MATLAB: Multithreaded FILTER

filtermulti-threading

I've found several references which tell that Matlab's filter is multi-threaded since R2007a, e.g. MathWorks:Solution 1-4PG4AN.
The test:
function myFilterTest
x  = rand(1e6, 2);
x1 = x(:,1);
x2 = x(:,2); 
% [B, A] = butter(3, 0.2, 'low');  % Butterworth 3rd order lowpass filter
B = [0.01809893300751, 0.05429679902254, 0.05429679902254, 0.01809893300751];
A = [1, -1.760041880343, 1.182893262037, -0.2780599176345];
tic;
for i=1:100
   y = filter(B, A, x);   % Matrix
   % clear('y');          % Avoid smart JIT interferences => same effects!
end
toc
tic;
for i=1:100
   y1 = filter(B, A, x1);     % Two vectors
   y2 = filter(B, A, x2);
   % clear('y1', 'y2');       % No qualitative changes
end
toc
[EDITED, 12-Dec-2012 22:38 UTC]: Explicite A and B instead of calling butter of SPT
Results on a Windows7/64 Core2Duo:
 Matlab 2009b/64:
   5.34 sec  (matrix)
   5.22 sec  (two vectors)
 Matlab 2009b/64 started with -singleCompThread:
   5.23 sec  (matrix)
   5.24 sec  (two vectors) 
 Matlab 2011b:
   4.75 sec  (matrix)
   4.99 sec  (two vectors)
My expectations: 1. The value of a filtered signal to a specific time depends on the complete history for an IIR filter like the Butterworth. Therefore the filtering of a vector cannot take advantage from multi-threading (is this correct?). 2. In opposite to this, filtering a [n x 2] signal should occupy two cores, such that a multi-threaded filter should need approximately the same time as for a [n x 1] signal (is this correct?).
But my double-core processor has a load of 57% during the calculations and the filtering needs nearly the same time, when I start Matlab with the -singleCompThread flag.
My conclusion: It looks like filter is not multi-threaded. Can somebody confirm this impression for 4 or 8 cores? Then with "x = rand(1e6, 8)" and "x1" to "x8". I get equivalent results for FIR filter parameters with A=1. For a 12th order Butterworth the matrix method gets an advantage of 10%.
Thanks.

Best Answer

I ran this on my 8-core machine using R2009a:
function myFilterTest
x  = rand(1e6, 8);
x1 = x(:,1);
x2 = x(:,2); 
x3 = x(:,3);
x4 = x(:,4); 
x5 = x(:,5);
x6 = x(:,6); 
x7 = x(:,7);
x8 = x(:,8); 
[B, A] = butter(3, 0.2, 'low');
tic;
for i=1:100
 y = filter(B, A, x);   % Matrix
 % clear('y');          % Avoid smart JIT interferences => same effects!
end
toc
tic;
for i=1:100
 y1 = filter(B, A, x1);     % Eight vectors
 y2 = filter(B, A, x2);
 y3 = filter(B, A, x3);
 y4 = filter(B, A, x4);
 y5 = filter(B, A, x5);
 y6 = filter(B, A, x6);
 y7 = filter(B, A, x7);
 y8 = filter(B, A, x8);
   % clear('y1', 'y2');       % No qualitative changes
end
toc
clear all;
And got this:
Elapsed time is 16.865596 seconds. 
Elapsed time is 16.117599 seconds.
Only one core was active during each test.
I ran this on my 8-core machine using R2011a and got:
Elapsed time is 12.542615 seconds.
Elapsed time is 16.268821 seconds.
All eight cores were active for the first test (on the matrix) and only a single core for the seconds test (on individual vectors).
I added this to the bottom of the test:
y_par = zeros(size(x));
matlabpool(8);tic;  
parfor j = 1:8
 for i=1:100 
     y_par(:,j) = filter(B, A, x(:,j));
 end   
 % clear('y_par');       % No qualitative changes
end
toc; matlabpool close;
And got this when using R2011a:
Elapsed time is 13.305009 seconds.
Elapsed time is 16.398203 seconds.
Starting matlabpool using the 'local' configuration ... connected to 8 labs.
Elapsed time is 3.542021 seconds.
Sending a stop signal to all the labs ... stopped.
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