Applying a function to a matrix, which depends on the indices? - matlab

Question

Suppose I have a matrix A and I want to apply a function f to each of its elements. I can then use f(A), if f is vectorized or arrayfun(f,A) if it's not.
But what if I had a function that depends on the entry and its indices: f = #(i,j,x) something. How do I apply this function to the matrix A without using a for loop like the following?
for j=1:size(A,2)
for i=1:size(A,1)
fA(i,j) = f(i,j,A(i,j));
end
end
I'd like to consider the function f to be vectorized. Hints on shorter notation for non-vectorized functions are welcome, though.

Answer 1

I have read your answers and I came up with another idea using indexing, which is the fastest way. Here is my test script:
%// 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
I get the result
tfor =
0.6813
tnd =
0.0341
tsub =
10.7477
tmy =
0.0171

Answer 2

Assuming that the function is vectorized ( no dependency or recursions involved), as mentioned in the comments earlier, you could use ndgrid to create 2D meshes corresponding to the two nested loop iterators i and j and of the same size as A. When these are fed to the particular function f, it would operate on the input 2D arrays in a vectorized manner. Thus, the implementation would look something like this -
[I,J] = ndgrid(1:size(A,1),1:size(A,2));
out = f(I,J,A);
Sample run -
>> f = #(i,j,k) i.^2+j.^2+sin(k);
A = rand(4,5);
for j=1:size(A,2)
for i=1:size(A,1)
fA(i,j) = f(i,j,A(i,j));
end
end
>> fA
fA =
2.3445 5.7939 10.371 17.506 26.539
5.7385 8.282 13.538 20.703 29.452
10.552 13.687 18.076 25.804 34.012
17.522 20.684 25.054 32.13 41.331
>> [I,J] = ndgrid(1:size(A,1),1:size(A,2)); out = f(I,J,A);
>> out
out =
2.3445 5.7939 10.371 17.506 26.539
5.7385 8.282 13.538 20.703 29.452
10.552 13.687 18.076 25.804 34.012
17.522 20.684 25.054 32.13 41.331

Answer 3

Using arrayfun(), ind2sub() and reshape() you can create the indexes matching the form of A. This way arrayfun() is applicable. There might be a better version as this feels a little bit like a hack, it should work on vectorized and unvectorized functions though.
[I,J] = ind2sub(size(A),1:numel(A));
fA = arrayfun(f,reshape(I,size(A)),reshape(J,size(A)),A)