1c Copyright (C) 2008, 2009 VZLU Prague, a.s., Czech Republic 2c 3c Author: Jaroslav Hajek <highegg@gmail.com> 4c 5c This file is part of qrupdate. 6c 7c qrupdate is free software; you can redistribute it and/or modify 8c it under the terms of the GNU General Public License as published by 9c the Free Software Foundation; either version 3 of the License, or 10c (at your option) any later version. 11c 12c This program is distributed in the hope that it will be useful, 13c but WITHOUT ANY WARRANTY; without even the implied warranty of 14c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15c GNU General Public License for more details. 16c 17c You should have received a copy of the GNU General Public License 18c along with this software; see the file COPYING. If not, see 19c <http://www.gnu.org/licenses/>. 20c 21 subroutine sqrshc(m,n,k,Q,ldq,R,ldr,i,j,w) 22c purpose: updates a QR factorization after circular shift of 23c columns. 24c i.e., given an m-by-k orthogonal matrix Q, an k-by-n 25c upper trapezoidal matrix R and index j in the range 26c 1:n+1, this subroutine updates the matrix Q -> Q1 and 27c R -> R1 so that Q1 is again orthogonal, R1 upper 28c trapezoidal, and 29c Q1*R1 = A(:,p), where A = Q*R and p is the permutation 30c [1:i-1,shift(i:j,-1),j+1:n] if i < j or 31c [1:j-1,shift(j:i,+1),i+1:n] if j < i. 32c (real version) 33c arguments: 34c m (in) number of rows of the matrix Q. 35c n (in) number of columns of the matrix R. 36c k (in) number of columns of Q1, and rows of R1. Must be 37c either k = m (full Q) or k = n <= m (economical form). 38c Q (io) on entry, the unitary m-by-k matrix Q. 39c on exit, the updated matrix Q1. 40c ldq (in) leading dimension of Q. ldq >= m. 41c R (io) on entry, the original matrix R. 42c on exit, the updated matrix R1. 43c ldr (in) leading dimension of R. ldr >= k. 44c i (in) the first index determining the range (see above) 45c j (in) the second index determining the range (see above) 46c w (o) a workspace vector of size 2*k. 47c 48 integer m,n,k,ldq,ldr,i,j 49 real Q(ldq,*),R(ldr,*),w(*) 50 external xerbla,scopy,sqrtv1,sqrqh,sqhqr 51 integer info,jj,kk,l 52c quick return if possible. 53 if (m == 0 .or. n == 1) return 54 info = 0 55c check arguments. 56 if (m < 0) then 57 info = 1 58 else if (n < 0) then 59 info = 2 60 else if (k /= m .and. (k /= n .or. n > m)) then 61 info = 3 62 else if (i < 1 .or. i > n) then 63 info = 6 64 else if (j < 1 .or. j > n) then 65 info = 7 66 end if 67 if (info /= 0) then 68 call xerbla('SQRSHC',info) 69 return 70 end if 71 72 if (i < j) then 73c shift columns 74 call scopy(k,R(1,i),1,w,1) 75 do l = i,j-1 76 call scopy(k,R(1,l+1),1,R(1,l),1) 77 end do 78 call scopy(k,w,1,R(1,j),1) 79c retriangularize 80 if (i < k) then 81 kk = min(k,j) 82 call sqhqr(kk+1-i,n+1-i,R(i,i),ldr,w(k+1),w) 83c apply rotations to Q. 84 call sqrot('F',m,kk+1-i,Q(1,i),ldq,w(k+1),w) 85 end if 86 else if (j < i) then 87c shift columns 88 call scopy(k,R(1,i),1,w,1) 89 do l = i,j+1,-1 90 call scopy(k,R(1,l-1),1,R(1,l),1) 91 end do 92 call scopy(k,w,1,R(1,j),1) 93c retriangularize 94 if (j < k) then 95 jj = min(j+1,n) 96 kk = min(k,i) 97c eliminate the introduced spike. 98 call sqrtv1(kk+1-j,R(j,j),w(k+1)) 99c apply rotations to R 100 call sqrqh(kk+1-j,n-j,R(j,jj),ldr,w(k+1),R(j+1,j)) 101c apply rotations to Q 102 call sqrot('B',m,kk+1-j,Q(1,j),ldq,w(k+1),R(j+1,j)) 103c zero spike. 104 do l = j+1,kk 105 R(l,j) = 0e0 106 end do 107 end if 108 end if 109 end subroutine 110