!
! Parallel Sparse BLAS version 3.5
! (C) Copyright 2006-2018
! Salvatore Filippone
! Alfredo Buttari
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions
! are met:
! 1. Redistributions of source code must retain the above copyright
! notice, this list of conditions and the following disclaimer.
! 2. Redistributions in binary form must reproduce the above copyright
! notice, this list of conditions, and the following disclaimer in the
! documentation and/or other materials provided with the distribution.
! 3. The name of the PSBLAS group or the names of its contributors may
! not be used to endorse or promote products derived from this
! software without specific written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
! POSSIBILITY OF SUCH DAMAGE.
!
!
!**********************************************************************
! *
! The communication step among processors at each *
! matrix-vector product is a variable all-to-all *
! collective communication that we reimplement *
! in terms of point-to-point communications. *
! The data in input is a list of dependencies: *
! for each node a list of all the nodes it has to *
! communicate with. The lists are guaranteed to be *
! symmetric, i.e. for each pair (I,J) there is a *
! pair (J,I). The idea is to organize the ordering *
! so that at each communication step as many *
! processors as possible are communicating at the *
! same time, i.e. a step is defined by the fact *
! that all edges (I,J) in it have no common node. *
! *
! Formulation of the problem is: *
! Given an undirected graph (forest): *
! Find the shortest series of steps to cancel all *
! graph edges, where at each step all edges belonging *
! to a matching in the graph are canceled. *
! *
! An obvious lower bound to the optimum number of steps *
! is the largest degree of any node in the graph. *
! *
! The algorithm proceeds as follows: *
! 1. Build a list of all edges, e.g. copy the *
! dependencies lists keeping only (I,J) with I<J *
! 2. Compute an auxiliary vector with the degree of *
! each node of the graph. *
! 3. While there are edges in the graph do: *
! 4. Weight the edges with the sum of the degrees *
! of their nodes and sort them into descending order *
! 5. Scan the list of edges; if neither node of the *
! edge has been marked yet, cancel the edge and mark *
! the two nodes *
! 6. If no edge was chosen but the graph is nonempty *
! raise an error condition *
! 7. Queue the edges in the matchin to the output *
! sequence; *
! 8. Decrease by 1 the degree of all marked nodes, *
! then clear all marks *
! 9. Cycle to 3. *
! 10. For each node: scan the edge sequence; if an *
! edge has the node as an endpoint, queue the other *
! node in the dependency list for the current one *
! *
!**********************************************************************
subroutine psi_i_csr_sort_dl(dl_ptr,c_dep_list,l_dep_list,ictxt,info)
use psi_mod, psb_protect_name => psi_i_csr_sort_dl
use psb_const_mod
use psb_error_mod
use psb_sort_mod
implicit none
integer(psb_ipk_), intent(inout) :: c_dep_list(:), dl_ptr(0:), l_dep_list(0:)
integer(psb_ipk_), intent(in) :: ictxt
integer(psb_ipk_), intent(out) :: info
! Local variables
integer(psb_ipk_), allocatable :: dg(:), dgp(:),&
& idx(:), upd(:), edges(:,:), ich(:)
integer(psb_ipk_) :: i, j, nedges, ip1, ip2, nch, ip, iedge,&
& i1, ix, ist, iswap(2)
logical :: internal_error
integer(psb_ipk_) :: me, np
info = 0
call psb_info(ictxt,me,np)
nedges = size(c_dep_list)
allocate(dg(0:np-1),dgp(nedges),edges(2,nedges),upd(0:np-1),&
& idx(nedges),ich(nedges),stat = info)
if (info /= 0) then
info = -9
return
end if
!
! 1. Compute an auxiliary vector with the degree of
! each node of the graph.
dg(0:np-1) = l_dep_list(0:np-1)
!
! 2. Build a list of all edges, e.g. copy the
! dependencies lists keeping only (I,J) with I<J
!
nedges = 0
do i = 0, np-1
do j = dl_ptr(i),dl_ptr(i+1) - 1
ip = c_dep_list(j)
if (i<=ip) then
nedges = nedges + 1
edges(1,nedges) = i
edges(2,nedges) = ip
end if
end do
end do
!
! 3. Loop over all edges
!
ist = 1
do while (ist <= nedges)
!
! 4. Weight the edges with the sum of the degrees
! of their nodes and sort them into descending order
upd(:) = 0
do i = ist, nedges
dgp(i) = (dg(edges(1,i)) + dg(edges(2,i)))
end do
call psb_msort(dgp(ist:nedges),ix=idx(ist:nedges),dir=psb_sort_down_)
! 5. Scan the list of edges; if neither node of the
! edge has been marked yet, take out the edge and mark
! the two nodes
i1 = ist
nch = 0
do i = ist, nedges
ix = idx(i)+ist-1
ip1 = edges(1,ix)
ip2 = edges(2,ix)
if ((upd(ip1)==0).and.(upd(ip2)==0)) then
upd(ip1) = -1
upd(ip2) = -1
nch = nch + 1
ich(nch) = ix
end if
end do
!
! 6. If no edge was chosen but the graph is nonempty
! raise an error condition
if (nch == 0) then
write(psb_err_unit,*)&
& 'srtlist ?????? impossible error !!!!!?????',&
& nedges,ist
do i=ist, nedges
ix = idx(i)+ist-1
write(psb_err_unit,*)&
& 'SRTLIST: Edge:',ix,edges(1,ix),&
& edges(2,ix),dgp(ix)
end do
info = psb_err_input_value_invalid_i_
return
end if
!
! 7. Queue the edges in the matching to the output
! sequence; decrease by 1 the degree of all marked
! nodes, then clear all marks
!
call psb_msort(ich(1:nch))
do i=1, nch
iswap(1:2) = edges(1:2,ist)
edges(1:2,ist) = edges(1:2,ich(i))
edges(1:2,ich(i)) = iswap(1:2)
ist = ist + 1
end do
do i=0, np-1
dg(i) = dg(i) + upd(i)
end do
end do
internal_error = .false.
do i=0, np-1
if (dg(i) /= 0) then
internal_error = .true.
if (me == 0) write(psb_err_unit,*)&
& 'csr_SRTLIST Error on exit:',i,dg(i)
end if
dg(i) = 0
end do
if (internal_error .and. (me==0)) then
write(0,*) 'Error on srt_list. Input:'
do i = 0, np-1
write(0,*) 'Proc: ',i,' list: '
write(0,*) c_dep_list(dl_ptr(i):dl_ptr(i+1) - 1)
end do
end if
!
! 10. Scan the edge sequence;
! for each edge, take each one of its
! endpoints and queue the other
! node in the endpoint dependency list
!
do j=1,nedges
i = edges(1,j)
ix = dl_ptr(i)
c_dep_list(ix+dg(i)) = edges(2,j)
dg(i) = dg(i)+1
i = edges(2,j)
ix = dl_ptr(i)
c_dep_list(ix+dg(i)) = edges(1,j)
dg(i) = dg(i)+1
!
! If there are any self loops, adjust for error condition
! check
!
if (edges(1,j) == edges(2,j)) dg(i) = dg(i) -1
end do
do i=0, np-1
if (dg(i) /= l_dep_list(i)) then
if (me == 0) write(psb_err_unit,*) &
& 'SRTLIST Mismatch on output',i,dg(i),l_dep_list(i)
end if
end do
end subroutine psi_i_csr_sort_dl