Generate matrix combinations with parameters
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I have the following matrix (8x6):
M = [T_1 T_2 T_3 0 0 0
T_1 0 T_2 T_3 0 0
T_1 0 0 T_2 T_3 0
T_1 T_2 0 0 T_3 0
0 T_1 T_2 0 0 T_3
0 0 T_1 T_2 0 T_3
0 0 0 T_1 T_2 T_3
0 T_1 0 0 T_2 T_3]
where T has the following possibilities: {1,0,0}, {0,1,0}, {0,0,1} or {1,1,1} and T_i is the i-component of T.
How can I create all possible combinations for M?
Accepted Answer
Shantanu Dixit
on 11 Jul 2024
Edited: Shantanu Dixit
on 11 Jul 2024
Hi Catarina,
It is my understanding that you are trying to generate the all possible combinations for the matrix M using T row vectors.
I am assuming that for each row T can take one of following possible 4 values
1. {1,0,0}
2. {0,1,0}
3. {0,0,1}
4. {1,1,1}
So for each row, there are 4 options available to fill that row.
No. possible combinations = 4*4*4*.. (8 times) = 4^8 = 65536
To generate all possible combinations recursion can come handy, you can see the below code for reference.
% All possibilities for T
% The initial matrix with symbolic placeholders (1, 2, 3)
% representing t1, t2, t3
T_possibilities = [
1, 0, 0;
0, 1, 0;
0, 0, 1;
1, 1, 1
];
% Initialize the original matrix M with symbolic placeholders
M_template = [
1, 2, 3, 0, 0, 0;
1, 0, 2, 3, 0, 0;
1, 0, 0, 2, 3, 0;
1, 2, 0, 0, 3, 0;
0, 1, 2, 0, 0, 3;
0, 0, 1, 2, 0, 3;
0, 0, 0, 1, 2, 3;
0, 1, 0, 0, 2, 3
];
% All possibilities for T
% The initial matrix with symbolic placeholders (1, 2, 3)
% representing t1, t2, t3
T_possibilities = [
1, 0, 0;
0, 1, 0;
0, 0, 1;
1, 1, 1
];
% Initialize the original matrix M with symbolic placeholders
M_template = [
1, 2, 3, 0, 0, 0;
1, 0, 2, 3, 0, 0;
1, 0, 0, 2, 3, 0;
1, 2, 0, 0, 3, 0;
0, 1, 2, 0, 0, 3;
0, 0, 1, 2, 0, 3;
0, 0, 0, 1, 2, 3;
0, 1, 0, 0, 2, 3
];
% Function to generate all combinations recursively
function combinations = generate_combinations(M_template, T_possibilities, row, combinations)
if row > size(M_template, 1)
combinations{end+1} = M_template;
return;
end
for i = 1:size(T_possibilities, 1)
T = T_possibilities(i, :);
M_row = M_template(row, :);
for j = 1:3
% replace the placeholders (1, 2, 3) with the corresponding
% elements from T
M_row(M_row == j) = T(j);
end
new_template = M_template;
new_template(row, :) = M_row;
combinations = generate_combinations(new_template, T_possibilities, row + 1, combinations);
end
end
% Generate all possible combinations
all_combinations = generate_combinations(M_template, T_possibilities, 1, {});
% Display the number of combinations
fprintf('Total combinations: %d\n', length(all_combinations));
disp('Example combinations:');
%% Display sample combination
disp(all_combinations{1});
disp(all_combinations{2});
The above MATLAB code defines a matrix M with symbolic placeholders (1, 2, 3) and a set of possible transformation matrices T. It recursively generates all combinations of M by replacing placeholders with elements from T. Each combination results in a modified matrix M, and all such combinations are stored in 'all_combinations'.
Thanks
1 Comment
Catarina Pina
on 11 Jul 2024
More Answers (4)
Hi Catarina,
To generate all possible combinations for the matrix M with the given parameters, you can use MATLAB to iterate through all possible values of T. Here’s a step-by-step approach to achieve this:
- We iterate through each possible T value from T_values.
- For each T value, we replace all placeholders for T_1, T_2, and T_3 in M with the corresponding components of the current T value.
- We directly store each generated matrix in the all_combinations cell array.
Below is a MATLAB script to accomplish this:
% Define the matrix M with placeholders
M = [1 2 3 0 0 0;
1 0 2 3 0 0;
1 0 0 2 3 0;
1 2 0 0 3 0;
0 1 2 0 0 3;
0 0 1 2 0 3;
0 0 0 1 2 3;
0 1 0 0 2 3];
% Define the possible values of T
T_values = {[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1]};
% Initialize a cell array to store all possible combinations of M
all_combinations = {};
% Iterate through all possible values of T
for T_idx = 1:length(T_values)
% Extract the current T value
T = T_values{T_idx};
% Create a copy of M to modify
M_comb = M;
% Replace placeholders with the corresponding T values
for i = 1:8
for j = 1:6
if M(i, j) == 1
M_comb(i, j) = T(1);
elseif M(i, j) == 2
M_comb(i, j) = T(2);
elseif M(i, j) == 3
M_comb(i, j) = T(3);
end
end
end
% Add the matrix to the combinations list
all_combinations{end+1} = M_comb;
end
% Display the number of unique combinations
disp(['Total number of unique combinations: ', num2str(length(all_combinations))]);
% Display all unique combinations
for k = 1:length(all_combinations)
disp(['Combination ', num2str(k), ':']);
disp(all_combinations{k});
end
I hope this helps!
1 Comment
Catarina Pina
on 10 Jul 2024
Catarina Pina
on 11 Jul 2024
0 votes
Catarina Pina
on 11 Jul 2024
0 votes
Catarina Pina
on 11 Jul 2024
0 votes
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