求实对称矩阵特征值的经典jacobi方法的matlab代码

以下是求实对称矩阵特征值的经典Jacobi方法的MATLAB代码：

function [D, V] = jacobi(A)
% JACOBI  Classic Jacobi method for finding eigenvalues and eigenvectors
%         of a real symmetric matrix A.
%
% Input:
%   A - real symmetric matrix
%
% Output:
%   D - diagonal matrix of eigenvalues
%   V - matrix of eigenvectors

% Initialize
n = size(A, 1);
V = eye(n);
D = diag(A);

% Jacobi method
while true
    % Find off-diagonal element with maximum modulus
    [p, q] = find_pq(A);
    if abs(A(p,q)) < eps
        break;
    end
    
    % Compute Jacobi rotation matrix
    theta = 0.5 * atan2(2*A(p,q), (A(p,p)-A(q,q)));
    c = cos(theta);
    s = sin(theta);
    J = eye(n);
    J(p,p) = c;
    J(q,q) = c;
    J(p,q) = -s;
    J(q,p) = s;
    
    % Update A, D, and V
    A = J' * A * J;
    D = diag(A);
    V = V * J;
end
end

function [p, q] = find_pq(A)
% FIND_PQ  Find off-diagonal element with maximum modulus.
n = size(A, 1);
maxval = 0;
for i = 1:n-1
    for j = i+1:n
        if abs(A(i,j)) > maxval
            maxval = abs(A(i,j));
            p = i;
            q = j;
        end
    end
end
end

使用方法：

% Example
A = [1 2 3; 2 2 1; 3 1 4];
[D, V] = jacobi(A);
disp(D); % diagonal matrix of eigenvalues
disp(V); % matrix of eigenvectors