# How can I create a set of N diagnal matrices range from diag(1, 1, ... , 1) to diag(-1, -1, ... , -1) for testing purposes?

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Zac Minson on 20 Sep 2021 at 16:02
Edited: Matt J on 21 Sep 2021 at 19:17
I am needing to create 16 4x4 diagnal matrices consisting of all of the combinations of "1" and "-1" and have them be able to be called for use in a loop. Besides creating each individual matrix, how can I go about accomplishing this?
for instance:
Z1 = diag(1,1,1,1);
.
Z8 = diag(1,-1,-1,1);
.
Z16 = diag(-1,-1,-1,-1);
Thank you for any guidance.
Stephen on 21 Sep 2021 at 18:33
@Zac Minson: using a cell array is a very general method, which works for any number of matrices.

Matt J on 20 Sep 2021 at 16:36
Edited: Matt J on 21 Sep 2021 at 19:17
Do you really need all Z{i} at the same time?
[C{1:N}]=ndgrid([-1,1]);
C=reshape( cat(N+1,C{:}) ,[],N);
Z=zeros(N^2,2^N); %EDITED - removed loops
Z(1:N+1:N^2,:)=C;
Z=reshape(Z, N,N,[])
Zac Minson on 21 Sep 2021 at 18:51
Thank you so much. I was really wracking my brain over how to generalize this problem. I appreciate your time.

Fangjun Jiang on 20 Sep 2021 at 16:46
a=(dec2bin(15:-1:0)-48)*2-1;
z=zeros(4,4,16);
for k=1:16
z(:,:,k)=diag(a(k,:));
end
the cyclist on 20 Sep 2021 at 18:10
Here is a generalization of this solution:
N = 4; % Set this value
a=(dec2bin((2^N-1):-1:0)-48)*2-1;
z=zeros(N,N,2^N);
for k=1:2^N
z(:,:,k)=diag(a(k,:));
end

Jan on 20 Sep 2021 at 17:20
Edited: Jan on 21 Sep 2021 at 15:47
z = repmat(eye(4), 1, 1, 16);
z(z==1) = 1 - rem(floor((0:15) ./ [1; 2; 4; 8]), 2) * 2; % Inlined DEC2BIN
Generalized:
n = 3;
z = repmat(eye(n), 1, 1, 2^n);
z(z==1) = 1 - rem(floor((0:2^n-1) ./ pow2(0:n-1).'), 2) * 2;
Now z(:,:,i) is the i.th matrix. This is more efficient than storing them in a cell. But if you want this:
zC = num2cell(z, [1,2]);

R2021a

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