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annotate libcruft/qrupdate/cqrinc.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 c Copyright (C) 2008 VZLU Prague, a.s., Czech Republic
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2 c
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3 c Author: Jaroslav Hajek <highegg@gmail.com>
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4 c
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5 c This source is free software; you can redistribute it and/or modify
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6 c it under the terms of the GNU General Public License as published by
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7 c the Free Software Foundation; either version 2 of the License, or
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8 c (at your option) any later version.
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9 c
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10 c This program is distributed in the hope that it will be useful,
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11 c but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 c GNU General Public License for more details.
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14 c
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15 c You should have received a copy of the GNU General Public License
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16 c along with this software; see the file COPYING. If not, see
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17 c <http://www.gnu.org/licenses/>.
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18 c
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19 subroutine cqrinc(m,n,k,Q,R,R1,j,x)
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20 c purpose: updates a QR factorization after inserting a new
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21 c column.
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22 c i.e., given an m-by-k unitary matrix Q, an m-by-n
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23 c upper trapezoidal matrix R and index j in the range
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24 c 1:n+1, this subroutine updates the matrix Q -> Q1 and
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25 c forms an m-by-(n+1) matrix R1 so that Q1 is again unitary,
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26 c R1 upper trapezoidal, and
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27 c Q1*R1 = [A(:,1:j-1); Q*Q'*x; A(:,j:n-1)], where A = Q*R.
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28 c (complex version)
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29 c arguments:
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30 c m (in) number of rows of the matrix Q.
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31 c n (in) number of columns of the matrix R.
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32 c k (in) number of columns of Q, and rows of R. k <= m.
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33 c Q (io) on entry, the unitary matrix Q.
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34 c on exit, the updated matrix Q1
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35 c R (in) the original upper trapezoidal matrix R
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36 c R1 (out) the updated matrix R1
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37 c j (in) the position of the new column in R1
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38 c x (in) the column being inserted
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39 c
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40 integer m,n,k,j
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41 complex Q(m,k),R(k,n),R1(k,n+1),x(m)
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42 complex w
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43 external xerbla,ccopy,cqrqhv,cgemv
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44 integer info,i,jj
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45 c quick return if possible
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46 if (m <= 0) return
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47 c check arguments
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48 info = 0
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49 if (n < 0) then
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50 info = 2
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51 else if (j < 1 .or. j > n+1) then
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52 info = 6
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53 end if
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54 if (info /= 0) then
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55 call xerbla('CQRINC',info)
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56 end if
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57 c copy leading portion of R
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58 call ccopy(k*(j-1),R,1,R1,1)
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59 if (j <= n) then
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60 call ccopy(k*(n+1-j),R(1,j),1,R1(1,j+1),1)
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61 end if
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62 call cgemv('C',m,min(k,j-1),cmplx(1e0),Q,m,x,1,
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63 + cmplx(0e0),R1(1,j),1)
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64 if (j < k) then
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65 c eliminate tail, updating Q(:,j:k) and R1(j:k,j+1:n+1)
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66 jj = min(j,n)+1
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67 call cqrqhv(m,n+1-j,k-j+1,Q(1,j),m,R1(j,jj),m,x,w)
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68 c assemble inserted column
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69 R1(j,j) = w
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70 do i = j+1,k
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71 R1(i,j) = 0e0
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72 end do
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73 end if
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74 end