-iHSrSSKrSSKJrJrJrJrJr SSK J r J r Sr Sr g)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 dURSnUn[X5n[[U5[U55n[R"[ Xg5VV s/sHup[ X5(aSOUPM sn n5n[US- US- S5Hdn [XjS-5S:dM[XjU S-5n [USS2XS-/4U R5USS2XS-/4'[XjU S-6Xj'Mf X4:a2[Xc5[S-:a[ XcXs5(dUS- nUS- S:aUS- U:a XcS- X#S- '[(aLXSs=::a[US-U5::de eU[U5s=::aU::de eURXD4:XdeXU4$s sn nf)aH This function updates the QR factorization of an MxN matrix A of full column rank, attempting to add a new column C to this matrix as the LAST column while maintaining the full-rankness. Case 1. If C is not in range(A) (theoretically, it implies N < M), then the new matrix is np.hstack([A, C]) Case 2. If C is in range(A), then the new matrix is np.hstack([A[:, :n-1], C]) N.B.: 0. Instead of R, this subroutine updates Rdiag, which is np.diag(R), with a size at most M and at least min(m, n+1). The number is min(m, n+1) rather than min(m, n) as n may be augmented by 1 in the function. 1. With the two cases specified as above, this function does not need A as an input. 2. The function changes only Q[:, nsave:m] (nsave is the original value of n) and R[:, n-1] (n takes the updated value) 3. Indeed, when C is in range(A), Powell wrote in comments that "set iOUT to the index of the constraint (here, column of A --- Zaikun) to be deleted, but branch if no suitable index can be found". The idea is to replace a column of A by C so that the new matrix still has full rank (such a column must exist unless C = 0). But his code essentially sets iout=n always. Maybe he found this worked well enough in practice. Meanwhile, Powell's code includes a snippet that can never be reached, which was probably intended to deal with the case that IOUT != n rrN)shaperabsnparrayziprrangerTrr r minlen) cQRdiagnmnsavecqcqacqicqaikGs S/var/www/html/venv/lib/python3.13/site-packages/scipy/_lib/pyprima/common/powalg.py qradd_Rdiagr$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. rrN)rrrrrrr)Arrirrr!r"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 8OGs'E)__doc__numpyrlinalgrrrrrconstsr r r$r(r#r/s#=="9x7r.