Advanced logical matrix indexing

Is it possible to use one line of code to achieve the following

given an NxN matrix A construct an N-1xN matrix B where each column _n in B eliminates the _nth element from the _n column in A

e.g.

A = [1 1 1;2 2 2;3 3 3] gives B = [2 1 1;3 3 2]

I can do this in a for-loop, but given MATLAB is really bad at handling these I was hoping there is a faster solution

Thanks,

~K

Answer 1

[James Tursa]

Another variation of Matt J's approach:

B = A(:);
B(1:(N+1):(N*N)) = [];
B = reshape(B,N-1,N);

[Matt J]

Interestingly, there's no need for B=A(:). It works just as well with B=A.

[James Tursa]

I noticed that too, but the result is a 1D vector so you still need the reshape at the end.

Answer 2

[Matt Fig]

Given this array:

A = [1 1 1;2 2 2;3 3 3] % Must be n-by-n
% Remove the ith element of each ith column.
B = reshape(A(~eye(size(A))),size(A,1)-1,size(A,1))

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.

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EDIT

One could write a nifty little function to do this:

function A = removediag(A)
% Removes the diagonal elements of a square matrix.
% Author:  Matt Fig

S = size(A);
if S(1)~=S(2)
   error('REMOVEDIAG is only for square arrays');
end

A = reshape(A(~diag(true(1,S(1)))),S(1)-1,S(1));

[Matt J]

OK, so I guess there is a 1-line solution! I would slightly prefer mine, though, because it uses sparse indexing.

[Matt Fig]

One could use speye(size(A)) instead I would think. SPEYE(args) creates the sparse version of the EYE(args).

[Matt J]

Yes, but ~speye(size(A)) will make it dense.

[Matt Fig]

I see. It is still sparse, but the space saving is ruined. True enough.

[Matt Fig]

One could avoid the intermediate double (eye(size(A))) by using:

B = reshape(A(~diag(true(1,size(A,1)))),size(A,1)-1,size(A,1))

In fact this is 40% faster than my original solution for very large arrays.

Answer 3

[Matt J]

I don't think there's a 1-line solution (without creating your own mfile function), but you don't need loops:

B=A;
B(logical(speye(N)))=[];
B=reshape(B,N-1,N);