Create symbolic matrix from triplets with repeated indices

Hi everyone,

I am trying to build a symbolic matrix from the triplets iRow, jCol, aElm such that

A(iRow(k),jCol(k)) = A(iRow(k),jCol(k))+aElm(k)

the work can be easily done with 'sparse' or 'accumarray', but my vector aElm is symbolic and these functions do not defined for input arguments of type 'sym'. I may use linear indexing, however the iRow and jCol vectors contains repeated indices and the values must be summed up in the final matrix. A for-loop gets the job done, but I am looking for a cleaner vectorised way, if possible. Suggestions?

Example

syms a1 a2 a3 a4
iRow = [1 2 1 2];
jCol = [1 1 1 2];
aElm = [a1 a2 a3 a4];

% expected result
A = 
[ a1 + a3,  0]
[      a2, a4]

Thank you in advance!

Fabio

[Karan Gill]

I didn't understand the correspondence between your equation

    A(...,...) = A(...,...) + aElm(...)

and your code. From your equation, "A" is predefined, and then elements of "aElm" get added to it? But in your code, "A" is not predefined. I didn't understand how "A" results from your variable definitions.

Answer 1

[Andrei Bobrov]

iRow = [1 2 1 2];
jCol = [1 1 1 2];
aElm = sym('a',[1 4])

k = accumarray([iRow(:),jCol(:)],(1:numel(iRow))',[],@(x){x});
s = size(k);
out = zeros(s,'sym');
for jj = 1:numel(k)
    out(jj) = sum(aElm(k{jj}));
end
out = reshape(out,s)

Answer 2

[John D'Errico]

Not a big problem. If you do this often, then just write a function for it, that will take the vectors of indices, as well as the symbolic elements.

function A = populateSymArray(rind,cind,symvals,n,m)
  % populates an array of symbolic elements
  % rind, cind - lists of row and column indices
  % symvals - list of symbolic elements to be populate the array
  % n, m - final size of the array

    A = zeros(n,m,'sym');

    rc = [rind(:),cind(:)];
    symvals = symvals(:);

    [rc,tags] = sortrows(rc);
    symvals = symvals(tags);

    % this loop will be a short one
    while ~isempty(rc)
      k = find(any(diff(rc,[],1),2));
      if isempty(k)
        k = size(rc,1);
      end
      ind = rc(k,1) + (rc(k,2)-1)*n;
      A(ind) = A(ind) + symvals(k);

      rc(k,:) = [];
      symvals(k) = [];
    end

That code has a loop in it, but the loop will be an efficient one as long as your elements are scattered around the array.