ftj7dZddlZddlmZmZmZmZddlmZdZ dZ dZ d Z d Z d Zd Zd ZdZdZddZddZdZdZddZdZdZdZddZddZdZdS)z This module provides some basic linear algebra procedures. Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA. Dedicated to late Professor M. J. D. Powell FRS (1936--2015). Python translation by Nickolai Belakovski. N) DEBUGGINGEPSREALMAXREALMIN)presentFctstj||Sd}tt |D]}|||||zz }|S)Nr)USE_NAIVE_MATHnpdotrangelenxyresultis ^/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/_lib/pyprima/common/linalg.pyinprodrsW va|| F 3q66]]!A$1+ Mctj|jd}t|jdD]}t ||dd|f||< |S)Nr)r zerosshaper rrs r matprod12r%sZ Xagaj ! !F 171:  ''1a1g&&q Mrctj|jd}t|jdD]}||dd|f||zz }|SNrrr rrr rs r matprod21r,sY Xagaj ! !F 171:  !!!AAAqD'AaD.  Mrc $tj|jd|jdf}t|jdD]H}t|jdD]+}|dd|fxx|dd|f|||fzz cc<,I|Srr)rrrrjs r matprod22r!3s Xqwqz171:. / /F 171:  ..qwqz"" . .A 111a4LLLAaaadGa1g- -LLLL . MrcXts||zSt|jdkr(t|jdkrt||St|jdkr(t|jdkrt ||St|jdkr(t|jdkrt ||St|jdkr(t|jdkrt ||Std|jd|j)NrzInvalid shapes for x and y: z and )r rrrrrr! ValueError)rrs rmatprodr%;s s  17||qS\\Q..a|| QW  s17||q00A QW  s17||q00A QW  s17||q00AOOOagOOPPPrctstj||Stjt |t |f}t t |D]}|||z|dd|f<|SN)r r outerrrr rs routprodr)Jsu x1~~ Xs1vvs1vv& ' 'F 3q66]]$$qt8F111a4LL Mrc ^ts(tj||ddS|jd}|jd}t ||}tj|}|}t|dz ddD]} t||dd| f} ttj |tj |dd| f} t| | rd|| <p| || z || <||| |dd| fzz }|S)N)rcondrr) r r linalglstsqrminrcopyr rabsisminor) AbQRdiagmnrankrrryqyqas rlsqrr<Ss 4yq!40033  A  A q!99D  A A 4!8R $ $## AqAw  RVAYYqAw00 2s   #AaDDa=AaDAaD1QQQT7N"AA Hrctstj||Stj|st |}n6tj|st |}nt tj||g}tjt |t|g}|dtjtkrK|dtjtdz kr%tjt||z}nP|ddkrB|dtj|d|dz |d|dz zdzz}nd}|S)Nrr@) r r hypotisfiniter1arrayr/maxsqrtrrsum)x1x2rrs rr?r?js4  xB ;r??  GG [__  GG "b"" # # Hc!ffc!ff% & & Q4"''"" " "qtbggck.B.B'B'BAaC!!AA qTAXX!rw!QqT AaD1I6:;;;AAA Hrctstj|Stjt d|D}|S)Ncg|]}||zSrJ).0xis r znorm..s,,,B"R%,,,r)r r r-normrCrD)rrs rrNrN}sK !y~~a   WS,,!,,,-- . .F Mrctt|tjt|z |kSr')primasumr1r trilr3tols ristrilrT. CFFRWSVV__, - - 44rctt|tjt|z |kSr')rPr1r triurRs ristriurXrUrcntstj|S|}|jd}t |r|j}tj||f}t|D]M}d|||fz |||f<t|d|d|f|d||f |||fz |d||f<N|jSt|rttj||f}t|D]M}d|||fz |||f<t|d|d|f|d||f |||fz |d||f<Nnt|\}}}|j}tj||f}t|dz ddD]M}|dd|ft|dd|dz|f||dz||fz |||fz |dd|f<Ntj|t}tjd|dz |||<|dd|fj}|S)Nrrr,dtype)r r r-invr0rrTTrr r%rXqrintlinspace)r3r8RBrr5PInvPs rr\r\sm  y}}Q A  A ayy C HaV  q ? ?A!AqD'kAadG"1"bqb& 1RaRU8444qAw>Abqb!eHHs  HaV  q ? ?A!AqD'kAadG"1"bqb& 1RaRU8444qAw>Abqb!eHH ? Q%%1a C HaV  q1ub"%% R RAAw111a!eAg:!a%'1* !F!FF!AqD'QAaaadGGx%%%+a1a((Q aaagJL Hrc |jd}|jd}tj|}|j}tjd|dz |t }t |D]Q}tjtt|||dz||dzfdd}|dkr?|||z dz kr3||z }||||c||<||<|||gddf|||gddf<t |dz |dD]}t||||gfj} tj t|||f|||fd||||gf<t||dz|dz||gf| ||dz|dz||gf<t|dd||gf| |dd||gf<S|j} || |fS)NrrrZaxisr,)rr eyer]r`r_r argmaxrP primapow2planerotappendr?r%) r3r7r8r5r]rcr krGras rr^r^s  A  A q A A AqsAS)))A 1XX 4 4 Ihy1QqS5!AaC%<99BBB K K K q55Q!a%!)^^ FA1qtJAaD!A$aVQQQY)r#r#)rr)rr)rr)rrg|=皙?g.AzG @ X = [||X||, 0])rranyr isnanallisinfrCsignr1r logical_andrrrNrBrArr@maximumminimumisorthr-)rcsrGturnrSs rrkrks!31vv{{{2{{{ BHQKK/   bhqkk  +  NRWQqT]] *  NRWQqT]] * ad))q..S1YY!^^   ad))sS1YY & & GAaDMM  ad))sS1YY & &  GAaDMM rww//"&));RVAYYQX[^Q^I_I_=_`` a a QA!qA!qAA!A$ii#ad))##!qt AAs1vvrwq1Q3w//00A 1 AAAAAA!qt AQAAaC 0 0122A 1 AAAAA 1a&A2q'"##AUw%vbk!nn%%%%%1T7QtW$%%AdGag,=(>(>>!CCCCj"*VUS["A"ABBa~~~ r~bk!nnbfQii"''C-:P:P.PQQ R R U q!!As1Q3!Q<(())ScAg->->>>>@T>>> Hrcd}t||t|zz}t|d|zt|zz}tjt||k||kS)a# This function tests whether x is minor compared to ref. It is used by Powell, e.g., in COBYLA. In precise arithmetic, isminor(x, ref) is true if and only if x == 0; in floating point arithmetic, isminor(x, ref) is true if x is 0 or its nonzero value can be attributed to computer rounding errors according to ref. Larger sensitivity means the function is more strict/precise, the value 0.1 being due to Powell. For example: isminor(1e-20, 1e300) -> True, because in floating point arithmetic 1e-20 cannot be added to 1e300 without being rounded to 1e300. isminor(1e300, 1e-20) -> False, because in floating point arithmetic adding 1e300 to 1e-20 dominates the latter number. isminor(3, 4) -> False, because 3 can be added to 4 without being rounded off rsr#)r1r logical_or)rref sensitivityrefarefbs rr2r2Esd K s88kCFF* *D s88a+oA. .D =ST)44< 8 88rc *tj|d}trtj|dtj|dksJtj|dtj|dksJtj|dtj|dksJt|r|dksJt|r|nXtjddt ztjtj|dtj|dz}tj||tjt|z|tjt|zg}tt||tj |z |k pGtt||tj |z |k }|S)zJ This procedure tests whether A = B^{-1} up to the tolerance TOL. rrgMbP?gY@) r sizerrr{rrzrBr1r%rhrv)r3rbrSr8is_invs risinvr[s 1 Awq!}}1 ----wq!}}1 ----wq!}}1 ---- 3<< !8888  i##2:dC#I 27STVW==Z\ZabcefZgZg@h@h4h#i#iC &#sRVCFF^^+S26#a&&>>-AB C CC71a==!!BF1II-#5 : : < < o#gaQRmmVXV\]^V_V_F_B`B`ehAh@m@m@o@oF Mrc trt|r|dksJtj|d}|tj|dkrd}ntjt t |rd}nt|rt t|j|tj |z tj ||tj t |zk }nMt t|j|tj |z dk }|S)zc This function tests whether the matrix A has orthonormal columns up to the tolerance TOL. rrF) rrr rrurPr1r%r]rhrzrBrv)r3rSnum_varsis_orths rr|r|ys*  3<< !8888 wq!}}H"'!Q-- (8CFF## $ $K 3<< K713??RVH-=-==>>"*SRUXZX^_bcd_e_eXfXfRfBgBggllnnGG713??RVH-=-==>>!CHHJJG Nrct|dkrtdtd|D}td|D}dtzt|dz|zS)aS Get a relative tolerance for a set of arrays. Borrowed from COBYQA Parameters ---------- *arrays: tuple Set of `numpy.ndarray` to get the tolerance for. Returns ------- float Relative tolerance for the set of arrays. Raises ------ ValueError If no array is provided. rz$At least one array must be provided.c3$K|] }|jV dSr')rrKrAs r z!get_arrays_tol..s$..euz......rc 3K|]D}tjtj|tj|dVEdS)?)initialN)r rBr1r@rs rrz!get_arrays_tol..s^  rveBK../00#>>>rg$@r)rr$rBr)arraysrweights rget_arrays_tolrs& 6{{a?@@@ ..v... . .D F #:D# & //r)rr')__doc__numpyr constsrrrrrr rrrr!r%r)r<r?rNrTrXr\r^rPrjrkr2rr|rrJrrrs444444444444 Q Q Q   .   &55555555   >24X X X v999,<@00000r