How to generate random projection matrices?
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As it is said in the question, I am looking for a Matlab function that generates random projection matrices, so that I can use it for linear programming.
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Answers (3)
KALYAN ACHARJYA
on 24 Jul 2019
Edited: KALYAN ACHARJYA
on 24 Jul 2019
function P=projection_mat(n)
A=colbasis(magic(n));
P=A*inv(A'*A)*A';
end
The colbasis function is here
Here n represent size of square matrix. Please note that I have answered this question from here
Command Window:
>> y=projection_mat(6)
y =
0.7500 -0.0000 0.2500 0.2500 -0.0000 -0.2500
-0.0000 1.0000 0.0000 -0.0000 -0.0000 0.0000
0.2500 0.0000 0.7500 -0.2500 -0.0000 0.2500
0.2500 -0.0000 -0.2500 0.7500 -0.0000 0.2500
-0.0000 -0.0000 -0.0000 -0.0000 1.0000 -0.0000
-0.2500 0.0000 0.2500 0.2500 -0.0000 0.7500
You can generate any size matries, just pass the same size matrix to colbasis function.
Hope it helps!
4 Comments
KALYAN ACHARJYA
on 25 Jul 2019
Edited: KALYAN ACHARJYA
on 25 Jul 2019
Is there any necessity having fixed size matrices?
>> y=projection_mat(6)
y =
0.7500 -0.0000 0.2500 0.2500 -0.0000 -0.2500
-0.0000 1.0000 0.0000 -0.0000 -0.0000 0.0000
0.2500 0.0000 0.7500 -0.2500 -0.0000 0.2500
0.2500 -0.0000 -0.2500 0.7500 -0.0000 0.2500
-0.0000 -0.0000 -0.0000 -0.0000 1.0000 -0.0000
-0.2500 0.0000 0.2500 0.2500 -0.0000 0.7500
>> y=projection_mat(5)
y =
1.0000 -0.0000 -0.0000 -0.0000 -0.0000
-0.0000 1.0000 -0.0000 -0.0000 -0.0000
-0.0000 -0.0000 1.0000 -0.0000 0.0000
-0.0000 -0.0000 -0.0000 1.0000 0.0000
-0.0000 -0.0000 -0.0000 -0.0000 1.0000
>>
Bruno Luong
on 25 Jul 2019
Edited: Bruno Luong
on 25 Jul 2019
n = 5
r = 3; % rank, dimension of the projection subspace
[Q,~] = qr(randn(n));
Q = Q(:,1:r);
P = Q*Q' % random projection matrix P^2 = P, rank P = r
5 Comments
Bruno Luong
on 25 Jul 2019
Edited: Bruno Luong
on 25 Jul 2019
Sorry I think the only projection matrix that is orthogonal is diagonal matrix with 1 or 0 on the diagonal. So there is no really randomness for what you ask.
Bruno Luong
on 26 Jul 2019
Edited: Bruno Luong
on 26 Jul 2019
I wonder if you mistaken "orthogonal projection matrix" and "projection matrix that is orthogonal". They are not the same.
Mine is "orthogonal projection matrix", which is projection matrix (P^2==P) that has additional properties
- symmetric
- all eigen values are 0 or 1.
Image Analyst
on 25 Jul 2019
Not sure what you mean by projection, but the radon transform does projections. That's its claim to fame. It basically projects a matrix along any angle and gives you the sum of the interpolated values along the projection angle. This is the crucial function for reconstructing 3-D volumetric CT images from 2-D projections.
The radon() function requires the Image Processing Toolbox.
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