double eigenPartialPivLUSpeed(const Eigen::MatrixXd & inputMatrix){
int matrixSize = inputMatrix.rows();
Eigen::MatrixXd inputF = Eigen::VectorXd::LinSpaced(Eigen::Sequential,matrixSize,-2,2);
double startTime = clock();
Eigen::PartialPivLU<Eigen::MatrixXd> LU (inputMatrix);
Eigen::VectorXd solverSoln = LU.solve(inputF);
double endTime = clock();
return (endTime - startTime)/CLOCKS_PER_SEC;
}
void ctms_decompositions()
{
const int maxSize = 16;
const int size = 12;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> Matrix;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, 1,
0,
maxSize, 1> Vector;
typedef Eigen::Matrix<std::complex<Scalar>,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> ComplexMatrix;
const Matrix A(Matrix::Random(size, size));
const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
const Matrix saA = A.adjoint() * A;
// Cholesky module
Eigen::LLT<Matrix> LLT; LLT.compute(A);
Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
// Eigenvalues module
Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
// LU module
Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
// QR module
Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
// SVD module
Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
}
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;
}
///////////////////////////////// MAIN /////////////////////////////////////////
int main( int argc, char* argv[] )
{
// Wrap everything in a try block. Do this every time,
// because exceptions will be thrown for problems.
try {
// Define the command line object.
TCLAP::CmdLine cmd("Solve linear least square fit.",
' ', "LeSLiE 0.1");
// add the input file as a required unlabeled value to the command line
TCLAP::UnlabeledValueArg<int>
lsqOrder( "order", "integer indicating maximal degree of polynomial basis",
true, 1, "int", cmd );
TCLAP::UnlabeledValueArg<std::string>
inpFile( "filename", ".csv file containing x and y values",
true, "default", "string", cmd );
// Parse the args.
cmd.parse( argc, argv );
const int degree = lsqOrder.getValue();
const std::string filename = inpFile.getValue();
// typedefs
typedef double scalar_type;
typedef Eigen::Matrix<scalar_type,Eigen::Dynamic,Eigen::Dynamic>
matrix_type;
typedef Eigen::Matrix<scalar_type,Eigen::Dynamic,1>
vector_type;
//////////////////////////// READ FROM FILE //////////////////////////////////
filereader<scalar_type,vector_type> myreader(filename);
// set up data pair
// std::cout << myreader.getFileName() << std::endl;
vector_type xs, ys;
myreader(xs,ys);
//////////////////////////////////////////////////////////////////////////////
///////////////////// SETTING UP PURE FUNCTION SPACE /////////////////////////
// initialize dim-0 space
FunctionSpace1d<scalar_type,vector_type,matrix_type,
Function1d<scalar_type,vector_type,Polynomial1d> >
mySpace(0);
// fill in basis
for (unsigned int k=0; k<=degree; ++k)
{
mySpace.addFunction(Function1d<scalar_type,vector_type,Polynomial1d>(k));
}
/////////// ALTERNATIVE OF SETTING UP MIXED FUNCTION SPACE ///////////////////
vector_type myShape(1);
myShape(0) = 3;
std::cout << POLYNOMIAL<scalar_type,vector_type>(5,myShape) << std::endl;
scalar_type (*myfunpt)(scalar_type,vector_type) =
POLYNOMIAL<scalar_type,vector_type>;
std::cout << myfunpt(6,myShape) << std::endl;
Function1d_PT<scalar_type,vector_type> myPoly(myfunpt,myShape);
std::cout << myPoly.evaluate(29) << std::endl;
// set up space for testing purposes
FunctionSpace1d<scalar_type,vector_type,matrix_type,
Function1d_PT<scalar_type,vector_type> >
testSpace(0);
// fill in basis
// ADD ARRAY OF FUNCTIONS
for (int p=0; p<=degree; ++p)
{
myShape(0) = p;
scalar_type (*myfunpt)(scalar_type,vector_type) =
POLYNOMIAL<scalar_type,vector_type>;
testSpace.addFunction(
Function1d_PT<scalar_type,vector_type>(myfunpt,myShape) );
}
// ADD A SINGLE FUNCTION - SPACE ENRICHED WITH LOG (COMPARED TO mySpace)
scalar_type (*lastpt)(scalar_type,vector_type) =
LOG<scalar_type,vector_type>;
myShape(0) = 1;
std::cout << myShape << std::endl;
testSpace.addFunction(Function1d_PT<scalar_type,vector_type>(lastpt,myShape));
///////////// END OF ALTERNATIVE OF SETTING UP MIXED FUNCTION SPACE //////////
// Define matrix
/*
// CASE A - mySpace
matrix_type Mat(xs.size(),mySpace.getDim());
Mat.setZero();
vector_type rhs(mySpace.getDim()), sol(mySpace.getDim());
// Compute matrix
mySpace.evaluate(xs,Mat);
*/
// CASE B - testSpace
matrix_type Mat(xs.size(),testSpace.getDim());
Mat.setZero();
vector_type rhs(testSpace.getDim()), sol(testSpace.getDim());
// Compute matrix
testSpace.evaluate(xs,Mat);
// compute rhs
rhs.noalias() = Mat.transpose()*ys;
// TODO: ADD ROUTINE THAT CHECKS SOLVABILITY OF THE SYSTEM
// This is an issue especially when MIXED function spaces are allowed.
Eigen::PartialPivLU<matrix_type> plu;
plu.compute(Mat.transpose()*Mat);
sol = plu.solve(rhs);
// Display solution - SHORT
std::cout << std::endl;
std::cout << "Solution:" << std::endl;
std::cout << sol << std::endl << std::endl;;
// Display solution - LONG
std::cout << "Solution:" << std::endl;
for (unsigned int i=0; i<sol.size(); ++i)
{
std::cout << "beta_" << i << "\t=\t" << sol(i) << std::endl;
}
// Display solution - CSV OPTIMIZED
std::cout << "Solution:" << std::endl;
for (unsigned int i=0; i<sol.size(); ++i)
{
std::cout << "beta_" << i << "," << sol(i) << std::endl;
}
//filewriter<scalar_type,vector_type> mywriter(filename+".OUT");
//mywriter(sol);
return 0;
} catch (TCLAP::ArgException &e) // catch any exceptions
{ std::cerr << "error: " << e.error() << " for arg " << e.argId()
<< std::endl;
}
}