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annotate libcruft/qrupdate/zch1dn.f @ 7948:af10baa63915 ss-3-1-50

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3.1.50 snapshot
author John W. Eaton <jwe@octave.org>
date Fri, 18 Jul 2008 17:42:48 -0400
parents 7c9ba697a479
children
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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 zch1dn(n,R,u,w,info)
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20 c purpose: given an upper triangular matrix R that is a Cholesky
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21 c factor of a hermitian positive definite matrix A, i.e.
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22 c A = R'*R, this subroutine downdates R -> R1 so that
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23 c R1'*R1 = A - u*u'
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24 c (complex version)
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25 c arguments:
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26 c n (in) the order of matrix R
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27 c R (io) on entry, the upper triangular matrix R
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28 c on exit, the updated matrix R1
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29 c u (io) the vector determining the rank-1 update
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30 c on exit, u is destroyed.
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31 c w (w) a workspace vector of size n
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32 c
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33 c NOTE: the workspace vector is used to store the rotations
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34 c so that R does not need to be traversed by rows.
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35 c
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36 integer n,info
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37 double complex R(n,n),u(n)
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38 double precision w(n)
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39 external ztrsv,zlartg,dznrm2
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40 double precision rho,dznrm2
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41 double complex crho,rr,ui,t
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42 integer i,j
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43
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44 c quick return if possible
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45 if (n <= 0) return
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46 c check for singularity of R
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47 do i = 1,n
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48 if (R(i,i) == 0d0) then
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49 info = 2
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50 return
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51 end if
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52 end do
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53 c form R' \ u
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54 call ztrsv('U','C','N',n,R,n,u,1)
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55 rho = dznrm2(n,u,1)
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56 c check positive definiteness
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57 rho = 1 - rho**2
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58 if (rho <= 0d0) then
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59 info = 1
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60 return
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61 end if
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62 crho = sqrt(rho)
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63 c eliminate R' \ u
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64 do i = n,1,-1
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65 ui = u(i)
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66 c generate next rotation
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67 call zlartg(crho,ui,w(i),u(i),rr)
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68 crho = rr
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69 end do
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70 c apply rotations
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71 do i = n,1,-1
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72 ui = 0d0
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73 do j = i,1,-1
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74 t = w(j)*ui + u(j)*R(j,i)
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75 R(j,i) = w(j)*R(j,i) - conjg(u(j))*ui
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76 ui = t
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77 end do
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78 end do
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79
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80 info = 0
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81 end