在Matlab中从向量生成3-d矩阵

Question

I have a vector A in Matlab of dimension (N-1)x1

A=[0:1:N-2]'

with N>=3 , eg with N=4 A=[0 1 2]

I want to construct a 3-dimensional matrix B of dimension Mx(N-1)x(N-1) without using loops such that eg with N=4 , M=5

B(:,:,1)=[0 0 0 0;
          0 0 0 0;
          0 0 0 0;
          0 0 0 0;
          0 0 0 0]

B(:,:,2)=[1 1 1 1;
          1 1 1 1;
          1 1 1 1;
          1 1 1 1;
          1 1 1 1]

...

B(:,:,end)=[N-2 N-2 N-2 N-2;
            N-2 N-2 N-2 N-2;
            N-2 N-2 N-2 N-2;
            N-2 N-2 N-2 N-2;
            N-2 N-2 N-2 N-2]

Answer 1

Here's one approach with kron and reshape :

A = 0:N-2;
B = reshape(kron(A, ones(M, N-1)), M, N-1, []);

We use kron to produce M x (N-1) 2D matrices that are stacked for as many elements as there are in A and each matrix is multiplied by the corresponding value in A . The next step is to take each of the concatenated 2D matrices and place them as individual slices in the third dimension, done by reshape .

Example with M = 5, N = 4

>> B

B(:,:,1) =

     0     0     0
     0     0     0
     0     0     0
     0     0     0
     0     0     0


B(:,:,2) =

     1     1     1
     1     1     1
     1     1     1
     1     1     1
     1     1     1


B(:,:,3) =

     2     2     2
     2     2     2
     2     2     2
     2     2     2
     2     2     2

Answer 2

Is this what you want?

B = repmat(reshape(A,1,1,[]), M, N-1); %// or change N-1 to N, according to your example

Another possibility:

B = bsxfun(@times, reshape(A,1,1,[]), ones(M, N-1)); %// or change N-1 to N

Yet another:

B = reshape(A(ceil((1:numel(A)*M*(N-1))/M/(N-1))), M, N-1, []); %// or change N-1 to N

Answer 3

我将继续使用permute直到掌握了...

B = ones(M,N-1,N-1).*permute(A,[3,2,1])