# How to get around sparse row deletion for least squares calculation

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### Answers (2)

Matt J
on 6 Mar 2023

Edited: Matt J
on 6 Mar 2023

##### 1 Comment

Matt J
on 6 Mar 2023

Edited: Matt J
on 6 Mar 2023

With the speed-up from pagemldivide, you might be able to offset the cost of rebuilding the matrices every time:

Psi=repmat({rand(30)},1,500); blocks=cellfun(@sparse,Psi,'uni',0);

A=cat(3,Psi{:}); b=A(:,1,:); %paged form (full)

S=blkdiag(blocks{:}); %block diagonal form (sparse)

timeit( @()S\b(:) )

timeit( @() pagemldivide(A,b) )

Bruno Luong
on 6 Mar 2023

Edited: Bruno Luong
on 6 Mar 2023

I'm nit sure why you formalize as block sparse, since it is like solving d independent linear systems of the same size, and can be performed by pagemrdivide as Matt has pointed out.

Now back too your question, you could probably reformulate the row-deletion to a weigted lsq system:

m = 10;

n = 3;

p = 1;

format long

% Full solution

A = rand(m,n);

b = rand(m,p);

x = A\b

% solution after removed 10th row

xd = A(1:m-1,:)\b(1:m-1,:)

% weigthed least-square solution w

w = ones(m,1);

w (m) = 0;

xw = (w.*A)\(w.*b)

##### 3 Comments

Bruno Luong
on 6 Mar 2023

Edited: Bruno Luong
on 6 Mar 2023

OP asks to keep the original SPARSE matrix, so I propose a solution for him to avoid : "I'm essentially asking for a new sparse block diagonal matrix of for each iteration".

Furthermore he could use sparse algorithms that requires matrix product vector so instead of doing (w.*A)*x, it only needs w.*(A*x).

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