Solving a least squares problem using QR decomposition

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Pascale Bou Chahine 2020-11-15

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https://ww2.mathworks.cn/matlabcentral/answers/648603-solving-a-least-squares-problem-using-qr-decomposition

编辑： Image Analyst 2020-11-15

"Given the least squares problem ||b - Ax||_2 = min_{y in R^n} ||b - Ax||_2 where A in R^{mxn} and b in R^m are given, and A is full-rank.

Write a MATLAB algorithm that solves the problem using the Matlab’s built-in QR Decomposition (qr) assuming m => n. "

Here's my code, but whenever I run it, I get an error in line 3: "Too many output arguments". What is the problem?

function[x] = ded(A,b)
[m,n] = size(A);
[Q, R, P] = qr(A);
c = Q'*b;
tol = max(size(A))*eps*abs(R(1,1));
r = 1;
while ( abs(R(r+1,r+1)) >= tol && r < n ); r = r+1; end
y1 = R(1:r,1:r) \ c(1:r);
y2 = zeros(n-r,1);
x = P*[y1;y2]

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Answer 1

Image Analyst 2020-11-15

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How are you calling ded()? What are you passing in for A and b? And according to the error you're expecting more than one output, so you're calling it like

[x, x2, x3] = ded(A,b)

with 2 or more outputs when ded returns only one output. Try with only one output:

x = ded(A,b)

Also, in

function[x] = ded(A,b)

you must have a space after the function key word and before the left bracket.

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Pascale Bou Chahine 2020-11-15

I'm taking A - rand(3,2), and b = rand(3,1)

I still don't know why I'm getting this error, can you edit my code to see where I went wrong please?

Image Analyst 2020-11-15

编辑：Image Analyst 2020-11-15

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OK, so that's how you're defining A and b, but what about my first, and most important question? Again:

"How are you calling ded()? "

You have not supplied us with your code, so we can't edit anything yet. I don't see anywhere in your posted code where you said you're calling it something like

[x, x2, x3] = ded(A,b)

Why not? Why won't you tell us how you're calling this function? Just to be super explicit, that will be on line 3 of your main script (not this function). Please attach the main script m-file, and the ded function m-file with the paper clip icon.

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