Matlab中某些索引的所有可能组合的矩阵 [英] Matrix of all possible combinations of some indices in Matlab

问题描述

考虑大小为1xL的Matlab向量A，报告一些严格的正整数.我想构造一个尺寸为prod(A,2)xL的矩阵T，报告来自1:1:A(1)，1:1:A(2)，...，1:1:A(L)的所有可能的L元组.

Consider a Matlab vector A of size 1xL, reporting some strictly positive integers. I want to construct a matrix T of size prod(A,2)xL reporting all the possible L-tuples from 1:1:A(1), 1:1:A(2), ..., 1:1:A(L).

例如，取L=3和A=[2 3 1].然后T可以构造为

For example, take L=3 and A=[2 3 1]. Then T can be constructed as

[ca, cb, cc] = ndgrid(1:1:A(1), 1:1:A(2), 1:1:A(3));
T= [ca(:), cb(:), cc(:)]; 

如何将以上代码概括为通用的L?

How can I generalise the code above to a generic L?

推荐答案

对此答案的较小修改.所需的更改是:

A minor modification of this answer works. The required changes are:

在载体中定义要组合"的载体.基于A.
1. 在此处用{:}索引替换{end:-1:1}索引，以相反的字典顺序获得结果.

1. Define the vectors to be "combined" based on A.
2. Replace {end:-1:1} indexing there by {:} indexing here, to get the results in reverse lexicographical order.

A = [2 3 1];
vectors = arrayfun(@(x) {1:x}, A); % 1. Define input vectors from A
n = numel(vectors);
T = cell(1,n);
[T{:}] = ndgrid(vectors{:}); % 2. Results will be in reverse lexicographical order 
T = cat(n+1, T{:});
T = reshape(T,[],n); 

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