jacobi_eig.cpp File Reference

Sequential cyclic Jacobi eigensolver. More...

#include "impl.hpp"
#include <cmath>
#include <algorithm>
#include <stdexcept>

Go to the source code of this file.

Namespaces
namespace	num
namespace	num::backends
namespace	num::backends::seq

Functions
EigenResult	num::backends::seq::eig_sym (const Matrix &A, real tol, idx max_sweeps)

Detailed Description

Sequential cyclic Jacobi eigensolver.

Reference: Golub & Van Loan "Matrix Computations" section 8.4

Each sweep visits every off-diagonal pair (p,q) and applies a 2x2 similarity rotation that zeros A[p,q]. The rotation angle satisfies:

tau = (A[q,q] - A[p,p]) / (2*A[p,q]) t = sign(tau) / (|tau| + sqrt(1 + tau^2)) c = 1/sqrt(1+t^2), s = c*t

Definition in file jacobi_eig.cpp.