Generate matrix combinations with parameters

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Catarina Pina
Catarina Pina 2024-7-10
回答： Catarina Pina 2024-7-11
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?

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采纳的回答

Shantanu Dixit
Shantanu Dixit 2024-7-11
编辑：Shantanu Dixit 2024-7-11
Ran in:
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));
Total combinations: 65536
disp('Example combinations:');
Example combinations:
%% Display sample combination
disp(all_combinations{1});
1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
disp(all_combinations{2});
1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
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 个评论
Catarina Pina
Catarina Pina 2024-7-11
The length of all_combinations is 65536. If I have a condition to impose to these combinations and eliminate some of them (I have already made this with if ... all_combinations{i} = []), how can I update the size of all_combinations? The entries remain in the structure, although empty, but I want to eliminate them completely (shifting all the others). For instance, if I delete 2 entries, how can I update the size of all_combinations to 65534?

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更多回答（4 个）

Omega
Omega 2024-7-10
编辑：Omega 2024-7-10
Ran in:
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:
  1. We iterate through each possible T value from T_values.
  2. 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.
  3. 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))]);
Total number of unique combinations: 4
% Display all unique combinations
for k = 1:length(all_combinations)
disp(['Combination ', num2str(k), ':']);
disp(all_combinations{k});
end
Combination 1:
1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
Combination 2:
0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0
Combination 3:
0 0 1 0 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 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
Combination 4:
1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1
I hope this helps!
  1 个评论
Catarina Pina
Catarina Pina 2024-7-10
Sorry, the problem is a little more complicated, I forgot to mention that T can vary in each line of M, that is, what we want is T_ij, with i =1,....,8, and j = 1,2,3,4, i.e., for example, in line 1 T could be 1 0 0, and in line 2 be 1,1,1, and so on.

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Catarina Pina
Catarina Pina 2024-7-11
First of all, thank you for your solution! In fact, it solves the problem I described. But I ended up not explaining the problem completely well. Apologies for the entropy. In fact, I have the following matrix (8x6):
M = [T_11 T_12 T_13 0 0 0
T_21 0 T_22 T_23 0 0
T_31 0 0 T_32 T_33 0
T_41 T_42 0 0 T_43 0
0 T_51 T_52 0 0 T_53
0 0 T_61 T_62 0 T_63
0 0 0 T_71 T_72 T_73
0 T_81 0 0 T_82 T_83]
where T_ij, where i =1,....,8 corresponds to the row of the matrix, and T_i: has the following possibilities: {1,0,0}, {0,1,0}, {0,0,1} or {1,1,1} .
For instance, if T_{1:} = (1,0,0), T_{2:} = (1,1,1), T_{3:} = (0,1,0}), ..., we have the following combination:
[1 0 0 0 0 0
1 0 1 1 0 0
0 0 0 1 0 0
...
]
How can I create all possible combinations for M?
Catarina Pina
Catarina Pina 2024-7-11
Thank you very much, it works perfectly!
Catarina Pina
Catarina Pina 2024-7-11
The length of all_combinations is 65536. If I have a condition to impose to these combinations and eliminate some of them (I have already made this with if ... all_combinations{i} = []), how can I update the size of all_combinations? The entries remain in the structure, although empty, but I want to eliminate them completely (shifting all the others). For instance, if I delete 2 entries, how can I update the size of all_combinations to 65534?

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