MATLAB: How to concatenate -x:x for x=0,1,2,3,..n without a loop

bsxfunfor loop

Hi,
I want to populate a matrix with rows in the form of
0,-1,0,1,-2,-1,0,1,2,-3,-2,-1,0,1,2,3
0,-1,0,1,-2,-1,0,1,2,-3,-2,-1,0,1,2,3
0,-1,0,1,-2,-1,0,1,2,-3,-2,-1,0,1,2,3
… ie -x:x for multiple x values. After this, I will call a function on the whole matrix to convert these numbers to something else. eg takesquare(Matrix) will give the elementwise squares of 0,-1,0,1,…
1. How to concatenate -x:x for x=0,1,2,3,..n without a loop? With a loop, solution is trivial and super slow.
2. How can I call the takesquare with additional parameters? So the idea is adding different values to each row, ie takesquare(Matrix, [column vector=2,0,7,1,5,6..]). I know bsxfun can be used, but since the operations should be elementwise, I'll need to repmat the columnvector to all entries then. Is there a better/less memory occupying way?
Thanks!

Best Answer

Constructing it as a vector is possible in theory.
The value range -N to +N is in the (N+1)'th group and is a vector of length (2*N+1). The total length of the vector to the end of the -N:+N group can be found to be (N+1)^2 . Therefore for any given position, M, floor(sqrt(M-1)-1) tells you how many complete N have been gone through, and M minus that gives you the relative position in progress:
Nb = floor(sqrt(M-1)-1);
value_at_M = M - (Nb+1).^2 - 1 + -(Nb+1);
For any given final N, Nf, you can run that vectorized:
M = 1 : (Nf+1).^2;
Nb = floor(sqrt(M-1)-1);
value_at_M = M - (Nb+1).^2 - 1 + -(Nb+1);
"2. How can I call the takesquare with additional parameters? So the idea is adding different values to each row"
You only have one row.
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