numerics/api/jacobi_8hpp_source.html

/// @file jacobi.hpp

/// @brief Jacobi iterative solver

#pragma once

#include "core/matrix.hpp"

#include "core/policy.hpp"

#include "core/vector.hpp"

#include "linalg/solvers/solver_result.hpp"


namespace num {


/// @brief Jacobi iterative solver for Ax = b

///

/// Updates all components simultaneously using only values from the previous

/// iteration. Converges for strictly diagonally dominant A. Trivially

/// parallelisable with Backend::omp.

///

/// @param A        Square matrix

/// @param b        Right-hand side vector

/// @param x        Solution vector (initial guess on input, solution on output)

/// @param tol      Convergence tolerance on residual norm (default 1e-10)

/// @param max_iter Maximum iterations (default 1000)

/// @param backend  Execution backend (default: default_backend)

/// @return SolverResult with convergence info

SolverResult jacobi(const Matrix &A, const Vector &b, Vector &x,

                    real tol = 1e-10, idx max_iter = 1000,

                    Backend backend = default_backend);


} // namespace num

policy.hpp
Backend enum for linear algebra operations.

matrix.hpp
Matrix operations.

num
Definition quadrature.hpp:8

num::real
double real
Definition types.hpp:10

num::Backend
Backend
Selects which backend handles a linalg operation.
Definition policy.hpp:19

num::idx
std::size_t idx
Definition types.hpp:11

num::e
constexpr real e
Definition math.hpp:43

num::Vector
BasicVector< real > Vector
Real-valued dense vector with full backend dispatch (CPU + GPU)
Definition vector.hpp:130

num::jacobi
SolverResult jacobi(const Matrix &A, const Vector &b, Vector &x, real tol=1e-10, idx max_iter=1000, Backend backend=default_backend)
Jacobi iterative solver for Ax = b.
Definition jacobi.cpp:7

num::default_backend
constexpr Backend default_backend
Definition policy.hpp:92

solver_result.hpp
Common result type shared by all iterative solvers.

vector.hpp
Vector operations.