How to convert matrix to a stack of diagonal matrices based on every row?

Question

I have a matrix:

A = [1 1 1
     2 2 2
     3 3 3]

Is there a vectorized way of obtaining:

B = [1 0 0 
     0 1 0
     0 0          


        

Answer 1

This is one solution using mod and sub2ind:

%// example data
data = reshape(1:9,3,3).' %'
n = 3;  %// assumed to be known

data =

     1     2     3
     4     5     6
     7     8     9

---

%// row indices
rows = 1:numel(data);
%// column indices
cols = mod(rows-1,n) + 1;
%// pre-allocation
out = zeros(n*n,n);
%// linear indices
linIdx = sub2ind(size(out),rows,cols);
%// assigning
out(linIdx) = data.'

---

out =

     1     0     0
     0     2     0
     0     0     3
     4     0     0
     0     5     0
     0     0     6
     7     0     0
     0     8     0
     0     0     9

---

Or if you prefer saving lines of code, instead of readability:

out = zeros(n*n,n);
out(sub2ind(size(out),1:numel(data),mod((1:numel(data))-1,n) + 1)) = data.'

---

Two other fast solutions, but not faster than the others:

%// #1
Z = blockproc(A,[1 size(A,2)],@(x) diag(x.data));

%// #2
n = size(A,2);
Z = zeros(n*n,n);
Z( repmat(logical(eye(n)),n,1) ) = A;

---

For the sake of competition - Benchmark

function [t] = bench()
    A = magic(200);

    % functions to compare
    fcns = {
        @() thewaywewalk(A);
        @() lhcgeneva(A);
        @() rayryeng(A);
        @() rlbond(A);
    };

    % timeit
    t = zeros(4,1);
    for ii = 1:10;
        t = t + cellfun(@timeit, fcns);
    end
    format long
end

function Z = thewaywewalk(A) 
    n = size(A,2);
    rows = 1:numel(A);
    cols = mod(rows-1,n) + 1;
    Z = zeros(n*n,n);
    linIdx = sub2ind(size(Z),rows,cols);
    Z(linIdx) = A.';
end
function Z = lhcgeneva(A) 
    sz = size(A);
    Z = zeros(sz(1)*sz(2), sz(2));
    for i = 1 : sz(1)
        Z((i-1)*sz(2)+1:i*sz(2), :) = diag(A(i, :));
    end
end
function Z = rayryeng(A)  
    A = A.';
    Z = full(sparse(1:numel(A), repmat(1:size(A,2),1,size(A,1)), A(:)));
end
function Z = rlbond(A)  
    D = cellfun(@diag,mat2cell(A, ones(size(A,1), 1), size(A,2)), 'UniformOutput', false);
    Z = vertcat(D{:});
end

---

ans =

   0.322633905428601  %// thewaywewalk
   0.550931853207228  %// lhcgeneva
   0.254718792359946  %// rayryeng - Winner!
   0.898236688657039  %// rlbond