Modifying the elements of matrix from indices (MATLAB)
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I have a number of elements m for example m=4. And the matrix is square of dimensions m*m
P =
1 2 3 4
2 3 4 3
3 4 3 2
4 3 2 1
using the following program to replace the indices 1, 2, 3...m with its sub-matrices:
m=input('Initialize a number of elements'); % Number of elements in the matrix
P=hankel(1:m,m:-1:1);
% Initialisation of sub-matrices of dimensions (m-1 x m-1)
a=zeros(m-1,m-1,m-2);
a(:,:,1)=eye(m-1); % First sub-matrix is always an identity matrix with indice = 1 in P
for k=2:m-1
a(:,:,k)=circshift(a(:,:,k-1),1,2 ); % Other sub-matrices of indice = 2 to m-1
end
a(:,:,m) = zeros(m-1); % Final sub-matrix of indice = m (always null)
% Replacing the sub-matrices of indices 1,2,...m in P
N = zeros(m*(m-1));
a = num2cell(a,[1 2]);
for ii = 1:m
for jj = 1:m
N((m-1)*(ii-1)+1:(m-1)*ii,(m-1)*(jj-1)+1:(m-1)*jj) = a{P(ii,jj)};
end
end
I added this part of program to find always two indices of sum=m. For example in the case of m=4 the indices are 1 and 3 to find 1+3=m
indice=0;
while sum(indice)~=m
indice=randi([1,m-1],[1,2]);
end
So the indice 2 is not used here. We use just 1, 3 and m.
I need to add a part in the prgram that replace all the sub-matrices of indices that are not used (in this example indice 2) with null matrices in the matrix N. How can I do that please.
4 Comments
randi() can return [2 2], so it's not true that index 2 can never be used.
m = 4;
indice = 0;
while sum(indice) ~= m
indice = randi([1,m-1],[1 2]);
end
disp(indice)
high speed
on 11 Mar 2022
Voss
on 11 Mar 2022
Are you saying that you have some code to prevent repeated indices, e.g., [2 2], or that you still need to write such code?
Also, what do you mean by null matrices? A matrix of the appropriate size which is all NaNs?
high speed
on 11 Mar 2022
Accepted Answer
Voss
on 11 Mar 2022
Here is a function you can use to get a pair of random indices that sum to m but are never [m/2 m/2]:
function idx = get_random_index(m)
if mod(m,2) % m is odd: no chance of getting m/2 from randi()
idx = randi([1 m-1]); % just use the result from randi()
else % m is even: could get m/2 from randi(), so use randi()
% to get an integer between 1 and m-2, then increase it
% by 1 if it is >= m/2, so you end up with a random index
% between 1 and m-1 excluding m/2
% e.g., for m == 4:
% randi() returns 1: idx = 1
% randi() returns 2: idx = 3
% e.g., for m == 6:
% randi() returns 1: idx = 1
% randi() returns 2: idx = 2
% randi() returns 3: idx = 4
% randi() returns 4: idx = 5
idx = randi([1 m-2]);
if idx >= m/2
idx = idx+1;
end
end
idx = [idx m-idx]; % return the 2 indices whose sum is m
end
6 Comments
high speed
on 11 Mar 2022
Since N is initialized with zeros, you can simply skip populating the relevant part of N when P(ii,jj) == m/2:
% m=input('Initialize a number of elements'); % Number of elements in the matrix
m = 4;
P=hankel(1:m,m:-1:1)
% Initialisation of sub-matrices of dimensions (m-1 x m-1)
a=zeros(m-1,m-1,m-2);
a(:,:,1)=eye(m-1); % First sub-matrix is always an identity matrix with indice = 1 in P
for k=2:m-1
a(:,:,k)=circshift(a(:,:,k-1),1,2 ); % Other sub-matrices of indice = 2 to m-1
end
a(:,:,m) = zeros(m-1); % Final sub-matrix of indice = m (always null)
% Replacing the sub-matrices of indices 1,2,...m in P
N = zeros(m*(m-1));
a = num2cell(a,[1 2]);
for ii = 1:m
for jj = 1:m
% if P(ii,jj) == m/2, then the corresponding sub-matrix in N needs
% to be all zeros, which it already is, so there is nothing to do
% in that case.
% Just set the sub-matrix when P(ii,jj) ~= m/2:
if P(ii,jj) ~= m/2
N((m-1)*(ii-1)+1:(m-1)*ii,(m-1)*(jj-1)+1:(m-1)*jj) = a{P(ii,jj)};
end
end
end
disp(N);
high speed
on 11 Mar 2022
OK. I wasn't sure how getting the random indices related to populating N with sub-matrices, but I think it makes sense now. You want to get a single pair of random indices and only populate N where P is one of those indices, right? If so, then it might look like this:
% m=input('Initialize a number of elements'); % Number of elements in the matrix
m = 5;
P=hankel(1:m,m:-1:1)
% Initialisation of sub-matrices of dimensions (m-1 x m-1)
a=zeros(m-1,m-1,m-2);
a(:,:,1)=eye(m-1); % First sub-matrix is always an identity matrix with indice = 1 in P
for k=2:m-1
a(:,:,k)=circshift(a(:,:,k-1),1,2 ); % Other sub-matrices of indice = 2 to m-1
end
a(:,:,m) = zeros(m-1); % Final sub-matrix of indice = m (always null)
idx = get_random_index(m)
% Replacing the sub-matrices of indices 1,2,...m in P
N = zeros(m*(m-1));
a = num2cell(a,[1 2]);
for ii = 1:m
for jj = 1:m
if ismember(P(ii,jj),idx)
N((m-1)*(ii-1)+1:(m-1)*ii,(m-1)*(jj-1)+1:(m-1)*jj) = a{P(ii,jj)};
end
end
end
disp(N);
function idx = get_random_index(m)
if mod(m,2) % m is odd: no chance of getting m/2 from randi()
idx = randi([1 m-1]); % just use the result from randi()
else % m is even: could get m/2 from randi(), so use randi()
% to get an integer between 1 and m-2, then increase it
% by 1 if it is >= m/2, so you end up with a random index
% between 1 and m-1 excluding m/2
% e.g., for m == 4:
% randi() returns 1: idx = 1
% randi() returns 2: idx = 3
% e.g., for m == 6:
% randi() returns 1: idx = 1
% randi() returns 2: idx = 2
% randi() returns 3: idx = 4
% randi() returns 4: idx = 5
idx = randi([1 m-2]);
if idx >= m/2
idx = idx+1;
end
end
idx = [idx m-idx]; % return the 2 indices whose sum is m
end
high speed
on 12 Mar 2022
Voss
on 12 Mar 2022
You're welcome!
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