Matlab中的qr分解算法中的错误

Question

I am supposed to implement the QR factorization using Matlab, and then test it on the matrix A = [1 2; 1 1; 2 3; 2 2]. This is the code I tried to write until now. But I am getting some errors and I'm not sure where the problem is. Can anyone spot it?

A = [1 2; 1 1; 2 3; 2 2];
m = 4
Q=A;
Q(:,1) = A(:,1)/norm(A(:,1));
K = eye(m);
for j=2:n 
Q(:,j) = ((K - Q(:,j-1)*Q(:,j-1)')*A(:,j))/norm((K - Q(:,j-1)*Q(:,j-1)')*A(:,j));
K = K - Q(:,j-1)*Q(:,j-1)';
end
R=Q'*A;

Answer 1

Your for loop runs from 2:n , but you haven't defined n. You simply need to define n with:

A = [1 2; 1 1; 2 3; 2 2];
[m,n] = size(A);

When I make this addition, I can evaluate Q*R and get

>> Q*R

ans =

    1.0000    2.0000
    1.0000    1.0000
    2.0000    3.0000
    2.0000    2.0000

Note that defining m,n this way lets you generalize to use any matrix A (assuming m>=n).