How to rewrite this high dimensional matrix calculation

3 次查看（过去 30 天）
Hancheng Zhu
Hancheng Zhu 2024-10-9
评论： Hancheng Zhu 2024-10-10
Here is the code:
X = randn(A,B,C);
Z = zeros(A,B,A,B,C);
for a=1:A
for b=1:B
Z(a,b,:,:,:) = X - X(a,b,:);
Z(a,b,a,b,:) = X(a,b,:);
end
end
X is a given three dimensional matrix with dimension A*B*C, i want to obtain the 5 dimension matrix Z. I am not familiar with the high dimension matrix manipulation so i just write with for loop, but it is really time-consuming. Is there any way to accelerate the calculation of Z?

请先登录，再回答此问题。

采纳的回答

Bruno Luong
Bruno Luong 2024-10-9
编辑：Bruno Luong 2024-10-9
Fully vectorized
Y = reshape(X, [], 1, C);
Z = reshape(Y, 1, [], C)-Y;
Z = reshape(Z, [], C);
Z(1:A*B+1:end,:) = Y;
Z = reshape(Z,[A B A B C]);
  5 个评论
显示 3更早的评论
Bruno Luong
Bruno Luong 2024-10-10
编辑：Bruno Luong 2024-10-10
Y = reshape(X, A, 1, []);
Z = reshape(X, 1, A, [])-Y;
Z = reshape(Z, [], B*C);
Z(1:A+1:end,:) = Y;
Z = reshape(Z,[A A B C]);
S = reshape(prod(Z,2), [A B C]);
I recommend to keep your original code; at least as comment while you don't fully master the vectorized version, which is not obviously clear.

请先登录，再进行评论。

更多回答（1 个）

Zinea
Zinea 2024-10-9
编辑：Zinea 2024-10-9
Hi @Hancheng Zhu,
To accelerate the calculation of the 5-dimensional matrix Z, you can make the following changes:
  1. Preallocate the matrix Z with zeros.
Z = zeros(A, B, A, B, C);
2. Use reshape to manipulate the dimensions of X. Also, element-wise operations is used to compute the difference for each element in X without explicit loops.
X_expanded = reshape(X, [1, 1, A, B, C]);
Z = X_expanded - reshape(X, [A, B, 1, 1, C]);
You may refer to the following documention on vectorization for more information:
https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html
3. A loop is still used to assign values where the indices of Z match (a,b) in the 3rd and 4th dimensions, but this is a relatively small operation compared to the entire matrix computation.
for a = 1:A
for b = 1:B
Z(a, b, a, b, :) = X(a, b, :);
end
end

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

产品


版本

R2024b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by