array_almost_equalÚassert_allcloseÚassert_array_equalÚassert_equal)Úraises)ÚodeintÚodeÚcomplex_odec                   ó,   a € ] tR t^t o R tR tRtV tR# )Ú
TestOdeintc           	     ób  a€ \        R SP                  R4      p\        SP                  SP                  VRR7      w  r4\        SP                  W24      4       \        V3R lSP                  VRRR7      w  r4\        SP                  W24      4       \        SR4      '       dŒ   \        SP                  SP                  VSP                  RR7      w  r4\        SP                  W24      4       \        V3R lSP                  VV3R	 lRRR
7      w  r4\        SP                  W24      4       R# R# )ç        gš™™™™™©?T©Úfull_outputc                 ó&   <€ SP                  W4      # ©N©Úf©ÚtÚyÚproblems   &&€Úu/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/integrate/tests/test_integrate.pyÚ<lambda>Ú(TestOdeint._do_problem.<locals>.<lambda>    s   ø€ ¨'¯)©)°A¬/ó    )r   ÚtfirstÚjac)ÚDfunr   c                 ó&   <€ SP                  W4      # r   r   r    s   &&€r$   r%   r&   +   s   ø€ ¨g¯i©i¸¬or'   c                 ó&   <€ SP                  W4      # r   ©r)   r    s   &&€r$   r%   r&   ,   s   ø€ °7·;±;¸qÔ3Dr'   )r*   r   r(   N)	r   Ústop_tr   r   Úz0r   ÚverifyÚhasattrr)   )Úselfr#   r!   ÚzÚinfodicts   &f   r$   Ú_do_problemÚTestOdeint._do_problem   sì   ø€ Ü�3˜Ÿ™¨Ó-ˆô ˜WŸY™Y¨¯
©
°AÀ4ÔH‰ˆÜ�—‘˜qÓ$Ô%ô Ô9¸7¿:¹:ÀqØ)-°dô<‰ˆä�—‘˜qÓ$Ô%ä�7˜E×"Ò"ä  §¡¨G¯J©J¸ÀÇÁØ-1ô3‰KˆAä�G—N‘N 1Ó(Ô)ô !Ô!=¸w¿z¹zÈ1Ü&DØ-1¸$ô@‰KˆAô �G—N‘N 1Ó(Ö)ñ #r'   c                óx   € \          F/  pV! 4       pVP                  '       d   K  V P                  V4       K1  	  R # r   ©ÚPROBLEMSÚcmplxr5   ©r2   Úproblem_clsr#   s   &  r$   Útest_odeintÚTestOdeint.test_odeint0   s-   € ß#ˆKÙ!“mˆGØ�}�}ˆ}ÙØ×Ñ˜WÖ%ó	 $r'   © N)Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__r5   r=   Ú__static_attributes__Ú__classdictcell__©Ú__classdict__s   @r$   r   r      s   ø‡ € ò*÷0&ð &r'   r   c                   ó.   a € ] tR t^8t o RtRR ltRtV tR# )ÚTestODEClassNc           	     óÌ  a€ V3R  lpRp\        SR4      '       d   V3R lp/ pSP                  f   SP                  e   SP                  VR&   SP                  VR&   V P                  WE4      pVP                  ! V3RSP
                  ^
,          RSP                  ^
,          RV/VB  VP                  SP                  R	R
7       VP                  SP                  4      p\        W‡P                  4       \        VP                  4       SV34       \        VP                  4       ^ 8„  SV34       \        SP!                  \#        V.4      SP                  4      SV34       R# )c                 ó&   <€ SP                  W4      # r   r   ©r!   r3   r#   s   &&€r$   r   Ú#TestODEClass._do_problem.<locals>.f?   s   ø€ Ø—9‘9˜Q“?Ð"r'   Nr)   c                 ó&   <€ SP                  W4      # r   r-   rL   s   &&€r$   r)   Ú%TestODEClass._do_problem.<locals>.jacC   s   ø€ Ø—{‘{ 1Ó(Ð(r'   ÚubandÚlbandÚatolÚrtolÚmethodr   )r!   )r1   rQ   rP   Ú	ode_classÚset_integratorrR   rS   Úset_initial_valuer/   Ú	integrater.   r   r"   r   Ú
successfulÚget_return_coder0   r   )	r2   r#   Ú
integratorrT   r   r)   Úintegrator_paramsÚigr3   s	   &f&&     r$   r5   ÚTestODEClass._do_problem<   s7  ø€ õ	#àˆÜ�7˜E×"Ò"õ)ð ÐØ�=‰=Ò$¨¯©Ò(AØ)0¯©Ð˜gÑ&Ø)0¯©Ð˜gÑ&à�^‰^˜AÓ#ˆØ
×Ò˜*ñ 	/Ø&Ÿ|™|¨B�ð	/à&Ÿ|™|¨B�ð	/ð "(ð	/ð .ò		/ð 	×Ñ˜WŸZ™Z¨3ÐÔ/Ø�L‰L˜Ÿ™Ó(ˆä˜1Ÿd™dÔ#Ü�—‘“ '¨6Ð!2Ô3Ü�×"Ñ"Ó$ qÑ(¨7°FÐ*;Ô<Ü�—‘œu a S›z¨7¯>©>Ó:¸WÀfÐ<MÖNr'   r?   )Úadams)r@   rA   rB   rC   rU   r5   rD   rE   rF   s   @r$   rI   rI   8   s   ø‡ € à€I÷Oò Or'   rI   c                   óN   a € ] tR t^[t o ]tR tR tR tR t	R t
R tR tRtV tR	# )
ÚTestOdec                óÆ   € \          FV  pV! 4       pVP                  '       d   K  VP                  '       g   V P                  VR R4       V P                  VR R4       KX  	  R# ©Úvoder_   ÚbdfN)r9   r:   Ústiffr5   r;   s   &  r$   Ú	test_vodeÚTestOde.test_vode_   sL   € ç#ˆKÙ!“mˆGØ�}�}ˆ}ÙØ—=—=�=Ø× Ñ  ¨&°'Ô:Ø×Ñ˜W f¨eÖ4ó $r'   c                óž   € \          FB  pV! 4       pVP                  '       g   V P                  VR R4       V P                  VR R4       KD  	  R# )Úzvoder_   re   N©r9   rf   r5   r;   s   &  r$   Ú
test_zvodeÚTestOde.test_zvodei   s@   € ç#ˆKÙ!“mˆGØ—=—=�=Ø× Ñ  ¨'°7Ô;Ø×Ñ˜W g¨uÖ5ó	 $r'   c                óz   € \          F0  pV! 4       pVP                  '       d   K  V P                  VR 4       K2  	  R# ©ÚlsodaNr8   r;   s   &  r$   Ú
test_lsodaÚTestOde.test_lsodaq   s/   € ç#ˆKÙ!“mˆGØ�}�}ˆ}ÙØ×Ñ˜W gÖ.ó	 $r'   c                óÊ   € \          FX  pV! 4       pVP                  '       d   K  VP                  '       d   K2  \        VR 4      '       d   KF  V P	                  VR4       KZ  	  R# ©r)   Údopri5N©r9   r:   rf   r1   r5   r;   s   &  r$   Útest_dopri5ÚTestOde.test_dopri5y   óK   € ç#ˆKÙ!“mˆGØ�}�}ˆ}ÙØ�}�}ˆ}ÙÜ�w ×&Ò&ÙØ×Ñ˜W hÖ/ó $r'   c                óÊ   € \          FX  pV! 4       pVP                  '       d   K  VP                  '       d   K2  \        VR 4      '       d   KF  V P	                  VR4       KZ  	  R# ©r)   Údop853Nrv   r;   s   &  r$   Útest_dop853ÚTestOde.test_dop853…   ry   r'   c                óÊ  € R FÜ  pR p\        V4      P                  V4      pVP                  ^ ^ 4       \        V4      P                  V4      pVP                  ^ ^ 4       VP                  VP                  R,           4       VP                  VP                  R,           4       VP                  VP                  R,           4       VP                  4       '       d   KÜ  Q h	  R# )rd   c                 ó   € R # ©ç      ð?r?   ©r!   r"   s   &&r$   r   Ú'TestOde.test_concurrent_fail.<locals>.f–   s   € Ùr'   çš™™™™™¹?N)rd   rj   rp   )r   rV   rW   rX   r!   rY   )r2   Úsolr   ÚrÚr2s   &    r$   Útest_concurrent_failÚTestOde.test_concurrent_fail‘   s«   € ó .ˆCòô �A“×%Ñ% cÓ*ˆAØ×Ñ  1Ô%ä�Q“×&Ñ& sÓ+ˆBØ× Ñ   AÔ&à�K‰K˜Ÿ™˜c�	Ô"Ø�L‰L˜Ÿ™ �Ô$ð �K‰K˜Ÿ™˜c�	Ô"Ø—<‘<—>”>Ð!�>ó .r'   c                ó¬  € R  p\        ^4       EF@  pR Fý  pVR9   d
   V^8”  d   K  \        V4      P                  V4      pVP                  ^ ^ 4       \        V4      P                  V4      pVP                  ^ ^ 4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       \        VP                  R4       \        VP                  R4       Kÿ  	  R EF2  p\        V4      P                  V4      pVP                  ^ ^ 4       \        V4      P                  V4      pVP                  ^ ^ 4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       VP	                  VP
                  R,           4       \        VP                  R4       \        VP                  R4       EK5  	  EKC  	  R# )c                 ó   € R # r�   r?   rƒ   s   &&r$   r   Ú%TestOde.test_concurrent_ok.<locals>.f§   s   € Ùr'   r…   gš™™™™™É?g333333Ó?N)rd   rj   rp   ru   r|   >   rd   rp   rj   ©ru   r|   )Úranger   rV   rW   rX   r!   r   r"   )r2   Únum_parallel_threadsr   Úkr†   r‡   rˆ   s   &&     r$   Útest_concurrent_okÚTestOde.test_concurrent_ok¦   s«  € ò	ô �q—ˆAÛE�ØÐ4Ô4Ð9MÐPQÔ9QÙÜ˜“F×)Ñ)¨#Ó.�Ø×#Ñ# A qÔ)ä˜“V×*Ñ*¨3Ó/�Ø×$Ñ$ Q¨Ô*à—‘˜AŸC™C #�IÔ&Ø—‘˜RŸT™T C�ZÔ(Ø—‘˜RŸT™T C�ZÔ(ä §¡ SÔ)Ü §¡ cÖ*ñ Fô  ,�Ü˜“F×)Ñ)¨#Ó.�Ø×#Ñ# A qÔ)ä˜“V×*Ñ*¨3Ó/�Ø×$Ñ$ Q¨Ô*à—‘˜AŸC™C #�IÔ&Ø—‘˜AŸC™C #�IÔ&Ø—‘˜RŸT™T C�ZÔ(Ø—‘˜AŸC™C #�IÔ&Ø—‘˜RŸT™T C�ZÔ(ä §¡ SÔ)Ü §¡ c×*ô ,ó# r'   r?   N)r@   rA   rB   rC   r   rU   rg   rl   rq   rw   r}   r‰   r’   rD   rE   rF   s   @r$   ra   ra   [   s2   ø‡ € à€Iò5ò6ò/ò
0ò
0ò"÷*#+ð #+r'   ra   c                   ó<   a € ] tR t^Ìt o ]tR tR tR tR t	Rt
V tR# )ÚTestComplexOdec                ó¢   € \          FD  pV! 4       pVP                  '       g   V P                  VR R4       K1  V P                  VR R4       KF  	  R# rc   rk   r;   s   &  r$   rg   ÚTestComplexOde.test_vodeÐ   s@   € ç#ˆKÙ!“mˆGØ—=—=�=Ø× Ñ  ¨&°'Ö:à× Ñ  ¨&°%Ö8ó $r'   c                óR   € \          F  pV! 4       pV P                  VR 4       K  	  R# ro   )r9   r5   r;   s   &  r$   rq   ÚTestComplexOde.test_lsodaÙ   s%   € ÷ $ˆKÙ!“mˆGØ×Ñ˜W gÖ.ó $r'   c                ó¢   € \          FD  pV! 4       pVP                  '       d   K  \        VR 4      '       d   K2  V P                  VR4       KF  	  R# rt   ©r9   rf   r1   r5   r;   s   &  r$   rw   ÚTestComplexOde.test_dopri5à   ó?   € ç#ˆKÙ!“mˆGØ�}�}ˆ}ÙÜ�w ×&Ò&ÙØ×Ñ˜W hÖ/ó $r'   c                ó¢   € \          FD  pV! 4       pVP                  '       d   K  \        VR 4      '       d   K2  V P                  VR4       KF  	  R# r{   r›   r;   s   &  r$   r}   ÚTestComplexOde.test_dop853ê   r�   r'   r?   N)r@   rA   rB   rC   r   rU   rg   rq   rw   r}   rD   rE   rF   s   @r$   r•   r•   Ì   s#   ø‡ € à€Iò9ò/ò0÷0ð 0r'   r•   c                   óD   a € ] tR t^õt o R tR tR tR tR tR t	Rt
V tR# )	Ú
TestSoloutc                óh  a	a
€ . o	. o
R pRpRR.pV	V
3R lpR p\        V4      P                  V4      pVP                  V4       VP                  WB4       VP	                  V4      p\        S
^ ,          V4       \        S
R,          V4       \        S	^ ,          V4       \        S	R,          V4       R# )r   ç      $@r‚   ç       @c                 óh   <€ SP                  V 4       SP                  VP                  4       4       R # r   ©ÚappendÚcopy©r!   r"   ÚtsÚyss   &&€€r$   ÚsoloutÚ+TestSolout._run_solout_test.<locals>.soloutÿ   ó    ø€ Ø�I‰I�aŒLØ�I‰I�a—f‘f“hÖr'   c                 óR   € V^ ,          V^,          ,           V^,          ^,          ) .# ©é    r?   rƒ   s   &&r$   ÚrhsÚ(TestSolout._run_solout_test.<locals>.rhs  ó#   € Ø�a•D˜1˜Q�4•K ! A¥$¨¥' Ð*Ð*r'   Néÿÿÿÿ)r   rV   Ú
set_soloutrW   rX   r   r   ©r2   r[   Út0ÚtendÚy0r¬   r²   r]   Úretrª   r«   s   &&       @@r$   Ú_run_solout_testÚTestSolout._run_solout_test÷   s    ù€ àˆØˆØˆØˆØ�3ˆZˆö	 ò	+ô �‹X×$Ñ$ ZÓ0ˆØ
�‰�fÔØ
×Ñ˜RÔ$Ø�l‰l˜4Ó ˆÜ˜2˜a�5 "Ô%Ü˜2˜b�6 3Ô'Ü�R˜•U˜BÔÜ�R˜•V˜TÖ"r'   c                ó:   € R F  pV P                  V4       K  	  R# ©ru   NrŽ   ©r¼   ©r2   r[   s   & r$   Útest_soloutÚTestSolout.test_solout  ó   € Û.ˆJØ×!Ñ! *Ö-ó /r'   c                óh  a	a
€ . o	. o
R pRpRR.pV	V
3R lpR p\        V4      P                  V4      pVP                  WB4       VP                  V4       VP	                  V4      p\        S
^ ,          V4       \        S
R,          V4       \        S	^ ,          V4       \        S	R,          V4       R# )r   r£   r‚   r¤   c                 óh   <€ SP                  V 4       SP                  VP                  4       4       R # r   r¦   r©   s   &&€€r$   r¬   Ú9TestSolout._run_solout_after_initial_test.<locals>.solout  r®   r'   c                 óR   € V^ ,          V^,          ,           V^,          ^,          ) .# r°   r?   rƒ   s   &&r$   r²   Ú6TestSolout._run_solout_after_initial_test.<locals>.rhs  r´   r'   Nrµ   )r   rV   rW   r¶   rX   r   r   r·   s   &&       @@r$   Ú_run_solout_after_initial_testÚ)TestSolout._run_solout_after_initial_test  s    ù€ àˆØˆØˆØˆØ�3ˆZˆö	 ò	+ô �‹X×$Ñ$ ZÓ0ˆØ
×Ñ˜RÔ$Ø
�‰�fÔØ�l‰l˜4Ó ˆÜ˜2˜a�5 "Ô%Ü˜2˜b�6 3Ô'Ü�R˜•U˜BÔÜ�R˜•V˜TÖ"r'   c                ó:   € R F  pV P                  V4       K  	  R# r¿   )rÊ   rÁ   s   & r$   Útest_solout_after_initialÚ$TestSolout.test_solout_after_initial+  s   € Û.ˆJØ×/Ñ/°
Ö;ó /r'   c                ó¨  aa	a
€ . o	. o
R pRoRR.pVV	V
3R lpR p\        V4      P                  V4      pVP                  V4       VP                  W24       VP	                  S4      p\        S
^ ,          V4       \        S
R,          V4       \        S	^ ,          V4       \        S	R,          SR,          8„  4       \        S	R,          S8  4       R# )r   r£   r‚   r¤   c                 óˆ   <€ SP                  V 4       SP                  VP                  4       4       V SR ,          8”  d   R# R# ©r¤   Nrµ   r¦   ©r!   r"   r¹   rª   r«   s   &&€€€r$   r¬   Ú1TestSolout._run_solout_break_test.<locals>.solout7  ó5   ø€ Ø�I‰I�aŒLØ�I‰I�a—f‘f“hÔØ�4˜•8Œ|Ø�	ñ r'   c                 óR   € V^ ,          V^,          ,           V^,          ^,          ) .# r°   r?   rƒ   s   &&r$   r²   Ú.TestSolout._run_solout_break_test.<locals>.rhs=  r´   r'   Nrµ   )r   rV   r¶   rW   rX   r   r   r   ©r2   r[   r¸   rº   r¬   r²   r]   r»   r¹   rª   r«   s   &&      @@@r$   Ú_run_solout_break_testÚ!TestSolout._run_solout_break_test/  s·   ú€ àˆØˆØˆØˆØ�3ˆZˆ÷	ò	+ô �‹X×$Ñ$ ZÓ0ˆØ
�‰�fÔØ
×Ñ˜RÔ$Ø�l‰l˜4Ó ˆÜ˜2˜a�5 "Ô%Ü˜2˜b�6 3Ô'Ü�R˜•U˜BÔÜ��2•˜˜c�Ñ!Ô"Ü��2•˜‘Ör'   c                ó:   € R F  pV P                  V4       K  	  R# r¿   ©rØ   rÁ   s   & r$   Útest_solout_breakÚTestSolout.test_solout_breakJ  ó   € Û.ˆJØ×'Ñ'¨
Ö3ó /r'   r?   N)r@   rA   rB   rC   r¼   rÂ   rÊ   rÍ   rØ   rÜ   rD   rE   rF   s   @r$   r¡   r¡   õ   s(   ø‡ € ò#ò0.ò#ò0<ò÷64ð 4r'   r¡   c                   ó8   a € ] tR tRt o R tR tR tR tRtV t	R# )ÚTestComplexSoloutiO  c                óf  a	a
€ . o	. o
R pRpR .pV	V
3R lpR p\        V4      P                  V4      pVP                  V4       VP                  WB4       VP	                  V4      p\        S
^ ,          V4       \        S
R,          V4       \        S	^ ,          V4       \        S	R,          V4       R# )r   ç      4@c                 óh   <€ SP                  V 4       SP                  VP                  4       4       R # r   r¦   r©   s   &&€€r$   r¬   Ú2TestComplexSolout._run_solout_test.<locals>.soloutY  r®   r'   c                 ó2   € R V R,
          R,
          ,          .# ©r‚   r£   ù              ð?r?   rƒ   s   &&r$   r²   Ú/TestComplexSolout._run_solout_test.<locals>.rhs]  ó   € Ø˜˜T� B�Õ'Ð(Ð(r'   Nrµ   )r   rV   r¶   rW   rX   r   r   r·   s   &&       @@r$   r¼   Ú"TestComplexSolout._run_solout_testQ  sŸ   ù€ àˆØˆØˆØˆØˆUˆö	 ò	)ô ˜Ó×,Ñ,¨ZÓ8ˆØ
�‰�fÔØ
×Ñ˜RÔ$Ø�l‰l˜4Ó ˆÜ˜2˜a�5 "Ô%Ü˜2˜b�6 3Ô'Ü�R˜•U˜BÔÜ�R˜•V˜TÖ"r'   c                ó:   € R F  pV P                  V4       K  	  R# r¿   rÀ   rÁ   s   & r$   rÂ   ÚTestComplexSolout.test_solouti  rÄ   r'   c                ó¦  aa	a
€ . o	. o
R pRoR .pVV	V
3R lpR p\        V4      P                  V4      pVP                  V4       VP                  W24       VP	                  S4      p\        S
^ ,          V4       \        S
R,          V4       \        S	^ ,          V4       \        S	R,          SR,          8„  4       \        S	R,          S8  4       R# )r   râ   c                 óˆ   <€ SP                  V 4       SP                  VP                  4       4       V SR ,          8”  d   R# R# rÑ   r¦   rÒ   s   &&€€€r$   r¬   Ú8TestComplexSolout._run_solout_break_test.<locals>.soloutu  rÔ   r'   c                 ó2   € R V R,
          R,
          ,          .# ræ   r?   rƒ   s   &&r$   r²   Ú5TestComplexSolout._run_solout_break_test.<locals>.rhs{  ré   r'   r¤   Nrµ   )r   rV   r¶   rW   rX   r   r   r   r×   s   &&      @@@r$   rØ   Ú(TestComplexSolout._run_solout_break_testm  s¶   ú€ àˆØˆØˆØˆØˆUˆ÷	ò	)ô ˜Ó×,Ñ,¨ZÓ8ˆØ
�‰�fÔØ
×Ñ˜RÔ$Ø�l‰l˜4Ó ˆÜ˜2˜a�5 "Ô%Ü˜2˜b�6 3Ô'Ü�R˜•U˜BÔÜ��2•˜˜c�Ñ!Ô"Ü��2•˜‘Ör'   c                ó:   € R F  pV P                  V4       K  	  R# r¿   rÛ   rÁ   s   & r$   rÜ   Ú#TestComplexSolout.test_solout_breakˆ  rÞ   r'   r?   N)
r@   rA   rB   rC   r¼   rÂ   rØ   rÜ   rD   rE   rF   s   @r$   rà   rà   O  s   ø‡ € ò#ò0.ò÷64ð 4r'   rà   c                   ó:   € ] tR tRtRtRtRt^t. tRt	Rt
RtRtRtR# )ÚODEi’  z
ODE problem
FNg�íµ ÷Æ°>gñhãˆµøä>r?   )r@   rA   rB   rC   Ú__doc__rf   r:   r.   r/   rQ   rP   rR   rS   rD   r?   r'   r$   rö   rö   ’  s1   † ñð €EØ€EØ€FØ	€Bà€EØ€Eà€DØ„Dr'   rö   c                   óR   a € ] tR tRt o RtR
t]! RR.]4      tRt	Rt
R tR tRtV tR	# )ÚSimpleOscillatori¢  z³
Free vibration of a simple oscillator::
    m \ddot{u} + k u = 0, u(0) = u_0 \dot{u}(0) \dot{u}_0
Solution::
    u(t) = u_0*cos(sqrt(k/m)*t)+\dot{u}_0*sin(sqrt(k/m)*t)/sqrt(k/m)
r‚   r…   g      @c                ó„   € \        R\        4      pRVR&   V P                  ) V P                  ,          VR&   \	        W14      # )é   r‚   )rû   rû   ©r±   é   )rý   r±   )r   Úfloatr‘   Úmr   )r2   r3   r!   Útmps   &&& r$   r   ÚSimpleOscillator.f¯  s9   € Ü�FœEÓ"ˆØˆˆD‰	Ø—V‘V�G˜dŸf™fÕ$ˆˆD‰	Ü�3‹{Ðr'   c                ó\  € \        V P                  V P                  ,          4      pV P                  ^ ,          \	        W2,          4      ,          V P                  ^,          \        W2,          4      ,          V,          ,           p\        WAR,          V P                  V P                  R7      # )r±   ©rR   rS   )ºNNNr±   )	r   r‘   rÿ   r/   r   r   r   rR   rS   )r2   Úzsr!   ÚomegaÚus   &&&  r$   r0   ÚSimpleOscillator.verifyµ  sh   € Ü�T—V‘V˜dŸf™f•_Ó%ˆØ�G‰G�A�J”s˜5�7“|Õ# d§g¡g¨a¥j´°UµW³Õ&=¸eÕ&CÕCˆÜ˜˜d�8¨$¯)©)¸$¿)¹)ÔDÐDr'   r?   Ngq=
×£pñ?)r@   rA   rB   rC   r÷   r.   r   rþ   r/   r‘   rÿ   r   r0   rD   rE   rF   s   @r$   rù   rù   ¢  s<   ø‡ € ñð €FÙ	��Sˆz˜5Ó	!€Bà€AØ€Aò÷Eð Er'   rù   c                   ó`   a € ] tR tRt o RtR],          t]! . R
O4      tRt	R t
R tR tRtV tR	# )Ú
ComplexExpi»  zThe equation :lm:`\dot u = i u`g®Gáz®ó?Tc                ó   € R V,          # ©rç   r?   ©r2   r3   r!   s   &&&r$   r   ÚComplexExp.fÁ  s   € Ø�!�tˆr'   c                ó&   € R \        ^4      ,          # r  )r	   r  s   &&&r$   r)   ÚComplexExp.jacÄ  s   € Ø”#�a“&�yÐr'   c                óŒ   € V P                   \        R V,          4      ,          p\        W1V P                  V P                  R7      # )rç   r  )r/   r   r   rR   rS   ©r2   r  r!   r  s   &&& r$   r0   ÚComplexExp.verifyÇ  s/   € Ø�G‰G”c˜"˜Q�$“iÕˆÜ˜ D§I¡I°D·I±IÔ>Ð>r'   r?   N)rç   ù               @y              @y              @y              @)r@   rA   rB   rC   r÷   r
   r.   r   r/   r:   r   r)   r0   rD   rE   rF   s   @r$   r
  r
  »  s5   ø‡ € Ù*Ø�"�W€FÙ	Ò!Ó	"€BØ€Eòò÷?ð ?r'   r
  c                   ó>   a € ] tR tRt o Rt^t^ .tRtR tR t	Rt
V tR# )ÚPiiÌ  z'Integrate 1/(t + 1j) from t=-10 to t=10Tc                óD   € \        R V^
,
          R,           ,          .4      # )r‚   rç   ©r   r  s   &&&r$   r   ÚPi.fÒ  s   € Ü�b˜!˜b�& 2�+Õ&Ð'Ó(Ð(r'   c                óŽ   € R\         P                  ! ^
4      ,          p\        W1R,          V P                  V P                  R7      # )r  r  y       €       À)rµ   r  )ÚnpÚarctanr   rR   rS   r  s   &&& r$   r0   Ú	Pi.verifyÕ  s/   € Ø”"—)’)˜B“-ÕˆÜ˜˜e�9¨4¯9©9¸4¿9¹9ÔEÐEr'   r?   N)r@   rA   rB   rC   r÷   r.   r/   r:   r   r0   rD   rE   rF   s   @r$   r  r  Ì  s*   ø‡ € Ù2Ø€FØ
ˆ€BØ€Eò)÷Fð Fr'   r  c                   óV   a € ] tR tRt o RtRtRt. R
Ot^t^ t	. ROt
R tR tR tRtV tR	# )ÚCoupledDecayiÚ  zY
3 coupled decays suited for banded treatment
(banded mode makes it necessary when N>>3)
Tç      à?c                ó@  € V P                   p\        P                  ! V^ ,          ) V^ ,          ,          V^,          ) V^,          ,          V^ ,          V^ ,          ,          ,           V^,          ) V^,          ,          V^,          V^,          ,          ,           .4      # r°   )Úlmbdr  r   )r2   r3   r!   r"  s   &&& r$   r   ÚCoupledDecay.fè  su   € Ø�y‰yˆÜ�xŠx˜$˜q�'˜ ! A¥$�Ø˜q�'˜ ! A¥$�¨¨a­°°1µ­Õ5Ø˜q�'˜ ! A¥$�¨¨a­°°1µ­Õ5ð7ó 8ð 	8r'   c                óX  a a€ S P                   p\        P                  ! S P                  S P                  ,           ^,           ^3RR7      oVV 3R lpV! ^ ^ V^ ,          ) 4       V! ^^ V^ ,          4       V! ^^V^,          ) 4       V! ^^V^,          4       V! ^^V^,          ) 4       S# )rý   ÚF©Úorderc                 óF   <€ VSSP                   V ,           V,
          V3&   R # r   )rP   )ÚriÚciÚvalÚjr2   s   &&&€€r$   Úset_jÚCoupledDecay.jac.<locals>.set_jþ  s   ø€ Ø*-ˆAˆd�j‰j˜2�o Õ" BÐ&Ó'r'   )r"  r  r   rQ   rP   )r2   r3   r!   r"  r-  r,  s   f&&  @r$   r)   ÚCoupledDecay.jacî  s•   ù€ ð �y‰yˆÜ�HŠH�d—j‘j 4§:¡:Õ-°Õ1°1Ð5¸SÔAˆö	.áˆa��T˜!•W�HÔÙˆa��D˜•GÔÙˆa��T˜!•W�HÔÙˆa��D˜•GÔÙˆa��T˜!•W�HÔØˆr'   c           
     ó–  € \         P                  ! V P                  4      pV^,          V^ ,          ,
          pV^,          V^,          ,
          pV^,          V^ ,          ,
          p\         P                  ! V^ ,          ) V,          4      p\         P                  ! V^,          ) V,          4      p\         P                  ! V^,          ) V,          4      p	\         P                  ! V P
                  ^ ,          V,          V P
                  ^,          V,          V P
                  ^ ,          V^ ,          ,          V,          Wx,
          ,          ,           V P
                  ^,          V	,          V P
                  ^,          V^,          ,          V,          W‰,
          ,          ,           V^,          V^ ,          ,          V P
                  ^ ,          ,          V,          ^V,          Wy,
          ,          ^V,          W‰,
          ,          ,
          ,          ,           34      P                  4       p
\        W¡V P                  V P                  R7      # )rý   r  )
r  r   r"  r   Úvstackr/   Ú	transposer   rR   rS   )r2   r  r!   r"  Úd10Úd21Úd20Úe0Úe1Úe2r  s   &&&        r$   r0   ÚCoupledDecay.verify  s†  € ä�xŠx˜Ÿ	™	Ó"ˆØ�1�g˜˜Q�ÕˆØ�1�g˜˜Q�ÕˆØ�1�g˜˜Q�ÕˆÜ�VŠV�T˜!•W�H˜q•LÓ!ˆÜ�VŠV�T˜!•W�H˜q•LÓ!ˆÜ�VŠV�T˜!•W�H˜q•LÓ!ˆÜ�IŠIØ�G‰G�A�J˜�OØ�G‰G�A�J˜�O˜dŸg™g a�j¨4°­7Õ2°SÕ8¸B½GÕDÕDØ�G‰G�A�J˜�O˜dŸg™g a�j¨4°­7Õ2°SÕ8¸B½GÕDÕDØ��G�d˜1•gÕ §¡¨¥
Õ*¨SÕ0Ø��W˜�Õ  1 s¥7¨b­gÕ#6Õ6õ8õ8ð9ó :÷
 ;D¹)»+ð 	
ô ˜ D§I¡I°D·I±IÔ>Ð>r'   r?   N)g      @g      @g      *@)gÃõ(\�ÂÅ?gq=
×£pÍ?g�Âõ(\�Ò?)r@   rA   rB   rC   r÷   rf   r.   r/   rQ   rP   r"  r   r)   r0   rD   rE   rF   s   @r$   r  r  Ú  s>   ø‡ € ñð
 €EØ€FÚ	€BØ€EØ€Eâ€Dò8ò÷2?ð ?r'   r  c                 ó,   € V^,          V^ ,          ) .pV# ©rý   r?   )r!   ÚxÚdxdts   && r$   r   r     s   € Øˆa�D�1�Q•4�%ˆ=€DØ€Kr'   c                 ó(   € \        R R.RR ..4      pV# )r   r‚   ç      ð¿r  )r!   r<  r,  s   && r$   r)   r)   #  s#   € Ü��SˆzØ�cˆ{ðó 	€Aà€Hr'   c                 óF   € W!^,          ,          V) V^ ,          ,          .pV# r;  r?   ©r!   r<  r  r=  s   &&& r$   Úf1rB  )  s!   € Ø�A•$�J˜˜˜q �t�Ð$€DØ€Kr'   c                 ó*   € \        R V.V) R ..4      pV# ©r   r  ©r!   r<  r  r,  s   &&& r$   Újac1rF  .  s%   € Ü��Uˆ|Ø�˜ˆ}ðó 	€Aà€Hr'   c                 óF   € W!^,          ,          V) V^ ,          ,          .pV# r;  r?   )r!   r<  Úomega1Úomega2r=  s   &&&& r$   Úf2rJ  4  s!   € Ø�Q•4�K˜&˜  1¥�Ð&€DØ€Kr'   c                 ó*   € \        R V.V) R ..4      pV# rD  r  )r!   r<  rH  rI  r,  s   &&&& r$   Újac2rL  9  s%   € Ü��Vˆ}Ø�˜ˆ~ðó 	 €Aà€Hr'   c                 ód   € V^ ,          V^,          ,          V^,          ) V^ ,          ,          .pV# r°   r?   rA  s   &&& r$   ÚfvrN  ?  s+   € Ø�!�H�Q�q•T�M˜E !�H˜9 Q q¥T�>Ð*€DØ€Kr'   c                 óF   € \        R V^ ,          .V^,          ) R ..4      pV# rD  r  rE  s   &&& r$   ÚjacvrP  D  s.   € Ü��U˜1•XˆØ�q•�	˜3Ðð!ó 	"€Aà€Hr'   c                   óV   a € ] tR tRt o RtRtRtR tR tR t	R t
R	 tR
 tR tRtV tR# )ÚODECheckParameterUseiJ  z=Call an ode-class solver with several cases of parameter use.Ú Fc                óÒ   € \        W4      pV P                  '       d,   VP                  V P                  R RV P                  R7       V# VP                  V P                  R RR7       V# )g•Ö&è.>gH¯¼šò×z>)rR   rS   Úwith_jacobianr  )r   Úsolver_uses_jacrV   Úsolver_name)r2   r   r)   Úsolvers   &&& r$   Ú_get_solverÚ ODECheckParameterUse._get_solverS  si   € Ü�Q“ˆØ××ÐØ×!Ñ! $×"2Ñ"2¸ÀDØ04×0DÑ0Dð "ô Fð ˆð ×!Ñ! $×"2Ñ"2¸ÀDÐ!ÔIØˆr'   c                óŒ   € R R.pVP                  VR4       VP                  \        4       \        VP                  RR.4       R# )r‚   r   Nr?  )rW   rX   r
   r   r"   ©r2   rX  Úics   && r$   Ú_check_solverÚ"ODECheckParameterUse._check_solver_  s;   € Ø�3ˆZˆØ× Ñ   SÔ)Ø×ÑœÔÜ! &§(¡(¨T°3¨KÖ8r'   c                ó\   € V P                  \        \        4      pV P                  V4       R # r   )rY  r   r)   r^  )r2   rX  s   & r$   Útest_no_paramsÚ#ODECheckParameterUse.test_no_paramse  s"   € Ø×!Ñ!¤!¤SÓ)ˆØ×Ñ˜6Ö"r'   c                óÈ   € V P                  \        \        4      pR pVP                  V4       V P                  '       d   VP                  V4       V P                  V4       R# ©r‚   N)rY  rB  rF  Úset_f_paramsrV  Úset_jac_paramsr^  ©r2   rX  r  s   &  r$   Útest_one_scalar_paramÚ*ODECheckParameterUse.test_one_scalar_parami  sO   € Ø×!Ñ!¤"¤dÓ+ˆØˆØ×Ñ˜EÔ"Ø××ÐØ×!Ñ! %Ô(Ø×Ñ˜6Ö"r'   c                óÌ   € V P                  \        \        4      pR pR pVP                  W#4       V P                  '       d   VP                  W#4       V P                  V4       R# rd  )rY  rJ  rL  re  rV  rf  r^  )r2   rX  rH  rI  s   &   r$   Útest_two_scalar_paramsÚ+ODECheckParameterUse.test_two_scalar_paramsq  sT   € Ø×!Ñ!¤"¤dÓ+ˆØˆØˆØ×Ñ˜FÔ+Ø××ÐØ×!Ñ! &Ô1Ø×Ñ˜6Ö"r'   c                óÌ   € V P                  \        \        4      pR R .pVP                  V4       V P                  '       d   VP                  V4       V P                  V4       R# rd  )rY  rN  rP  re  rV  rf  r^  rg  s   &  r$   Útest_vector_paramÚ&ODECheckParameterUse.test_vector_paramz  sS   € Ø×!Ñ!¤"¤dÓ+ˆØ�c�
ˆØ×Ñ˜EÔ"Ø××ÐØ×!Ñ! %Ô(Ø×Ñ˜6Ö"r'   c                óH  € V P                  \        \        4      pVP                  V P                  ^R7       RR.pVP                  VR4       \        P                  ! \        4      ;_uu_ 4        VP                  \        4       RRR4       R#   + '       g   i     R# ; i)rý   )Únstepsr‚   r   N)rY  r   r)   rV   rW  rW   ÚpytestÚwarnsÚUserWarningrX   r
   r\  s   &  r$   Útest_warns_on_failureÚ*ODECheckParameterUse.test_warns_on_failure‚  sr   € à×!Ñ!¤!¤SÓ)ˆØ×Ñ˜d×.Ñ.°qÐÔ9Ø�3ˆZˆØ× Ñ   SÔ)Ü�\Š\œ+×&Õ&Ø×ÑœRÔ ÷ '×&×&Ò&ús   Á0BÂB!	r?   N)r@   rA   rB   rC   r÷   rW  rV  rY  r^  ra  rh  rk  rn  ru  rD   rE   rF   s   @r$   rR  rR  J  s<   ø‡ € ÙGð
 €KØ€Oò
ò9ò#ò#ò#ò#÷!ð !r'   rR  c                   ó   € ] tR tRtRtRtRtR# )ÚTestDOPRI5CheckParameterUseiŒ  ru   Fr?   N©r@   rA   rB   rC   rW  rV  rD   r?   r'   r$   rx  rx  Œ  ó   † Ø€KØ„Or'   rx  c                   ó   € ] tR tRtRtRtRtR# )ÚTestDOP853CheckParameterUsei‘  r|   Fr?   Nry  r?   r'   r$   r|  r|  ‘  rz  r'   r|  c                   ó   € ] tR tRtRtRtRtR# )ÚTestVODECheckParameterUsei–  rd   Tr?   Nry  r?   r'   r$   r~  r~  –  s   † Ø€KØ„Or'   r~  c                   ó   € ] tR tRtRtRtRtR# )ÚTestZVODECheckParameterUsei›  rj   Tr?   Nry  r?   r'   r$   r€  r€  ›  ó   † Ø€KØ„Or'   r€  c                   ó   € ] tR tRtRtRtRtR# )ÚTestLSODACheckParameterUsei   rp   Tr?   Nry  r?   r'   r$   rƒ  rƒ     r�  r'   rƒ  c                  óv   € ^p ^ .p\        R WRR7      w  r#\        V\        P                  ! V ..4      4       R# )rý   c                 ó   € V ) # r   r?   )r"   r!   s   &&r$   r%   Ú*test_odeint_trivial_time.<locals>.<lambda>ª  s   €  1¡"r'   Tr   N)r   r   r  r   )rº   r!   r"   Úinfos       r$   Útest_odeint_trivial_timerˆ  ¥  s7   € ð 
€BØ	
ˆ€AÜ‘_ b¸Ô>�G€AÜ�qœ"Ÿ(š( R D 6Ó*Ö+r'   c                  óˆ  aaa€ R  oR oR p R oV3R lp\        . RO. RO. RO. RO.4      p\        P                  ! ^4      p\        P                   ! . RO4      p\        SW4V3RRRRSR	7	      w  rV\        SW4V3RRRRV RR
7
      w  rx\        SW4V3RRRRS^^R7      w  rš\        SW4V3RRRRV^^RR7      w  r¼\	        WWRR7       \	        WYRRR7       \	        W›RR7       \        VR,          VR,          4       \        V
R,          VR,          4       \        V3R lW4V3RRRRV3R lRR7
      w  rÞ\	        W]RRR7       R# )c                 ó$   € VP                  V 4      # r   )r   ©r"   r!   Úcs   &&&r$   ÚfuncÚ)test_odeint_banded_jacobian.<locals>.func±  s   € Ø�u‰u�Q‹xˆr'   c                 ó   € V# r   r?   r‹  s   &&&r$   r)   Ú(test_odeint_banded_jacobian.<locals>.jac´  s   € Øˆr'   c                 ó:   € VP                   P                  R R7      # ©ÚCr&  ©ÚTr¨   r‹  s   &&&r$   Újac_transposeÚ2test_odeint_banded_jacobian.<locals>.jac_transpose·  s   € Ø�s‰s�x‰x˜cˆxÓ"Ð"r'   c           
      ól  € \         P                  ! \         P                  ^ \         P                  ! V^4      3,          \         P                  ! V4      \         P                  \         P                  ! VR4      ^ 3,          \         P                  \         P                  ! VR4      ^ ^ 3,          34      pV# )r±   rµ   éþÿÿÿ)r  r1  Úr_Údiag)r"   r!   rŒ  r)   s   &&& r$   Ú	bjac_rowsÚ.test_odeint_banded_jacobian.<locals>.bjac_rowsº  sy   € Ü�iŠiœŸ™˜q¤"§'¢'¨!¨Q£-Ð/Õ0ÜŸGšG A›JÜŸE™E¤"§'¢'¨!¨R£.°!Ð"3Õ4ÜŸE™E¤"§'¢'¨!¨R£.°!°QÐ"6Õ7ð9ó :ˆð ˆ
r'   c                 óJ   <€ S! WV4      P                   P                  R R7      # r’  r”  )r"   r!   rŒ  rœ  s   &&&€r$   Ú	bjac_colsÚ.test_odeint_banded_jacobian.<locals>.bjac_colsÁ  s$   ø€ Ù˜˜qÓ!×#Ñ#×(Ñ(¨sÐ(Ó3Ð3r'   Tg‚vIhÂ%<=g•dyáý¥=i'  )Úargsr   rR   rS   Úmxstepr*   )r¡  r   rR   rS   r¢  r*   Ú	col_deriv)r¡  r   rR   rS   r¢  r*   ÚmlÚmu)	r¡  r   rR   rS   r¢  r*   r¤  r¥  r£  zsol1 != sol2)Úerr_msgçê-�™—q=zsol1 != sol3)rR   r¦  zsol3 != sol4Únjec                 ó   <€ S! WV4      # r   r?   )r!   r"   rŒ  r�  s   &&&€r$   r%   Ú-test_odeint_banded_jacobian.<locals>.<lambda>í  s   ø€ ©T°!¸¬]r'   c                 ó   <€ S! WV4      # r   r?   )r!   r"   rŒ  r)   s   &&&€r$   r%   rª  ð  s   ø€ ±#°a¸A´,r'   )r¡  r   rR   rS   r¢  r*   r(   zsol1 != sol1ty)rS   r¦  N)i3ÿÿÿç{®Gáz„?r   r   )r…   g      Àg{®Gáz”?r   )gü©ñÒMbP?r¬  g       Àr¬  )r   r   r…   r?  )r±   é   é
   éd   )r   r  Úonesr   r   r   )r–  rŸ  rŒ  rº   r!   Úsol1Úinfo1Úsol2Úinfo2Úsol3Úinfo3Úsol4Úinfo4Úsol1tyÚinfo1tyrœ  r�  r)   s                  @@@r$   Útest_odeint_banded_jacobianr»  ®  si  ú€ òòò#òõ4ô 	Ò&Ú&Ú'Ú&ð(ó 	)€Aô
 
�Š�‹€BÜ
�Š’Ó!€Aô ˜˜r¨A¨4¸TØ#¨%¸Ø!ô#�K€Dô
 ˜˜r¨A¨4¸TØ#¨%¸Ø+°tô=�K€Dô
 ˜˜r¨A¨4¸TØ#¨%¸Ø'¨A°!ô5�K€Dô
 ˜˜r¨A¨4¸TØ#¨%¸Ø'¨A°!¸tôE�K€Dô �D¨Õ7Ü�D U°NÕCÜ�D¨Õ7ô �u˜U•| U¨5¥\Ô2Ü�u˜U•| U¨5¥\Ô2ô Ô:¸BÈÈØ)-°EÀØ$)Ü">ÀtôM�O€Fô �D uÐ6F×Gr'   c            	      ó:  € R  p R pR pR pR pR pR p\        \        \        VR^ ^.4       \        \        \        VR^ ^.4       \        \        \        V R^ ^.VR7       \        \        \        V R^ ^.VR7       \        \        \        VRR.^ ^.VR7       R	# )
c                 ó   € RV ,          # ©r¯  éœÿÿÿr?   ©r<  r!   s   &&r$   Úsys1dÚ!test_odeint_errors.<locals>.sys1dø  ó   € Ø�A�vˆr'   c                 ó   € R ^ ,          # r�   r?   rÀ  s   &&r$   Úbad1Ú test_odeint_errors.<locals>.bad1û  ó   € Ø�1�uˆr'   c                 ó   € R # ©Úfoor?   rÀ  s   &&r$   Úbad2Ú test_odeint_errors.<locals>.bad2þ  s   € Ùr'   c                 ó   € R ^ ,          # r�   r?   rÀ  s   &&r$   Úbad_jac1Ú$test_odeint_errors.<locals>.bad_jac1  rÇ  r'   c                 ó
   € R ..# rÉ  r?   rÀ  s   &&r$   Úbad_jac2Ú$test_odeint_errors.<locals>.bad_jac2  s   € Ø�ˆyÐr'   c                 óB   € RV ^ ,          ,          RV ^,          ,          .# )r¯  r¿  çš™™™™™¹¿r?   rÀ  s   &&r$   Úsys2dÚ!test_odeint_errors.<locals>.sys2d  s   € Ø�Q�q•T•	˜4  !¥�9Ð%Ð%r'   c                 ó    € R ^ ,          ^ .^ R..# )r‚   rÔ  r?   rÀ  s   &&r$   Úsys2d_bad_jacÚ)test_odeint_errors.<locals>.sys2d_bad_jac
  s   € Ø�Q•˜�
˜Q ˜IÐ&Ð&r'   r‚   ©r*   N)Úassert_raisesÚZeroDivisionErrorr   Ú
ValueError)rÁ  rÅ  rË  rÎ  rÑ  rÕ  rØ  s          r$   Útest_odeint_errorsrÞ  ÷  s›   € òòòòòò&ò'ô Ô#¤V¨T°3¸¸A¸Ô?Ü”*œf d¨C°!°Q°Ô8äÔ#¤V¨U°C¸!¸Q¸ÀhÕOÜ”*œf e¨S°1°a°&¸xÕHäÔ#¤V¨U°S¸#°JÀÀAÀØ$÷&r'   c            	      ó  € R  p R pR p^ ^ .^ ^ ..p\        \        \        W^ ^.4       ^ ^.^^..p\        \        \        VR.V4       \        \        \        V ^
^ ^.4       \        \        \        V^
^
.^ ^.VR7       R# )c                 ó
   € ^R.# )rý   rµ   r?   rÀ  s   &&r$   ÚbadrhsÚ&test_odeint_bad_shapes.<locals>.badrhs  s   € Ø�2ˆwˆr'   c                 ó   € RV ,          # r¾  r?   rÀ  s   &&r$   Úsys1Ú$test_odeint_bad_shapes.<locals>.sys1  rÃ  r'   c                 ó   € . RO.# )r±   )r±   r±   r±   r?   rÀ  s   &&r$   ÚbadjacÚ&test_odeint_bad_shapes.<locals>.badjac   s
   € Úˆ{Ðr'   r£   rÚ  N)rÛ  rÝ  r   ÚRuntimeError)rá  rä  rç  Úbad_y0Úbad_ts        r$   Útest_odeint_bad_shapesrì    s�   € òòòð �!ˆf�q˜!�fÐ€FÜ”*œf d°Q¸°FÔ;ð �ˆV�a˜�VÐ€EÜ”*œf d¨T¨F°EÔ:ô ”,¤¨°°Q¸°FÔ;ô ”,¤¨¨r°2¨h¸¸A¸ÀV×Lr'   c                 óÜ  € R p \         P                  ! ^
4      p\        V R.V4      p\        V\         P                  ! \        V4      ^34      4       ^\         P                  ! ^4      ,          p^ .^	,          V^V,          ^V,          ^V,          .,           p\        V ^^.VRRR7      p\         P                  ! RR..^	,          RR.RR.RR.RR..,           4      p\        W$4       \        V R.. 4      p\        V\         P                  ! . \         P                  R	7      P                  R4      4       \        \        \        V R.. RO4       \        \        \        V . RO. RO4       R
# )zRegression test for gh-8217.c                 ó   € RV ,          # )ç      Ð?g      Ð¿r?   rÀ  s   &&r$   r�  Ú$test_repeated_t_values.<locals>.func5  s   € Ø�Q�wˆr'   r‚   r§  )rS   rR   r¤   r   rï  g      À?)ÚdtypeNrü   )r±   rý   r   r±   )rý   rû   é   )r±   rµ   r™  rò  )r  r   r   r   r°  ÚlenÚlogr   r   Úfloat64ÚreshaperÛ  rÝ  )r�  r!   r†   ÚtauÚexpected_sols        r$   Útest_repeated_t_valuesrù  2  s1  € òô 	�Š�‹€AÜ
�˜�t˜QÓ
€CÜ�sœBŸGšG¤S¨£V¨Q KÓ0Ô1à
ŒB�FŠF�1‹I�+€CØ	
ˆˆA���a˜•e˜Q˜s�U A c¥EÐ*Õ*€AÜ
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