Matlab 将N^2 3x3矩阵串联成3Nx3N矩阵

我有N^2个矩阵。 每一个都是一个3x3矩阵。 将它们连接到3Nx3N矩阵的一种方法是写入

A（：，：，i）=#3x3矩阵i=1:N^2

B=[A11 A12..A1N；A21…A2N；…]

但当N很大时，这是一项乏味的工作。

---

您提供什么服务？

请尝试以下代码：

N = 4;
A = rand(3,3,N^2);                     %# 3-by-3-by-N^2

c1 = squeeze( num2cell(A,[1 2]) );
c2 = cell(N,1);
for i=0:N-1
    c2{i+1} = cat(2, c1{i*N+1:(i+1)*N});
end

B = cat(1, c2{:});                     %# 3N-by-3N

---

另一种可能涉及

mat2cell

和

重塑

N = 2;
A = rand(3,3,N^2);  

C = mat2cell(A,3,3,ones(N^2,1));
C = reshape(C,N,N)'; %'# make a N-by-N cell array and transpose

%# catenate into 3N-by-3N cell array
B = cell2mat(C);

如果你更喜欢的话，这一行也一样

B = cell2mat(reshape(mat2cell(A,2,2,ones(N^2,1)),N,N)');

对于N=2

>> A = rand(3,3,N^2)
A(:,:,1) =
      0.40181      0.12332      0.41727
     0.075967      0.18391     0.049654
      0.23992      0.23995      0.90272
A(:,:,2) =
      0.94479      0.33772       0.1112
      0.49086      0.90005      0.78025
      0.48925      0.36925      0.38974
A(:,:,3) =
      0.24169      0.13197      0.57521
      0.40391      0.94205      0.05978
     0.096455      0.95613      0.23478
A(:,:,4) =
      0.35316     0.043024      0.73172
      0.82119      0.16899      0.64775
     0.015403      0.64912      0.45092

B =
      0.40181      0.12332      0.41727      0.94479      0.33772       0.1112
     0.075967      0.18391     0.049654      0.49086      0.90005      0.78025
      0.23992      0.23995      0.90272      0.48925      0.36925      0.38974
      0.24169      0.13197      0.57521      0.35316     0.043024      0.73172
      0.40391      0.94205      0.05978      0.82119      0.16899      0.64775
     0.096455      0.95613      0.23478     0.015403      0.64912      0.45092

---

为什么不进行老式的预分配和循环呢？应该很快

N = 4;
A = rand(3,3,N^2);  % Assuming column major order for Aij
8
B = zeros(3*N, 3*N);
for j = 1:N^2
    ix = mod(j-1, N)*3 + 1;
    iy = floor((j-1)/N)*3 + 1;
    fprintf('%02d - %02d\n', ix, iy);
    B(ix:ix+2, iy:iy+2) = A(:,:,j);
end

编辑：这里是速度迷的排名：

N = 200;
A = rand(3,3,N^2);  % test set

@gnovice solution: Elapsed time is 0.013069 seconds.
@Amro    solution: Elapsed time is 0.203308 seconds.
@Rich C  solution: Elapsed time is 0.887077 seconds.
@Jonas   solution: Elapsed time is 7.065174 seconds.

---

这里有一个非常快速的单行程序，只使用和：

还有一个测试：

>> N=2;
>> A = rand(3,3,N^2)
A(:,:,1) =
    0.5909    0.6571    0.8082
    0.7118    0.6090    0.7183
    0.4694    0.9588    0.5582
A(:,:,2) =
    0.1791    0.6844    0.6286
    0.4164    0.4140    0.5833
    0.1380    0.1099    0.8970
A(:,:,3) =
    0.2232    0.2355    0.1214
    0.1782    0.6873    0.3394
    0.5645    0.4745    0.9763
A(:,:,4) =
    0.5334    0.7559    0.9984
    0.8454    0.7618    0.1065
    0.0549    0.5029    0.3226

>> B = reshape(permute(reshape(A,3,3*N,N),[2 1 3]),3*N,3*N).'
B =
    0.5909    0.6571    0.8082    0.1791    0.6844    0.6286
    0.7118    0.6090    0.7183    0.4164    0.4140    0.5833
    0.4694    0.9588    0.5582    0.1380    0.1099    0.8970
    0.2232    0.2355    0.1214    0.5334    0.7559    0.9984
    0.1782    0.6873    0.3394    0.8454    0.7618    0.1065
    0.5645    0.4745    0.9763    0.0549    0.5029    0.3226

---

在此之前我有一个相关的假设，它是：我可以确认这比+1快一个数量级

>> N=2;
>> A = rand(3,3,N^2)
A(:,:,1) =
    0.5909    0.6571    0.8082
    0.7118    0.6090    0.7183
    0.4694    0.9588    0.5582
A(:,:,2) =
    0.1791    0.6844    0.6286
    0.4164    0.4140    0.5833
    0.1380    0.1099    0.8970
A(:,:,3) =
    0.2232    0.2355    0.1214
    0.1782    0.6873    0.3394
    0.5645    0.4745    0.9763
A(:,:,4) =
    0.5334    0.7559    0.9984
    0.8454    0.7618    0.1065
    0.0549    0.5029    0.3226

>> B = reshape(permute(reshape(A,3,3*N,N),[2 1 3]),3*N,3*N).'
B =
    0.5909    0.6571    0.8082    0.1791    0.6844    0.6286
    0.7118    0.6090    0.7183    0.4164    0.4140    0.5833
    0.4694    0.9588    0.5582    0.1380    0.1099    0.8970
    0.2232    0.2355    0.1214    0.5334    0.7559    0.9984
    0.1782    0.6873    0.3394    0.8454    0.7618    0.1065
    0.5645    0.4745    0.9763    0.0549    0.5029    0.3226