ЏkhHdZddlZddlmZmZmZmZmZddl m Z m Z dZ dZ y)a This module provides some Powell-style 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)isminorplanerotmatprodinprodhypot) DEBUGGINGEPSc J|jd}|}t||}tt|t|}tjt ||D cgc]\}} t || rdn|c} }}t|dz |dz dD]g} t|| dzdkDst|| | dz} t|dd| | dzgf| j|dd| | dzgf<t|| | dz|| <i||kr/t||tdzkDrt ||||s|dz }|dz dk\r|dz |kr||dz ||dz <trI||cxkrt|dz|ksJJ|t|cxkr|ksJJ|j||fk(sJ|||fScc} }w)a This function updates the QR factorization of an MxN matrix A of full column rank, attempting to add a new column C to this matrix as the LAST column while maintaining the full-rankness. Case 1. If C is not in range(A) (theoretically, it implies N < M), then the new matrix is np.hstack([A, C]) Case 2. If C is in range(A), then the new matrix is np.hstack([A[:, :n-1], C]) N.B.: 0. Instead of R, this subroutine updates Rdiag, which is np.diag(R), with a size at most M and at least min(m, n+1). The number is min(m, n+1) rather than min(m, n) as n may be augmented by 1 in the function. 1. With the two cases specified as above, this function does not need A as an input. 2. The function changes only Q[:, nsave:m] (nsave is the original value of n) and R[:, n-1] (n takes the updated value) 3. Indeed, when C is in range(A), Powell wrote in comments that "set iOUT to the index of the constraint (here, column of A --- Zaikun) to be deleted, but branch if no suitable index can be found". The idea is to replace a column of A by C so that the new matrix still has full rank (such a column must exist unless C = 0). But his code essentially sets iout=n always. Maybe he found this worked well enough in practice. Meanwhile, Powell's code includes a snippet that can never be reached, which was probably intended to deal with the case that IOUT != n rrN)shaperabsnparrayziprrangerTrr r minlen) cQRdiagnmnsavecqcqacqicqaikGs \/var/www/teggl/fontify/venv/lib/python3.12/site-packages/scipy/_lib/pyprima/common/powalg.py qradd_Rdiagr$s(  A E AB #a&#a& !C SS\R TT*13R SB 1Q3!R & r!A#w= L >= N. Most often L = M or N. 2. This function changes only Q[:, i:] and Rdiag[i:] 3. (NDB 20230919) In Python, i is either icon or nact - 2, whereas in FORTRAN it is either icon or nact - 1. rrN)rrrrrrr)Arrirrr!r"s r# qrexc_Rdiagr(Ls 77DAq 6a1f  6a!e  u:?? 771:?qwwqzQ1771:?B B  1uQ%x1ac]8 eAaCj&1a4!AqsF)"<= > 1qsAh;!##7!a1X+89>a1 F1F1QT7Aa1fI.FE!AaCL!QqS& 1QT7+E!A#J e8OGs?$E)__doc__numpyrlinalgrrrrrconstsr r r$r(r#r/s#=="9x7r.