生成包含元素的所有组合的矩阵从n个向量取 [英] Generate a matrix containing all combinations of elements taken from n vectors

问题描述

这个问题的一种形式经常弹出或其他（例如，见这里或的这里）。所以，我想我会美元的一般格式P $ psent它，并提供一个答案可能成为以供将来参考。

  

给定一个任意数量的 N 可能不同大小的矢量，产生一个 N -column矩阵，其行描述从这些向量（笛卡尔乘积）。

元素所采取的所有组合

例如，

  =向量{[1〜2]，[3 6 9]，[10 20]}
 

应该给

 梳子= [1 3 10
          1 3 20
          1 6 10
          1 6 20
          1 9 10
          1 9 20
          2 3 10
          2 3 20
          2 6 10
          2 6 20
          2 9 10
          2 9 20]
 

解决方案

ndgrid 功能几乎给出了答案，但有一点需要注意： N 输出变量必须显式定义调用它。由于 N 是任意的，最好的办法是使用<一个href=\"http://www.mathworks.es/es/help/matlab/matlab_prog/comma-separated-lists.html?s_tid=doc_12b\">comma-separated列表（从单元阵列产生与 N 细胞）作为输出。由此产生的 N 然后矩阵连接成所需的 N -column矩阵：

  =向量{[1〜2]，[3 6 9]，[10 20]}; //％输入数据：向量单元阵列N = numel（矢量）; //％向量的数量
梳=细胞（1，n）的; //％pre-定义生成逗号分隔的列表
[梳子{结束：-1：1}] = ndgrid（向量{结束：-1：1}）; ％//在这两个相反的顺序
％//逗号分隔的列表，需要以产生结果矩阵的行
//％字典序
梳=猫（n + 1个，梳子{：}）;沿着维数n + 1％// CONCAT的N，N-二暗淡阵列
梳子=重塑（梳子，[]，N）; //％重塑，以获得所需的矩阵
 

This question pops up quite often in one form or another (see for example here or here). So I thought I'd present it in a general form, and provide an answer which might serve for future reference.

Given an arbitrary number n of vectors of possibly different sizes, generate an n-column matrix whose rows describe all combinations of elements taken from those vectors (Cartesian product) .

For example,

vectors = { [1 2], [3 6 9], [10 20] }

should give

combs = [ 1     3    10
          1     3    20
          1     6    10
          1     6    20
          1     9    10
          1     9    20
          2     3    10
          2     3    20
          2     6    10
          2     6    20
          2     9    10
          2     9    20 ]

解决方案

The ndgrid function almost gives the answer, but has one caveat: n output variables must be explicitly defined to call it. Since n is arbitrary, the best way is to use a comma-separated list (generated from a cell array with ncells) to serve as output. The resulting n matrices are then concatenated into the desired n-column matrix:

vectors = { [1 2], [3 6 9], [10 20] }; %// input data: cell array of vectors

n = numel(vectors); %// number of vectors
combs = cell(1,n); %// pre-define to generate comma-separated list
[combs{end:-1:1}] = ndgrid(vectors{end:-1:1}); %// the reverse order in these two
%// comma-separated lists is needed to produce the rows of the result matrix in
%// lexicographical order 
combs = cat(n+1, combs{:}); %// concat the n n-dim arrays along dimension n+1
combs = reshape(combs,[],n); %// reshape to obtain desired matrix

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