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

Answer 1

[Walter Roberson]

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.

[ailbeildce]

First of all, thanks for the answer. For the second one I should be more clear: I have 4 2D arrays of same size, I have a function fn(Arg1,Arg2,Arg3,Arg4). I want to elementwise call this function with these 4 arrays. In other words, Arg1 will be picked from first 2D array, Arg2 from 2nd and so on.

[Walter Roberson]

arrayfun(@fn, FirstArray, SecondArray, ThirdArray, FourthArray)