readsdpa

 READSDPA - Read a linear SDP problem from a Sparse SDPA file
  separate the linear constraint matrix, return
 the problem in the following structure:
  
 Elements of the structure
   name ... filename of the input file
   Nx ..... number of primal variables
   Na ..... number of linear matrix inequalities (or diagonal blocks of the
            matrix constraint)
   Ng ..... number of linear inequalitites
   B ...... matrix defining the linear inequality constraints Bx<=d
            dimension Ng x Nx
   d ...... rhs for linear constraints
   c ...... dim (Nx,1), coefficients of the linear objective function
   NaDims . vector of sizes of matrix constraints (diagonal blocks)
   A ...... cell array (matrix) of A{k,l} for k=1,...,Na matrix constraint
            for l=1 ~ absolute term, l=2..Nx+1 coeficient matrices
            (some of them might be empty)
   Adep ... dependency list for each matrix constraint

 See also sdp_define, pen2bmi

0001 function sdpdata = readsdpa(filename); 
0002 % READSDPA - Read a linear SDP problem from a Sparse SDPA file
0003 %  separate the linear constraint matrix, return
0004 % the problem in the following structure:
0005 %
0006 % Elements of the structure
0007 %   name ... filename of the input file
0008 %   Nx ..... number of primal variables
0009 %   Na ..... number of linear matrix inequalities (or diagonal blocks of the
0010 %            matrix constraint)
0011 %   Ng ..... number of linear inequalitites
0012 %   B ...... matrix defining the linear inequality constraints Bx<=d
0013 %            dimension Ng x Nx
0014 %   d ...... rhs for linear constraints
0015 %   c ...... dim (Nx,1), coefficients of the linear objective function
0016 %   NaDims . vector of sizes of matrix constraints (diagonal blocks)
0017 %   A ...... cell array (matrix) of A{k,l} for k=1,...,Na matrix constraint
0018 %            for l=1 ~ absolute term, l=2..Nx+1 coeficient matrices
0019 %            (some of them might be empty)
0020 %   Adep ... dependency list for each matrix constraint
0021 %
0022 % See also sdp_define, pen2bmi
0023 
0024 % This file is a part of PENLAB package distributed under GPLv3 license
0025 % Copyright (c) 2013 by  J. Fiala, M. Kocvara, M. Stingl
0026 % Last Modified: 4 Dec 2013
0027 
0028   sdpdata=[];
0029 
0030   % open file
0031   fid=fopen(filename,'r');
0032   if (fid==-1)
0033     error(sprintf('Cannot open file "%s"',filename));
0034   end
0035 
0036   nline=0;
0037   phase=0;
0038   nx=0;
0039   nblocks=0;
0040   msizes=[];
0041   c=[];
0042   nentries=0;
0043   maxentries=0;
0044   alldata=[];
0045   while 1
0046     line=fgetl(fid);
0047     nline=nline+1;
0048     if (~ischar(line))
0049       % end of file
0050       break;
0051     end
0052     %fprintf('line %d: >>%s<<\n',nline,line);
0053 
0054     % skip comments or empty lines
0055     if (isempty(line) || line(1)=='*' || line(1) =='"')
0056       continue;
0057     end
0058 
0059     switch (phase)
0060     case 0
0061       % expecting number of variables
0062       [nx,count]=sscanf(line,'%d',1);
0063       if (count~=1)
0064         error(sprintf('Line %d, cannot read number of variables.',nline));
0065       elseif (nx<=0)
0066         error(sprintf('Line %d, wrong number of variables.',nline));
0067       end
0068       phase=phase+1;
0069       %nx
0070 
0071     case 1
0072       % expecting number of matrix constraints (=blocks)
0073       [nblocks,count]=sscanf(line,'%d',1);
0074       if (count~=1)
0075         error(sprintf('Line %d, cannot read number of blocks.',nline));
0076       elseif (nblocks<=0)
0077         error(sprintf('Line %d, wrong number of blocks.',nline));
0078       end
0079       phase=phase+1;
0080       %nblocks
0081 
0082     case 2
0083       % expecting block sizes which might be separated by foreign
0084       % characters such as {,},(,),... Add space at the beginning
0085       % of the line in case there is nothing
0086       [msizes,count]=sscanf([' ' line],'%*[^0-9+-]%d',nblocks);
0087       if (count~=nblocks)
0088         error(sprintf('Line %d, cannot read block sizes.',nline));
0089       elseif (any(msizes==0))
0090         error(sprintf('Line %d, block sizes are incorrect.',nline));
0091       end
0092       phase=phase+1;
0093       %msizes
0094 
0095     case 3
0096       % expecting the objective vector perhaps mixed with some garbage
0097       [c,count]=sscanf([' ' line],'%*[^0-9eE.+-]%lg',nx);
0098       if (count~=nx)
0099         error(sprintf('Line %d, cannot read the objective vector.',nline));
0100       end
0101       phase=phase+1;
0102       %c
0103 
0104     case 4
0105       % expecting a data line
0106       [data,count]=sscanf(line,'%i %i %i %i %lg',5);
0107       if (count~=5)
0108         error(sprintf('Line %d, cannot read the data line.',nline));
0109       end
0110       nentries=nentries+1;
0111       if (nentries>maxentries)
0112         alldata=[alldata,zeros(5,2500)];
0113         maxentries=maxentries+2500;
0114       end
0115       alldata(:,nentries)=data;
0116       %alldata(:,1:nentries)
0117 
0118     end
0119 
0120   end
0121 
0122   % close file
0123   fclose(fid);
0124 
0125   if (nx<=0 || nblocks<=0 || isempty(msizes) || isempty(c) || nentries<=0)
0126     error('The file seems to be incomplete.');
0127   end
0128 
0129   % remove empty entries
0130   alldata=alldata(:,1:nentries);
0131 
0132   % check the correctness of the data lines
0133   if (any(alldata(1,:)<0 | alldata(1,:)>nx))
0134     error('Some of the data lines have matrix_number out of range.');
0135   end
0136   if (any(alldata(2,:)<1 | alldata(2,:)>nblocks))
0137     error('Some of the data lines have block_number out of range.');
0138   end
0139 
0140   % extract the linear constraints
0141   % turn 1-size matrix blocks into linear constraints
0142   idx=find(msizes==1);
0143   msizes(idx)=-1;
0144   linblk=find(msizes<0);
0145   nlin=sum(abs(msizes(linblk)));
0146   nnzlin=length(find(msizes(alldata(2,:))<0));
0147   % accummulate data into B matrix
0148   B=sparse([],[],[],nx,nlin,nnzlin);
0149   d=zeros(nlin,1);
0150   ng=0;    % no of the constraint written so far
0151   for iblk=linblk'
0152     dim=-msizes(iblk);
0153     idxentries=find(alldata(2,:)==iblk);
0154     thisblock=alldata(:,idxentries);
0155     if (any(thisblock(3,:)<1 | thisblock(3,:)>dim | ...
0156       thisblock(3,:)~=thisblock(4,:)))
0157       error(sprintf('Diagonal block %d have indices nondiag. or out of range elements.',iblk));
0158     end
0159     % extract RHS
0160     idx=find(thisblock(1,:)==0);
0161     if (~isempty(idx))
0162       d(ng+thisblock(3,idx))=thisblock(5,idx);
0163     end
0164     % extract linear constraints bodies
0165     idx=find(thisblock(1,:)>0);
0166     if (~isempty(idx))
0167       B(:,ng+1:ng+dim)=sparse(thisblock(1,idx),thisblock(3,idx),thisblock(5,idx),nx,dim);
0168     end
0169     ng=ng+dim;
0170   end
0171   %d
0172   %spy(B)
0173   
0174   % extract matrix constraints
0175   matblk=find(msizes>0);
0176   na=length(matblk);
0177   A=cell(na,nx+1);
0178   for iblk=matblk'
0179     dim=msizes(iblk);
0180     idxentries=find(alldata(2,:)==iblk);
0181     thisblock=alldata(:,idxentries);
0182     if (any(thisblock(3,:)<1 | thisblock(3,:)>dim | thisblock(4,:)<1 | ...
0183       thisblock(4,:)>dim))
0184       error(sprintf('Block %d have indices not matching its dim=%d.',iblk,dim));
0185     end
0186     % if i>j --> lower triangle which is not allowed
0187     if (any(thisblock(3,:)>thisblock(4,:)))
0188       error(sprintf('Block %d have elements outside upper triangle.',iblk));
0189     end
0190     % extract each of the matrices in this block
0191     for i=0:nx
0192       idx=find(thisblock(1,:)==i);
0193       if (isempty(idx))
0194         A{iblk,i+1}=sparse(dim,dim);
0195       else
0196         M=sparse(thisblock(3,idx),thisblock(4,idx),thisblock(5,idx),dim,dim);
0197         A{iblk,i+1}=M+triu(M,1)';
0198       end
0199     end
0200   end
0201 
0202   % put everything together into one structure
0203   sdpdata.name=filename;
0204   sdpdata.Nx=nx;
0205   sdpdata.Na=na;
0206   sdpdata.Ng=nlin;
0207   sdpdata.B=B';
0208   sdpdata.d=d;
0209   sdpdata.c=c;
0210   sdpdata.NaDims=msizes;
0211   sdpdata.A=A;
0212 
0213 
0214 %  if 0
0215 
0216 
0217 % create dependency table, Adep(k) = vector of all x indices which Ak depends on
0218 sdpdata.Adep=cell(sdpdata.Na,1);
0219 for k=1:sdpdata.Na
0220   list=[];
0221   for i=2:nx+1
0222     if (~isempty(sdpdata.A{k,i}) && nnz(sdpdata.A{k,i})>0)
0223       list=[list,i-1];
0224     end
0225   end
0226   sdpdata.Adep{k}=list;
0227 end
0228 
0229 
0230 end
0231