5 vues (au cours des 30 derniers jours)
Adam Fitchett le 29 Sep 2022
I have a 3e6*4 matrix1 and a 7e6*4 matrix2. For each element in matrix1 I need to replace it with the row index of the element in the 4th column of matrix2 that is equal to the value of that element in matrix1. I have written a nested for loop which does this but it takes 4 hours. How can I do it more efficiently?
for i = 1:size(matrix1,1)
for j = 1:size(matrix1,2)
matrix1(i,j) = find(matrix2(:,4)==matrix1(i,j))
end
end
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Adam Fitchett le 29 Sep 2022
When I did tic/toc it told me each iteration was taking 0.01 seconds but for 12 million iterations that ends up being hours
Adam Fitchett le 29 Sep 2022
Pre-allocation isn't necessary because the result matrix already exists
matrix1 already exists, i am simply assiging a value to each element iteratively

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### Réponses (1)

Jan le 29 Sep 2022
Modifié(e) : Jan le 1 Oct 2022
[~, Result] = ismember(A, B(:, 4));
A look up table is even faster: Instead of searching the element A(i,j) in B(:, 4), create a vector, which contains the index of the elements of B at the corresponding vector. A limitation is, that look up tables work for positive integer values only and the maximum value must match into the available RAM. If this is not the case, use ismember, or the ismembc approach.
Some timings using input data which are a factor of 100 smaller: (Win10, R2018b, 4 Core i7)
index = randperm(12e4, 7e4).';
B = [zeros(7e4, 3), index];
A0 = index(randi([1, numel(index)], 3e4, 4));
% ISMEMBER:
tic;
[~, Result] = ismember(A0, B(:, 4));
toc
% Look up table:
tic;
n = max(A0(:));
LUT = zeros(n, 1);
LUT(B(:, 4)) = 1:size(B, 1);
A = LUT(A0);
toc;
assert(isequal(Result, A), 'wrong result');
% 2 loops:
A = A0;
tic
for i = 1:size(A,1)
for j = 1:size(A,2)
A(i,j) = find(B(:,4) == A(i,j));
end
end
toc
assert(isequal(Result, A), 'wrong result');
% 1 FOR loop
A = A0;
tic
V = B(:, 4);
for k = 1:numel(A)
A(k) = find(V == A(k));
end
toc
assert(isequal(Result, A), 'wrong result');
% 1 PARFOR loop:
A = A0;
gcp; % Open a parallel pool
tic
V = B(:, 4);
parfor k = 1:numel(A)
A(k) = find(V == A(k));
end
toc
assert(isequal(Result, A), 'wrong result');
% ISMEMBC2 (undocumented):
A = A0;
tic
[Vs, idx] = sort(B(:, 4));
A = idx(ismembc2(A, Vs)); % [EDITED, without a loop over indices of A]
toc
assert(isequal(Result, A), 'wrong result');
% Elapsed time is 0.008757 seconds. ismember
% Elapsed time is 0.002307 seconds. look up table
% Elapsed time is 8.971745 seconds. 2 loops
% Elapsed time is 9.019042 seconds. 1 loop
% Elapsed time is 3.829381 seconds. 1 PARFOR loop
% Elapsed time is 0.006160 seconds. ismembc2
For the input data of the original size:
index = randperm(12e6, 7e6).';
B = [zeros(7e6, 3), index];
A0 = index(randi([1, numel(index)], 3e6, 4));
I get 1.8 seconds for ismember and 0.53 seconds for the look up table. A speed up by a factor 27'000 compared with your 4 hours. Nice.
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Bruno Luong le 4 Oct 2022
Déplacé(e) : Bruno Luong le 4 Oct 2022
Timings with my brand new laptop with Jan's code
Elapsed time is 0.004218 seds. % ISMEMBER
Elapsed time is 0.001169 seconds. % LUT
Elapsed time is 8.071717 seconds. % 2 forloop
Elapsed time is 4.558228 seconds. % 1 for loop
Elapsed time is 1.017994 seconds. % par for
Elapsed time is 0.002874 seconds. % ISMEMBC2
Jan le 4 Oct 2022
Do you mean this one:
Result = zeros(size(A)); % Pre-allocation!!!
B4 = B(:, 4);
for k = 1:numel(A)
Result(k) = find(A(k) == B4, 1);
end
But this ismember, ismembc2 and look-up-table methods are some tenthousands times faster.
Use at least the binary search with:
Result = zeros(size(A)); % Pre-allocation!!!
[Vs, idx] = sort(B(:, 4));
for k = 1:numel(A)
A(k) = idx(ismembc2(A(k), Vs));
end
Avoiding the loop by
A = idx(ismembc2(A, Vs));
speeds this up another time.

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