Efficient method for finding elements in MATLAB matrix

Question

I would like to know how can the bottleneck be treated in the given piece of code.

%% Points is an Nx3 matrix having the coordinates of N points where N ~ 10^6
Z = points(:,3)
listZ = (Z >= a & Z < b); % Bottleneck
np = sum(listZ); % For later usage
slice = points(listZ,:);

Currently for N ~ 10^6, np ~ 1000 and number of calls to this part of code = 1000, the bottleneck statement is taking around 10 seconds in total, which is a big chunk of time compared to the rest of my code.

Some more screenshots of a sample code for only the indexing statement as requested by @EitanT

Answer 1

If the equality on one side is not important you can reformulate it to a one-sided comparison and it gets one order of magnitude faster:

Z = rand(1e6,3);
a=0.5; b=0.6;
c=(a+b)/2;
d=abs(a-b)/2;
tic
for k=1:100,
    listZ1 = (Z >= a & Z < b); % Bottleneck
end
toc

tic
for k=1:100,
    listZ2 = (abs(Z-c)<d);
end
toc

isequal(listZ1, listZ2)

returns

Elapsed time is 5.567460 seconds.
Elapsed time is 0.625646 seconds.

ans =

     1

Answer 2

Assuming the worst case:

• element-wise & is not short-circuited internally
• the comparisons are single-threaded

You're doing 2*1e6*1e3 = 2e9 comparisons in ~10 seconds. That's ~200 million comparisons per second (~200 MFLOPS).

Considering you can do some 1.7 GFLops on a single core, this indeed seems rather low.

Are you running Windows 7? If so, have you checked your power settings? You are on a mobile processor, so I expect that by default, there will be some low-power consumption scheme in effect. This allows windows to scale down the processing speed, so...check that.

Other than that....I really have no clue.

Answer 3

Try doing something like this:

for i = 1:1000
    x = (a >= 0.5);
    x = (x < 0.6);
end

I found it to be faster than:

for i = 1:1000
    x = (a >= 0.5 & a < 0.6);
end

by about 4 seconds:

Elapsed time is 0.985001 seconds. (first one)
Elapsed time is 4.888243 seconds. (second one)

I think the reason for your slowing is the element wise & operation.