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implementation of QR factorization updating
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 04 Mar 2008 21:47:11 -0500
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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 dqrder(m,n,Q,Q1,R,R1,j)
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20 c purpose: updates a QR factorization after deleting a row.
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21 c i.e., given an m-by-m orthogonal matrix Q, an m-by-n
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22 c upper trapezoidal matrix R and index j in the range
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23 c 1:m, this subroutine forms the (m-1)-by-(m-1) matrix
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24 c Q1 and an (m-1)-by-n matrix R1 so that Q1 is again
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25 c orthogonal, R1 upper trapezoidal, and
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26 c Q1*R1 = [A(1:j-1,:); A(j+1:m,:)], where A = Q*R.
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27 c (real version)
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28 c
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29 c arguments:
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30 c m (in) number of rows of the matrix R.
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31 c n (in) number of columns of the matrix R
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32 c Q (in) the orthogonal matrix Q
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33 c Q1 (out) the updated matrix Q1
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34 c R (in) the upper trapezoidal matrix R
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35 c R1 (out) the updated matrix R1
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36 c j (in) the position of the new row in R1
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37 c
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38 integer m,n,j
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39 double precision Q(m,m),Q1(m-1,m-1),R(m,n),R1(m-1,n)
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40 double precision c
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41 double precision s,rr,w
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42 external xerbla,dlacpy,dlartg,drot,dscal,daxpy
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43 integer i
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44 c quick return if possible
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45 if (m == 1) return
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46 c check arguments
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47 info = 0
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48 if (m < 1) then
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49 info = 1
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50 else if (j < 1 .or. j > n) then
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51 info = 7
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52 end if
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53 if (info /= 0) then
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54 call xerbla('DQRDER',info)
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55 end if
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56 c setup the new matrix Q1
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57 c permute the columns of Q and rows of R so that the deleted row ends
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58 c up being the topmost row.
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59 if (j > 1) then
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60 call dlacpy('0',j-1,m-1,Q(1,2),m,Q1(1,1),m-1)
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61 end if
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62 if (j < m) then
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63 call dlacpy('0',m-j,m-1,Q(j+1,2),m,Q1(j,1),m-1)
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64 end if
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65 c setup the new matrix R1
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66 call dlacpy('0',m-1,n,R(2,1),m,R1(1,1),m-1)
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67 c eliminate Q(j,2:m)
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68 w = Q(j,m)
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69 do i = m-1,2,-1
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70 call dlartg(Q(j,i),w,c,s,rr)
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71 w = rr
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72 c apply rotation to rows of R1
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73 if (i <= n) then
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74 call drot(n-i+1,R1(i-1,i),m-1,R1(i,i),m-1,c,s)
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75 end if
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76 c apply rotation to columns of Q1
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77 call drot(m-1,Q1(1,i-1),1,Q1(1,i),1,c,s)
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78 end do
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79 c the last iteration is special, as we don't have the first row of
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80 c R and first column of Q
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81 call dlartg(Q(j,1),w,c,s,rr)
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82 w = rr
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83 call dscal(n,c,R1(1,1),m-1)
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84 call daxpy(n,-s,R(1,1),m,R1(1,1),m-1)
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85 c apply rotation to columns of Q1
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86 call dscal(m-1,c,Q1(1,1),1)
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87 if (j > 1) then
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88 call daxpy(j-1,-s,Q(1,1),1,Q1(1,1),1)
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89 end if
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90 if (j < m) then
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91 call daxpy(m-j,-s,Q(j+1,1),1,Q1(j,1),1)
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92 end if
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93 end