cg.hpp File Reference

Conjugate gradient solvers. More...

#include "core/matrix.hpp"
#include "core/policy.hpp"
#include "core/vector.hpp"
#include "linalg/matrix_properties.hpp"
#include "linalg/solvers/solver_result.hpp"
#include "core/concepts.hpp"
#include <cmath>
#include <stdexcept>

Go to the source code of this file.

Namespaces
namespace	num
namespace	num::detail

Functions
SolverResult	num::cg (const Matrix &A, const Vector &b, Vector &x, real tol=1e-10, idx max_iter=1000, Backend backend=default_backend)
SolverResult	num::cg (const linalg::SPDMatrix< Matrix > &A, const Vector &b, Vector &x, real tol=1e-10, idx max_iter=1000, Backend backend=default_backend)
template<class Op > requires LinearOperator<Op, Vector, Vector>
SolverResult	num::detail::cg_operator_impl (const Op &A, const Vector &b, Vector &x, real tol, idx max_iter, Backend backend)
template<class Op > requires SPDLinearOperator<Op, Vector, Vector>
SolverResult	num::cg (const Op &A, const Vector &b, Vector &x, real tol=1e-10, idx max_iter=1000, Backend backend=default_backend)
	Operator CG for a declared SPD operator.

Detailed Description

Conjugate gradient solvers.

Solves \(Ax=b\) for symmetric positive definite \(A\) using \(\mathcal{K}_k(A,r_0)=\mathrm{span}\{r_0,Ar_0,\ldots,A^{k-1}r_0\}\).

Definition in file cg.hpp.