ftjȱddlZddlZddlmZddlmZejej Z ejej Z dZ dZdZdZd Zd Zd Zd ZdS) N)qr)get_arrays_tolc |r7t|tjr |jdksJt j||sJt|tjr|j|jksJt|tjr|j|jksJt|tsJt|tsJt||}tj ||ksJtj || ksJtj |r|dksJtj |d}tj|d}|j}tj|}tj|} |dk|dkz|dk|dkzz} tj|} tj| } ||  | | <d} d}d}| tj| kr|| z}|dt&z|zt)dtj|zkrnc t/| | |}n#t0$rYnCwxYw| |zd|zkrn0|| }| |z}|t2t5|zkrt)| |z d}n tj}t9||}| |d|z|zzzd|zkrn|tj k| t2 tj|| z zkz}|tjk| t2tj|| z zkz}tj| tj}tj| tj}tj||| |z | |z d||<tj||| |z | |z d||<tj|}tj|}t9||}t9||}|dkrPtj| | || | zz|| || | | <|||zz }|||d|z|zzzz}|t9||kr7|| || z|z }|| | z|| z | | <d| | <| dz } n||kr_||kr tj|}||| |<ntj|}||| |<d| |<||  | | <d| | <d} nM||krtA|}||| |<d| |<||krtA|}||| |<d| |<d }n| tj| k|!d d r|rtj| }| |zd|z||zz} tj| dkr;| | | | z}!|| || z}"|| | | z}#tj"t)|!|"z|#d zz d }|#| | z|!|| zz | | <d| | <|d |zks9tj#|t2 tj| | zkrnx| | xx| zcc<tj$|}$tj$|}%| | d z| | d zz|| d zz |$| <| | d z| | d zz|| d zz |%| <tj"|$|$dk| |$dkz |$|$dk<tj"|%|%dk| |%dkz|%|%dk<tj| |z d}&tj|| z d}'|$t2|&zk}|%t2|'zk}tj%|}(tj%|})tj |(||&||$|z |(|<tj |)||'||%|z |)|<tj|(}*tj|)}+t9|*|+},|| }-|| }| |-z}.| |z}| |z}/d }0tM|0dz |,zdz}0tj'|,|0z |,|0}1d |1zd|1d zzz }2|2|#|1z|z |1|.zz |2|1|/zd||.z zz zzz}3tj |3dkrntj(|3}4d|1|4d zz d|1|4d zzz }5|5| | z|2|4| | zz| | <||5dz |-z|2|4|zzz }||3|4z }|,dkrT|4|0dz krK|*|,krtA|(}||| |<d| |<|+|,krtA|)}||| |<d| |<nntj| dk;| | zd| z|| zz| kr|} |r\tj || ksJtj | |ksJtj| d|zksJ| S)ad Minimize approximately a quadratic function subject to bound constraints in a trust region. This function solves approximately .. math:: \min_{s \in \mathbb{R}^n} \quad g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u\\ \lVert s \rVert \le \Delta, \end{array} \right. using an active-set variation of the truncated conjugate gradient method. Parameters ---------- grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. hess_prod : callable Product of the Hessian matrix :math:`H` with any vector. ``hess_prod(s) -> `numpy.ndarray`, shape (n,)`` returns the product :math:`H s`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Other Parameters ---------------- improve_tcg : bool, optional If True, a solution generated by the truncated conjugate gradient method that is on the boundary of the trust region is improved by moving around the trust-region boundary on the two-dimensional space spanned by the solution and the gradient of the quadratic function at the solution (default is True). Notes ----- This function implements Algorithm 6.2 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. rF$?:0yE>?T improve_tcg@:0yE皙?)) isinstancenpndarrayndiminspect signaturebindshapefloatboolrallisfiniteminimummaximumsizecopy zeros_like count_nonzeroEPSmaxlinalgnorm _alpha_trZeroDivisionErrorTINYabsinfmin full_likeclipargmin_argmingetsqrtanyzerosonesintlinspaceargmax)6grad hess_prodxlxudeltadebugkwargstoln grad_origfree_bdstepsdkreductboundary_reachedgrad_sdalpha_trhess_sdcurv_sd alpha_quadalphai_xli_xu all_alpha_xl all_alpha_xualpha_xlalpha_xualpha_bdbetai_new step_basestep_comparatorstep_sqgrad_sq grad_steptemp_xltemp_xudist_xldist_xuall_t_xlall_t_xut_xlt_xut_bd hess_step curv_step curv_step_sd n_samples t_samples sin_values all_reducti_max cos_values6 `/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/_lib/cobyqa/subsolvers/optim.pytangential_byrd_omojokunrr s @ 2$ ++> Q> ++0066666"bj))Dbh$*.D.D.DD"bj))Dbh$*.D.D.DD%'''''%&&&&&R$$vbCi     vbSDj!!!!!{5!!1eckkk1 B  B B  B A 74==D ISTCZ(b3h4#:-FGG =  D t  B=.BwK A F bw'' ' ') eckAoC1E1E(F(FF F F   r511HH     E  9w $- / / )B--w, TCLL( ( (gX/55JJJHj)) 6WsU{W44 5 F F bfW tebfR$Y.?.?&?!?@RV TBF29,=,=%= =>|D"&11 |D"&11 Z XT "bh .   T Z XT "bh .   T6,''6,''x**E8$$ 3;;GW 7 337 7 DM EGO #D ewuw)>>? ?F 3x** * *MGG$44?DG,tG}L IY]d2Q677I D9$4dIFFIyC)S.,@AJ#I%i'(|+cWy5H.IIKKJvjC'(( Ij))Ey/366i&#--IDM)Ju,=7 ,KK M Y_ 1Ju4E4OO OD j' 'F czzey1}444<<#H--E"$U)DK%*GEN4<<#H--E"$U)DK%*GENIw''!++P t cDj99T??: :_ L LD 2vbDj!!!!!vdbj!!!!!y~~d##cEk1111 Ks I I)(I)c  8|r t|tjr |jdksJt j||sJt|tjr|j|jksJt|tjr|j|jksJt|tjr!|jdkr|jd|jksJt|tjr!|jdkr|j|jdksJt|tjr!|jdkr|jd|jksJt|tsJt|tsJt||} tj || ksJtj || ksJtj || ksJtj |r|dksJtj|d}tj|d}tj|d}|j} tj|}tj|} |dk|dkz} |dk|dkz}|dk||zdkz}t#||| ||\}}tj|}|dd|df |dd|dfj|zz}tj|}d}d}d}|| |z kr||z}|dt(z| zt+dtj|zkrn[ t1|||}n#t2$rYn;wxYw| |zd |zkrn(||}||z}|t4t7|zkrt+| |z d}n tj}t;||}| |d |z|zzzd |zkrn| |tj kz|t4 tj||z zkz}||tjkz|t4tj||z zkz}tj|tj} tj|tj}!tj||||z ||z d| |<tj||||z ||z d|!|<tj| }"tj|!}#t;|"|#}$||z}%||%t4tj|zkz}&tj|tj}'||&|%|&z |'|&<tj|'tj }(t;||$|(}|dkrPtj|||zz||}|||zz }tjd|||%zz }|||d |z|zzzz}|t;||$|(kr<|dd|df|dd|dfj|zz})|)|z|z }*|*|z|)z }|dz }n1||kr|"|kr%tj | }+||+||+<d| |+<nD|#|kr%tj |!}+||+||+<d||+<ntj |'}+d||+<t#||| ||\}}|dd|df |dd|dfj|zz}d}n}|"|krtC| }+||+||+<d| |+<|#|krtC|!}+||+||+<d||+<|(|krtC|'}+d||+<t#||| ||\}}d }n || |z k| "d d r |r || krtj|},|| kr|dd|df|dd|dfj|zz}-|dd|df|dd|dfj|zz})|-|-z}.|)|)z}/|)|-z}0tj#t+|.|/z|0dzz d }|dd|df|dd|dfj|0|z|.|zz zz}|d|zks3tj$|t4 tj|zkrn|| z}tj%| }1tj%| }2tj||z d}3tj||z d}4|| dz|3| |3| d|-| zz zz |1| <||dz|4||4|d|-|zzzz |2|<tj#|1|1dk||1dkz |1|1dk<tj#|2|2dk||2dkz|2|2dk<|1t4|3zk}|2t4|4zk}tj&| }5tj&| }6tj|5||3||1|z |5|<tj|6||4||2|z |6|<tj|5}7tj|6}8t;|7|8}9tj|}:||-z};||z}%|%|dz||||d|;|zzzz |:|<tj#|:|:dk|%|:dkz|:|:dk<|:t4|zk}&tj'|}||-}?||}|-|?z}@||z}|-|z}Ad}BtQ|Bdz |>zdz}Btj)|>|Bz |>|B}Cd|Czd|Cdzzz }D|D|0|Cz|z |Dd |Cdzz|@zd|Cz|Azz d |zzzz z}Etj |Edkrn:tj*|E}Fd|C|Fdzz d|C|Fdzzz }Gtj||Gdz |-zz|D|F|zz||}||Gdz |?z|D|F|zzz }tjd||Gdz |;zz |D|F|%zz }||E|Fz }|>dkr|F|Bdz kr{|7|>krtC|5}+||+||+<d| |+<|8|>krtC|6}+||+||+<d| |+<|=|>krtC|<}+d||+<t#||| ||\}}nn|| k| |zd |z||zz| |,zd |,z||,zzkr|,}|rt||} tj ||ksJtj ||ksJtj ||z|| zksJtj tj||z| ksJtj|d|zksJ|S)af Minimize approximately a quadratic function subject to bound and linear constraints in a trust region. This function solves approximately .. math:: \min_{s \in \mathbb{R}^n} \quad g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ A_{\scriptscriptstyle I} s \le b_{\scriptscriptstyle I},\\ A_{\scriptscriptstyle E} s = 0,\\ \lVert s \rVert \le \Delta, \end{array} \right. using an active-set variation of the truncated conjugate gradient method. Parameters ---------- grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. hess_prod : callable Product of the Hessian matrix :math:`H` with any vector. ``hess_prod(s) -> `numpy.ndarray`, shape (n,)`` returns the product :math:`H s`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. aub : `numpy.ndarray`, shape (m_linear_ub, n) Coefficient matrix :math:`A_{\scriptscriptstyle I}` as shown above. bub : `numpy.ndarray`, shape (m_linear_ub,) Right-hand side :math:`b_{\scriptscriptstyle I}` as shown above. aeq : `numpy.ndarray`, shape (m_linear_eq, n) Coefficient matrix :math:`A_{\scriptscriptstyle E}` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Other Parameters ---------------- improve_tcg : bool, optional If True, a solution generated by the truncated conjugate gradient method that is on the boundary of the trust region is improved by moving around the trust-region boundary on the two-dimensional space spanned by the solution and the gradient of the quadratic function at the solution (default is True). Notes ----- This function implements Algorithm 6.3 of [1]_. It is assumed that the origin is feasible with respect to the bound and linear constraints, and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. rrrrNFr r r r initialTr rrrrr)+rrrrrrrrr!rrrrrrr r"qr_tangential_byrd_omojokunr#Tr%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7 ones_liker8r9r:)Hr;r<r=r>aubbubaeqr?r@rArBrCrDfree_xlfree_xufree_ubn_actqrFrGresidrHrIrJrKrLrMrNrOrPrQrRrSrTrUrVrWaub_sdi_ub all_alpha_ubalpha_ub grad_projrXrYrZ step_projr\r]r^r_r`rarbrcrdrerfrgtemp_ubaub_stepall_t_ubt_ubt_minrhrirjrkrlrmrnrorpsH rq$constrained_tangential_byrd_omojokunrCs^f 2$ ++> Q> ++0066666"bj))Dbh$*.D.D.DD"bj))Dbh$*.D.D.DD sBJ ' ' A  !  ))) * sBJ ' ' A CIaL((( ) sBJ ' ' A  !  ))) *%'''''%&&&&&R$$vbCi     vbSDj!!!!!vccTk"""""{5!!1eckkk1 B  B B  B *S#  C A 74==D ICxD3J'GCxD3J'GSyS4Z#-.G*3WgwOOHE1 =  D AAAuvvI,!AAAuvvI,.4/ 0B GCLLE A F a%i--) eckAoC1E1E(F(FF F F   r511HH     E  9w $- / / )B--w, TCLL( ( (gX/55JJJHj)) 6WsU{W44 5 F F "w,'2rDy8I8I0I+IJ"rv+&"tbfR$Y6G6G/G*GH|D"&11 |D"&11 Z XT "bh .   T Z XT "bh .   T6,''6,''x**r&4"&--#778|C00 "4[6$<7 T6,777E8X.. 3;;74%"*,b"55D EGO #DJsEEFN$:;;E ewuw)>>? ?F 3x844 4 4!!!UVV) !!!UVV) (=>I'72DY&B FAA X  5   ,// iU !&U"" ,// iU !& ,//!&2 HE1AAAuvvI,!AAAuvvI,.4"78BAA 5   -- iU !&5   -- iU !&5   --!&2 HE1 $  k a%i--pzz-&&Z+;Z GDMM aii!!!UVV) !!!UVV) (=>I!!!UVV) !!!UVV) (=>I)+G)+G!I-Iws7W#4y#~#EsKKLLLG111eff9!!!UVV) )d"2Wt^"CDB%&.((BFD526"::----( 7(NB hqkkGhqkkGjC00GjdC00G!'{c1GG4D 37);#;;5 GG  "'{c1GG4D 37);#;;5 GG # .//"Ws]2CC GcM "# .//"Ws]2CC GcM "TG^+DTG^+DwqzzHwqzzHZ  -HTN Z  -HTN6(##D6(##DtT??DmE**GYH2XF%g#5ggx'8!889 GG # .//&32GG GcM "TE\)D|E**HZd gdm+HTN6(C000DdOOE" ),,IimmG!I-I7lG$w.L IY]e3a788I EI$5uiHHIyC)S.,@AJ#I%)S.(94Io 45Gm$ JvjC'(( Ij))Ey/366i&#--I7 C944z%7H27MMD Y_ 1Ju4E4OO ODJs?h./U#f,-E j' 'F s{{u A 555==#H--E"$U)DK%*GEN5==#H--E"$U)DK%*GEN5==#H--E%*GEN6 qqcaiij t cDj99 , ,    !C)Oii 6J6J$J J K KD 2R$$vbDj!!!!!vdbj!!!!!vcDjC#I-.....vbfS4Z((C/00000y~~d##cEk1111 Ks M22 N?Nc |rt|tjr |jdksJt|tjr!|jdkr|j|jdksJt|tjr'|jdkr|jd|jdksJt|tjr!|jdkr|j|jdksJt|tjr|j|jdfksJt|tjr|j|jdfksJt|t sJt|tsJt||} tj || ksJtj || ksJtj |r|dksJtj |d}tj |d}|j\} } tj |j| ztj d| f} |dk| d| dkz} |dk| d| dkz}|dk}|dk|| d| z| | dz dkz}t|| |||\}}tj||z| | d| | dzz}tj| }|dd|df |dd|dfj| zz}|| | dz}d}d}d}|| | z|z kr| |z}|dt$z| zt'dtj| zkrn t-||d| |}n#t.$rtj}YnwxYw t3|t-| | d|| d|}n#t.$rYnwxYw| |zd |zkrn&tj |j||d| zz|| df}||z}|t4t7|zkrt'| |z d}n tj}t3||}| |d |z|zzzd |zkrn| |tj kz|d| t4 tj||z zkz} ||tjkz|d| t4tj||z zkz}!||| dt4 tj| | dzkz}"tj|tj}#tj|tj}$tj|tj}%tj || || z |d| | z d|#| <tj ||!||!z |d| |!z d|$|!<tj | | d|" || d|"z d|%|"<tj|#}&tj|$}'tj|%tj }(t3|&|'|(})||d| z|| dz }*||*t4tj|zkz}+tj|tj},||+|*|+z |,|+<tj|,tj }-t3||)|-}|dkrXtj|||d| zz||}| ||zz } tj d|||*zz }|||d |z|zzzz}|t3||)|-kr<|dd|df|dd|dfj| zz}.|.|z|z }/|/|z|.z }|dz }n!||kr|&|kr%tj|#}0||0||0<d| |0<nd|'|kr%tj|$}0||0||0<d||0<n9|(|krtj|%}0d||0<ntj|,}0d||0<t|| |||\}}|dd|df |dd|dfj| zz}d}nM|&|krt?|#}0||0||0<d| |0<|'|krt?|$}0||0||0<d||0<d }n || | z|z k| d d r|rtj!|}1| |z}2|jtj ||z|z dz|j||z|z zz} tj| }tj"|2dkr||2||2z}3| |2| |2z}4| |2||2z}5tjt'|3|4z|5dzz d }|5||2z|3| |2zz ||2<d||2<|d|zks9tj#|t4 tj||2zkrn9||2xx| zcc<tj| }6tj| }7||2dz||2dzz||2dzz |6|2<||2dz||2dzz||2dzz |7|2<tj|6|6dk||6dkz |6|6dk<tj|7|7dk||7dkz|7|7dk<tj ||z d}8tj ||z d}9|6t4|8zk} |7t4|9zk}!tj$| }:tj$| };tj |:| |8| |6| z |:| <tj |;|!|9|!|7|!z |;|!<tj|:}d}?tK|?dz |>zdz}?tj&|>|?z |>|?}@tj ||z|z d}A||z|z }Btj!|}Cd|C|2<tj'|?}DtQ|?D]}Ed|@|Ezd|@|Edzzz }Ftj||F||@|E|Czz zz||}Gtj ||Gz|z d}H||Gz|z }Id |A|Az|B|Bzz|H|Hzz |I|Izz z|D|E<tj |Ddkrntj)|D}Jd|@|Jdzz d|@|Jdzzz }Kd|@|Jzd|@|Jdzzz }F|K||2z|F||2zz||2<|jtj ||z|z dz|j||z|z zz} ||D|Jz }|>dkrT|J|?dz krK|<|>krt?|:}0||0||0<d|2|0<|=|>krt?|;}0||0||0<d|2|0<nntj"|2dktj ||z|z d}Atj ||1z|z d}L||z|z }B||1z|z }M|A|Az|B|Bzz|L|Lz|M|Mzzkr|1}|r\tj ||ksJtj ||ksJtj|d|zksJ|S)a Minimize approximately a linear constraint violation subject to bound constraints in a trust region. This function solves approximately .. math:: \min_{s \in \mathbb{R}^n} \quad \frac{1}{2} \big( \lVert \max \{ A_{\scriptscriptstyle I} s - b_{\scriptscriptstyle I}, 0 \} \rVert^2 + \lVert A_{\scriptscriptstyle E} s - b_{\scriptscriptstyle E} \rVert^2 \big) \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right. using a variation of the truncated conjugate gradient method. Parameters ---------- aub : `numpy.ndarray`, shape (m_linear_ub, n) Matrix :math:`A_{\scriptscriptstyle I}` as shown above. bub : `numpy.ndarray`, shape (m_linear_ub,) Vector :math:`b_{\scriptscriptstyle I}` as shown above. aeq : `numpy.ndarray`, shape (m_linear_eq, n) Matrix :math:`A_{\scriptscriptstyle E}` as shown above. beq : `numpy.ndarray`, shape (m_linear_eq,) Vector :math:`b_{\scriptscriptstyle E}` as shown above. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Other Parameters ---------------- improve_tcg : bool, optional If True, a solution generated by the truncated conjugate gradient method that is on the boundary of the trust region is improved by moving around the trust-region boundary on the two-dimensional space spanned by the solution and the gradient of the quadratic function at the solution (default is True). Notes ----- This function implements Algorithm 6.4 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. rrrrNFr r r r rtTr rrrrr)*rrrrr!rrrrrrrr r_rwqr_normal_byrd_omojokunr4r6r%r&r'r(r)r*r-r.r+r,r/r0r1r2r3r"r$r5r7r8r9emptyranger:)Nryrzr{beqr=r>r?r@rArB m_linear_ubrCr;r|r} free_slackr~rr delta_slackrFrGrrHrIrJrKrLrMrNrOrPrQrRi_slackrSrTall_alpha_slackrUrV alpha_slackrWrrrrrrXrYrZrEr\r]r^r_r`rarbrcrdrerfrgrkrlresid_ubresid_eqrrni sin_valuestep_alt resid_ub_alt resid_eq_altrorp resid_ub_base resid_eq_basesN rqnormal_byrd_omojokunrsF 2#rz**>? ?F 3x844 4 4!!!UVV) !!!UVV) (=>I'72DY&B FAA X  5   ,// iU !&U"" ,// iU !&%% /22$) 5!! ,//!&.Wgz7HE1AAAuvvI,!AAAuvvI,.4"78BAA 5   -- iU !&5   -- iU !&#  q a+o% % %vzz-&&~+;~GDMM G#urz#*s"2C88835 $J <  Xa[[w''!++7md7m3G7md7m3GW W 5Iws7W#4y#~#EsKKLLLG#d7m3gW 6MMBwKBxL%&.((BFD526"W+#6#666--( wKKKG8 #KKK hqkkGhqkkGW $r'{c'99BwK3DD "X~3 #x')*"\12#\12! 1 vjC'(( Ij))Ey/366i&#--Iy//)E"2c"99;I%W 5 BwK8OODM52:cDj3&6<<> :#i#- x (X"5 5m+mm.KK L LD 2vbDj!!!!!vdbj!!!!!y~~d##cEk1111 Ks$9NN,+N,0/O O-,O-c 2|j}tj|}ttj|g||ddfg||ddf g||ddfggjd\}}} tjtjtj|dtz|ztj |dtj |j dtj |j fdzk} | |fSNT)pivotingg$@r)axis)r!reyerblockrwr$r,diagr%r'r(r.r) ryr{r|r}r~rCidentityrr_rs rqrvrvcs' AvayyH gXqqq[!"G8QQQ;''(7(AAA+&'        GAq!   rwqzz      )..,RVAG__,.?qw.??@q. I I J J  E !8Oc|j\}}tj|}tj|}ttj||ddf||ddf gtj|tj|z |f||ddf g||ddf tj|tj|z |fg||ddftj|tj|z |fggjd\} } } tjtjtj | dtz||zztj | dtj | jdtj | jfdzk} | | fSr)rrrrrr6r$rwr,rr%r'r(r.) ryr|r}rr~rrC identity_n identity_mrrrrs rqrr{sYNKJ $$J !!! $!!! ,, HkB,> ? ?D#~~%$TG^)<)<"<<<w%/55 TG^  tj0 0 0zTG^4c:: OrcVtj|tj|kSN)r flatnonzeror&xs rq_argmaxr >!rvayy. ) ))rcVtj|tj|kSr)rrr.rs rqr2r2rr)rnumpyr scipy.linalgrutilsrfinfortinyr+epsr%rrrrrvrr)rr2rrqrs""""""rxbhuoosssl ```F zzzz 0"""J   ********r