[英]Generate all possible combinations of the elements of some vectors (Cartesian product)
I would like to generate all the possible combinations of the elements of a given number of vectors.我想生成给定数量向量的元素的所有可能组合。
For example, for [1 2]
, [1 2]
and [4 5]
I want to generate the elements:例如,对于
[1 2]
、 [1 2]
和[4 5]
我想生成元素:
[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.问题是我不知道需要计算组合的向量数量。 There might be 3 as in this case, or there may be 10, and I need a generalization .
在这种情况下可能有 3 个,或者可能有 10 个,我需要一个概括。 Can you please help me to this in MATLAB?
你能在 MATLAB 中帮我解决这个问题吗? Is there already a predefined function that can do this task?
是否已经有预定义的 function 可以执行此任务?
Consider this solution using the NDGRID function: 考虑使用NDGRID函数的此解决方案:
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: 或者,如果您想为任意数量的集合提供通用解决方案(而不必手动创建变量),请使用以下函数定义:
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: 请注意,如果您愿意,可以对结果进行排序:
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]}
). 另外,上面的代码不检查集合是否没有重复值(例如:
{[1 1] [1 2] [4 5]}
)。 Add this one line if you want to: 如果您要添加这一行:
sets = cellfun(@unique, sets, 'UniformOutput',false);
Try ALLCOMB function at FileExchange. 在FileExchange尝试ALLCOMB函数。
If you store you vectors in a cell array, you can run it like this: 如果将向量存储在单元格数组中,则可以这样运行它:
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, 最新的答案提供了另外两个解决方案,其中第二个是解决方案 (我认为),并且通过应用MATLAB强大的逗号分隔列表而不是单元格数组来提高Amro对
ndgrid
的答案解决方案的性能,
combvec
combvec
Just as Amro did in his answer, the comma-separated lists syntax ( v{:}
) supplies both the inputs and outputs of ndgrid
. 就像Amro在回答中所做的那样,逗号分隔的列表语法(
v{:}
)提供ndgrid
的输入和输出。 The difference (fourth line) is that it avoids cellfun
and cell2mat
by applying comma-separated lists, again, now as the inputs to cat
: 区别(第四行)是,它再次应用逗号分隔的列表作为
cat
的输入,从而避免了cellfun
和cell2mat
:
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. 使用
cat
和reshape
将执行时间减少近一半。 This approach was demonstrated in my answer to an different question , and more formally by Luis Mendo . 路易斯·门多(Luis Mendo)在我对另一个问题的回答中 更详细地说明了这种方法。
we can also use the 'combvec' instruction in matlab 我们也可以在matlab中使用'combvec'指令
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. 希望能帮助到你。 Good luck.
祝好运。
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