I have a program which I copied from a textbook, and which times the difference in program execution runtime when calculating the same thing with uninitialized, initialized array and vectors.
However, although the program runs somewhat as expected, if running several times every once in a while it will give out a crazy result. See below for program and an example of crazy result.
clear all; clc;
% Purpose:
% This program calculates the time required to calculate the squares of
% all integers from 1 to 10000 in three different ways:
% 1. using a for loop with an uninitialized output array
% 2. Using a for loop with a pre-allocated output array
% 3. Using vectors
% PERFORM CALCULATION WITH AN UNINITIALIZED ARRAY
% (done only once because it is so slow)
maxcount = 1;
tic;
for jj = 1:maxcount
clear square
for ii = 1:10000
square(ii) = ii^2;
end
end
average1 = (toc)/maxcount;
% PERFORM CALCULATION WITH A PRE-ALLOCATED ARRAY
% (averaged over 10 loops)
maxcount = 10;
tic;
for jj = 1:maxcount
clear square
square = zeros(1,10000);
for ii = 1:10000
square(ii) = ii^2;
end
end
average2 = (toc)/maxcount;
% PERFORM CALCULATION WITH VECTORS
% (averaged over 100 executions)
maxcount = 100;
tic;
for jj = 1:maxcount
clear square
ii = 1:10000;
square = ii.^2;
end
average3 = (toc)/maxcount;
% Display results
fprintf('Loop / uninitialized array = %8.6f\n', average1)
fprintf('Loop / initialized array = %8.6f\n', average2)
fprintf('Vectorized = %8.6f\n', average3)
Result - normal:
Loop / uninitialized array = 0.195286
Loop / initialized array = 0.000339
Vectorized = 0.000079
Result - crazy:
Loop / uninitialized array = 0.203350
Loop / initialized array = 973258065.680879
Vectorized = 0.000102
Why is this happening ?
(sometimes the crazy number is on vectorized, sometimes on loop initialized)
Where did MATLAB "find" that number?
That is indeed crazy. Don't know what could cause it, and was unable to reproduce on my own Matlab R2010a copy over several runs, invoked by name or via F5.
Here's an idea for debugging it.
When using tic/toc inside a script or function, use the "tstart = tic" form that captures the output. This makes it safe to use nested tic/toc calls (e.g. inside called functions), and lets you hold on to multiple start and elapsed times and examine them programmatically.
t0 = tic;
% ... do some work ...
te = toc(t0); % "te" for "time elapsed"
You can use different "t0_label" suffixes for each of the tic and toc returns, or store them in a vector, so you preserve them until the end of your script.
t0_uninit = tic;
% ... do the uninitialized-array test ...
te_uninit = toc(t0_uninit);
t0_prealloc = tic;
% ... test the preallocated array ...
te_prealloc = toc(t0_prealloc);
Have the script break in to the debugger when it finds one of the large values.
if any([te_uninit te_prealloc te_vector] > 5)
keyboard
end
Then you can examine the workspace and the return values from tic, which might provide some clues.
EDIT: You could also try testing tic() on its own to see if there's something odd with your system clock, or whatever tic/toc is calling. tic()'s return value looks like a native timestamp of some sort. Try calling it many times in a row and comparing the subsequent values. If it ever goes backwards, that would be surprising.
function test_tic
t0 = tic;
for i = 1:1000000
t1 = tic;
if t1 <= t0
fprintf('tic went backwards: %s to %s\n', num2str(t0), num2str(t1));
end
t0 = t1;
end
On Matlab R2010b (prerelease), which has int64 math, you can reproduce a similar ridiculous toc result by jiggering the reference tic value to be "in the future". Looks like an int rollover effect, as suggested by gary comtois.
>> t0 = tic; toc(t0+999999)
Elapsed time is 6148914691.236258 seconds.
This suggests that if there were some jitter in the timer that toc were using, you might get rollover if it occurs while you're timing very short operations. (I assume toc() internally does something like tic() to get a value to compare the input to.) Increasing the number of iterations could make the effect go away because a small amount of clock jitter would be less significant as part of longer tic/toc periods. Would also explain why you don't see this in your non-preallocated test, which takes longer.
UPDATE: I was able to reproduce this behavior. I was working on some unrelated code and found that on one particular desktop with a CPU model we haven't used before, a Core 2 Q8400 2.66GHz quad core, tic was giving inaccurate results. Looks like a system-dependent bug in tic/toc.
On this particular machine, tic/toc will regularly report bizarrely high values like yours.
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
elapsed: 6934787980.471930500
elapsed: 6934787980.471931500
elapsed: 6934787980.471899000
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
elapsed: 6934787980.471928600
elapsed: 6934787980.471913300
>>
It goes past that. On this machine, tic/toc will regularly under-report elapsed time for operations, especially for low CPU usage tasks.
>> t0 = tic; c0 = clock; pause(4); toc(t0); fprintf('Wall time is %.6f seconds.\n', etime(clock, c0));
Elapsed time is 0.183467 seconds.
Wall time is 4.000000 seconds.
So it looks like this is a bug in tic/toc that is related to particular CPU models (or something else specific to the system configuration). I've reported the bug to MathWorks.
This means that tic/toc is probably giving you inaccurate results even when it doesn't produce those insanely large numbers. As a workaround, on this machine, use etime() instead, and time only longer chunks of work to compensate for etime's lower resolution. You could wrap it in your own tick/tock functions that use the for i=1:50000 test to detect when tic is broken on the current machine, use tic/toc normally, and have them warn and fall back to using etime() on broken-tic systems.
UPDATE 2012-03-28: I've seen this in the wild for a while now, and it's highly likely due to an interaction with the CPU's high resolution performance timer and speed scaling, and (on Windows) QueryPerformanceCounter, as described here: http://support.microsoft.com/kb/895980/. It is not a bug in tic/toc, the issue is in the OS features that tic/toc is calling. Setting a boot parameter can work around it.
Here's my theory about what might be happening, based on these two pieces of data I found:
There is a function maxNumCompThreads which controls the maximum number of computational threads used by MATLAB to perform tasks. Quoting the documentation:
By default, MATLAB makes use of the
multithreading capabilities of the
computer on which it is running.
Which leads me to think that perhaps multiple copies of your script are running at the same time.
This newsgroup thread discusses a bug in an older version of MATLAB (R14) "in the way that MATLAB accelerates M-code with global structure variables", which it appears the TIC/TOC functions may use. The solution there was to disable the accelerator using the undocumented FEATURE function:
feature accel off
Putting these two things together, I'm wondering if the multiple versions of your script that are running in the workspace may be simultaneously resetting global variables used by the TIC/TOC functions and screwing one another up. Maybe this isn't a problem when converting your script to a function as Amro did since this would separate the workspaces that the two programs are running in (i.e. they wouldn't both be running in the main workspace).
This could also explain the exceedingly large numbers you get. As gary and Andrew have pointed out, these numbers appear to be due to an integer roll-over effect (i.e. an integer overflow) whereby the starting time (from TIC) is larger than the ending time (from TOC). This would result in a huge number that is still positive because TIC/TOC are internally using unsigned 64-bit integers as time measures. Consider the following possible scenario with two scripts running at the same time on different threads:
The first thread calls TIC, initializing a global variable to a starting time measure (i.e. the current time).
The first thread then calls TOC, and the immediate action the TOC function is likely to make is to get the current time measure.
The second thread calls TIC, resetting the global starting time measure to the current time, which is later than the time just measured by the TOC function for the first thread.
The TOC function for the first thread accesses the global starting time measure to get the difference between it and the measure it previously took. This difference would result in a negative number, except that the time measures are unsigned integers. This results in integer overflow, giving a huge positive number for the time difference.
So, how might you avoid this problem? Changing your scripts to functions like Amro did is probably the best choice, as that seems to circumvent the problem and keeps the workspace from becoming cluttered. An alternative work-around you could try is to set the maximum number of computational threads to one:
maxNumCompThreads(1);
This should keep multiple copies of your script from running at the same time in the main workspace.
There are at least two possible error sources. Can you try to differentiate between 'tic/toc' and 'fprintf' by just looking at the computed values without formatting them.
I don't understand the braces around 'toc' but they shouldn't do any harm.
Here is a hypothesis which is testable. Matlab's tic()/toc() have to be using some high-resolution timer. On Windows, because their return value looks like clock cycles, I think they're using the Win32 QueryPerformanceCounter() call, or maybe something else hitting the CPU's RDTSC time stamp counter. These apparently have glitches on some multiprocessor systems, mentioned in the linked articles. Perhaps your machine is one of those, getting different results if the Matlab process is moved from core to core by the process scheduler.
http://msdn.microsoft.com/en-us/library/ms644904(VS.85).aspx
http://www.virtualdub.org/blog/pivot/entry.php?id=106
This would be hardware and system configuration dependent, which would explain why other posters haven't been able to reproduce it.
Try using Windows Task Manager to set the affinity on your Matlab.exe process to a single CPU. (On the Processes tab, right-click MATLAB.exe, "Set affinity...", un-check all but CPU 0.) If the crazy timing goes away while affinity is set, looks like you found the cause.
Regardless, the workaround looks like to just increase maxcount so you're timing longer pieces of work, and the noise you're apparently getting in tic()/toc() is small compared to the measured value. (You don't want to have to muck around with CPU affinity; Matlab is supposed to be easy to run.) If there's a problem in there that's causing int overflow, the other small positive numbers are a bit suspect too. Besides, hi-res timing in a high level language like Matlab is a bit problematic. Timing workloads down to a couple hundred microseconds subjects them to noise from other transient conditions in your machine's state.
Related
I wrote a MATLAB code for finding seismic signal (ex. P wave) from SAC(seismic) file (which is read via another code). This algorithm is called STA/LTA trigger algorithm (actually not that important for my question)
Important thing is that actually this code works well, but since my seismic file is too big (1GB, which is for two months), it takes almost 40 minutes for executing to see the result. Thus, I feel the need to optimize the code.
I heard that replacing loops with advanced functions would help, but since I am a novice in MATLAB, I cannot get an idea about how to do it, since the purpose of code is scan through the every time series.
Also, I heard that preallocation might help, but I have mere idea about how to actually do this.
Since this code is about seismology, it might be hard to understand, but my notes at the top might help. I hope I can get useful advice here.
Following is my code.
function[pstime]=classic_LR(tseries,ltw,stw,thresh,dt)
% This is the code for "Classic LR" algorithm
% 'ns' is the number of measurement in STW-used to calculate STA
% 'nl' is the number of measurement in LTW-used to calculate LTA
% 'dt' is the time gap between measurements i.e. 0.008s for HHZ and 0.02s for BHZ
% 'ltw' and 'stw' are long and short time windows respectively
% 'lta' and 'sta' are long and short time windows average respectively
% 'sra' is the ratio between 'sta' and 'lta' which will be each component
% for a vector containing the ratio for each measurement point 'i'
% Index 'i' denotes each measurement point and this will be converted to actual time
nl=fix(ltw/dt);
ns=fix(stw/dt);
nt=length(tseries);
aseries=abs(detrend(tseries));
sra=zeros(1,nt);
for i=1:nt-ns
if i>nl
lta=mean(aseries(i-nl:i));
sta=mean(aseries(i:i+ns));
sra(i)=sta/lta;
else
sra(i)=0;
end
end
[k]=find(sra>thresh);
if ~isempty(k)
pstime=k*dt;
else
pstime=0;
end
return;
If you have MATLAB 2016a or later, you can use movmean instead of your loop (this means you also don't need to preallocate anything):
lta = movmean(aseries(1:nt-ns),nl+1,'Endpoints','discard');
sta = movmean(aseries(nl+1:end),ns+1,'Endpoints','discard');
sra = sta./lta;
The only difference here is that you will get sra with no leading and trailing zeros. This is most likely to be the fastest way. If for instance, aseries is 'only' 8 MB than this method takes less than 0.02 second while the original method takes almost 6 seconds!
However, even if you don't have Matlab 2016a, considering your loop, you can still do the following:
Remove the else statement - sta(i) is already zero from the preallocating.
Start the loop from nl+1, instead of checking when i is greater than nl.
So your new loop will be:
for i=nl+1:nt-ns
lta = mean(aseries(i-nl:i));
sta = mean(aseries(i:i+ns));
sra(i)=sta/lta;
end
But it won't be so faster.
I run a Matlab code with an iteration loop, and during each iteration it sample random numbers and uses the function intlinprog. My issue is that, due to the large amount of data I provide to the intlinprog function and to the stochastic values I assign to part of its variables, some of the iterations take a really long time.
My code is more or less like this:
rounds = 1E3;
Total_PF = zeros(rounds,4893);
for i=1:rounds
i
cT = zeros (4894,1);
cT(4894,1) = 1;
xint = linspace(1,4893,4893);
xint = xint';
AT = rand(4,4894);
beT = ones(4,1);
lb = zeros(4894,1);
ub = ones (4894,1);
ub(4894,1) = Inf;
[x] = intlinprog(cT,xint,AT,beT,[],[],lb,ub);
Total_PF(i,:)= (x(1:length(x)-1)');
end
Now in the minimal working example I provided, all the iterations are quite fast, but in my real code, sometimes intlinprog takes really long time ( I mean hours) to do a single iteration.
Therefore, I was wondering: is there a way to break the intlinprog while the intlinprog line is being executed? I was thinking that it may be done by modifying the matlab function but first of all I do not know if I am allowed to do it, secondly I am afraid that may be very dangerous.
This is very difficult to do effectively.
You could try using a timer object to watch the value. However, since you are using inherent Matlab functions and not executing external functions, you could set a time limit value and utilize tic and toc in a while loop while you execute the intlinprog and checking the value of toc against your time limit and break your code if toc exceeds the limit.
(correctly and instructively asnwered, see below)
I'm beginning to do experiments with matlab and gpu (nvidia gtx660).
Now, I wrote this simple monte carlo algorithm to calculate PI. The following is the CPU version:
function pig = mc1vecnocuda(n)
countr=0;
A=rand(n,2);
for i=1:n
if norm(A(i,:))<1
countr=countr+1;
end
end
pig=(countr/n)*4;
end
This takes very little time to be executed on CPU with 100000 points "thrown" into the unit circle:
>> tic; mc1vecnocuda(100000);toc;
Elapsed time is 0.092473 seconds.
See, instead, what happens with gpu-ized version of the algorithm:
function pig = mc1veccuda(n)
countr=0;
gpucountr=gpuArray(countr);
A=gpuArray.rand(n,2);
parfor (i=1:n,1024)
if norm(A(i,:))<1
gpucountr=gpucountr+1;
end
end
pig=(gpucountr/n)*4;
end
Now, this takes a LONG time to be executed:
>> tic; mc1veccuda(100000);toc;
Elapsed time is 21.137954 seconds.
I don't understand why. I used parfor loop with 1024 workers, because querying my nvidia card with gpuDevice, 1024 is the maximum number of simultaneous threads allowed on the gtx660.
Can someone help me? Thanks.
Edit: this is the updated version that avoids IF:
function pig = mc2veccuda(n)
countr=0;
gpucountr=gpuArray(countr);
A=gpuArray.rand(n,2);
parfor (i=1:n,1024)
gpucountr = gpucountr+nnz(norm(A(i,:))<1);
end
pig=(gpucountr/n)*4;
end
And this is the code written following Bichoy's guidelines (the
right code to achieve result):
function pig = mc3veccuda(n)
countr=0;
gpucountr=gpuArray(countr);
A=gpuArray.rand(n,2);
Asq = A.^2;
Asqsum_big_column = Asq(:,1)+Asq(:,2);
Anorms=Asqsum_big_column.^(1/2);
gpucountr=gpucountr+nnz(Anorms<1);
pig=(gpucountr/n)*4;
end
Please note execution time with n=10 millions:
>> tic; mc3veccuda(10000000); toc;
Elapsed time is 0.131348 seconds.
>> tic; mc1vecnocuda(10000000); toc;
Elapsed time is 8.108907 seconds.
I didn't test my original cuda version (for/parfor), for its execution would require hours with n=10000000.
Great Bichoy! ;)
I guess the problem is with parfor!
parfor is supposed to run on MATLAB workers, that is your host not the GPU!
I guess what is actually happening is that you are starting 1024 threads on your host (not on your GPU) and each of them is trying to call the GPU. This result in the tremendous time your code is taking.
Try to re-write your code to use matrix and array operations, not for-loops! This will show some speed-up. Also, remember that you should have much more calculations to do in the GPU otherwise, memory transfer will just dominate your code.
Code:
This is the final code after including all corrections and suggestions from several people:
function pig = mc2veccuda(n)
A=gpuArray.rand(n,2); % An nx2 random matrix
Asq = A.^2; % Get the square value of each element
Anormsq = Asq(:,1)+Asq(:,2); % Get the norm squared of each point
gpucountr = nnz(Anorm<1); % Check the number of elements < 1
pig=(gpucountr/n)*4;
Many reasons like:
Movement of data between host & device
Computation within each loop is very small
Call to rand on GPU may not be parallel
if condition within the loop can cause divergence
Accumulation to a common variable may run in serial, with overhead
It is difficult to profile Matlab+CUDA code. You should probably try in native C++/CUDA and use parallel Nsight to find the bottleneck.
As Bichoy said, CUDA code should always be done vectorized. In MATLAB, unless you're writing a CUDA Kernal, the only large speedup that you're getting is that the vectorized operations are called on the GPU which has thousands of (slow) cores. If you don't have large vectors and vectorized code, it won't help.
Another thing that hasn't been mentioned is that for highly parallel architectures like GPUs you want to use different random number generating algorithms than the "standard" ones. So to add to Bichoy's answer, adding the parameter 'Threefry4x64' (64-bit) or 'Philox4x32-10' (32-bit and a lot faster! Super fast!) can lead to large speedups in CUDA code. MATLAB explains this here: http://www.mathworks.com/help/distcomp/examples/generating-random-numbers-on-a-gpu.html
I have written the following code in MATLAB to process large images of the order of 3000x2500 pixels. Currently the operation takes more than half hour to complete. Is there any scope to improve the code to consume less time? I heard parallel processing can make things faster, but I have no idea on how to implement it. How do I do it, given the following code?
function dirvar(subfn)
[fn,pn] = uigetfile({'*.TIF; *.tiff; *.tif; *.TIFF; *.jpg; *.bmp; *.JPG; *.png'}, ...
'Select an image', '~/');
I = double(imread(fullfile(pn,fn)));
ld = input('Enter the lag distance = '); % prompt for lag distance
fh = eval(['#' subfn]); % Function handles
I2 = uint8(nlfilter(I, [7 7], fh));
imshow(I2); % Texture Layer Image
imwrite(I2,'result_mat.tif');
% Zero Degree Variogram
function [gamma] = ewvar(I)
c = (size(I)+1)/2; % Finds the central pixel of moving window
EW = I(c(1),c(2):end); % Determines the values from central pixel to margin of window
h = length(EW) - ld; % Number of lags
gamma = 1/(2 * h) * sum((EW(1:ld:end-1) - EW(2:ld:end)).^2);
end
The input lag distance is usually 1.
You really need to use the profiler to get some improvements out of it. My first guess (as I haven't run the profiler, which you should as suggested already), would be to use as little length operations as possible. Since you are processing every image with a [7 7] window, you can precalculate some parts,
such that you won't repeat these actions
function dirvar(subfn)
[fn,pn] = uigetfile({'*.TIF; *.tiff; *.tif; *.TIFF; *.jpg; *.bmp; *.JPG; *.png'}, ...
'Select an image', '~/');
I = double(imread(fullfile(pn,fn)));
ld = input('Enter the lag distance = '); % prompt for lag distance
fh = eval(['#' subfn]); % Function handles
%% precalculations
wind = [7 7];
center = (wind+1)/2; % Finds the central pixel of moving window
EWlength = (wind(2)+1)/2;
h = EWlength - ld; % Number of lags
%% calculations
I2 = nlfilter(I, wind, fh);
imshow(I2); % Texture Layer Image
imwrite(I2,'result_mat.tif');
% Zero Degree Variogram
function [gamma] = ewvar(I)
EW = I(center(1),center(2):end); % Determines the values from central pixel to margin of window
gamma = 1/(2 * h) * sum((EW(1:ld:end-1) - EW(2:ld:end)).^2);
end
end
Note that by doing so, you trade performance for clearness of your code and coupling (between the function dirvar and the nested function ewvar). However, since I haven't profiled your code (you should do that yourself using your own inputs), you can find what line of your code consumes the most time.
For batch processing, I would also recommend to leave out any input, imshow, imwrite and uigetfile. Those are commands that you typically call from a more high-level function/script and that will force you to enter these inputs even when you want them to stay the same. So instead of that code, make each of the variables they produce (/process) a parameter (/return value) for your function. That way, you could leave MATLAB running during the weekend to process everything (without having manually enter to all those values), even if you are unable to speed up the code.
A few general purpose tricks:
1 - use the MATLAB profiler to determine all the computational bottlenecks
2 - parallel processing can make things faster and there are a lot of tools that you can use, but it depends on how your entire code is set up and whether the code is optimized for it. By far the easiest trick to learn is parfor, where you can replace the top level for loop by parfor. This does mean you must open the MATLAB pool with matlabpool open.
3 - If you have a rather recent Nvidia GPU as well as MATLAB 2011, you can also write some CUDA code.
All in all 30 mins to me is peanuts, so don't fret it too much.
First of all, I strongly suggest you follow the advice by #Egon: Write a separate function that collects a list of files (the excellent UIPICKFILES from the FEX is your friend here), and then runs your filtering code in a loop for each image. Note that you should definitely keep the call to imwrite in your filtering code: In case the analysis crashes at image 48 (e.g. due to power failure), you don't want to lose all the previous work.
Running thusly in batch mode has two big advantages: (1) you can start running your code and go home for the week-end, and (2) you can easily parallelize this outside loop using PARFOR. However, with only a dual-core machine, it is unlikely that you get any significant improvements from parallelization - your OS also wants to run stuff at times, and the overhead of parallelization might be more than the gain from running two workers. Also, 2.5GB of RAM is seriously limiting.
As to your specific code: in my experience using IM2COL is often faster than NLFILTER. im2col creates a nElementsInMask-by-nMasks array out of your image, so that you can apply the filtering in one single operation. With a 7x7 window, the output of im2col will be 3000*2500*49 bytes, which is close to 400MB. Thus, it should just work. All that you need to do is rewrite ewvar so that it works on a 49x1 array of pixels that make up the pixels your mask, which will require some index juggling, if I understand your code correctly.
I'm going to write a program in MATLAB that takes a function, sets the value D from 10 to 100 (the for loop), integrates the function with Simpson's rule (the while loop) and then displays it. Now, this works fine for the first 7-8 values, but then it takes longer time and eventually I run out of memory, and I don't understand the reason for this. This is the code so far:
global D;
s=200;
tolerance = 9*10^(-5);
for D=10:1:100
r = Simpson(#f,0,D,s);
error = 1;
while(error>tolerance)
s = 2*s;
error = (1/15)*(Simpson(#f,0,D,s)-r);
r = Simpson(#f,0,D,s);
end
clear error;
disp(r)
end
mtrw's comment probably already answers the question in part: s should be reinitialized inside the for loop. The posted code results in s increasing irreversibly every time the error was too large, so for larger values of D the largest s so far will be used.
Additionally, since the code re-evaluates the entire integration instead of reusing the previous integration from [0, D-1] you waste lots of resources unless you want to explicitly show the error tolerance of your Simpson function - s will have to increase a lot for large D to maintain the same low error (since you integrate over a larger range you have to sum up more points).
Finally, your implementation of Simpson could of course do funny stuff as well, which no one can tell without seeing it...