Reshaping, overlapping columns of array into vector in MATLAB - arrays

Question

I want to reshape an array into a vector by its columns, and I want to have an offset between each column, with the overlapping elements added together.
Any ideas? I've done it using a double for-loop but I was hoping for something more efficient...
for i=1:b
for j=1:a
overlap=j+(i-1)*offset;
vector(overlap) = vector(overlap) + (array(j,i));
end
end
for example I want to have:
[ 1 4 7 ]
[ 2 5 8 ]
[ 3 6 9 ]
and an offset of 1 between columns, then I want to get as a vector the following:
[ 1 2 7 5 13 8 9 ]
edit I thought of appending zeros and then adding per column like this
[ 1 2 3 0 0 0 0 ]
[ 0 0 4 5 6 0 0 ]
[ 0 0 0 0 7 8 9 ]
and then use sum per column in order to get a new vector with elements the sum of the columns.
Does anyone know of a quick way to create such diagonal matrices?

Answer 1

Basically what you need is a general formula for this matrix:
[ 1 2 3 0 0 0 0 ]
[ 0 0 4 5 6 0 0 ]
[ 0 0 0 0 7 8 9 ]
This is a little easier if we rewrite the matrix as follows:
[ 1 2 3 0 0 0 0 0 0 4 5 6 0 0 0 0 0 0 7 8 9 ]
I'll state without proof that the number of zeros between each set of non-zero numbers is equal to:
nz = (size(array,1) - overlap) * size(array,2);
You should be able to convince yourself that this is true fairly easily. Now we can do the following:
vector = [array;zeros(nz,size(array,2)];
vector = vector(1:end-nz);
which gives
vector = [ 1 2 3 0 0 0 0 0 0 4 5 6 0 0 0 0 0 0 7 8 9 ]
then we just reshape and sum:
vector = sum(reshape(vector,[],size(array,2))');
vector =
1 2 7 5 13 8 9