基于matlab，用Jacobi算法利用旋转参数构造矩阵旋转模块,并将旋转矩阵输出出来

以下是基于Jacobi算法的矩阵旋转模块的matlab代码：

function [R] = jacobi_rotation(A)
% This function uses Jacobi algorithm to construct rotation matrix R from
% matrix A such that A is transformed into diagonal matrix D = R'*A*R.

% Initialize R as identity matrix
n = size(A,1);
R = eye(n);

% Find maximum off-diagonal element of A
max_offdiag = max(max(triu(abs(A),1)) );

% Keep rotating until all off-diagonal elements are negligible
while max_offdiag > 1e-10

% Find index of maximum off-diagonal element
[i,j] = find(abs(A)==max_offdiag,1);

% Calculate rotation angle
if A(i,i) == A(j,j)
theta = pi/4;
else
theta = 0.5*atan(2*A(i,j)/(A(i,i)-A(j,j)));
end

% Construct rotation matrix G
G = eye(n);
G(i,i) = cos(theta);
G(j,j) = cos(theta);
G(i,j) = -sin(theta);
G(j,i) = sin(theta);

% Update R and A
R = R*G;
A = G'*A*G;

% Find new maximum off-diagonal element of A
max_offdiag = max(max(triu(abs(A),1)) );
end

% Output rotation matrix R
end

我们可以通过调用该函数来得到旋转矩阵，以下是一个示例：

% Define a symmetric matrix A
A = [1,2,3; 2,4,5; 3,5,6];

% Use Jacobi algorithm to construct rotation matrix R
R = jacobi_rotation(A);

% Verify that A is transformed into diagonal matrix D = R'*A*R
D = R'*A*R % should be a diagonal matrix