o Xi#@sfdZddlmZddlmZddlmZmZmZddl Z ddl m Z dgZ d d Zddefd dZdS) z&Byrd-Omojokun Trust-Region SQP method.)eye) projections)modified_dogleg projected_cgbox_intersectionsN)normequality_constrained_sqpcCst|\}t|S)N)npshapespeye)xnrb/tmp/pip-target-1s0edx8b/lib/python/scipy/optimize/_trustregion_constr/equality_constrained_sqp.pydefault_scaling s rcO Csd}d}d}d}d}d}d}d}d}d}d}t|\}| d ur(t|tj } |d ur3t|tj}t|}| }| }|}|} |}!|}"||}#z t|"| \}$}%}&Wntyk}'z t|'d kretd |'|'d }'~'ww|%|  }(|||(})t | |"j |(tj}*t |!d krt |!tjnd }+d d d d},d }-|| ||-|*|+|||,s>t |"|&|!|||| ||}.|)|.| }/t |!}0t|dtj |.d}1| |.}2||.}3t|)|/|$|&|0|1|2|3\}4},|.|4}5d|)|5|5| j |5}6|"|5|!}7t |!t |7}8td|8}8|}9|6d kr |6d||8}:t||:}|6 ||8};||t |!}<||#|5}=||=\}>}?|>|t |?}@|<|@}A|A|;}B|B|krt |.|t |4kr|&|? }Ct|5|C| |\}D}E}F||#|5|E|C}G||G\}H}I|H|t |I}J|<|J}K|K|;}L|Fr|L|kr|G}=|H}>|I}?|L}B|B|krt|t |5|}n<|B|krt|t |5|}n-|B|krd|d|B}M|Mt |5}N|N||kr||9}n|N||kr|N}n||9}|B|kr/|=}|>|?}}!||\} }"||}#t|"| \}$}%}&|%|  }(|||(})d }-t | |"j |(tj}*t |!d kr,t |!tjnd }+n|9}d}-|| ||-|*|+|||,r|| fS)auSolve nonlinear equality-constrained problem using trust-region SQP. Solve optimization problem: minimize fun(x) subject to: constr(x) = 0 using Byrd-Omojokun Trust-Region SQP method described in [1]_. Several implementation details are based on [2]_ and [3]_, p. 549. References ---------- .. [1] Lalee, Marucha, Jorge Nocedal, and Todd Plantenga. "On the implementation of an algorithm for large-scale equality constrained optimization." SIAM Journal on Optimization 8.3 (1998): 682-706. .. [2] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. "An interior point algorithm for large-scale nonlinear programming." SIAM Journal on Optimization 9.4 (1999): 877-900. .. [3] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006). g333333?g?g:0yE>g@g@g?g?g?Nzexpected square matrixzThe 'expected square matrix' error can occur if there are more equality constraints than independent variables. Consider how your constraints are set up, or use factorization_method='SVDFactorization'.rF)niter stop_cond hits_boundarygؗҜs