Modifying the elements of matrix from indices (MATLAB)

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high speed 2022-3-11

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评论： Voss 2022-3-12

I have a number of elements m for example m=4. And the matrix is square of dimensions m*m

P = 
   2     3     4
   3     4     3
   4     3     2
   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.

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Voss 2022-3-11

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 2022-3-11

@_ For the repeated indices, I still need to modify this part in such a way it prevents this repetition.

By null matrix I mean zero matrix (its elements are all zeros)

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Answer 1

Voss 2022-3-11

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https://ww2.mathworks.cn/matlabcentral/answers/1669269-modifying-the-elements-of-matrix-from-indices-matlab#answer_915664

在 MATLAB Online 中打开

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

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Voss 2022-3-11

在 MATLAB Online 中打开

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)
P = 4×4
     1     2     3     4
     2     3     4     3
     3     4     3     2
     4     3     2     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);
     1     0     0     0     0     0     0     0     1     0     0     0
     0     1     0     0     0     0     1     0     0     0     0     0
     0     0     1     0     0     0     0     1     0     0     0     0
     0     0     0     0     0     1     0     0     0     0     0     1
     0     0     0     1     0     0     0     0     0     1     0     0
     0     0     0     0     1     0     0     0     0     0     1     0
     0     0     1     0     0     0     0     0     1     0     0     0
     1     0     0     0     0     0     1     0     0     0     0     0
     0     1     0     0     0     0     0     1     0     0     0     0
     0     0     0     0     0     1     0     0     0     1     0     0
     0     0     0     1     0     0     0     0     0     0     1     0
     0     0     0     0     1     0     0     0     0     0     0     1

Voss 2022-3-11

在 MATLAB Online 中打开

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)
P = 5×5
     1     2     3     4     5
     2     3     4     5     4
     3     4     5     4     3
     4     5     4     3     2
     5     4     3     2     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)
idx = 1×2
     4     1
% 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);
     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0
     0     1     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0
     0     0     1     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0
     0     0     0     1     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1
     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0
     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0
     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0
     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0
     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0
     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0
     0     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0
     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0
     0     0     1     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     1     0     0     0
     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0
     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     1
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 2022-3-12

@_ Thank you so much! it works exactly as I want

I appreciate your help

Voss 2022-3-12

You're welcome!

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Modifying the elements of matrix from indices (MATLAB)

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