Matlab:从k张量列表创建(k + 1)张量 [英] Matlab: creating a (k+1)-tensor from a list of k-tensors

问题描述

假设您得到了一堆k张量，为简单起见，我们假设它们是2张量/矩阵:

Assume you are given a bunch of k-tensors, for simplicity let's say they are 2-tensors/matrices:

 X = rand(5,5); Y = rand(5,5);

是否存在将它们组合成3张量的惯用法，其中第一个维度索引矩阵?一种方法是

Is there an idiom for combining them into a 3-tensor, where the first dimension indexes the matrix? One way to do it is

P(1,:,:) = X;
P(2,:,:) = Y;

，现在P根据需要具有尺寸2x5x5.有一个更好的方法吗? 例如，在numpy中，只需输入:

and now P has dimensions 2x5x5 as required. Is there a better way to do this? For example, in numpy one could simply type:

P = array((X,Y))

，但是在matlab中键入P=[X Y]或P=[X; Y]会分别给出10x5和5x10矩阵，而不是预期的2x5x5.

but in matlab typing P=[X Y] or P=[X; Y] would give 10x5 and 5x10 matrices respectively rather than the intended 2x5x5.

推荐答案

使用 cat 命令.

假设您有5个大小为(x,y,z)的矩阵

Suppose you have 5 matrices of size (x,y,z),

A = rand(x,y,z); B = rand(x,y,z); C = rand(x,y,z); D = rand(x,y,z); E = rand(x,y,z);

串联的矩阵将是

M = cat(4, A, B, C, D, E);

其中，4是第4维.输出M的大小为(x,y,z,5).在MATLAB中，每个矩阵A,B,...的大小为(x,y,z,1,1,...)，即它们的第4维长度为1.

where 4 refers to the 4-th dimension. The output M has size (x,y,z,5). In MATLAB, each of the matrices A,B,... has a size of (x,y,z,1,1,...), i.e. their 4-th dimensional length is 1.

在连接之后，可能有必要更改维度索引的顺序，以便第一个维度是新创建的维度.使用 permute 命令.

After the concatenation, it might be necessary to change the order of dimensional indices so that the first dimension is the newly-created dimension. Use the permute command.

N = permute(M, [4, 1, 2, 3]);

输出矩阵N的大小为(5,x,y,z).

编辑历史记录

Edit history

1. 将输入矩阵的大小从(3,3,3)更改为(x,y,z)，以在区分和排列时清楚地区分每个维度.
2. 添加了permute，这是满足OP的尺寸索引要求所必需的.

1. Changed input matrix size from (3,3,3) to (x,y,z) to clearly distinguish each dimension during concatenation and permutation.
2. Added permute, which was necessary in order to satisfy OP's dimensional index requirement.

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