重新排列 ND 陣列可以提高整體效能

在某些情況下，我們需要將函式應用於一組 ND 陣列。讓我們看看這個簡單的例子。

A(:,:,1) = [1 2; 4 5];
A(:,:,2) = [11 22; 44 55];
B(:,:,1) = [7 8; 1 2];
B(:,:,2) = [77 88; 11 22];

A =

ans(:,:,1) =

   1   2 
   4   5 

ans(:,:,2) =

   11   22
   44   55

>> B
B =

ans(:,:,1) =

   7   8
   1   2

ans(:,:,2) =

   77   88
   11   22

兩個矩陣都是 3D，假設我們必須計算以下內容：

result= zeros(2,2);
...
for k = 1:2 
   result(i,j) = result(i,j) + abs( A(i,j,k) - B(i,j,k) );
...

if k is very large, this for-loop can be a bottleneck since MATLAB order the data in a column major fashion. So a better way to compute "result" could be:

% trying to exploit the column major ordering
Aprime = reshape(permute(A,[3,1,2]), [2,4]);
Bprime = reshape(permute(B,[3,1,2]), [2,4]);

>> Aprime
Aprime =

    1    4    2    5
   11   44   22   55

>> Bprime
Bprime =

    7    1    8    2
   77   11   88   22

現在我們將以上迴圈替換為：

result= zeros(2,2);
....
temp = abs(Aprime - Bprime);
for k = 1:2
    result(i,j) = result(i,j) + temp(k, i+2*(j-1));
...

我們重新安排了資料，以便我們可以利用快取。置換和重塑可能是昂貴的，但是當使用大型 ND 陣列時，與這些操作相關的計算成本遠低於未安排陣列的計算成本。