Linear span of a vector in MATLAB - matlab

Question

I'm looking for a way to generate the spans of a given vector in MATLAB.
For example:
if a = [ 0 1 0 1] I need all vectors of the form [0 x 0 y], 1 <= x <= max1, 1 <= y <= max2,.
or if
a = [ 0 1 0 1 1 0] I need all vectors of the form [0 x 0 y z 0], 1 <= x <= max1, 1 <= y <= max2, 1<= z <= max3.
Note that the vector can have a variable number of 1's.
My first impression is that I would need a variable number of for loops, though I don't know if that is doable in MATLAB. Also any other ideas are welcome!

Answer 1

You don't need multiple for loops for this. The code below generates all required vectors as rows of a tall matrix. It actually creates the columns of the matrix one at a time. Each column will have numbers 1:m(i) arranged in the pattern where
each term repeats the number of times equal to the product of all m-numbers after m(i)
the whole pattern repeats the number of times equal to the product of all m-numbers before m(i)
This is what repmat(kron(1:m(i),ones(1,after)),1,before)' does. (Starting with R2015a you can use repelem to simplify this by replacing the kron command, but I don't have that release yet.)
a = [0 1 0 1 1 0];
m = [2 4 3]; // the numbers max1, max2, max3
A = zeros(prod(m), length(a));
i = 1; // runs through elements of m
for j=1:length(a) // runs through elements of a
if (a(j)>0)
before = prod(m(1:i-1));
after = prod(m(i+1:end));
A(:,j) = repmat(kron(1:m(i),ones(1,after)),1,before)';
i = i+1;
end
end
Output:
0 1 0 1 1 0
0 1 0 1 2 0
0 1 0 1 3 0
0 1 0 2 1 0
0 1 0 2 2 0
0 1 0 2 3 0
0 1 0 3 1 0
0 1 0 3 2 0
0 1 0 3 3 0
0 1 0 4 1 0
0 1 0 4 2 0
0 1 0 4 3 0
0 2 0 1 1 0
0 2 0 1 2 0
0 2 0 1 3 0
0 2 0 2 1 0
0 2 0 2 2 0
0 2 0 2 3 0
0 2 0 3 1 0
0 2 0 3 2 0
0 2 0 3 3 0
0 2 0 4 1 0
0 2 0 4 2 0
0 2 0 4 3 0