+ /iJRt^RIt^RIHtHtHtHtHt^RI H t H t Rt Rt R#)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 VP^,pTp\W4p\\V4\V44p\P!\ Wg4UU u.uFwr\ W4'd^MTNK up p4p\V^, V^, R4F~p \Wj^,,4^8gK"\WjV ^,4p \VRW^,.3,V P4VRW^,.3&\WjV ^,!Wj&K W48dI\Wc,4\^,8d(\ Wc,Ws,4'g V^, pV^, ^8d'V^, V8dWc^, ,W#^, &\'dVYSu;8:d\V^,V48:gQhQhV\V4u;8:d V8:gQhQhVPWD38XgQhWV3#uup pi)aH 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 NNN)shaperabsnparrayziprrangerTrrrminlen) cQRdiagnmnsavecqcqacqicqaikGs &&&& ^/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/_lib/pyprima/common/powalg.py qradd_Rdiagr"s(  A E B #a&#a& !C S\R\ **13\R SB 1Q3!R  rA#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. r )r rrrrrr)Arrirrrr s&&&& r! qrexc_Rdiagr&Lsn 77DA 6af  6ae  u:?? 771:?qwwqzQ1771:?B B  1ux1c] eaCj&1a4!AqsF)"<= > 1qsAh;!##7!a1X+9>a1 F 1F1QT7Aa1fI. FEAaCL!QqS& 1QT7+EA#J 8OGs8.F#)__doc__numpyrlinalgrrrrrconstsrrr"r&r!r-s#=="9x7r,