matlab - 将函数应用于矩阵，这取决于索引？

Question

假设我有一个矩阵A，我想对它的每个元素应用一个函数f。然后我可以使用 f(A)，如果 f 是矢量化的，或者 arrayfun(f,A) 如果不是。

但是如果我有一个依赖于条目及其索引的函数怎么办:f = @(i,j,x) something。如何在不使用如下所示的 for 循环的情况下将此函数应用于矩阵 A？

for j=1:size(A,2)
   for i=1:size(A,1)
      fA(i,j) = f(i,j,A(i,j));
   end
end

我想考虑将函数 f 向量化。不过，欢迎提供有关非矢量化函数的更短符号的提示。

Answer 1

我已经阅读了您的回答，并且想到了另一个使用索引的想法，这是最快的方法。这是我的测试脚本:

%// Test function
f = @(i,j,x) i.*x + j.*x.^2;

%// Initialize times
tfor = 0;
tnd = 0;
tsub = 0;
tmy = 0;

%// Do the calculation 100 times
for it = 1:100

   %// Random input data
   A = rand(100);

   %// Clear all variables
   clear fA1 fA2 fA3 fA4;

   %// Use the for loop
   tic;
   fA1(size(A,1),size(A,2)) = 0;
   for j=1:size(A,2)
      for i=1:size(A,1)
         fA1(i,j) = f(i,j,A(i,j));
      end
   end
   tfor = tfor + toc;

   %// Use ndgrid, like @Divakar suggested
   clear I J;
   tic;
   [I,J] = ndgrid(1:size(A,1),1:size(A,2));
   fA2 = f(I,J,A);
   tnd = tnd + toc;

   %// Test if the calculation is correct
   if max(max(abs(fA2-fA1))) > 0
      max(max(abs(fA2-fA1)))
   end

   %// Use ind2sub, like @DennisKlopfer suggested
   clear I J;
   tic;
   [I,J] = ind2sub(size(A),1:numel(A));
   fA3 = arrayfun(f,reshape(I,size(A)),reshape(J,size(A)),A);
   tsub = tsub + toc;

   %// Test if the calculation is correct
   if max(max(abs(fA3-fA1))) > 0
      max(max(abs(fA3-fA1)))
   end

   %// My suggestion using indexing
   clear sA1 sA2 ssA1 ssA2;
   tic;
   sA1=size(A,1);
   ssA1=1:sA1;
   sA2=size(A,2);
   ssA2=1:sA2;
   fA4 = f(ssA1(ones(1,sA2),:)', ssA2(ones(1,sA1,1),:), A); %'
   tmy = tmy + toc;

   %// Test if the calculation is correct
   if max(max(abs(fA4-fA1))) > 0
      max(max(abs(fA4-fA1)))
   end   
end

%// Print times
tfor
tnd
tsub
tmy

我得到了结果

tfor =
    0.6813

tnd =
    0.0341

tsub =
   10.7477

tmy =
    0.0171