^MhdZddlmZddlZddlZddlZddlZddlZddl m Z ddl m Z m Z mZddlmZddlmZddlmZdd lmZdd lmZd gZ ddddZGddZGddZGddZdS)z`). Alternatively supply a map-like callable, such as `multiprocessing.Pool.map` for parallel evaluation. This evaluation is carried out as ``workers(func, iterable)``. Requires that `func` be pickleable. .. versionadded:: 1.11.0 Returns ------- res : OptimizeResult The optimization result represented as a `OptimizeResult` object. Important attributes are: ``x`` the solution array corresponding to the global minimum, ``fun`` the function output at the global solution, ``xl`` an ordered list of local minima solutions, ``funl`` the function output at the corresponding local solutions, ``success`` a Boolean flag indicating if the optimizer exited successfully, ``message`` which describes the cause of the termination, ``nfev`` the total number of objective function evaluations including the sampling calls, ``nlfev`` the total number of objective function evaluations culminating from all local search optimizations, ``nit`` number of iterations performed by the global routine. Notes ----- Global optimization using simplicial homology global optimization [1]_. Appropriate for solving general purpose NLP and blackbox optimization problems to global optimality (low-dimensional problems). In general, the optimization problems are of the form:: minimize f(x) subject to g_i(x) >= 0, i = 1,...,m h_j(x) = 0, j = 1,...,p where x is a vector of one or more variables. ``f(x)`` is the objective function ``R^n -> R``, ``g_i(x)`` are the inequality constraints, and ``h_j(x)`` are the equality constraints. Optionally, the lower and upper bounds for each element in x can also be specified using the `bounds` argument. While most of the theoretical advantages of SHGO are only proven for when ``f(x)`` is a Lipschitz smooth function, the algorithm is also proven to converge to the global optimum for the more general case where ``f(x)`` is non-continuous, non-convex and non-smooth, if the default sampling method is used [1]_. The local search method may be specified using the ``minimizer_kwargs`` parameter which is passed on to ``scipy.optimize.minimize``. By default, the ``SLSQP`` method is used. In general, it is recommended to use the ``SLSQP``, ``COBYLA``, or ``COBYQA`` local minimization if inequality constraints are defined for the problem since the other methods do not use constraints. The ``halton`` and ``sobol`` method points are generated using `scipy.stats.qmc`. Any other QMC method could be used. References ---------- .. [1] Endres, SC, Sandrock, C, Focke, WW (2018) "A simplicial homology algorithm for lipschitz optimisation", Journal of Global Optimization. .. [2] Joe, SW and Kuo, FY (2008) "Constructing Sobol' sequences with better two-dimensional projections", SIAM J. Sci. Comput. 30, 2635-2654. .. [3] Hock, W and Schittkowski, K (1981) "Test examples for nonlinear programming codes", Lecture Notes in Economics and Mathematical Systems, 187. Springer-Verlag, New York. http://www.ai7.uni-bayreuth.de/test_problem_coll.pdf .. [4] Wales, DJ (2015) "Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape", Journal of Chemical Physics, 142(13), 2015. .. [5] https://docs.scipy.org/doc/scipy/tutorial/optimize.html#constrained-minimization-of-multivariate-scalar-functions-minimize Examples -------- First consider the problem of minimizing the Rosenbrock function, `rosen`: >>> from scipy.optimize import rosen, shgo >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] >>> result = shgo(rosen, bounds) >>> result.x, result.fun (array([1., 1., 1., 1., 1.]), 2.920392374190081e-18) Note that bounds determine the dimensionality of the objective function and is therefore a required input, however you can specify empty bounds using ``None`` or objects like ``np.inf`` which will be converted to large float numbers. >>> bounds = [(None, None), ]*4 >>> result = shgo(rosen, bounds) >>> result.x array([0.99999851, 0.99999704, 0.99999411, 0.9999882 ]) Next, we consider the Eggholder function, a problem with several local minima and one global minimum. We will demonstrate the use of arguments and the capabilities of `shgo`. (https://en.wikipedia.org/wiki/Test_functions_for_optimization) >>> import numpy as np >>> def eggholder(x): ... return (-(x[1] + 47.0) ... * np.sin(np.sqrt(abs(x[0]/2.0 + (x[1] + 47.0)))) ... - x[0] * np.sin(np.sqrt(abs(x[0] - (x[1] + 47.0)))) ... ) ... >>> bounds = [(-512, 512), (-512, 512)] `shgo` has built-in low discrepancy sampling sequences. First, we will input 64 initial sampling points of the *Sobol'* sequence: >>> result = shgo(eggholder, bounds, n=64, sampling_method='sobol') >>> result.x, result.fun (array([512. , 404.23180824]), -959.6406627208397) `shgo` also has a return for any other local minima that was found, these can be called using: >>> result.xl array([[ 512. , 404.23180824], [ 283.0759062 , -487.12565635], [-294.66820039, -462.01964031], [-105.87688911, 423.15323845], [-242.97926 , 274.38030925], [-506.25823477, 6.3131022 ], [-408.71980731, -156.10116949], [ 150.23207937, 301.31376595], [ 91.00920901, -391.283763 ], [ 202.89662724, -269.38043241], [ 361.66623976, -106.96493868], [-219.40612786, -244.06020508]]) >>> result.funl array([-959.64066272, -718.16745962, -704.80659592, -565.99778097, -559.78685655, -557.36868733, -507.87385942, -493.9605115 , -426.48799655, -421.15571437, -419.31194957, -410.98477763]) These results are useful in applications where there are many global minima and the values of other global minima are desired or where the local minima can provide insight into the system (for example morphologies in physical chemistry [4]_). If we want to find a larger number of local minima, we can increase the number of sampling points or the number of iterations. We'll increase the number of sampling points to 64 and the number of iterations from the default of 1 to 3. Using ``simplicial`` this would have given us 64 x 3 = 192 initial sampling points. >>> result_2 = shgo(eggholder, ... bounds, n=64, iters=3, sampling_method='sobol') >>> len(result.xl), len(result_2.xl) (12, 23) Note the difference between, e.g., ``n=192, iters=1`` and ``n=64, iters=3``. In the first case the promising points contained in the minimiser pool are processed only once. In the latter case it is processed every 64 sampling points for a total of 3 times. To demonstrate solving problems with non-linear constraints consider the following example from Hock and Schittkowski problem 73 (cattle-feed) [3]_:: minimize: f = 24.55 * x_1 + 26.75 * x_2 + 39 * x_3 + 40.50 * x_4 subject to: 2.3 * x_1 + 5.6 * x_2 + 11.1 * x_3 + 1.3 * x_4 - 5 >= 0, 12 * x_1 + 11.9 * x_2 + 41.8 * x_3 + 52.1 * x_4 - 21 -1.645 * sqrt(0.28 * x_1**2 + 0.19 * x_2**2 + 20.5 * x_3**2 + 0.62 * x_4**2) >= 0, x_1 + x_2 + x_3 + x_4 - 1 == 0, 1 >= x_i >= 0 for all i The approximate answer given in [3]_ is:: f([0.6355216, -0.12e-11, 0.3127019, 0.05177655]) = 29.894378 >>> def f(x): # (cattle-feed) ... return 24.55*x[0] + 26.75*x[1] + 39*x[2] + 40.50*x[3] ... >>> def g1(x): ... return 2.3*x[0] + 5.6*x[1] + 11.1*x[2] + 1.3*x[3] - 5 # >=0 ... >>> def g2(x): ... return (12*x[0] + 11.9*x[1] +41.8*x[2] + 52.1*x[3] - 21 ... - 1.645 * np.sqrt(0.28*x[0]**2 + 0.19*x[1]**2 ... + 20.5*x[2]**2 + 0.62*x[3]**2) ... ) # >=0 ... >>> def h1(x): ... return x[0] + x[1] + x[2] + x[3] - 1 # == 0 ... >>> cons = ({'type': 'ineq', 'fun': g1}, ... {'type': 'ineq', 'fun': g2}, ... {'type': 'eq', 'fun': h1}) >>> bounds = [(0, 1.0),]*4 >>> res = shgo(f, bounds, n=150, constraints=cons) >>> res message: Optimization terminated successfully. success: True fun: 29.894378159142136 funl: [ 2.989e+01] x: [ 6.355e-01 1.137e-13 3.127e-01 5.178e-02] # may vary xl: [[ 6.355e-01 1.137e-13 3.127e-01 5.178e-02]] # may vary nit: 1 nfev: 142 # may vary nlfev: 35 # may vary nljev: 5 nlhev: 0 >>> g1(res.x), g2(res.x), h1(res.x) (-5.062616992290714e-14, -2.9594104944408173e-12, 0.0) ) args constraintsniterscallbackminimizer_kwargsoptionssampling_methodrNz/Successfully completed construction of complex.rTzCFailed to find a feasible minimizer point. Lowest sampling point = )mesz%Optimization terminated successfully.) isinstancerr lbublenSHGO iterate_all break_routinedisplogginginfoLMCxl_mapsfind_lowest_vertex fail_routinef_lowestresfunx_lowestxfnnfev n_sampledtnevmessagesuccess) funcboundsrrrrrrrrrshcs T/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/_shgo.pyr r sN &&!!I"69fiVYHH dF;!X 0    $'    L 8 L LJ K K K 37?q        G8; GG H H Hl L v }    A 7NsA>>BBceZdZ d(dZdZdZdZd Zd Zd Z d Z d Z dZ dZ dZdZdZdZdZdZdZd)dZdZdZdZdZd*dZd*dZdZd+d!Zd)d"Zd#Zd$Z d%Z!d,d'Z"dS)-r!rNrrc Lddlm} gd} t| tr9| | vr5t dd|  |ddurBt|ds-t|_ j j }||d<j }n|_ n#ttf$r |_ YnwxYwt||_ |_|_|_t#j|t&}t#j|d_t#j|}d||dddfdf<d ||ddd fd f<|dddf|ddd fk}|r0t d dd |Dd |_|_||_g_g_t9|t#jjt&d_jD]x}|ddvrlj|d j|dN#t$rjdYtwxYwyt?j_t?j_nd_d_djijd_ |j !|n ddij d<j d"dvr|d|vr|jjj d<| #| nTd_$d_%d_&d_'d_(d_)d_$d_*d_+d_,d_-d_.gd_/idgdd gd!gd"dgd#dgd$gd%d&dd'gd(dd'gd)dd*gd+gd,d-gd.d/dd0gd1gd%d2gd%d3dd0gd4gd5}j d}xj/||"z c_/d6}|j j/|j dj/dgzd_0d_1|_2d_3|_4d_5d_6d_7d_8d_9d_:j4&j2| d7krd8jzd z_4d_5j2d _2j4| d7ksd9x_4_4d_5j4d9kr| d7krd8jzd z_4j&j'j(j*j$d_2twjjj dj+j| :_<| d7krj=_>| _?n| d;vst| tsЉj@_>| d;vr| d_?| Fjdd=_Efd?} nd@_?jG_H| _Id_Jd_Kg_Lt_Nt_PdjP_QdjP_RdjP_SdjP_TdS)ANr)qmc)haltonsobolrz4Unknown sampling_method specified. Valid methods: {}z, jacTgd~Qgd~QJrzError: lb > ub in bounds c34K|]}t|VdSN)str).0bs r9 z SHGO.__init__..s()A)AQ#a&&)A)A)A)A)A)A.oldtypeineqr-rrSLSQP)methodr7rrftolg-q=rrL)slsqpcobylacobyqa trust-constrrF)r-x0rrrrL_custom)r?hesshesspr7rz nelder-meadpowellcgbfgsz newton-cgr?rTrUzl-bfgs-br7tncrOcatolrP)r7rfeasibility_tolrN)r?r7rdoglegrTz trust-ncgz trust-krylovz trust-exactrQ)r?rTrUrczt|}|t|z D]}||ddS)z8Remove keys from dictionary if not in goodkeys - inplaceN)setpop) dictionarygoodkeys existingkeyskeys r9_restrict_to_keysz(SHGO.__init__.._restrict_to_keyssHz??L#c(mm3 * *sD)))) * *rFrr)dimdomainsfield sfield_argssymmetryrr)r=r>r>)dscrambleseedr=c8j|SrA) qmc_enginerandom)rrlselfs r9rz&SHGO.__init__..sampling_methods?11!444rFcustom)U scipy.statsr<rrB ValueErrorformatjoincallablerr6 derivative TypeErrorKeyErrorr r7rrnparrayfloatshapergisfiniteanyrmin_consg_consg_argsr emptyappendtuplerupdatelower init_options f_min_trueminimize_every_itermaxitermaxfevmaxevmaxtimeminhgrdrkinfty_cons_sampl local_iterr$min_solver_args stop_globalr#r iters_donerncn_prcr2r0hgrqhull_incrementalr HCiterate_hypercubeiterate_complexriterate_delaunayintceillog2SobolrpHaltonsampling_customsamplingsampling_function stop_l_iterstop_complex_iterminimizer_pool LMapCacher'rr,r1nlfevnljevnlhev)rrr6r7rrrrrrrrrr<methodsr?aboundinfindbnderrcons solver_argsrLres` r9__init__z SHGO.__init__s $#####333 os + + Pw0N0N34:F499W;M;M4N4NPP P !%(D00!"25"9::1&t,, i**- 'y  8$   DIII %T400     &%((8F##A&+f%%%"'vaaad|Q"&vaaad|Q1qqq!t , ::<< FE $ )A)A&)A)A)A A AEEEFF F '  "'DMDKDK 75))  D  ( / /&>!>??DF DG+2D(&)ii$(U56'0'8'8DOO,4D(&)jj48d67'1'9'9DO555555 (0$ 0DM%4D "!!&!;;"## s%AB//C  C  I22$JJc|jd|dD]9}||jdvr(|jd||j|<:|dd|_|dd|_|dd|_|dd|_tj|_ |d d|_ d |vr)|d |_ |d d |_ nd|_ |d d|_ |dd|_|jrdgt|jz|_nd|_|dd|_|dd|_|dd|_dS)z Initiates the options. Can also be useful to change parameters after class initiation. Parameters ---------- options : dict Returns ------- None rrYrTrNrrrf_minf_tolg-C6?rrkFrrinfty_constraintsr$)rrr`getrrrrtimeinitrrrrrkr r7rrr$)rrropts r9rzSHGO.init_optionss" i(//888, ? ?Cd+I666))488==%c*$+;;/Dd#K#K {{9d33 kk(D11 [[$// IKK {{9d33 g  %g.DO Wd33DJJ"DO{{9d33  J66 = !E#dk"2"22DMM DM"++lE:: ' ,? F FKK.. rFc|SrArrrs r9 __enter__zSHGO.__enter__-s rFc4|jjjj|SrA)rV _mapwrapper__exit__)rrrs r9rz SHGO.__exit__0s-twy$-t44rFcJ|jrtjd|js7|jrn/|||j7|js|js||j |j _ |j j j|_dS)z Construct for `iters` iterations. If uniform sampling is used, every iteration adds 'n' sampling points. Iterations if a stopping criteria (e.g., sampling points or processing time) has been met. zSplitting first generationN)r$r%r&rr#iteratestopping_criteriar find_minimarr,nitrrr1r0rs r9r"zSHGO.iterate_all5s 9 7 L5 6 6 6" %!  LLNNN  " " $ $ $ " %' #% #  """ ').rFc|jrtjd|t |jdkrQ||j||j j |_ |j j |_ n||jrtjd|jdSdS)z Construct the minimizer pool, map the minimizers to local minima and sort the results into a global return object. zSearching for minimizer pool...rzMinimiser pool = SHGO.X_min = N)r$r%r& minimizersr X_min minimise_poolr sort_resultr,r-r+r/r.r)rs r9rzSHGO.find_minimaSs 9 < L: ; ; ;  tz??a     t / / /      !HLDM HJDMM  # # % % % 9 H LF$*FF G G G G G H HrFc`tj|_|jjjD]}|jj|j|jkrk|jr,tj d|jj|j|jj|j|_|jj|j |_ |j jD]K}|j |j |jkr.|j |j |_|j |j|_ L|jtjkrd|_d|_ dSdS)Nzself.HC.V[x].f = )r|infr+rrcachefr$r%r&x_ar.r'rx_l)rrr/lmcs r9r)zSHGO.find_lowest_vertexns  1 1Awy|~ --9GL!ETWYq\^!E!EFFF $ !  $ ! 0 8> 2 2Cx}"T]22 $ 3 $ 1 =BF " " DM DMMM # "rFctd|j|jfD}|jrt jd|jd||j|j|jkrd|_|j|j|jkrd|_|jS)Nc3K|]}||V dSrAr)rCr/s r9rEz)SHGO.finite_iterations..s"HHq!-----HHrFzIterations done =  / T)minrrr$r%r&rr)rrmis r9finite_iterationszSHGO.finite_iterationss HHTZ6HHH H H 9 H LFdoFF"FF G G G : !4:..#' < #4<00#' rFc|jr$tjd|jd|j|j|jkrd|_|jS)NzFunction evaluations done = rT)r$r%r&r0rrrs r9 finite_fevzSHGO.finite_fevsR 9 S LQQQDKQQ R R R 7dk ! !#D rFc|jr$tjd|jd|j|j|jkr d|_dSdS)NzSampling evaluations done = rT)r$r%r&r2rrrs r9 finite_evzSHGO.finite_evsg 9 , L+++"j++ , , , >TZ ' '#D    ( 'rFc|jr8tjdtj|jz d|jtj|jz |jkr d|_dSdS)NzTime elapsed = rT)r$r%r&rrrrrs r9 finite_timezSHGO.finite_times} 9 . L-49;;+B--"l-- . . . IKK$) # 4 4#D    5 4rFc4||jr8tjd|jtjd|j|j|jS|jdkr|j|jkrd|_n|j|jz t|jz }|j|jkrHd|_t|d|jzkr&tj d|jd|jd ||jkrd|_|jS) z Stop the algorithm if the final function value is known Specify in options (with ``self.f_min_true = options['f_min']``) and the tolerance with ``f_tol = options['f_tol']`` zLowest function evaluation = zSpecified minimum = NTrfz&A much lower value than expected f* = z was found f_lowest = ) stacklevel) r)r$r%r&r+rrrabswarningswarn)rrpes r9finite_precisionzSHGO.finite_precisions= !!! 9 C LHHH I I I LAAA B B B = # # ?c ! !} **#' -$/1S5I5IIB}//#' r77a$*n,,M@@@04 @@#$ TZ#' rFc|jjdkrdS|jj|jz |_|jj|_|j|jkrd|_|jr%tjd|jd|jd|jS)zV Stop the algorithm if homology group rank did not grow in iteration. rNTzCurrent homology growth = z (minimum growth = )) r'sizerhgrdrrr$r%r&rs r9finite_homology_growthzSHGO.finite_homology_growths 8=A   FHMDH, 8= 9 $ $#D  9 @ L?di??/3|??? @ @ @rFc|j||j||j||j||j||j | |j | |j S)zt Various stopping criteria ran every iteration Returns ------- stop : bool )rrrrrrrrrrrrrrrs r9rzSHGO.stopping_criterias < #  " " $ $ $ : !  " " $ $ $ ; " OO    : ! NN    < #       ? &  ! ! # # # < #  ' ' ) ) )rFc||jr|js||xjdz c_dSNr)rrr#rrrs r9rz SHGO.iteratesT   # #% #  """ 1rFc|jrtjd|j=|j|jj|_n4|j |j|xj|jz c_|jrtjdt|j j dkrY|j j D]L}|jj|}|}|jD]}||j}M|jj|jrtjd|jjj|_dS)z Iterate a subdivision of the complex Note: called with ``self.iterate_complex()`` after class initiation z G   !WY^^--DNN GNN46 " " " NNdf $NN 9 ; L: ; ; ; tx 1 $ $hn 0 0GIbM00A#\\!$//FF0  !!! 9 3 L1 2 2 2').rFc|xj|jz c_||j|jrLt jd|jt jd|jt jd|jdkrtj |j d|_ |j |_ g}t|j D]3\}}|dkr(||j |dz |dz4tj|}t!d d d g|j ||_i|_nP|j jd|jdzkr||j |j jd|_|jrt jd t-|d r/|j|jj|jj|jrt jd |jj|jrt jd|jjj|_|j|_dS)z Build a complex of Delaunay triangulated points Note: called with ``self.iterate_complex()`` after class initiation )rz self.n = z self.nc = zRConstructing and refining simplicial complex graph structure from sampling points.rfraxisrTripoints simplices)rrrN)rrsampled_surfacerr$r%r&rgr|argsortC Ind_sortedflatten enumeraterr}rrrrdelaunay_triangulationrhasattrrvf_to_vvrrrr1r0r2)rrtrisindind_ss r9rzSHGO.iterate_delaunay,sf 46 d.CDDD 9 < L-TV-- . . . L/dg// 0 0 0 L; < < < 8a<< ja888DO"o5577DOD'88 B B U77KKaa @AAA8D>>DAz%(K)@AA$&$OODHDKKv|AA--++$*+===aDJ 9 G LF G G G 4   B G  TX_dh.@ A A A 9 ; L: ; ; ;  !!! 9 3 L1 2 2 2').rFcg|_|jjjD]}d}t |jjdkrM|jjD]@}tjtj |tj |krd}A|rr|jj| rM|j rtj dtj d|jj|jdtj d|jj|jdtj d|jj||jvr*|j|jj||j rztj d tj d|jj|jD]&}tj d |jd |j'tj dg|_g|_i|_|jD]a}|j|j|j|j|j|jt-|j<btj |j|_tj |j|_||jS) z7 Returns the indexes of all minimizers FrTz<============================================================zv.x = z is minimizerzv.f = z==============================z Neighbors:zx = z || f = )rrrrr r'r(r|allr} minimiserr$r%r&rrrrr/minimizer_pool_Fr X_min_cacher sort_min_pool)rrr/in_LMCxlmivnrs r9rzSHGO.minimizerses! + +AF48#$$q(( H,&&DvbhqkkRXd^^;<<&!% wy|%%'' +9+L***L!I$')A,*:!I!I!IJJJL!G$')A,.!G!G!GHHHL***79Q ? ?Xdj))  zrFFcH||jd|jd}|d|js||r|dz}|dkrd|_nt j|jddkrd|_n}||j |j|j dddf}||j dddf|jd}|||jd|_dS)a; This processing method can optionally minimise only the best candidate solutions in the minimiser pool Parameters ---------- force_iter : int Number of starting minimizers to process (can be specified globally or locally) rrrTNF) rrr trim_min_poolrrr|r g_topographr/ZSs)rr force_iter lres_f_min ind_xmin_ls r9rzSHGO.minimise_pools4]]4:a=d6I!6L]MM  1" +  " " $ $ $ a ??'+D$x ##A&!++#'    Z\4: 6 6 62Jtwr111u~t7J27NOOJ   z * * *5" +:!rFctj|j|_tj|j|j|_tj|j|j|_dSrA)r|rr ind_f_minr}rrs r9rzSHGO.sort_min_poolsVD$9:: ht':;;DNK ")> ? ? 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J J i(;XFFrFcHtj|g}tj||d|_tj|jd|_||jd|_|j |j|_ |j d|_ |jS)a Returns the topographical vector stemming from the specified value ``x_min`` for the current feasible set ``X_min`` with True boolean values indicating positive entries and False values indicating negative entries. euclideanrrr) r|r}rdistancecdistYrrrr)rrx_minrs r9rzSHGO.g_topographs%!!!''ukBBDF,,,-""1$&9"1!4wrFcd|jD}|jD]x}t|jD]a\}}||j|kr|||dkr |||d<||j|kr|||dkr |||d<by|jr3t jd|jt jd||S)aM Construct locally (approximately) convex bounds Parameters ---------- v_min : Vertex object The minimizer vertex Returns ------- cbounds : list of lists List of size dimension with length-2 list of bounds for each dimension. c.g|]}|d|dgSrrrrCx_b_is r9 z1SHGO.construct_lcb_simplicial..%AAAEE!HeAh'AAArFrrzcbounds found for v_min.x_a = z cbounds = )r7rr rr$r%r&)rrv_mincboundsrix_is r9construct_lcb_simplicialzSHGO.construct_lcb_simplicials BAT[AAA( ( (B#BF++ ( (3%)A,&&S71:a=-@-@$'GAJqM%)A,&&S71:a=-@-@$'GAJqM ( 9 1 LE%)EE F F F L/g// 0 0 0rFc(d|jD}|S)aL Construct locally (approximately) convex bounds Parameters ---------- v_min : Vertex object The minimizer vertex Returns ------- cbounds : list of lists List of size dimension with length-2 list of bounds for each dimension. c.g|]}|d|dgSr0rr1s r9r3z/SHGO.construct_lcb_delaunay..r4rFr7)rrr5rr6s r9construct_lcb_delaunayzSHGO.construct_lcb_delaunaysBAT[AAArFc|jr!tjd|jj|j|j9tjd|j|j|j|jS|jtjd|d|jrtjd|d|jdkrt|}|j t|}t|}| |j j |}d |j vr)||jd <tj|jd nI||| }d |j vr)||jd <tj|jd |jr> HNNdi 'NN T>> HNNdi 'NN x{DHHI&    HHHH   X666 s&I99JJc|j}|d|j_|d|j_|d|j_|d|j_|j|jjz|j_ |jS)A Sort results and build the global return object rfunlr/r-) r'sort_cache_resultr,rrKr/r-r0rr1)rrresultss r9rzSHGO.sort_resultpsh (,,..dm  S\ u~ $(.0 xrFFailed to convergecTd|_d|j_dg|_||j_dS)NTF)r#r,r5rr4)rrrs r9r*zSHGO.fail_routines-! 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