How to find non-zero indexes (or value) in row in matrix, and make taken results i and j elements of another matrix Dij?

I have a matrix : A =

     1     0     0     4
     1     0     3     4
     1     2     0     4
     1     2     3     4

I need to find the non-zero elements in every row of matrix A, and making them i(number of row) and j(number of column) of the matrix Dij(shown below).

Then find that element in matrix Dij, and make summation of values if it needs.

Dij =

         0   22.2794   33.7859   45.0000
   22.2794         0   15.4008   23.0367
   33.7859   15.4008         0   14.9726
   45.0000   23.0367   14.9726         0

For example, I need a code which will find all non zero values of every row, results of matrix A should be:

1 4

1 3 4

1 2 4

1 2 3 4

Then the values of every rows should be ij elements of Dij matrix. For example:

1 4==============> D(1,4)=45

1 3 4============> D(1,3)+D(3,4)=33.7859+14.9726

1 2 4============> D(1,2)+D(2,4)=22.2794+23.0367

1 2 3 4==========> D(1,2)+D(2,3)+D(3,4)=22.2794+15.4008+14.9726

Could anyone help me?

Answer 1

[James Tursa]

E.g., using a loop:

m = size(A,1);
result = zeros(m,1);
for k=1:m
    x = find(A(k,:));
    for n=2:numel(x)
        result(k) = result(k) + Dij(x(n-1),x(n));
    end
end

Answer 2

[Stephen23]

A short version without explicit loops:

>> [Ra,Ca] = find(A~=0);
>> X = accumarray(Ra,Ca,[],@(n){n});
>> F = @(V)arrayfun(@(r,c)Dij(r,c),V(1:end-1),V(2:end));
>> Z = cellfun(@(V)sum(F(sort(V))),X)
Z =
         45
     48.758
     45.316
     52.653