/*===========================================================================* Scan through the variables and select those that are binary and are at a fractional level. *===========================================================================*/ void CglClique::selectFractionalBinaries(const OsiSolverInterface& si) { // extract the primal tolerance from the solver double lclPetol = 0.0; si.getDblParam(OsiPrimalTolerance, lclPetol); const int numcols = si.getNumCols(); if (petol<0.0) { // do all if not too many int n=0; for (int i = 0; i < numcols; ++i) { if (si.isBinary(i)) n++; } if (n<5000) lclPetol=-1.0e-5; } const double* x = si.getColSolution(); std::vector<int> fracind; int i; for (i = 0; i < numcols; ++i) { if (si.isBinary(i) && x[i] > lclPetol && x[i] < 1-petol) fracind.push_back(i); } sp_numcols = static_cast<int>(fracind.size()); sp_orig_col_ind = new int[sp_numcols]; sp_colsol = new double[sp_numcols]; for (i = 0; i < sp_numcols; ++i) { sp_orig_col_ind[i] = fracind[i]; sp_colsol[i] = x[fracind[i]]; } }
// Useful constructor CbcFollowOn::CbcFollowOn (CbcModel * model) : CbcObject(model) { assert (model); OsiSolverInterface * solver = model_->solver(); matrix_ = *solver->getMatrixByCol(); matrix_.removeGaps(); matrix_.setExtraGap(0.0); matrixByRow_ = *solver->getMatrixByRow(); int numberRows = matrix_.getNumRows(); rhs_ = new int[numberRows]; int i; const double * rowLower = solver->getRowLower(); const double * rowUpper = solver->getRowUpper(); // Row copy const double * elementByRow = matrixByRow_.getElements(); const int * column = matrixByRow_.getIndices(); const CoinBigIndex * rowStart = matrixByRow_.getVectorStarts(); const int * rowLength = matrixByRow_.getVectorLengths(); for (i = 0; i < numberRows; i++) { rhs_[i] = 0; double value = rowLower[i]; if (value == rowUpper[i]) { if (floor(value) == value && value >= 1.0 && value < 10.0) { // check elements bool good = true; for (int j = rowStart[i]; j < rowStart[i] + rowLength[i]; j++) { int iColumn = column[j]; if (!solver->isBinary(iColumn)) good = false; double elValue = elementByRow[j]; if (floor(elValue) != elValue || value < 1.0) good = false; } if (good) rhs_[i] = static_cast<int> (value); } } } }
// Create a list of rows which might yield cuts // The possible parameter is a list to cut down search void CglOddHole::createRowList( const OsiSolverInterface & si, const int * possible) { // Get basic problem information int nRows=si.getNumRows(); const CoinPackedMatrix * rowCopy = si.getMatrixByRow(); const int * column = rowCopy->getIndices(); const CoinBigIndex * rowStart = rowCopy->getVectorStarts(); const int * rowLength = rowCopy->getVectorLengths(); int rowIndex; delete [] suitableRows_; numberRows_=nRows; const double * rowElements = rowCopy->getElements(); const double * rowupper = si.getRowUpper(); const double * rowlower = si.getRowLower(); const double * collower = si.getColLower(); const double * colupper = si.getColUpper(); suitableRows_=new int[nRows]; if (possible) { memcpy(suitableRows_,possible,nRows*sizeof(int)); } else { int i; for (i=0;i<nRows;i++) { suitableRows_[i]=1; } } for (rowIndex=0; rowIndex<nRows; rowIndex++){ double rhs1=rowupper[rowIndex]; double rhs2=rowlower[rowIndex]; if (suitableRows_[rowIndex]) { int i; bool goodRow=true; for (i=rowStart[rowIndex]; i<rowStart[rowIndex]+rowLength[rowIndex];i++) { int thisCol=column[i]; if (colupper[thisCol]-collower[thisCol]>epsilon_) { // could allow general integer variables but unlikely if (!si.isBinary(thisCol) ) { goodRow=false; break; } if (fabs(rowElements[i]-1.0)>epsilon_) { goodRow=false; break; } } else { rhs1 -= collower[thisCol]*rowElements[i]; rhs2 -= collower[thisCol]*rowElements[i]; } } if (fabs(rhs1-1.0)>epsilon_&&fabs(rhs2-1.0)>epsilon_) { goodRow=false; } if (goodRow) { suitableRows_[rowIndex]=1; } else { suitableRows_[rowIndex]=0; } } } }
//------------------------------------------------------------------------------- // Generate three cycle cuts //------------------------------------------------------------------- void CglOddHole::generateCuts(const OsiSolverInterface & si, OsiCuts & cs, const CglTreeInfo info) { // Get basic problem information int nRows=si.getNumRows(); int nCols=si.getNumCols(); const CoinPackedMatrix * rowCopy = si.getMatrixByRow(); // Could do cliques and extra OSL cliques // For moment just easy ones // If no information exists then get a list of suitable rows // If it does then suitable rows are subset of information CglOddHole temp; int * checkRow = new int[nRows]; int i; if (!suitableRows_) { for (i=0;i<nRows;i++) { checkRow[i]=1; } } else { // initialize and extend rows to current size memset(checkRow,0,nRows*sizeof(int)); memcpy(checkRow,suitableRows_,CoinMin(nRows,numberRows_)*sizeof(int)); } temp.createRowList(si,checkRow); // now cut down further by only allowing rows with fractional solution double * solution = new double[nCols]; memcpy(solution,si.getColSolution(),nCols*sizeof(double)); const int * column = rowCopy->getIndices(); const CoinBigIndex * rowStart = rowCopy->getVectorStarts(); const int * rowLength = rowCopy->getVectorLengths(); const double * collower = si.getColLower(); const double * colupper = si.getColUpper(); int * suitable = temp.suitableRows_; // At present I am using new and delete as easier to see arrays in debugger int * fixed = new int[nCols]; // mark fixed columns for (i=0;i<nCols;i++) { if (si.isBinary(i) ) { fixed[i]=0; if (colupper[i]-collower[i]<epsilon_) { solution[i]=0.0; fixed[i]=2; } else if (solution[i]<epsilon_) { solution[i]=0.0; fixed[i]=-1; } else if (solution[i]>onetol_) { solution[i]=1.0; fixed[i]=+1; } } else { //mark as fixed even if not (can not intersect any interesting rows) solution[i]=0.0; fixed[i]=3; } } // first do packed const double * rowlower = si.getRowLower(); const double * rowupper = si.getRowUpper(); for (i=0;i<nRows;i++) { if (suitable[i]) { int k; double sum=0.0; if (rowupper[i]>1.001) suitable[i]=-1; for (k=rowStart[i]; k<rowStart[i]+rowLength[i];k++) { int icol=column[k]; if (!fixed[icol]) sum += solution[icol]; } if (sum<0.9) suitable[i]=-1; //say no good } } #ifdef CGL_DEBUG const OsiRowCutDebugger * debugger = si.getRowCutDebugger(); if (debugger&&!debugger->onOptimalPath(si)) debugger = NULL; #else const OsiRowCutDebugger * debugger = NULL; #endif temp.generateCuts(debugger, *rowCopy,solution, si.getReducedCost(),cs,suitable,fixed,info,true); // now cover //if no >= then skip bool doCover=false; int nsuitable=0; for (i=0;i<nRows;i++) { suitable[i]=abs(suitable[i]); if (suitable[i]) { int k; double sum=0.0; if (rowlower[i]<0.999) sum=2.0; if (rowupper[i]>1.001) doCover=true; for (k=rowStart[i]; k<rowStart[i]+rowLength[i];k++) { int icol=column[k]; if (!fixed[icol]) sum += solution[icol]; if (fixed[icol]==1) sum=2.0; //don't use if any at 1 } if (sum>1.1) { suitable[i]=-1; //say no good } else { nsuitable++; } } } if (doCover&&nsuitable) temp.generateCuts(debugger, *rowCopy,solution,si.getReducedCost(), cs,suitable,fixed,info,false); delete [] checkRow; delete [] solution; delete [] fixed; }
//----------------------------------------------------------------------------- // Generate Lift-and-Project cuts //------------------------------------------------------------------- void CglLiftAndProject::generateCuts(const OsiSolverInterface& si, OsiCuts& cs, const CglTreeInfo /*info*/) { // Assumes the mixed 0-1 problem // // min {cx: <Atilde,x> >= btilde} // // is in canonical form with all bounds, // including x_t>=0, -x_t>=-1 for x_t binary, // explicitly stated in the constraint matrix. // See ~/COIN/Examples/Cgl2/cgl2.cpp // for a general purpose "convert" function. // Reference [BCC]: Balas, Ceria, and Corneujols, // "A lift-and-project cutting plane algorithm // for mixed 0-1 program", Math Prog 58, (1993) // 295-324. // This implementation uses Normalization 1. // Given canonical problem and // the lp-relaxation solution, x, // the LAP cut generator attempts to construct // a cut for every x_j such that 0<x_j<1 // [BCC:307] // x_j is the strictly fractional binary variable // the cut is generated from int j = 0; // Get basic problem information // let Atilde be an m by n matrix const int m = si.getNumRows(); const int n = si.getNumCols(); const double * x = si.getColSolution(); // Remember - Atildes may have gaps.. const CoinPackedMatrix * Atilde = si.getMatrixByRow(); const double * AtildeElements = Atilde->getElements(); const int * AtildeIndices = Atilde->getIndices(); const CoinBigIndex * AtildeStarts = Atilde->getVectorStarts(); const int * AtildeLengths = Atilde->getVectorLengths(); const int AtildeFullSize = AtildeStarts[m]; const double * btilde = si.getRowLower(); // Set up memory for system (10) [BCC:307] // (the problem over the norm intersected // with the polar cone) // // min <<x^T,Atilde^T>,u> + x_ju_0 // s.t. // <B,w> = (0,...,0,beta_,beta)^T // w is nonneg for all but the // last two entries, which are free. // where // w = (u,v,v_0,u_0)in BCC notation // u and v are m-vectors; u,v >=0 // v_0 and u_0 are free-scalars, and // // B = Atilde^T -Atilde^T -e_j e_j // btilde^T e_0^T 0 0 // e_0^T btilde^T 1 0 // ^T indicates Transpose // e_0 is a (AtildeNCols x 1) vector of all zeros // e_j is e_0 with a 1 in the jth position // Storing B in column order. B is a (n+2 x 2m+2) matrix // But need to allow for possible gaps in Atilde. // At each iteration, only need to change 2 cols and objfunc // Sane design of OsiSolverInterface does not permit mucking // with matrix. // Because we must delete and add cols to alter matrix, // and we can only add columns on the end of the matrix // put the v_0 and u_0 columns on the end. // rather than as described in [BCC] // Initially allocating B with space for v_0 and u_O cols // but not populating, for efficiency. // B without u_0 and v_0 is a (n+2 x 2m) size matrix. int twoM = 2*m; int BNumRows = n+2; int BNumCols = twoM+2; int BFullSize = 2*AtildeFullSize+twoM+3; double * BElements = new double[BFullSize]; int * BIndices = new int[BFullSize]; CoinBigIndex * BStarts = new CoinBigIndex [BNumCols+1]; int * BLengths = new int[BNumCols]; int i, ij, k=0; int nPlus1=n+1; int offset = AtildeStarts[m]+m; for (i=0; i<m; i++){ for (ij=AtildeStarts[i];ij<AtildeStarts[i]+AtildeLengths[i];ij++){ BElements[k]=AtildeElements[ij]; BElements[k+offset]=-AtildeElements[ij]; BIndices[k]= AtildeIndices[ij]; BIndices[k+offset]= AtildeIndices[ij]; k++; } BElements[k]=btilde[i]; BElements[k+offset]=btilde[i]; BIndices[k]=n; BIndices[k+offset]=nPlus1; BStarts[i]= AtildeStarts[i]+i; BStarts[i+m]=offset+BStarts[i];// = AtildeStarts[m]+m+AtildeStarts[i]+i BLengths[i]= AtildeLengths[i]+1; BLengths[i+m]= AtildeLengths[i]+1; k++; } BStarts[twoM]=BStarts[twoM-1]+BLengths[twoM-1]; // Cols that will be deleted each iteration int BNumColsLessOne=BNumCols-1; int BNumColsLessTwo=BNumCols-2; const int delCols[2] = {BNumColsLessOne, BNumColsLessTwo}; // Set lower bound on u and v // u_0, v_0 will be reset as free const double solverINFINITY = si.getInfinity(); double * BColLowers = new double[BNumCols]; double * BColUppers = new double[BNumCols]; CoinFillN(BColLowers,BNumCols,0.0); CoinFillN(BColUppers,BNumCols,solverINFINITY); // Set row lowers and uppers. // The rhs is zero, for but the last two rows. // For these the rhs is beta_ double * BRowLowers = new double[BNumRows]; double * BRowUppers = new double[BNumRows]; CoinFillN(BRowLowers,BNumRows,0.0); CoinFillN(BRowUppers,BNumRows,0.0); BRowLowers[BNumRows-2]=beta_; BRowUppers[BNumRows-2]=beta_; BRowLowers[BNumRows-1]=beta_; BRowUppers[BNumRows-1]=beta_; // Calculate base objective <<x^T,Atilde^T>,u> // Note: at each iteration coefficient u_0 // changes to <x^T,e_j> // w=(u,v,beta,v_0,u_0) size 2m+3 // So, BOjective[2m+2]=x[j] double * BObjective= new double[BNumCols]; double * Atildex = new double[m]; CoinFillN(BObjective,BNumCols,0.0); Atilde->times(x,Atildex); // Atildex is size m, x is size n CoinDisjointCopyN(Atildex,m,BObjective); // Number of cols and size of Elements vector // in B without the v_0 and u_0 cols int BFullSizeLessThree = BFullSize-3; // Load B matrix into a column orders CoinPackedMatrix CoinPackedMatrix * BMatrix = new CoinPackedMatrix(true, BNumRows, BNumColsLessTwo, BFullSizeLessThree, BElements,BIndices, BStarts,BLengths); // Assign problem into a solver interface // Note: coneSi will cleanup the memory itself OsiSolverInterface * coneSi = si.clone(false); coneSi->assignProblem (BMatrix, BColLowers, BColUppers, BObjective, BRowLowers, BRowUppers); // Problem sense should default to "min" by default, // but just to be virtuous... coneSi->setObjSense(1.0); // The plot outline from here on down: // coneSi has been assigned B without the u_0 and v_0 columns // Calculate base objective <<x^T,Atilde^T>,u> // bool haveWarmStart = false; // For (j=0; j<n, j++) // if (!isBinary(x_j) || x_j<=0 || x_j>=1) continue; // // IMPROVEME: if(haveWarmStart) check if j attractive // add {-e_j,0,-1} matrix column for v_0 // add {e_j,0,0} matrix column for u_0 // objective coefficient for u_0 is x_j // if (haveWarmStart) // set warmstart info // solve min{objw:Bw=0; w>=0,except v_0, u_0 free} // if (bounded) // get warmstart info // haveWarmStart=true; // ustar = optimal u solution // ustar_0 = optimal u_0 solution // alpha^T= <ustar^T,Atilde> -ustar_0e_j^T // (double check <alpha^T,x> >= beta_ should be violated) // add <alpha^T,x> >= beta_ to cutset // endif // delete column for u_0 // this deletes all column info. // delete column for v_0 // endFor // clean up memory // return 0; int * nVectorIndices = new int[n]; CoinIotaN(nVectorIndices, n, 0); bool haveWarmStart = false; bool equalObj1, equalObj2; CoinRelFltEq eq; double v_0Elements[2] = {-1,1}; double u_0Elements[1] = {1}; CoinWarmStart * warmStart = 0; double * ustar = new double[m]; CoinFillN(ustar, m, 0.0); double* alpha = new double[n]; CoinFillN(alpha, n, 0.0); for (j=0;j<n;j++){ if (!si.isBinary(j)) continue; // Better to ask coneSi? No! // coneSi has no binInfo. equalObj1=eq(x[j],0); equalObj2=eq(x[j],1); if (equalObj1 || equalObj2) continue; // IMPROVEME: if (haveWarmStart) check if j attractive; // AskLL:wanted to declare u_0 and v_0 packedVec outside loop // and setIndices, but didn't see a method to do that(?) // (Could "insert". Seems inefficient) int v_0Indices[2]={j,nPlus1}; int u_0Indices[1]={j}; // CoinPackedVector v_0(2,v_0Indices,v_0Elements,false); CoinPackedVector u_0(1,u_0Indices,u_0Elements,false); #if CGL_DEBUG const CoinPackedMatrix *see1 = coneSi->getMatrixByRow(); #endif coneSi->addCol(v_0,-solverINFINITY,solverINFINITY,0); coneSi->addCol(u_0,-solverINFINITY,solverINFINITY,x[j]); if(haveWarmStart) { coneSi->setWarmStart(warmStart); coneSi->resolve(); } else { #if CGL_DEBUG const CoinPackedMatrix *see2 = coneSi->getMatrixByRow(); #endif coneSi->initialSolve(); } if(coneSi->isProvenOptimal()){ warmStart = coneSi->getWarmStart(); haveWarmStart=true; const double * wstar = coneSi->getColSolution(); CoinDisjointCopyN(wstar, m, ustar); Atilde->transposeTimes(ustar,alpha); alpha[j]+=wstar[BNumCols-1]; #if debug int p; double sum; for(p=0;p<n;p++)sum+=alpha[p]*x[p]; if (sum<=beta_){ throw CoinError("Cut not violated", "cutGeneration", "CglLiftAndProject"); } #endif // add <alpha^T,x> >= beta_ to cutset OsiRowCut rc; rc.setRow(n,nVectorIndices,alpha); rc.setLb(beta_); rc.setUb(solverINFINITY); cs.insert(rc); } // delete col for u_o and v_0 coneSi->deleteCols(2,delCols); // clean up memory } // clean up delete [] alpha; delete [] ustar; delete [] nVectorIndices; // BMatrix, BColLowers,BColUppers, BObjective, BRowLowers, BRowUppers // are all freed by OsiSolverInterface destructor (?) delete [] BLengths; delete [] BStarts; delete [] BIndices; delete [] BElements; }
//-------------------------------------------------------------------------- // test EKKsolution methods. void CglOddHoleUnitTest( const OsiSolverInterface * baseSiP, const std::string mpsDir ) { CoinRelFltEq eq(0.000001); // Test default constructor { CglOddHole aGenerator; } // Test copy & assignment { CglOddHole rhs; { CglOddHole bGenerator; CglOddHole cGenerator(bGenerator); rhs=bGenerator; } } // test on simple case { const int nRows=3; const int nCols=3; const int nEls=6; const double elem[]={1.0,1.0,1.0,1.0,1.0,1.0}; const int row[]={0,1,0,2,1,2}; const CoinBigIndex start[]={0,2,4}; const int len[]={2,2,2}; CoinPackedMatrix matrix(true,nRows,nCols,nEls,elem,row,start,len); const double sol[]={0.5,0.5,0.5}; const double dj[]={0,0,0}; const int which[]={1,1,1}; const int fixed[]={0,0,0}; OsiCuts cs; CglOddHole test1; CglTreeInfo info; info.randomNumberGenerator=NULL; test1.generateCuts(NULL,matrix,sol,dj,cs,which,fixed,info,true); CoinPackedVector check; int index[] = {0,1,2}; double el[] = {1,1,1}; check.setVector(3,index,el); //assert (cs.sizeRowCuts()==2); assert (cs.sizeRowCuts()==1); // sort Elements in increasing order CoinPackedVector rpv=cs.rowCut(0).row(); rpv.sortIncrIndex(); assert (check==rpv); } // Testcase /u/rlh/osl2/mps/scOneInt.mps // Model has 3 continous, 2 binary, and 1 general // integer variable. { OsiSolverInterface * siP = baseSiP->clone(); std::string fn = mpsDir+"scOneInt"; siP->readMps(fn.c_str(),"mps"); #if 0 CglOddHole cg; int nCols=siP->getNumCols(); // Test the siP methods for detecting // variable type int numCont=0, numBinary=0, numIntNonBinary=0, numInt=0; for (int thisCol=0; thisCol<nCols; thisCol++) { if ( siP->isContinuous(thisCol) ) numCont++; if ( siP->isBinary(thisCol) ) numBinary++; if ( siP->isIntegerNonBinary(thisCol) ) numIntNonBinary++; if ( siP->isInteger(thisCol) ) numInt++; } assert(numCont==3); assert(numBinary==2); assert(numIntNonBinary==1); assert(numInt==3); // Test initializeCutGenerator siP->initialSolve(); assert(xstar !=NULL); for (i=0; i<nCols; i++){ assert(complement[i]==0); } int nRows=siP->getNumRows(); for (i=0; i<nRows; i++){ int vectorsize = siP->getMatrixByRow()->getVectorSize(i); assert(vectorsize==2); } kccg.cleanUpCutGenerator(complement,xstar); #endif delete siP; } }
//-------------------------------------------------------------------------- void CglKnapsackCoverUnitTest( const OsiSolverInterface * baseSiP, const std::string mpsDir ) { int i; CoinRelFltEq eq(0.000001); // Test default constructor { CglKnapsackCover kccGenerator; } // Test copy & assignment { CglKnapsackCover rhs; { CglKnapsackCover kccGenerator; CglKnapsackCover cgC(kccGenerator); rhs=kccGenerator; } } // test exactSolveKnapsack { CglKnapsackCover kccg; const int n=7; double c=50; double p[n] = {70,20,39,37,7,5,10}; double w[n] = {31, 10, 20, 19, 4, 3, 6}; double z; int x[n]; int exactsol = kccg.exactSolveKnapsack(n, c, p, w, z, x); assert(exactsol==1); assert (z == 107); assert (x[0]==1); assert (x[1]==0); assert (x[2]==0); assert (x[3]==1); assert (x[4]==0); assert (x[5]==0); assert (x[6]==0); } /* // Testcase /u/rlh/osl2/mps/scOneInt.mps // Model has 3 continous, 2 binary, and 1 general // integer variable. { OsiSolverInterface * siP = baseSiP->clone(); int * complement=NULL; double * xstar=NULL; siP->readMps("../Mps/scOneInt","mps"); CglKnapsackCover kccg; int nCols=siP->getNumCols(); // Test the siP methods for detecting // variable type int numCont=0, numBinary=0, numIntNonBinary=0, numInt=0; for (int thisCol=0; thisCol<nCols; thisCol++) { if ( siP->isContinuous(thisCol) ) numCont++; if ( siP->isBinary(thisCol) ) numBinary++; if ( siP->isIntegerNonBinary(thisCol) ) numIntNonBinary++; if ( siP->isInteger(thisCol) ) numInt++; } assert(numCont==3); assert(numBinary==2); assert(numIntNonBinary==1); assert(numInt==3); // Test initializeCutGenerator siP->initialSolve(); assert(xstar !=NULL); for (i=0; i<nCols; i++){ assert(complement[i]==0); } int nRows=siP->getNumRows(); for (i=0; i<nRows; i++){ int vectorsize = siP->getMatrixByRow()->vectorSize(i); assert(vectorsize==2); } kccg.cleanUpCutGenerator(complement,xstar); delete siP; } */ // Testcase /u/rlh/osl2/mps/tp3.mps // Models has 3 cols, 3 rows // Row 0 yields a knapsack, others do not. { // setup OsiSolverInterface * siP = baseSiP->clone(); std::string fn(mpsDir+"tp3"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); OsiCuts cs; CoinPackedVector krow; double b=0; int nCols=siP->getNumCols(); int * complement=new int [nCols]; double * xstar=new double [nCols]; CglKnapsackCover kccg; // solve LP relaxation // a "must" before calling initialization siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); std::cout<<"Initial LP value: "<<lpRelaxBefore<<std::endl; assert( eq(siP->getObjValue(), 97.185) ); double mycs[] = {.627, .667558333333, .038}; siP->setColSolution(mycs); const double *colsol = siP->getColSolution(); int k; for (k=0; k<nCols; k++){ xstar[k]=colsol[k]; complement[k]=0; } // test deriveAKnapsack int rind = ( siP->getRowSense()[0] == 'N' ) ? 1 : 0; const CoinShallowPackedVector reqdBySunCC = siP->getMatrixByRow()->getVector(rind) ; int deriveaknap = kccg.deriveAKnapsack(*siP, cs, krow,b,complement,xstar,rind,reqdBySunCC); assert(deriveaknap ==1); assert(complement[0]==0); assert(complement[1]==1); assert(complement[2]==1); int inx[3] = {0,1,2}; double el[3] = {161, 120, 68}; CoinPackedVector r; r.setVector(3,inx,el); assert (krow == r); //assert (b == 183.0); ????? but x1 and x2 at 1 is valid // test findGreedyCover CoinPackedVector cover,remainder; #if 0 int findgreedy = kccg.findGreedyCover( 0, krow, b, xstar, cover, remainder ); assert( findgreedy == 1 ); int coveri = cover.getNumElements(); assert( cover.getNumElements() == 2); coveri = cover.getIndices()[0]; assert( cover.getIndices()[0] == 0); assert( cover.getIndices()[1] == 1); assert( cover.getElements()[0] == 161.0); assert( cover.getElements()[1] == 120.0); assert( remainder.getNumElements() == 1); assert( remainder.getIndices()[0] == 2); assert( remainder.getElements()[0] == 68.0); // test liftCoverCut CoinPackedVector cut; double * rowupper = ekk_rowupper(model); double cutRhs = cover.getNumElements() - 1.0; kccg.liftCoverCut(b, krow.getNumElements(), cover, remainder, cut); assert ( cut.getNumElements() == 3 ); assert ( cut.getIndices()[0] == 0 ); assert ( cut.getIndices()[1] == 1 ); assert ( cut.getIndices()[2] == 2 ); assert( cut.getElements()[0] == 1 ); assert( cut.getElements()[1] == 1 ); assert( eq(cut.getElements()[2], 0.087719) ); // test liftAndUncomplementAndAdd OsiCuts cuts; kccg.liftAndUncomplementAndAdd(*siP.getRowUpper()[0],krow,b,complement,0, cover,remainder,cuts); int sizerowcuts = cuts.sizeRowCuts(); assert ( sizerowcuts== 1 ); OsiRowCut testRowCut = cuts.rowCut(0); CoinPackedVector testRowPV = testRowCut.row(); OsiRowCut sampleRowCut; const int sampleSize = 3; int sampleCols[sampleSize]={0,1,2}; double sampleElems[sampleSize]={1.0,-1.0,-0.087719}; sampleRowCut.setRow(sampleSize,sampleCols,sampleElems); sampleRowCut.setLb(-DBL_MAX); sampleRowCut.setUb(-0.087719); bool equiv = testRowPV.equivalent(sampleRowCut.row(),CoinRelFltEq(1.0e-05) ); assert ( equiv ); #endif // test find PseudoJohnAndEllisCover cover.setVector(0,NULL, NULL); remainder.setVector(0,NULL,NULL); rind = ( siP->getRowSense()[0] == 'N' ) ? 1 : 0; int findPJE = kccg.findPseudoJohnAndEllisCover( rind, krow, b, xstar, cover, remainder ); assert( findPJE == 1 ); assert ( cover.getIndices()[0] == 0 ); assert ( cover.getIndices()[1] == 2 ); assert ( cover.getElements()[0] == 161 ); assert ( cover.getElements()[1] == 68 ); assert ( remainder.getIndices()[0] == 1 ); assert ( remainder.getElements()[0] == 120 ); OsiCuts cuts; kccg.liftAndUncomplementAndAdd((*siP).getRowUpper()[rind],krow,b, complement, rind, cover,remainder,cuts); assert (cuts.sizeRowCuts() == 1 ); OsiRowCut testRowCut = cuts.rowCut(0); CoinPackedVector testRowPV = testRowCut.row(); const int sampleSize = 3; int sampleCols[sampleSize]={0,1,2}; double sampleElems[sampleSize]={1.0, -1.0, -1.0}; OsiRowCut sampleRowCut; sampleRowCut.setRow(sampleSize,sampleCols,sampleElems); sampleRowCut.setLb(-COIN_DBL_MAX); sampleRowCut.setUb(-1.0); // test for 'close enough' assert( testRowPV.isEquivalent(sampleRowCut.row(),CoinRelFltEq(1.0e-05) ) ); // Reset complement & test next row for (i=0; i<nCols; i++){ complement[i]=0; } rind++; const CoinShallowPackedVector reqdBySunCC2 = siP->getMatrixByRow()->getVector(rind) ; deriveaknap = kccg.deriveAKnapsack(*siP,cuts,krow,b,complement,xstar,rind,reqdBySunCC2); assert(deriveaknap==0); // Reset complement & test next row for (i=0; i<nCols; i++){ complement[i]=0; } const CoinShallowPackedVector reqdBySunCC3 = siP->getMatrixByRow()->getVector(2) ; deriveaknap = kccg.deriveAKnapsack(*siP,cuts,krow,b,complement,xstar,2, reqdBySunCC3); assert(deriveaknap == 0); // Clean up delete [] complement; delete [] xstar; delete siP; } #if 0 // Testcase /u/rlh/osl2/mps/tp4.mps // Models has 6 cols, 1 knapsack row and // 3 rows explicily bounding variables // Row 0 yields a knapsack cover cut // using findGreedyCover which moves the // LP objective function value. { // Setup EKKContext * env=ekk_initializeContext(); EKKModel * model = ekk_newModel(env,""); OsiSolverInterface si(model); ekk_importModel(model, "tp4.mps"); CglKnapsackCover kccg; kccg.ekk_validateIntType(si); // Solve the LP relaxation of the model and // print out ofv for sake of comparison ekk_allSlackBasis(model); ekk_crash(model,1); ekk_primalSimplex(model,1); double lpRelaxBefore=ekk_getRobjvalue(model); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); #endif // Determine if lp sol is ip optimal // Note: no ekk_function to do this int nCols=ekk_getInumcols(model); double * optLpSol = ekk_colsol(model); int ipOpt = 1; i=0; while (i++<nCols && ipOpt){ if(optLpSol[i] < 1.0-1.0e-08 && optLpSol[i]> 1.0e-08) ipOpt = 0; } if (ipOpt){ #ifdef CGL_DEBUG printf("Lp solution is within ip optimality tolerance\n"); #endif } else { OsiSolverInterface iModel(model); OsiCuts cuts; // Test generateCuts method kccg.generateCuts(iModel,cuts); OsiSolverInterface::ApplyCutsReturnCode rc = iModel.applyCuts(cuts); ekk_mergeBlocks(model,1); ekk_dualSimplex(model); double lpRelaxAfter=ekk_getRobjvalue(model); #ifdef CGL_DEBUG printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif assert( lpRelaxBefore < lpRelaxAfter ); // This may need to be updated as other // minimal cover finders are added assert( cuts.sizeRowCuts() == 1 ); OsiRowCut testRowCut = cuts.rowCut(0); CoinPackedVector testRowPV = testRowCut.row(); OsiRowCut sampleRowCut; const int sampleSize = 6; int sampleCols[sampleSize]={0,1,2,3,4,5}; double sampleElems[sampleSize]={1.0,1.0,1.0,1.0,0.5, 2.0}; sampleRowCut.setRow(sampleSize,sampleCols,sampleElems); sampleRowCut.setLb(-DBL_MAX); sampleRowCut.setUb(3.0); bool equiv = testRowPV.equivalent(sampleRowCut.row(),CoinRelFltEq(1.0e-05) ); assert( testRowPV.equivalent(sampleRowCut.row(),CoinRelFltEq(1.0e-05) ) ); } // Exit out of OSL ekk_deleteModel(model); ekk_endContext(env); } #endif // Testcase /u/rlh/osl2/mps/tp5.mps // Models has 6 cols, 1 knapsack row and // 3 rows explicily bounding variables // Row 0 yields a knapsack cover cut // using findGreedyCover which moves the // LP objective function value. { // Setup OsiSolverInterface * siP = baseSiP->clone(); std::string fn(mpsDir+"tp5"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); CglKnapsackCover kccg; // Solve the LP relaxation of the model and // print out ofv for sake of comparison siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); assert( eq(lpRelaxBefore, -51.66666666667) ); double mycs[] = {.8999999999, .899999999999, .89999999999, 1.110223e-16, .5166666666667, 0}; siP->setColSolution(mycs); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); #endif // Determine if lp sol is 0/1 optimal int nCols=siP->getNumCols(); const double * optLpSol = siP->getColSolution(); bool ipOpt = true; i=0; while (i++<nCols && ipOpt){ if(optLpSol[i] > kccg.epsilon_ && optLpSol[i] < kccg.onetol_) ipOpt = false; } if (ipOpt){ #ifdef CGL_DEBUG printf("Lp solution is within ip optimality tolerance\n"); #endif } else { // set up OsiCuts cuts; CoinPackedVector krow; double b=0.0; int * complement=new int[nCols]; double * xstar=new double[nCols]; // initialize cut generator const double *colsol = siP->getColSolution(); for (i=0; i<nCols; i++){ xstar[i]=colsol[i]; complement[i]=0; } int row = ( siP->getRowSense()[0] == 'N' ) ? 1 : 0; // transform row into canonical knapsack form const CoinShallowPackedVector reqdBySunCC = siP->getMatrixByRow()->getVector(row) ; if (kccg.deriveAKnapsack(*siP, cuts, krow, b, complement, xstar, row,reqdBySunCC)){ CoinPackedVector cover, remainder; // apply greedy logic to detect violated minimal cover inequalities if (kccg.findGreedyCover(row, krow, b, xstar, cover, remainder) == 1){ // lift, uncomplements, and add cut to cut set kccg.liftAndUncomplementAndAdd((*siP).getRowUpper()[row],krow, b, complement, row, cover, remainder, cuts); } // reset optimal column solution (xstar) information in OSL const double * rowupper = siP->getRowUpper(); int k; if (fabs(b-rowupper[row]) > 1.0e-05) { for(k=0; k<krow.getNumElements(); k++) { if (complement[krow.getIndices()[k]]){ xstar[krow.getIndices()[k]]= 1.0-xstar[krow.getIndices()[k]]; complement[krow.getIndices()[k]]=0; } } } // clean up delete [] complement; delete [] xstar; } // apply the cuts OsiSolverInterface::ApplyCutsReturnCode rc = siP->applyCuts(cuts); siP->resolve(); double lpRelaxAfter=siP->getObjValue(); assert( eq(lpRelaxAfter, -30.0) ); #ifdef CGL_DEBUG printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif // test that expected cut was detected assert( lpRelaxBefore < lpRelaxAfter ); assert( cuts.sizeRowCuts() == 1 ); OsiRowCut testRowCut = cuts.rowCut(0); CoinPackedVector testRowPV = testRowCut.row(); OsiRowCut sampleRowCut; const int sampleSize = 6; int sampleCols[sampleSize]={0,1,2,3,4,5}; double sampleElems[sampleSize]={1.0,1.0,1.0,0.25,1.0,2.0}; sampleRowCut.setRow(sampleSize,sampleCols,sampleElems); sampleRowCut.setLb(-COIN_DBL_MAX); sampleRowCut.setUb(3.0); assert(testRowPV.isEquivalent(sampleRowCut.row(),CoinRelFltEq(1.0e-05))); } delete siP; } // Testcase /u/rlh/osl2/mps/p0033 // Miplib3 problem p0033 // Test that no cuts chop off the optimal solution { // Setup OsiSolverInterface * siP = baseSiP->clone(); std::string fn(mpsDir+"p0033"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); int nCols=siP->getNumCols(); CglKnapsackCover kccg; // Solve the LP relaxation of the model and // print out ofv for sake of comparison siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); assert( eq(lpRelaxBefore, 2520.5717391304347) ); double mycs[] = {0, 1, 0, 0, -2.0837010502455788e-19, 1, 0, 0, 1, 0.021739130434782594, 0.35652173913043478, -6.7220534694101275e-18, 5.3125906451789717e-18, 1, 0, 1.9298798670241979e-17, 0, 0, 0, 7.8875708048320448e-18, 0.5, 0, 0.85999999999999999, 1, 1, 0.57999999999999996, 1, 0, 1, 0, 0.25, 0, 0.67500000000000004}; siP->setColSolution(mycs); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); #endif OsiCuts cuts; // Test generateCuts method kccg.generateCuts(*siP,cuts); OsiSolverInterface::ApplyCutsReturnCode rc = siP->applyCuts(cuts); siP->resolve(); double lpRelaxAfter=siP->getObjValue(); assert( eq(lpRelaxAfter, 2829.0597826086955) ); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif assert( lpRelaxBefore < lpRelaxAfter ); // the CoinPackedVector p0033 is the optimal // IP solution to the miplib problem p0033 int objIndices[14] = { 0, 6, 7, 9, 13, 17, 18, 22, 24, 25, 26, 27, 28, 29 }; CoinPackedVector p0033(14,objIndices,1.0); // Sanity check const double * objective=siP->getObjCoefficients(); double ofv =0 ; int r; for (r=0; r<nCols; r++){ ofv=ofv + p0033[r]*objective[r]; } CoinRelFltEq eq; assert( eq(ofv,3089.0) ); int nRowCuts = cuts.sizeRowCuts(); OsiRowCut rcut; CoinPackedVector rpv; for (i=0; i<nRowCuts; i++){ rcut = cuts.rowCut(i); rpv = rcut.row(); double p0033Sum = (rpv*p0033).sum(); assert (p0033Sum <= rcut.ub() ); } delete siP; } // if a debug file is there then look at it { FILE * fp = fopen("knapsack.debug","r"); if (fp) { int ncol,nel; double up; int x = fscanf(fp,"%d %d %lg",&ncol,&nel,&up); if (x<=0) throw("bad fscanf"); printf("%d columns, %d elements, upper %g\n",ncol,nel,up); double * sol1 = new double[nel]; double * el1 = new double[nel]; int * col1 = new int[nel]; CoinBigIndex * start = new CoinBigIndex [ncol+1]; memset(start,0,ncol*sizeof(CoinBigIndex )); int * row = new int[nel]; int i; for (i=0;i<nel;i++) { x=fscanf(fp,"%d %lg %lg",col1+i,el1+i,sol1+i); if (x<=0) throw("bad fscanf"); printf("[%d, e=%g, v=%g] ",col1[i],el1[i],sol1[i]); start[col1[i]]=1; row[i]=0; } printf("\n"); // Setup OsiSolverInterface * siP = baseSiP->clone(); double lo=-1.0e30; double * upper = new double[ncol]; start[ncol]=nel; int last=0; for (i=0;i<ncol;i++) { upper[i]=1.0; int marked=start[i]; start[i]=last; if (marked) last++; } siP->loadProblem(ncol,1,start,row,el1,NULL,upper,NULL,&lo,&up); // use upper for solution memset(upper,0,ncol*sizeof(double)); for (i=0;i<nel;i++) { int icol=col1[i]; upper[icol]=sol1[i]; siP->setInteger(icol); } siP->setColSolution(upper); delete [] sol1; delete [] el1; delete [] col1; delete [] start; delete [] row; delete [] upper; CglKnapsackCover kccg; OsiCuts cuts; // Test generateCuts method kccg.generateCuts(*siP,cuts); // print out and compare to known cuts int numberCuts = cuts.sizeRowCuts(); if (numberCuts) { for (i=0;i<numberCuts;i++) { OsiRowCut * thisCut = cuts.rowCutPtr(i); int n=thisCut->row().getNumElements(); printf("Cut %d has %d entries, rhs %g %g =>",i,n,thisCut->lb(), thisCut->ub()); int j; const int * index = thisCut->row().getIndices(); const double * element = thisCut->row().getElements(); for (j=0;j<n;j++) { printf(" (%d,%g)",index[j],element[j]); } printf("\n"); } } fclose(fp); } } // Testcase /u/rlh/osl2/mps/p0201 // Miplib3 problem p0282 // Test that no cuts chop off the optimal ip solution { // Setup OsiSolverInterface * siP = baseSiP->clone(); std::string fn(mpsDir+"p0201"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); const int nCols=siP->getNumCols(); CglKnapsackCover kccg; // Solve the LP relaxation of the model and // print out ofv for sake of comparisn siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); assert( eq(lpRelaxBefore, 6875.) ); double mycs[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; siP->setColSolution(mycs); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); #endif OsiCuts cuts; // Test generateCuts method kccg.generateCuts(*siP,cuts); OsiSolverInterface::ApplyCutsReturnCode rc = siP->applyCuts(cuts); siP->resolve(); double lpRelaxAfter=siP->getObjValue(); assert( eq(lpRelaxAfter, 7125) ); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif assert( lpRelaxBefore < lpRelaxAfter ); // Optimal IP solution to p0201 int objIndices[22] = { 8, 10, 21, 38, 39, 56, 60, 74, 79, 92, 94, 110, 111, 128, 132, 146, 151,164, 166, 182,183, 200 }; CoinPackedVector p0201(22,objIndices,1.0); // Sanity check const double * objective=siP->getObjCoefficients(); double ofv =0 ; int r; for (r=0; r<nCols; r++){ ofv=ofv + p0201[r]*objective[r]; } CoinRelFltEq eq; assert( eq(ofv,7615.0) ); //printf("p0201 optimal ofv = %g\n",ofv); int nRowCuts = cuts.sizeRowCuts(); OsiRowCut rcut; CoinPackedVector rpv; for (i=0; i<nRowCuts; i++){ rcut = cuts.rowCut(i); rpv = rcut.row(); double p0201Sum = (rpv*p0201).sum(); assert (p0201Sum <= rcut.ub() ); } delete siP; } // see if I get the same covers that N&W get { OsiSolverInterface * siP=baseSiP->clone(); std::string fn(mpsDir+"nw460"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); CglKnapsackCover kccg; // Solve the LP relaxation of the model and // print out ofv for sake of comparison siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); assert( eq(lpRelaxBefore, -225.68951787852194) ); double mycs[] = {0.7099213482046447, 0, 0.34185802225477174, 1, 1, 0, 1, 1, 0}; siP->setColSolution(mycs); OsiCuts cuts; // Test generateCuts method kccg.generateCuts(*siP,cuts); OsiSolverInterface::ApplyCutsReturnCode rc = siP->applyCuts(cuts); siP->resolve(); double lpRelaxAfter=siP->getObjValue(); assert( eq(lpRelaxAfter, -176) ); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif #ifdef MJS assert( lpRelaxBefore < lpRelaxAfter ); #endif int nRowCuts = cuts.sizeRowCuts(); OsiRowCut rcut; CoinPackedVector rpv; for (i=0; i<nRowCuts; i++){ rcut = cuts.rowCut(i); rpv = rcut.row(); int j; printf("Row cut number %i has rhs = %g\n",i,rcut.ub()); for (j=0; j<rpv.getNumElements(); j++){ printf("index %i, element %g\n", rpv.getIndices()[j], rpv.getElements()[j]); } printf("\n"); } delete siP; } // Debugging: try "exmip1.mps" { // Setup OsiSolverInterface * siP = baseSiP->clone(); std::string fn(mpsDir+"exmip1"); siP->readMps(fn.c_str(),"mps"); // All integer variables should be binary. // Assert that this is true. for ( i = 0; i < siP->getNumCols(); i++ ) if ( siP->isInteger(i) ) assert(siP->getColUpper()[i]==1.0 && siP->isBinary(i)); CglKnapsackCover kccg; // Solve the LP relaxation of the model and // print out ofv for sake of comparison siP->initialSolve(); double lpRelaxBefore=siP->getObjValue(); assert( eq(lpRelaxBefore, 3.2368421052631575) ); double mycs[] = {2.5, 0, 0, 0.6428571428571429, 0.5, 4, 0, 0.26315789473684253}; siP->setColSolution(mycs); // Test generateCuts method OsiCuts cuts; kccg.generateCuts(*siP,cuts); OsiSolverInterface::ApplyCutsReturnCode rc = siP->applyCuts(cuts); siP->resolve(); double lpRelaxAfter=siP->getObjValue(); assert( eq(lpRelaxAfter, 3.2368421052631575) ); #ifdef CGL_DEBUG printf("\n\nOrig LP min=%f\n",lpRelaxBefore); printf("\n\nFinal LP min=%f\n",lpRelaxAfter); #endif assert( lpRelaxBefore <= lpRelaxAfter ); delete siP; } #ifdef CGL_DEBUG // See what findLPMostViolatedMinCover for knapsack with 2 elements does { int nCols = 2; int row = 1; CoinPackedVector krow; double e[2] = {5,10}; int ii[2] = {0,1}; krow.setVector(nCols,ii,e); double b=11; double xstar[2] = {.2,.9}; CoinPackedVector cover; CoinPackedVector remainder; CglKnapsackCover kccg; kccg.findLPMostViolatedMinCover(nCols, row, krow, b, xstar, cover, remainder); printf("num in cover = %i\n",cover.getNumElements()); int j; for (j=0; j<cover.getNumElements(); j++){ printf(" index %i element % g\n", cover.getIndices()[j], cover.getElements()[j]); } } #endif #ifdef CGL_DEBUG // see what findLPMostViolatedMinCover does { int nCols = 5; int row = 1; CoinPackedVector krow; double e[5] = {1,1,1,1,10}; int ii[5] = {0,1,2,3,4}; krow.setVector(nCols,ii,e); double b=11; double xstar[5] = {.9,.9,1,1,.1}; CoinPackedVector cover; CoinPackedVector remainder; CglKnapsackCover kccg; kccg.findLPMostViolatedMinCover(nCols, row, krow, b, xstar, cover, remainder); printf("num in cover = %i\n",cover.getNumElements()); int j; for (j=0; j<cover.getNumElements(); j++){ printf(" index %i element % g\n", cover.getIndices()[j], cover.getElements()[j]); } } #endif }