Givens rotation QR decomposition

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Duc Anh Le
Duc Anh Le 2020-2-11
评论： MmO 2021-9-30
Screen Shot 2020-02-11 at 2.08.39 PM.png
I'm trying to create a function that computes the Givens Rotation QR decomposition, following this pseudo-code.
function [Q,R] = givens(A)
[m,n] = size(A);
indexI = zeros(m,n);
indexJ = zeros(m,n);
C = zeros(m,n);
S = zeros(m,n);
for i = 1:n
for j = i+1:m
c = A(i,i)/((A(i,i))^2 + (A(j,i)^2))^0.5;
s = A(j,i)/((A(i,i))^2 + (A(j,i)^2))^0.5;
A(i,:) = c*A(i,:) + s*A(j,:);
A(j,:) = -s*A(i,:) + c*A(j,:);
indexI(j,i) = i;
indexJ(j,i) = j;
C(j,i) = c;
S(j,i) = s;
end
end
R = A;
Q = eye(m);
for i = 1:n
for j= j+1:m
Q(:,i) = c*Q(:,i) + s*Q(:,j);
Q(:,j) = -s*Q(:,i) + c*Q(:,j);
end
end
However, the R matrix, that I get, is not upper triangular. I can't seem to find the mistake here. Any help would be highly appreciated. Thanks in advance.
  2 个评论
Benjamin Ellis
Benjamin Ellis 2020-3-10
Hi! I'm in this class too. I added the lines c = C(j,i) and s = S(j,i) within the second for loop. Also the second for loop should iterate j = (i+1):m.
With these changes I got Q and R to agree with qr(A) up to a sign.
MmO
MmO 2021-9-30
Hello, Where you able to find the mistake? Where did you take this algorithm from? Best regards

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回答（1 个）

Jon
Jon 2020-2-11
It looks to me like your code reproduces what is in the pseudocode. Are you sure that the psuedocode that you based your code on is correct?
A few things look perhaps questionable about the psuedocode.
Why do we compute C, S, idxI idxJ and never use them?
In the second double loop you use the values c and s which are just the last values from the double loop in the first part of the algorithm. So they never change value as i and j change. Maybe that is ok but it looks strange.

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