Asked by WM
on 11 Oct 2019

I use the built-in fft() function on a 2D single matrix of size 71*110000. Initially, I looped over the first dimension. However, passing the whole matrix to fft() results in ~30% speedup, which is why I'd like to continue with that. What's puzzling me is that the results are similar but not the same. My understanding from the documentation is that Matlab would do the exact same computation, treating each row as a vector in the matrix case. I'd be thankful for any idea why the results differ.

Example:

%% generate random data

data = single(rand(71, 110000));

n = 111872;

%% loop version

for ichan = 1:size(data, 1)

dataX(ichan, :) = fft(data(ichan, :), n);

end

%% matrix version

alldataX = fft(data, n, 2);

%% test

isequal(dataX, alldataX)

isequaln(dataX, alldataX)

max(abs(dataX - alldataX)) %small difference, but not the same

Answer by Matt J
on 11 Oct 2019

Edited by Matt J
on 11 Oct 2019

Accepted Answer

The same dicrepancy exists with most Matlab functions that do operations along rows or columns. Here is the same test replacing fft with sum,

%% generate random data

data = single(rand(71, 110000));

dataX=data(:,1);

%% loop version

for ichan = 1:size(data, 1)

dataX(ichan) = sum(data(ichan, :), 2);

end

%% matrix version

alldataX = sum(data, 2);

%% test

isequal(dataX, alldataX)

isequaln(dataX, alldataX)

max(abs(dataX(:) - alldataX(:)))/max(alldataX(:))*100 %4.2499e-05

The reason for it is that Matlab's internal multi-threading splits the data up differently depending on the size of the array given as input to the function. This leads to summations being done in different orders and hence floating point discrepancies in the results.

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## dpb (view profile)

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## Bjorn Gustavsson (view profile)

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## WM (view profile)

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