why arrayfun does NOT improve my struct array operation performance - matlab

Question

here is the input data:
% #param Landmarks:
% Landmarks should be 1*m struct.
% m is the number of training set.
% Landmark(i).data is a n*2 matrix
old function:
function Landmarks=CenterOfGravity(Landmarks)
% align center of gravity
for i=1 : length(Landmarks)
Landmarks(i).data=Landmarks(i).data - ones(size(Landmarks(i).data,1),1)...
*mean(Landmarks(i).data);
end
end
new function which use arrayfun:
function [Landmarks] = center_to_gravity(Landmarks)
Landmarks = arrayfun(#(struct_data)...
struct('data', struct_data.data - repmat(mean(struct_data.data), [size(struct_data.data, 1), 1]))...
,Landmarks);
end %function center_to_gravity
when using profiler, I find the usage of time is NOT what I expected:
Function Total Time Self Time*
CenterOfGravity 0.011s 0.004 s
center_to_gravity 0.029s 0.001 s
Can someone tell me why?
BTW...I can't add "arrayfun" as a new tag for my reputation.

Answer 1

Using arrayfun does not count as "vectorizing your code" as described in every Matlab performance blog post ever written.
If your .data field is the same length for all entries of landmark, your could vectorize this code by first placing all of the data into a single DATASIZE-BY-LANDMARKSIZE martix, and then running this command
meanRemovedData = bsxfun(#minus, data, mean(data,1));
But you lose an awful lot of code clarity that way. (I'm pretty sure that bsxfun usually has vectorization-like speed advantages, but I haven't done any time testing this morning.)
In terms of why, I'm not really the right guy to ask. But many of the advantages of vectorization are dependent on performing simple operations of contiguous blocks of memory. Data stored in an array of structures is (I believe) stored as an array of pointers to disparate memory locations, which is why you can change the size or class of Landmarks(i).data without reallocating the whole structure array.

Answer 2

Thanks for Amro and Pursuit's enthusiastic to my question.
I get the best solution at Matlab answers from Jan Simon:
why arrayfun does NOT improve my struct array operation performance
There are some points that do improve the performance:
It is surprisingly that SUM/LENGTH is faster than MEAN
timeit can give more accurate result.
The fastest approach use tricks like this:
m = sum(data, 1) / size(data, 1);
data(:, 1) = data(:, 1) - m(1);

Answer 3

Consider the following three implementations (all vectorized using BSXFUN):
function s = func1(s)
for i=1:numel(s)
s(i).data = bsxfun(#minus, s(i).data, mean(s(i).data));
end
end
function v = func2(s)
v = arrayfun(#(ss) bsxfun(#minus,ss.data,mean(ss.data)), ...
s, 'UniformOutput',false);
v = struct('data',v);
end
function v = func3(s)
v = arrayfun(#(ss) struct('data',bsxfun(#minus,ss.data,mean(ss.data))), ...
s, 'UniformOutput',true);
end
Explanation:
First uses a for-loop to iterate over the array of structs.
Second uses ARRAYFUN to return a cell array of the data matrices, which are then passed to STRUCT to build the array of structures.
The last one uses ARRAYFUN and builds a structure directly at each iteration.
Here is a simple test to compare the timings:
function testArrayStruct()
%# sample array of structures
s = struct('data',[]);
for i=5000:-1:1
s(i).data = rand(randi(1000),2);
end
%# timing
tic; v1 = func1(s); toc
tic; v2 = func2(s); toc
tic; v3 = func3(s); toc
%# check all have the same output
assert(isequal(v1,v2,v3))
end
The results:
Elapsed time is 0.357796 seconds. %# func1
Elapsed time is 0.427568 seconds. %# func2
Elapsed time is 0.537971 seconds. %# func3
So you can see the loop-based solution is actually the fastest..