MATLAB, Julia Language, and QR Decomposition

I was trying to calculate so coefficients for a Savitsky Golay filter. MATLAB told me I was out of memory and would not solve the following code. My understanding of the deeper problem is naive at best. I switch to using Julia and Julia solved this no problem.

Matlab Code:

nl = 40000; % number of points to the left of current point
nr = 40000; % number of points to the right of current point
M = 3; % order of polynomial to local fit around current point

% construct A matrix
A = ones (nl+nr+1, M+1);
for j = M:-1:1,
  A (:, j) = (-nl:nr)' .* A (:, j+1);
end

% filter coefficients c
[Q, R] = qr (A);
c = Q (:, M+1) / R (M+1, M+1);

c = c(nl+nr+1:-1:1);

MATLAB Error and Resource Screenshot

 Error using qr
 Out of memory. Type HELP MEMORY for your options.

 Error in savGol (line 43)
 [Q, R] = qr (A);

The screen shot is from when nl = 25000 and nr = 25000 which means A is the size [50001 4]. A is the size of [80001 4] when the QR decomposition fails.

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Julia Language Version

nl = 40000; # number of points to the left of current point
nr = 40000; # number of points to the right of current point
M = 3; # order of polynomial to local fit around current point

# construct A matrix
A = ones(nl+nr+1, M+1);
for j = M:-1:1,
  A [:, j] = (-nl:nr).* A[:, j+1];
end

# filter coefficients c
(Q, R) = qr(A);
c = Q[:, M+1] / R[M+1, M+1];

c = c[nl+nr+1:-1:1];

The Julia Language solved the QR decomposition no problem when nl = 40000 and nr = 40000 and A is the size [80001 4]. Also, it solved the case nl = 25000 and nr = 25000 faster and with fewer resources than MATLAB. The screenshot is shown below.

Julia Language Resource Screenshot

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Question:

1. Can someone explain this difference?
2. Is there something I am doing wrong such that I can get the same behavior in MATLAB as the Julia Language?

Answer 1

[Matt J]

Possibly, you need to use the economy form of qr()

[Q, R] = qr (A,0);

[Jason Nicholson]

Yes you are correct. I should have seen this. Thank you.