I would like to generate all the possible combinations of the elements of a given number of vectors.
For example, for [1 2], [1 2] and [4 5] I want to generate the elements:
[1 1 4; 1 1 5; 1 2 4; 1 2 5; 2 1 4; 2 1 5; 2 2 4; 2 2 5]
The problem is that I don't know the number of vectors for which I need to calculate the combinations. There might be 3 as in this case, or there may be 10, and I need a generalization. Can you please help me to this in MATLAB? Is there already a predefined function that can do this task?
Consider this solution using the NDGRID function:
sets = {[1 2], [1 2], [4 5]};
[x y z] = ndgrid(sets{:});
cartProd = [x(:) y(:) z(:)];
cartProd =
1 1 4
2 1 4
1 2 4
2 2 4
1 1 5
2 1 5
1 2 5
2 2 5
Or if you want a general solution for any number of sets (without having to create the variables manually), use this function definition:
function result = cartesianProduct(sets)
c = cell(1, numel(sets));
[c{:}] = ndgrid( sets{:} );
result = cell2mat( cellfun(#(v)v(:), c, 'UniformOutput',false) );
end
Note that if you prefer, you can sort the results:
cartProd = sortrows(cartProd, 1:numel(sets));
Also, the code above does not check if the sets have no duplicate values (ex: {[1 1] [1 2] [4 5]}). Add this one line if you want to:
sets = cellfun(#unique, sets, 'UniformOutput',false);
Try ALLCOMB function at FileExchange.
If you store you vectors in a cell array, you can run it like this:
a = {[1 2], [1 2], [4 5]};
allcomb(a{:})
ans =
1 1 4
1 1 5
1 2 4
1 2 5
2 1 4
2 1 5
2 2 4
2 2 5
This late answers provides two additional solutions, where the second is the solution (in my opinion) and an improvement on Amro's answer solution with ndgrid by applying MATLAB's powerful comma-separated lists instead of cell arrays for high performance,
If you have the Neural Network Toolbox: use combvec
If you do not have the toolbox, as is usually the case: below is another way to generalize the Cartesian product for any number of sets.
Just as Amro did in his answer, the comma-separated lists syntax (v{:}) supplies both the inputs and outputs of ndgrid. The difference (fourth line) is that it avoids cellfun and cell2mat by applying comma-separated lists, again, now as the inputs to cat:
N = numel(a);
v = cell(N,1);
[v{:}] = ndgrid(a{:});
res = reshape(cat(N+1,v{:}),[],N);
The use of cat and reshape cuts execution time almost in half. This approach was demonstrated in my answer to an different question, and more formally by Luis Mendo.
we can also use the 'combvec' instruction in matlab
no_inp=3 % number of inputs we want...in this case we have 3 inputs
a=[1 2 3]
b=[1 2 3]
c=[1 2 3]
pre_final=combvec(c,b,a)';
final=zeros(size(pre_final));
for i=1:no_inp
final(:,i)=pre_final(:,no_inp-i+1);
end
final
Hope it helps.
Good luck.
Related
This question already has answers here:
Octave / Matlab: Extend a vector making it repeat itself?
(3 answers)
Closed 5 years ago.
I think it should be very easy, but i don´t know how to a append a vector by his own within a loop.
For example:
a = [1 2 3]
I would like to have:
b = [1 2 3 1 2 3 1 2 3]
So, there must be an empty array where i append the a vector 3 times via a loop?
The answer is to use the built-in function repmat
a = [1 2 3]
% Repeat 1x in the rows dimension, 3x in the columns dimension
b = repmat( a, 1, 3 );
% >> b = [1 2 3 1 2 3 1 2 3]
To append two vectors use the [a, b] notation.
For your example:
a = [1 2 3];
b = [];
for i=1:3
b = [b, a];
end
Edit in response to the comment about memory allocation time:
Consider pre-allocating the whole array before your loop.
a = [1 2 3];
b= zeros(1, size(a,2)*3);
s_a = size(a,2);
for i=1:3
b(((i-1)*s_a + 1):i*s_a) = a;
end
I would like to generate all the possible combinations of the elements of a given number of vectors.
For example, for [1 2], [1 2] and [4 5] I want to generate the elements:
[1 1 4; 1 1 5; 1 2 4; 1 2 5; 2 1 4; 2 1 5; 2 2 4; 2 2 5]
The problem is that I don't know the number of vectors for which I need to calculate the combinations. There might be 3 as in this case, or there may be 10, and I need a generalization. Can you please help me to this in MATLAB? Is there already a predefined function that can do this task?
Consider this solution using the NDGRID function:
sets = {[1 2], [1 2], [4 5]};
[x y z] = ndgrid(sets{:});
cartProd = [x(:) y(:) z(:)];
cartProd =
1 1 4
2 1 4
1 2 4
2 2 4
1 1 5
2 1 5
1 2 5
2 2 5
Or if you want a general solution for any number of sets (without having to create the variables manually), use this function definition:
function result = cartesianProduct(sets)
c = cell(1, numel(sets));
[c{:}] = ndgrid( sets{:} );
result = cell2mat( cellfun(#(v)v(:), c, 'UniformOutput',false) );
end
Note that if you prefer, you can sort the results:
cartProd = sortrows(cartProd, 1:numel(sets));
Also, the code above does not check if the sets have no duplicate values (ex: {[1 1] [1 2] [4 5]}). Add this one line if you want to:
sets = cellfun(#unique, sets, 'UniformOutput',false);
Try ALLCOMB function at FileExchange.
If you store you vectors in a cell array, you can run it like this:
a = {[1 2], [1 2], [4 5]};
allcomb(a{:})
ans =
1 1 4
1 1 5
1 2 4
1 2 5
2 1 4
2 1 5
2 2 4
2 2 5
This late answers provides two additional solutions, where the second is the solution (in my opinion) and an improvement on Amro's answer solution with ndgrid by applying MATLAB's powerful comma-separated lists instead of cell arrays for high performance,
If you have the Neural Network Toolbox: use combvec
If you do not have the toolbox, as is usually the case: below is another way to generalize the Cartesian product for any number of sets.
Just as Amro did in his answer, the comma-separated lists syntax (v{:}) supplies both the inputs and outputs of ndgrid. The difference (fourth line) is that it avoids cellfun and cell2mat by applying comma-separated lists, again, now as the inputs to cat:
N = numel(a);
v = cell(N,1);
[v{:}] = ndgrid(a{:});
res = reshape(cat(N+1,v{:}),[],N);
The use of cat and reshape cuts execution time almost in half. This approach was demonstrated in my answer to an different question, and more formally by Luis Mendo.
we can also use the 'combvec' instruction in matlab
no_inp=3 % number of inputs we want...in this case we have 3 inputs
a=[1 2 3]
b=[1 2 3]
c=[1 2 3]
pre_final=combvec(c,b,a)';
final=zeros(size(pre_final));
for i=1:no_inp
final(:,i)=pre_final(:,no_inp-i+1);
end
final
Hope it helps.
Good luck.
How to generate the different combinations possible for a certain number
Example:
m=2 gives:
[1 1;1 2;2 1;2 2]
m=3 gives:
[1 1;1 2;1 3;2 1;2 2;2 3;3 1;3 2;3 3]
and so on...
using perms([1 2]) generates [1 2;2 1] only
You can use ndgrid:
m = 3;
[A,B] = ndgrid(1:m);
Here A and B look like this:
A =
1 1 1
2 2 2
3 3 3
B =
1 2 3
1 2 3
1 2 3
So you can concatenate them vertically to get the combinations. Using the colon operator transforms the matrices into column-vectors, i.e. listing all the elements column-wise. Therefore, you could use either
P = sortrows([A(:), B(:)])
or
P = [B(:) A(:)] %// Thanks #knedlsepp :)
to get sorted combinations.
P now looks like this:
P =
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
Note that your question is highly related to the following, where the goal is to find combinations from 2 vectors.: How to generate all pairs from two vectors in MATLAB using vectorised code?. I suggest you look at it as well to get more ideas.
That being said the question might be a duplicate...anyhow hope that helps.
It's a little tricky, as nchoosek can not be used straight out of the box:
n = 3;
X = nchoosek([1:n, n:-1:1],2);
Y = unique(X,'rows','legacy');
respectively in one line:
Y = unique(nchoosek([1:n, n:-1:1],2),'rows','legacy');
I have two matrix and want to get difference(Subtraction) b/w two matrix
e.g, IF
A = [2 4 6]
B = [1 1 1]
Answer should be
ans = [1 3 5] % A-B
Note:
(Its not a set difference..)
Just use one of the following in Matlab:
A-B
minus(A,B)
You will get:
ans =
1 3 5
Check out here for more info.
I would like to generate all the possible combinations of the elements of a given number of vectors.
For example, for [1 2], [1 2] and [4 5] I want to generate the elements:
[1 1 4; 1 1 5; 1 2 4; 1 2 5; 2 1 4; 2 1 5; 2 2 4; 2 2 5]
The problem is that I don't know the number of vectors for which I need to calculate the combinations. There might be 3 as in this case, or there may be 10, and I need a generalization. Can you please help me to this in MATLAB? Is there already a predefined function that can do this task?
Consider this solution using the NDGRID function:
sets = {[1 2], [1 2], [4 5]};
[x y z] = ndgrid(sets{:});
cartProd = [x(:) y(:) z(:)];
cartProd =
1 1 4
2 1 4
1 2 4
2 2 4
1 1 5
2 1 5
1 2 5
2 2 5
Or if you want a general solution for any number of sets (without having to create the variables manually), use this function definition:
function result = cartesianProduct(sets)
c = cell(1, numel(sets));
[c{:}] = ndgrid( sets{:} );
result = cell2mat( cellfun(#(v)v(:), c, 'UniformOutput',false) );
end
Note that if you prefer, you can sort the results:
cartProd = sortrows(cartProd, 1:numel(sets));
Also, the code above does not check if the sets have no duplicate values (ex: {[1 1] [1 2] [4 5]}). Add this one line if you want to:
sets = cellfun(#unique, sets, 'UniformOutput',false);
Try ALLCOMB function at FileExchange.
If you store you vectors in a cell array, you can run it like this:
a = {[1 2], [1 2], [4 5]};
allcomb(a{:})
ans =
1 1 4
1 1 5
1 2 4
1 2 5
2 1 4
2 1 5
2 2 4
2 2 5
This late answers provides two additional solutions, where the second is the solution (in my opinion) and an improvement on Amro's answer solution with ndgrid by applying MATLAB's powerful comma-separated lists instead of cell arrays for high performance,
If you have the Neural Network Toolbox: use combvec
If you do not have the toolbox, as is usually the case: below is another way to generalize the Cartesian product for any number of sets.
Just as Amro did in his answer, the comma-separated lists syntax (v{:}) supplies both the inputs and outputs of ndgrid. The difference (fourth line) is that it avoids cellfun and cell2mat by applying comma-separated lists, again, now as the inputs to cat:
N = numel(a);
v = cell(N,1);
[v{:}] = ndgrid(a{:});
res = reshape(cat(N+1,v{:}),[],N);
The use of cat and reshape cuts execution time almost in half. This approach was demonstrated in my answer to an different question, and more formally by Luis Mendo.
we can also use the 'combvec' instruction in matlab
no_inp=3 % number of inputs we want...in this case we have 3 inputs
a=[1 2 3]
b=[1 2 3]
c=[1 2 3]
pre_final=combvec(c,b,a)';
final=zeros(size(pre_final));
for i=1:no_inp
final(:,i)=pre_final(:,no_inp-i+1);
end
final
Hope it helps.
Good luck.