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!
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! Parallel Sparse BLAS version 3.5
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! (C) Copyright 2006, 2010, 2015, 2017
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! Salvatore Filippone
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! Alfredo Buttari CNRS-IRIT, Toulouse
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!
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! Redistribution and use in source and binary forms, with or without
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! modification, are permitted provided that the following conditions
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! are met:
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! 1. Redistributions of source code must retain the above copyright
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! notice, this list of conditions and the following disclaimer.
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! 2. Redistributions in binary form must reproduce the above copyright
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! notice, this list of conditions, and the following disclaimer in the
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! documentation and/or other materials provided with the distribution.
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! 3. The name of the PSBLAS group or the names of its contributors may
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! not be used to endorse or promote products derived from this
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! software without specific written permission.
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!
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! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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! POSSIBILITY OF SUCH DAMAGE.
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!
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!
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!**********************************************************************
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! *
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! The communication step among processors at each *
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! matrix-vector product is a variable all-to-all *
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! collective communication that we reimplement *
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! in terms of point-to-point communications. *
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! The data in input is a list of dependencies: *
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! for each node a list of all the nodes it has to *
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! communicate with. The lists are guaranteed to be *
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! symmetric, i.e. for each pair (I,J) there is a *
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! pair (J,I). The idea is to organize the ordering *
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! so that at each communication step as many *
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! processors as possible are communicating at the *
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! same time, i.e. a step is defined by the fact *
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! that all edges (I,J) in it have no common node. *
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! *
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! Formulation of the problem is: *
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! Given an undirected graph (forest): *
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! Find the shortest series of steps to cancel all *
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! graph edges, where at each step all edges belonging *
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! to a matching in the graph are canceled. *
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! *
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! An obvious lower bound to the optimum number of steps *
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! is the largest degree of any node in the graph. *
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! *
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! The algorithm proceeds as follows: *
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! 1. Build a list of all edges, e.g. copy the *
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! dependencies lists keeping only (I,J) with I<J *
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! 2. Compute an auxiliary vector with the degree of *
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! each node of the graph. *
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! 3. While there are edges in the graph do: *
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! 4. Weight the edges with the sum of the degrees *
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! of their nodes and sort them into descending order *
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! 5. Scan the list of edges; if neither node of the *
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! edge has been marked yet, cancel the edge and mark *
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! the two nodes *
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! 6. If no edge was chosen but the graph is nonempty *
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! raise an error condition *
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! 7. Queue the edges in the matchin to the output *
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! sequence; *
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! 8. Decrease by 1 the degree of all marked nodes, *
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! then clear all marks *
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! 9. Cycle to 3. *
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! 10. For each node: scan the edge sequence; if an *
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! edge has the node as an endpoint, queue the other *
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! node in the dependency list for the current one *
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! *
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!**********************************************************************
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subroutine srtlist(dep_list,dl_lda,ldl,np,dg,dgp,upd, edges,idx,ich,info)
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use psb_serial_mod
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implicit none
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integer(psb_ipk_) :: np, dl_lda, info
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integer(psb_ipk_) :: dep_list(dl_lda,*), ldl(*),dg(*), dgp(*),&
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& idx(*), upd(*),edges(2,*),ich(*)
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integer(psb_ipk_) :: i,j, nedges,ip1,ip2,nch,ip,iedge,&
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& i1,ix,ist,iswap(2)
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integer(psb_ipk_) :: no_comm
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parameter (no_comm=-1)
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if (np .lt. 0) then
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info = 1
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return
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endif
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!
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! dg contains number of communications
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!
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do i=1, np
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dg(i)=ldl(i)
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enddo
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nedges = 0
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do i=1, np
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do j=1, dg(i)
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ip = dep_list(j,i) + 1
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if (ip.gt.i) nedges = nedges + 1
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enddo
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enddo
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iedge = 0
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do i=1, np
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do j=1, dg(i)
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ip = dep_list(j,i) + 1
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if (ip >= i) then
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iedge = iedge + 1
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edges(1,iedge) = i
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edges(2,iedge) = ip
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endif
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enddo
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enddo
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ist = 1
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do while (ist.le.nedges)
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do i=1, np
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upd(i) = 0
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enddo
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do i=ist, nedges
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dgp(i) = -(dg(edges(1,i))+dg(edges(2,i)))
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enddo
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call psb_msort(dgp(ist:nedges),ix=idx(ist:nedges))
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i1 = ist
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nch = 0
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do i = ist, nedges
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ix = idx(i)+ist-1
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ip1 = edges(1,ix)
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ip2 = edges(2,ix)
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if ((upd(ip1).eq.0).and.(upd(ip2).eq.0)) then
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upd(ip1) = -1
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upd(ip2) = -1
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nch = nch + 1
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ich(nch) = ix
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endif
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enddo
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if (nch.eq.0) then
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write(psb_err_unit,*)&
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& 'srtlist ?????? impossible error !!!!!?????',&
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& nedges,ist
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do i=ist, nedges
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ix = idx(i)+ist-1
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write(psb_err_unit,*)&
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& 'SRTLIST: Edge:',ix,edges(1,ix),&
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& edges(2,ix),dgp(ix)
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enddo
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info = psb_err_input_value_invalid_i_
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return
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endif
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call psb_msort(ich(1:nch))
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do i=1, nch
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iswap(1) = edges(1,ist)
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iswap(2) = edges(2,ist)
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edges(1,ist) = edges(1,ich(i))
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edges(2,ist) = edges(2,ich(i))
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edges(1,ich(i)) = iswap(1)
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edges(2,ich(i)) = iswap(2)
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ist = ist + 1
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enddo
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do i=1, np
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dg(i) = dg(i) + upd(i)
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enddo
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enddo
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do i=1, np
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if (dg(i).ne.0) then
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write(psb_err_unit,*)&
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& 'SRTLIST Error on exit:',i,dg(i)
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endif
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dg(i) = 0
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enddo
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do j=1,nedges
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i = edges(1,j)
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dg(i) = dg(i)+1
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dep_list(dg(i),i) = edges(2,j)-1
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i = edges(2,j)
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dg(i) = dg(i)+1
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dep_list(dg(i),i) = edges(1,j)-1
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if (edges(1,j) == edges(2,j)) dg(i) = dg(i) -1
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enddo
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do i=1, np
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if (dg(i).ne.ldl(i)) then
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write(psb_err_unit,*) &
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& 'SRTLIST Mismatch on output',i,dg(i),ldl(i)
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endif
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enddo
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return
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end subroutine srtlist
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