Algebra

include/PacsHPDG/Algebra/

Structs

include/PacsHPDG/Algebra/Vector.hpp

template<NumericType T> struct Vector {};

include/PacsHPDG/Algebra/Matrix.hpp

template<NumericType T> struct Matrix {};

include/PacsHPDG/Algebra/Sparse.hpp

template<NumericType T> struct Sparse {};

Methods

include/PacsHPDG/Algebra/Solvers.hpp

// Solvers and preconditioners (enums).
enum DenseSolver {LUD, QRD};
enum SparseSolver {GMRES, CGM, BICGSTAB};
enum SparseDSolver {DB};
enum Preconditioner {DI, DBI};

// Matrix solve wrappers.
template<NumericType T> Vector<T> solve(const Matrix<T> &, const Vector<T> &, const DenseSolver &S = QRD);
template<NumericType T> Matrix<T> solve(const Matrix<T> &, const Matrix<T> &, const DenseSolver &S = QRD);

// Sparse solve wrappers.
template<NumericType T> Vector<T> solve(const Sparse<T> &, const Vector<T> &, const SparseSolver &S = GMRES, const Real &TOL = 1E-8);
template<NumericType T> Vector<T> solve(const Sparse<T> &, const Vector<T> &, std::vector<std::array<std::vector<std::size_t>, 2>> &, const SparseSolver &S = GMRES, const Preconditioner &P = DBI, const Real &TOL = 1E-8);
template<NumericType T> Vector<T> solve(const Sparse<T> &, const Vector<T> &, std::vector<std::array<std::vector<std::size_t>, 2>> &, const SparseDSolver &S = DB);

// Matrix solvers.
template<NumericType T> Vector<T> _lu(const Matrix<T> &, const Vector<T> &);
template<NumericType T> Matrix<T> _lu(const Matrix<T> &, const Matrix<T> &);
template<NumericType T> Vector<T> _qr(const Matrix<T> &, const Vector<T> &);
template<NumericType T> Matrix<T> _qr(const Matrix<T> &, const Matrix<T> &);

// Sparse iterative solvers.
template<NumericType T> Vector<T> _gmres(const Sparse<T> &, const Vector<T> &, const Real &TOL = 1E-8);
template<NumericType T> Vector<T> _gmres(const Sparse<T> &, const Vector<T> &, const Vector<T> &guess, const Real &TOL = 1E-8);
template<NumericType T> Vector<T> _cgm(const Sparse<T> &, const Vector<T> &, const Real &TOL = 1E-8);
template<NumericType T> Vector<T> _bicgstab(const Sparse<T> &, const Vector<T> &, const Real &TOL = 1E-8);

// Sparse direct solvers.
template<NumericType T> Vector<T> _db(const Sparse<T> &, const Vector<T> &, const std::vector<std::array<std::vector<std::size_t>, 2>> &);

// Preconditioners.
template<NumericType T> Sparse<T> _di(const Sparse<T> &);
template<NumericType T> Sparse<T> _dbi(const Sparse<T> &, const std::vector<std::array<std::vector<std::size_t>, 2>> &);

include/PacsHPDG/Algebra/Methods/Vector.hpp

// Math.
template<NumericType T> inline T min(const Vector<T> &);
template<NumericType T> inline T max(const Vector<T> &);
template<NumericType T> inline T sum(const Vector<T> &);
template<NumericType T> inline T dot(const Vector<T> &, const Vector<T> &);
template<NumericType T> inline Real norm(const Vector<T> &);

namespace std { template<pacs::NumericType T> pacs::Vector<T> abs(const pacs::Vector<T> vector); }

// Tools.
template<NumericType T> Vector<T> stack(const Vector<T> &, const Vector<T> &);
template<NumericType T> Vector<T> flip(const Vector<T> &);
template<NumericType T> Mask highest(const Vector<T> &, const std::size_t &);
template<NumericType T> Mask lowest(const Vector<T> &, const std::size_t &);

include/PacsHPDG/Algebra/Methods/Matrix.hpp

// Math.
template<NumericType T> std::array<Matrix<T>, 2> LU(const Matrix<T> &);
template<NumericType T> std::array<Matrix<T>, 2> QR(const Matrix<T> &);
template<NumericType T> inline Matrix<T> identity(const std::size_t &);
template<NumericType T> T mtrace(const Matrix<T> &);

// Tools.
template<NumericType T> Vector<T> squash(const Matrix<T> &);

include/PacsHPDG/Algebra/Methods/Sparse.hpp

// Math.
template<NumericType T> T mtrace(const Sparse<T> &);