How to assign mutliple vectors to matrix diagonals

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A K 2016-10-18

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I have 3 vectors that I want to assign as diagonals to a matrix. Vector A is the center diagonal, Vector B is above the center diagonal, Vector C is below the centre diagonal.

So my final matrix should have 3 diagonals.

Now, say that these vectors each have 3 separate columns (now a matrix), how would i go about producing 3 matrices that demonstrate the above? How can i do this? I have tried to use the gallery('tridiag',A,B,C,

B=ones(3,22); 
M=zeros(23);
n=1; k=1;
for n=1:3;
    for k=1:23
        for g=1:22;
        super_diag(n,g)=B(n,g);
        diag(n,k)=-A(n,k); % -ve to make values -ve
        sub_diag(n,g)=C(n,g);
        end
        M{n}=gallery('tridiag',sub_diag(n,g),diag(n,k),super_diag(1,g));
    end
end

This does not seem to work, any ideas where I have gone wrong?

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Answer 1

Guillaume 2016-10-18

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I have no idea what you're trying to do with your code, it makes no sense, from the comment about creating a sparse matrix followed by no sparse matrix creation, to cell indexing into a matrix, through the pointless copying of scalar values.

Trying to decode what you say, you have 3 matrices (not vectors), A, B and C with 3 columns each and you want to create 3 tridiagonal matrices from the corresponding columns of each. In which case:

A = [1:9; 11:19; 21:29]';  %demo data
B = [101:110; 111:120; 121:130]'; %demo data
C = [201:209; 211:219; 221:229]'; %demo data
assert(size(A, 2) == size(B, 2) && size(A, 2) == size(C, 2), 'A, B, and C must have the same number of columns');
assert(size(A, 1) == size(C, 1) && size(B, 1) == size(A, 1) + 1, 'A and C must have the same number of rows. B must have one more row');
m = arrayfun(@(colidx) gallery('tridiag', A(:, colidx), B(:, colidx), C(:, colidx)), 1:size(A, 2), 'UniformOutput', false)

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A K 2016-10-18

yes, that's exactly what i'm trying to do, but i'm trying to approach it in the general case, which is why i'm indexing and using a loop.

Thanks for your answer.

Guillaume 2016-10-18

You're not going to get any more generic than what I've written. Notice that none of the sizes are hardcoded (unlike your loop solution). The code will work with A, B and C of any height as long as B is one element taller than A and C, and with any number of columns as long as A, B and C have the same number. It will generate as many matrices as there are columns.

This is ultra generic. I actually stated the only conditions required for the code to work in the two assert.