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c
c Authors:
c Reinhard Furrer
c
c Copyright (C) 2017 -- 2017 Reinhard Furrer
c
c This program is free software; you can redistribute it and/or
c modify it under the terms of the GNU General Public License
c as published by the Free Software Foundation; either version 3
c of the License, or (at your option) any later version.
c
c This program is distributed in the hope that it will be useful,
c but WITHOUT ANY WARRANTY; without even the implied warranty of
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c GNU General Public License for more details.
c
c You should have received a copy of the GNU General Public License
c along with this program; if not, write to the Free Software
c Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
subroutine backsolve(m,nsuper,nrhs,lindx,xlindx,lnz,
& xlnz,xsuper,b)
c see below...
implicit none
integer m,nsuper,nrhs,lindx(*),xlindx(m+1),
& xlnz(m+1),xsuper(m+1)
double precision lnz(*),b(m,nrhs)
integer j
do j = 1,nrhs
call blkslb(nsuper,xsuper,xlindx,lindx,xlnz,lnz,b(1,j))
enddo
return
end
subroutine forwardsolve(m,nsuper,nrhs,lindx,xlindx,
& lnz,xlnz,xsuper,b)
c INPUT:
c m -- the number of column in the matrix
c lindx -- an nsub-vector of interger which contains, in
c column major oder, the row subscripts of the nonzero
c entries in L in a compressed storage format
c xlindx -- an nsuper-vector of integer of pointers for lindx
c lnz -- First contains the non-zero entries of d; later
c contains the entries of the Cholesky factor
c xlnz -- column pointer for L stored in lnz
c xsuper -- array of length m+1 containing the supernode
c partitioning
c b -- the rhs of the equality constraint
c OUTPUT:
c b -- the solution
implicit none
integer m,nsuper,nrhs,lindx(*),xlindx(m+1),
& xlnz(m+1),xsuper(m+1)
double precision lnz(*),b(m,nrhs)
integer j
c
do j = 1,nrhs
call blkslf(nsuper,xsuper,xlindx,lindx,xlnz,lnz,b(1,j))
enddo
return
end
C***********************************************************************
C***********************************************************************
C
C Version: 0.4
C Last modified: December 27, 1994
C Authors: Esmond G. Ng and Barry W. Peyton
C Slight modification by Reinhard Furrer
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C
C***********************************************************************
subroutine pivotforwardsolve(m,nsuper,nrhs,lindx,xlindx,lnz,
& xlnz,invp,perm,xsuper,newrhs,sol,b)
c Sparse least squares solver via Ng-Peyton's sparse Cholesky
c factorization for sparse symmetric positive definite
c INPUT:
c m -- the number of column in the design matrix X
c nsubmax -- upper bound of the dimension of lindx
c lindx -- an nsub-vector of interger which contains, in
c column major oder, the row subscripts of the nonzero
c entries in L in a compressed storage format
c xlindx -- an nsuper-vector of integer of pointers for lindx
c lnz -- First contains the non-zero entries of d; later
c contains the entries of the Cholesky factor
c xlnz -- column pointer for L stored in lnz
c invp -- an m-vector of integer of inverse permutation
c vector
c perm -- an m-vector of integer of permutation vector
c xsuper -- array of length m+1 containing the supernode
c partitioning
c newrhs -- extra work vector for right-hand side and
c solution
c sol -- the least squares solution
c b -- an m-vector, usualy the rhs of the equality constraint
c X'a = (1-tau)X'e in the rq setting
c OUTPUT:
c y -- an m-vector of least squares solution
c WORK ARRAYS:
c b -- an m-vector, usually the rhs of the equality constraint
c X'a = (1-tau)X'e in the rq setting
implicit none
integer m,nsuper,nrhs,lindx(*),xlindx(m+1),
& invp(m),perm(m),xlnz(m+1), xsuper(m+1)
integer i,j
double precision lnz(*),b(m,nrhs),newrhs(m),sol(m,nrhs)
do j = 1,nrhs
do i = 1,m
newrhs(i) = b(perm(i),j)
enddo
call blkslf(nsuper,xsuper,xlindx,lindx,xlnz,lnz,newrhs)
do i = 1,m
sol(i,j) = newrhs(invp(i))
enddo
enddo
return
end
C***********************************************************************
subroutine pivotbacksolve(m,nsuper,nrhs,lindx,xlindx,lnz,
& xlnz,invp,perm,xsuper,newrhs,sol,b)
c see above
implicit none
integer m, nsuper,nrhs,lindx(*),xlindx(m+1),
& invp(m),perm(m),xlnz(m+1), xsuper(m+1)
double precision lnz(*),b(m,nrhs),newrhs(m),sol(m,nrhs)
integer i,j
do j = 1,nrhs
do i = 1,m
newrhs(i) = b(perm(i),j)
enddo
call blkslb(nsuper,xsuper,xlindx,lindx,xlnz,lnz,newrhs)
do i = 1,m
sol(i,j) = newrhs(invp(i))
enddo
enddo
return
end
C***********************************************************************
subroutine backsolves(m,nsuper,nrhs,lindx,xlindx,lnz,
& xlnz,invp,perm,xsuper,newrhs,b)
c MODIFIED, overwritting b now!! (M.Schlather, 4.4.15)
c
c Sparse least squares solver via Ng-Peyton's sparse Cholesky
c factorization for sparse symmetric positive definite
c INPUT:
c m -- the number of column in the design matrix X
c nsubmax -- upper bound of the dimension of lindx
c lindx -- an nsub-vector of interger which contains, in
c column major oder, the row subscripts of the nonzero
c entries in L in a compressed storage format
c xlindx -- an nsuper-vector of integer of pointers for lindx
c nnzlmax -- the upper bound of the non-zero entries in
c L stored in lnz, including the diagonal entries
c lnz -- First contains the non-zero entries of d; later
c contains the entries of the Cholesky factor
c xlnz -- column pointer for L stored in lnz
c invp -- an m-vector of integer of inverse permutation
c vector
c perm -- an m-vector of integer of permutation vector
c xsuper -- array of length m+1 containing the supernode
c partitioning
c newrhs -- extra work vector for right-hand side and
c solution
c ( sol -- the least squares solution)
c b -- an m-vector, usualy the rhs of the equality constraint
c X'a = (1-tau)X'e in the rq setting
c OUTPUT:
c y -- an m-vector of least squares solution
c WORK ARRAYS:
c b -- an m-vector, usually the rhs of the equality constraint
c X'a = (1-tau)X'e in the rq setting
implicit none
integer m,nsuper,nrhs,lindx(*),xlindx(m+1),
& invp(m),perm(m),xlnz(m+1), xsuper(m+1)
double precision lnz(*),b(m,nrhs),newrhs(m)
integer i,j
do j = 1,nrhs
do i = 1,m
newrhs(i) = b(perm(i),j)
enddo
call blkslv(nsuper,xsuper,xlindx,lindx,xlnz,lnz,newrhs)
do i = 1,m
b(i,j) = newrhs(invp(i))
enddo
enddo
return
end
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