void testBoundaryLRSolver(const std::string inputMatrixFileName,const std::string inputGraphFileName,const std::string outputFileName,const double iterInitTol,const int sizeThreshold,const int depth,user_IndexTree &usrTree){
Eigen::MatrixXd inputMatrix = readBinaryIntoMatrixXd(inputMatrixFileName);
Eigen::SparseMatrix<double> inputGraph = readMtxIntoSparseMatrix(inputGraphFileName);
HODLR_Matrix testHODLR(inputMatrix,inputGraph,sizeThreshold,usrTree);
int matrixSize = inputMatrix.rows();
Eigen::VectorXd exactSoln = Eigen::VectorXd::LinSpaced(Eigen::Sequential,matrixSize,-2,2);
Eigen::VectorXd inputF = inputMatrix * exactSoln;
testHODLR.set_BoundaryDepth(depth);
testHODLR.printResultInfo = true;
Eigen::VectorXd solverSoln = testHODLR.iterative_Solve(inputF,100,1e-10,iterInitTol,"PS_Boundary","recLU");
Eigen::VectorXd difference = solverSoln - exactSoln;
//double relError = difference.norm()/exactSoln.norm();
//std::cout<<relError<<std::endl;
testHODLR.saveSolverInfo(outputFileName);
double startTime = clock();
Eigen::PartialPivLU<Eigen::MatrixXd> LU (inputMatrix);
solverSoln = LU.solve(inputF);
double endTime = clock();
double LU_SolveTime = (endTime - startTime)/CLOCKS_PER_SEC;
std::cout<<"LU Solve Time = "<<LU_SolveTime<<" seconds"<<std::endl;
std::cout<<"Matrix Size = "<<inputMatrix.rows()<<std::endl;
}
int main(){
std::cout<<"+++++++++++++++++++++++++++++++++++++++++++++++++++"<<std::endl;
std::cout<<"Testing fast iterative solver on a 100k matrix...."<<std::endl;
//Eigen::SparseMatrix<double> inputSpMatrix = readMtxIntoSparseMatrix("../benchmarks/data/input_FETI/TardecAres/localmat1");
// Eigen::SparseMatrix<double> inputSpMatrix = readMtxIntoSparseMatrix("../benchmarks/data/stiffness/GenericHull/localmat0");
Eigen_IML_Matrix inputSpMatrix;
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/input_FETI/TardecAres/localmat1");
//loadMarket(inputSpMatrix,"../../../benchmarks/data/input_FETI/TardecAres/localmat1");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/AMD/G3_circuit/G3_circuit.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/Botonakis/thermomech_dM/thermomech_dM.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/CEMW/tmt_sym/tmt_sym.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/GHS_psdef/apache2/apache2.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/McRae/ecology2/ecology2.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/Wissgott/parabolic_fem/parabolic_fem.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/stiffness/unStructured/cylinderHead/2.3m/localmat0");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/SMatrices/linearElasticity/ElasticityS32_660k");
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/SMatrices/Poisson/PoissonS64_1M");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/input_FETI/structured/localmat1.800k");
//inputSpMatrix = readMtxIntoSparseMatrix("../../benchmarks/data/UF/Janna/Cube_Coup_dt6/Cube_Coup_dt6.mtx");
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/input_FETI/structured/localmat0.100k");
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/input_FETI/unStructured/cube/localmat0.500k");
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/stiffness/unStructured/beam/stiffness.300k");
//inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/stiffness/unStructured/cylinderHead/330k/localmat0");
// inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/input_FETI/structured/localmat0.400k");
inputSpMatrix = readMtxIntoSparseMatrix("../../../benchmarks/data/input_FETI/unStructured/engine/localmat4");
//inputSpMatrix = rowScaling(inputSpMatrix);
//testSolveSp(inputSpMatrix, "implicit");
//testSolveSp(inputSpMatrix, "fast_Iterative");
//Eigen_IML_Vector exactSoln_Sp = Eigen::VectorXd::LinSpaced(Eigen::Sequential,inputSpMatrix.rows(),-2,2);
//Eigen_IML_Vector RHS = inputSpMatrix * exactSoln_Sp;
Eigen_IML_Vector RHS = Eigen::MatrixXd::Random(inputSpMatrix.rows(),1);
fastSparse_IML_Precond precond(inputSpMatrix);
precond.printResultInfo = true;
Eigen_IML_Vector x1 = precond.implicit_Solve(RHS);
//Eigen_IML_Vector x0 = precond.solve(RHS);
//Eigen_IML_Vector soln_Sp = precond.iterative_Solve(RHS,10,1e-10,1e-1);
//Eigen_IML_Vector x0 = Eigen::MatrixXd::Zero(inputSpMatrix.rows(),1);
precond.printResultInfo = false;
std::cout<<"RHS norm = "<<RHS.norm()<<std::endl;
double tol = 1e-4;
int result, maxit = 5000,restart = 32;
Eigen::MatrixXd H =Eigen::MatrixXd::Zero(restart+1,restart);
//result = GMRES(inputSpMatrix,x0,RHS,precond,H,restart,maxit,tol);
std::cout<<"GMRES flag = "<<result<<std::endl;
std::cout<<"iterations performed "<<maxit<<std::endl;
std::cout<<"tolerance achieved : "<<tol<<std::endl;
diag_IML_Precond diagPrecond(inputSpMatrix);
Eigen_IML_Vector x2 = diagPrecond.solve(RHS);
H = Eigen::MatrixXd::Zero(restart+1,restart);
maxit = 1000;
tol = 1e-4;
std::cout<<"here"<<std::endl;
//result = GMRES(inputSpMatrix,x2,RHS,diagPrecond,H,restart,maxit,tol);
std::cout<<"GMRES flag = "<<result<<std::endl;
std::cout<<"iterations performed "<<maxit<<std::endl;
std::cout<<"tolerance achieved : "<<tol<<std::endl;
return 0;
}
void analyzeRank(const std::string inputMatrixFileName,const std::string inputGraphFileName,const std::string outputFileName,const int input_Min_i,const int input_Min_j, const int input_NumRows,const int input_NumCols,std::string mode){
Eigen::MatrixXd inputMatrix = readBinaryIntoMatrixXd(inputMatrixFileName);
Eigen::SparseMatrix<double> inputGraph = readMtxIntoSparseMatrix(inputGraphFileName);
int min_i,min_j,numRows,numCols;
int matrixSize = inputMatrix.rows();
if (mode == "topOffDiag"){
int split = matrixSize/2;
min_i = 0;
min_j = split + 1;
numRows = split + 1;
numCols = matrixSize - split - 1;
} else if (mode == "bottOffDiag"){
int split = matrixSize/2;
min_i = split + 1;
min_j = 0;
numRows = matrixSize - split - 1;
numCols = split + 1;
}else{
min_i = input_Min_i;
min_j = input_Min_j;
numRows = input_NumRows;
numCols = input_NumCols;
}
int currRank = 0;
int currRankComp1 = 0;
int currRankComp3 = 0;
int currRankComp5 = 0;
int nextRank = -1;
int depth = 0;
Eigen::MatrixXd currBlock = inputMatrix.block(min_i,min_j,numRows,numCols);
Eigen::MatrixXd U,V;
std::vector<double> numPoints,boundaryError,SVDError,singularValues;
std::vector<double> boundaryErrorComp1,boundaryErrorComp3,boundaryErrorComp5;
while (currRank != nextRank){
nextRank = currRank;
PS_Boundary_LowRankApprox(inputMatrix,inputGraph,U,V,min_i,min_j,numRows,numCols,1e-15,currRank,depth);
numPoints.push_back(currRank);
double relError = (U * V.transpose() - currBlock).norm()/currBlock.norm();
boundaryError.push_back(relError);
PS_Boundary_LowRankApprox(inputMatrix,inputGraph,U,V,min_i,min_j,numRows,numCols,1e-1,currRankComp1,depth);
relError = (U * V.transpose() - currBlock).norm()/currBlock.norm();
boundaryErrorComp1.push_back(relError);
PS_Boundary_LowRankApprox(inputMatrix,inputGraph,U,V,min_i,min_j,numRows,numCols,1e-3,currRankComp3,depth);
relError = (U * V.transpose() - currBlock).norm()/currBlock.norm();
boundaryErrorComp3.push_back(relError);
PS_Boundary_LowRankApprox(inputMatrix,inputGraph,U,V,min_i,min_j,numRows,numCols,1e-5,currRankComp5,depth);
relError = (U * V.transpose() - currBlock).norm()/currBlock.norm();
boundaryErrorComp5.push_back(relError);
depth ++;
}
saveVectorAsText(outputFileName + "numPointsVsBoundaryDistance",numPoints);
saveVectorAsText(outputFileName + "boundaryErrorVsBoundaryDistance",boundaryError);
saveVectorAsText(outputFileName + "boundaryErrorCompVsBoundaryDistance1",boundaryErrorComp1);
saveVectorAsText(outputFileName + "boundaryErrorCompVsBoundaryDistance3",boundaryErrorComp3);
saveVectorAsText(outputFileName + "boundaryErrorCompVsBoundaryDistance5",boundaryErrorComp5);
// Use svd to calculate the optimal low-rank approximation error
Eigen::JacobiSVD<Eigen::MatrixXd> svd(currBlock,Eigen::ComputeThinU|Eigen::ComputeThinV);
Eigen::VectorXd s = svd.singularValues();
for (unsigned int i = 0; i < s.rows(); i++)
singularValues.push_back(s(i));
for (unsigned int i = 0; i < numPoints.size(); i++){
int rank = numPoints[i];
U = svd.matrixU().leftCols(rank);
V = svd.matrixV().leftCols(rank);
Eigen::MatrixXd K = Eigen::MatrixXd::Zero(rank,rank);
for (int j = 0; j < rank; j++)
K(j,j) = singularValues[j];
double relError = (U * K * V.transpose() - currBlock).norm()/currBlock.norm();
SVDError.push_back(relError);
}
saveVectorAsText(outputFileName + "SVDErrorVsBoundaryDistance",SVDError);
saveVectorAsText(outputFileName + "SingularValueDecay",singularValues);
// Calculate distance from boundary vs pivot size
PS_Boundary_LowRankApprox(inputMatrix,inputGraph,U,V,min_i,min_j,numRows,numCols,1e-15,currRank,matrixSize,outputFileName + "distanceFromBoundaryVsPivotSize");
}