hi everyone , how can I built a matrix of circularly shifted array in efficient way

I have a given initial array of length M , I want to built a matrix of MxM , by circularly shifting this array, example

for array=[2,0,0] the matrix should be matrix=[2,0,0;0,2,0;0,0,2]

my code works but it not efficient for large M I would be happy if someone can gives me an efficient suggestion

my code:

array=[2,0,0]; % given Initial array

M=length(array);

mat=zeros(M,M);%matrix

mat(1,:)=array;

for i=2:M

array=circshift(array(1,1:M),[0 1]);

mat(i,:)=array;

end

Answer 1

[Stephen23]

Multiple circshift calls in a loop is not required. One call to toeplitz is simpler:

>> V = [2,0,0];
>> toeplitz(V([1,end:-1:2]),V)
ans =
   2   0   0
   0   2   0
   0   0   2

Or a clearer example:

>> V = [4,3,2,1,0];
>> toeplitz(V([1,end:-1:2]),V)
ans =
   4   3   2   1   0
   0   4   3   2   1
   1   0   4   3   2
   2   1   0   4   3
   3   2   1   0   4

[fatema hamodi]

thanks a lot !!

Answer 2

[Guillaume]

To be compared to a loop version, it's very possible that a loop is faster:

array = [2, 0, 0];
shiftidx = hankel(1:numel(array), circshift(1:numel(array), 1))
M = array(shiftidx)

Or, for a shift in the other direction:

array = [2, 0, 0];
shiftidx = toeplitz(1:numel(array), [1, numel(array):-1:2])
M = array(shiftidx.')