0^j7dZddlZddlmZmZmZmZddlmZdZ dZ dZ d Z d Z d Zd Zd ZdZdZddZddZdZdZddZdZdZdZddZddZdZy)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 p/var/www/ramen.bs-engineer-server.com/venv/lib/python3.12/site-packages/scipy/_external/pyprima/common/linalg.pyinprodrsL vva| F 3q6]!A$1+ Mctj|jd}t|jdD]}t ||dd|f||<|S)Nr)r zerosshaper rrs r matprod12r%sQ XXaggaj !F 1771: '1a1g&q ' Mrctj|jd}t|jdD]}||dd|f||zz }|SNrrr rrr rs r matprod21r,sS XXaggaj !F 1771: !!AqD'AaD. ! Mrc tj|jd|jdf}t|jdD]?}t|jdD]"}|dd|fxx|dd|f|||fzz cc<$A|Srr)rrrrjs r matprod22r!3s XXqwwqz1771:. /F 1771: .qwwqz" .A 1a4LAadGa1g- -L .. 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HQ%1a CC HHaV q1ub"% RAAw1a!eAg:!a%'1* !FF!AqD'QAadG Rxx%++a1a(Q agJLL Hrc B|jd}|jd}tj|}|j}tjd|dz |t }t |D]!}tjtt|||dz||dzfdd}|dkDr5|||z dz kr*||z }||||c||<||<|||gddf|||gddf<t |dz |dD]}t||||gfj} tjt|||f|||fd||||gf<t||dz|dz||gf| ||dz|dz||gf<t|dd||gf| |dd||gf<$|j} || |fS)NrrrVaxisr,)rr eyerYr\r[r argmaxrL primapow2planerotappendr?r%) r3r7r8r5rYr_r krGr]s rrZrZs  A  A q A A AqsAS)A 1X 4 IIhy1QqS5!AaC%<9B K q5Q!a%!)^ FA1qtJAaD!A$aVQY)r#r#)rr)rr)rr)rrg|=皙?g.AzG @ X = [||X||, 0])rranyr isnanallisinfrCsignr1r logical_andrrrIrBrArr@maximumminimumisorthr-)rcsrGturjrOs rrgrgs1v{222{ BHHQK   bhhqk   NRWWQqT] *  NRWWQqT] * ad)q.S1Y!^   ad)sS1Y & GGAaDM  ad)sS1Y &  GGAaDM rwww/"&&);RVVAYQX[^Q^I_=_` aQA!qA!qA!A$i#ad)#!qt AAs1vrwwq1Q3w/0A 1 AAAAA!qt AQAAaC 012A 1 AAAAA 1a&A2q'"#Aww%vvbkk!n%%%1T7QtW$%AdGag,=(>>!CCCjj"**VUS["ABa~~ r~~bkk!nbffQi"'''C-:P.PQ R q!As1Q3!Q<()ScAg->> T@T T> Hrcd}t||t|zz}t|d|zt|zz}tjt||k\||k\S)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 rpr#)r1r logical_or)rref sensitivityrefarefbs rr2r2EsY K s8kCF* *D s8a+oA. .D ==ST)44< 88rc tj|d}trtj|dtj|dk(sJtj|dtj|dk(sJtj|dtj|dk(sJt|r|dk\sJt|r|n[tjddt ztj tj|dtj|dz}tj||tjt|z|tjt|zg}tt||tj|z |kjxs<tt||tj|z |kj}|S)zJ This procedure tests whether A = B^{-1} up to the tolerance TOL. rrgMbP?gY@) r sizerrrxrrwrBr1r%rdrs)r3r^rOr8is_invs risinvr[su 1 Awwq!}1 ---wwq!}1 ---wwq!}1 --- 3<!8O8 #2::dC#I 277STVW=Z\ZaZabcefZg@h4h#iC &&#sRVVCF^+S266#a&>-AB CC71a=!BFF1I-#5 : : < o#gaQRmVXV\V\]^V_F_B`ehAh@m@m@oF Mrc trt|r|dk\sJtj|d}|tj|dkDrd}|Stjt t |rd}|St|r{t t|j|tj|z tj||tjt |zkj}|St t|j|tj|z dkj}|S)zc This function tests whether the matrix A has orthonormal columns up to the tolerance TOL. rrF) rrr rrrrLr1r%rYrdrwrBrs)r3rOnum_varsis_orths rryryys  3<!8O8 wwq!}H"''!Q- N ((8CF# $ N 3<7133?RVVH-==>"**SRUXZX^X^_bcd_eXfRfBggllnG N 7133?RVVH-==>!CHHJG Nrct|dk(r tdtd|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$At least one array must be provided.c34K|]}|jywr')r.0rAs r z!get_arrays_tol..s.euzz.sc 3K|]D}tjtj|tj|dFyw)?)initialN)r rBr1r@rs rrz!get_arrays_tol..s=  rvveBKK./0#>>sA A g$@r)rr$rBr)arraysrweights rget_arrays_tolrs_& 6{a?@@ .v. .D F #:D# & //r)rr')__doc__numpyr constsrrrrrr rrrr!r%r)r<r?rIrPrTrXrZrLrfrgr2rryrrnrrrs44 Q . &55 >24X v9,<@0r