ftjJdZddlZddlmZmZmZmZmZddl m Z m Z dZ dZ dS)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|jd}|}t||}tt|t|}tjdt ||D}t |dz |dz dD]}t||dzdkrat|||dz} t|dd||dzgf| j|dd||dzgf<t|||dz||<||krBt||tdzkr!t||||s|dz }|dz dkr|dz |kr||dz ||dz <trO||cxkrt|dz|ksnJ|t|cxkr|ksnJ|j||fksJ|||fS)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 rc<g|]\}}t||rdn|S)r)r).0cqicqais ^/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/_lib/pyprima/common/powalg.py zqradd_Rdiag..-s/RRR TT**311RRRrN)shaperabsnparrayziprangerTrr rr minlen) cQRdiagnmnsavecqcqakGs r qradd_Rdiagr(s(  A E AB #a&&#a&& ! !C RRSS\\RRR S 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. rrNc ^g|])}tdd|fdd|dzf*S)Nr)r)r r&Ars rrzqrexc_Rdiag..s?FFF1F1QQQT7Aaaa1fI..FFFr)rrrrrrr)r+rr ir"r!r&r's`` r qrexc_Rdiagr-Ls 7DAq 66a1fff  66a!eee  u::???? 71:??qwqzQ171:??? B  1uuQ%x1ac]]88 eAaCj&111a4!AAAqsF)"<"<= > > 111qsAh;!#77!!!a1X+GFFFFa1 FFFE!AaC%L!!!QqS& 1QQQT7++E!A#J e8Or)__doc__numpyrlinalgrrrrrconstsr r r(r-rrr3s==============""""""""999x77777r