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Projection using Modified Gram-Schmidt orthogonality

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Hello,
I need the Modified Gram-Schmidt orthogonalization method in my Research.
I wrote the following code for the projection using the Classic Gram-Schmidt:
function[Xp] = Project(A,B)
Xp = [] ;
u1 = B;
for i = 1:1:6
u2 = A(i,:)- (A(i,:)*u1)/(u1'*u1) * u1';
Xp = [Xp;u2] ;
end
end
I faced problems to convert the Modified Gram-Schmidt orthogonalization method into MATLAB code, which is illustrated in the following link https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
under section Numerical stability.
Can anyone help me in this problem please?
  22 Comments
Torsten
Torsten on 26 Jan 2023
Then I can assure you that from what you wrote, nobody will be able to understand what you are looking for.
Try to understand the problem first before looking for a solution.
Jan
Jan on 28 Jan 2023
@M: Please stop addressing specific users by messages like "Hi @xyz do you have any idea about my question please?"
Imagine what would happen, if all users do this: The most active users would receive a huge number of notifications and find less time to post answers.

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Accepted Answer

Matt J
Matt J on 25 Jan 2023
Edited: Matt J on 26 Jan 2023
Aorth=orth(A); %A orthogonalized
ProjB=Aorth*(Aorth.'*B); %projection of B
  38 Comments
Torsten
Torsten on 26 Jan 2023
I'm surprised you now found what you were searching for.
In the end, was it projecting a single vector onto a set of vectors or a set of vectors onto a single vector you were aiming at ?
M
M on 26 Jan 2023
@Torsten, my problem is an optimization problem. it contains equations and I need to know unknown values using several orthogonal techniques. Thanks

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