Speedup constrained shuffling. GPU (Tesla K40m), CPU parallel computations in MATLAB - matlab

Question

I have 100 lamps. They are blinking. I observe them during some time. For each lamp i calculate mean, std and autocorrelation of intervals between blinking.
Now I should resample observed data and keep permutations, where all parameters (mean, std, autocorrelation) are inside some range. Code which I have works good. But it takes to long time (week) for each round of experiment. I do it on computing server with 12 cores and 2 Tesla K40m GPUs (details are in the end).
My code:
close all
clear all
clc
% open parpool skip error if it was opened
try parpool(24); end
% Sample input. It is faked, just for demo.
% Number of "lamps" and number of "blinks" are similar to real.
NLamps = 10^2;
NBlinks = 2*10^2;
Events = cumsum([randg(9,NLamps,NBlinks)],2); % each row - different "lamp"
DurationOfExperiment=Events(:,end).*1.01;
%% MAIN
% Define parameters
nLags=2; % I need to keep autocorrelation with lags 1-2
alpha=[0.01,0.1]; % range of allowed relative deviation from observed
% parameters should be > 0 to avoid generating original
% sequence
nPermutations=10^2; % In original code 10^5
% Processing of experimental data
DurationOfExperiment=num2cell(DurationOfExperiment);
Events=num2cell(Events,2);
Intervals=cellfun(#(x) diff(x),Events,'UniformOutput',false);
observedParams=cellfun(#(x) fGetParameters(x,nLags),Intervals,'UniformOutput',false);
observedParams=cell2mat(observedParams);
% Constrained shuffling. EXPENSIVE PART!!!
while true
parfor iPermutation=1:nPermutations
% Shuffle intervals
shuffledIntervals=cellfun(#(x,y) fPermute(x,y),Intervals,DurationOfExperiment,'UniformOutput',false);
% get parameters of shuffled intervals
shuffledParameters=cellfun(#(x) fGetParameters(x,nLags),shuffledIntervals,'UniformOutput',false);
shuffledParameters=cell2mat(shuffledParameters);
% get relative deviation
delta=abs((shuffledParameters-observedParams)./observedParams);
% find shuffled Lamps, which are inside alpha range
MaximumDeviation=max(delta,[] ,2);
MinimumDeviation=min(delta,[] ,2);
LampID=find(and(MaximumDeviation<alpha(2),MinimumDeviation>alpha(1)));
% if shuffling of ANY lamp was succesful, save these Intervals
if ~isempty(LampID)
shuffledIntervals=shuffledIntervals(LampID);
shuffledParameters=shuffledParameters(LampID,:);
parsave( LampID,shuffledIntervals,shuffledParameters);
'DONE'
end
end
end
%% FUNCTIONS
function [ params ] = fGetParameters( intervals,nLags )
% Calculate [mean,std,autocorrelations with lags from 1 to nLags
R=nan(1,nLags);
for lag=1:nLags
R(lag) = corr(intervals(1:end-lag)',intervals((1+lag):end)','type','Spearman');
end
params = [mean(intervals),std(intervals),R];
end
%--------------------------------------------------------------------------
function [ Intervals ] = fPermute( Intervals,Duration )
% Create long shuffled time-series
Time=cumsum([0,datasample(Intervals,numel(Intervals)*3)]);
% Keep the same duration
Time(Time>Duration)=[];
% Calculate Intervals
Intervals=diff(Time);
end
%--------------------------------------------------------------------------
function parsave( LampID,Intervals,params)
save([num2str(randi(10^9)),'.mat'],'LampID','Intervals','params')
end
Server specs:
>>gpuDevice()
CUDADevice with properties:
Name: 'Tesla K40m'
Index: 1
ComputeCapability: '3.5'
SupportsDouble: 1
DriverVersion: 8
ToolkitVersion: 8
MaxThreadsPerBlock: 1024
MaxShmemPerBlock: 49152
MaxThreadBlockSize: [1024 1024 64]
MaxGridSize: [2.1475e+09 65535 65535]
SIMDWidth: 32
TotalMemory: 1.1979e+10
AvailableMemory: 1.1846e+10
MultiprocessorCount: 15
ClockRateKHz: 745000
ComputeMode: 'Default'
GPUOverlapsTransfers: 1
KernelExecutionTimeout: 0
CanMapHostMemory: 1
DeviceSupported: 1
DeviceSelected: 1
>> feature('numcores')
MATLAB detected: 12 physical cores.
MATLAB detected: 24 logical cores.
MATLAB was assigned: 24 logical cores by the OS.
MATLAB is using: 12 logical cores.
MATLAB is not using all logical cores because hyper-threading is enabled.
>> system('for /f "tokens=2 delims==" %A in (''wmic cpu get name /value'') do #(echo %A)')
Intel(R) Xeon(R) CPU E5-2630 v2 # 2.60GHz
Intel(R) Xeon(R) CPU E5-2630 v2 # 2.60GHz
>> memory
Maximum possible array: 496890 MB (5.210e+11 bytes) *
Memory available for all arrays: 496890 MB (5.210e+11 bytes) *
Memory used by MATLAB: 18534 MB (1.943e+10 bytes)
Physical Memory (RAM): 262109 MB (2.748e+11 bytes)
* Limited by System Memory (physical + swap file) available.
Question:
Is it possible to speedup my calculation? I think about CPU+GPU computing, but I could not understand how to do it (I have no experience with gpuArrays). Moreover, I am not sure it is a good idea. Sometimes some algorithm optimisation gives bigger profit, then parallel computing.
P.S.
Saving step is not the bottleneck- it happens once in 10-30 mins in best case.

Answer 1

GPU-based processing is only available on some functions and with the right cards (if I remember correctly).
For the GPU part of your question MATLAB has a list of available functions - that you can run on GPU - the most expensive part of your code is the function corr which unfortunately isn't on the list.
If the profiler isn't highlighting bottlenecks - something weird is going on... So I ran some tests on your code above:
nPermutations = 10^0 iteration takes ~0.13 seconds
nPermutations = 10^1 iteration takes ~1.3 seconds
nPermutations = 10^3 iteration takes ~130 seconds
nPermutations = 10^4 probably takes ~1300 seconds
nPermutations = 10^5 probably takes ~13000 seconds
Which is a lot less than a week...
Did I mention that I put a break out of your while statement - as I couldn't see in your code where you ever "break" out of the while loop - I hope for your sake that this isn't the reason that your function would run forever....
while true
parfor iPermutation=1:nPermutations
% Shuffle intervals
shuffledIntervals=cellfun(#(x,y) fPermute(x,y),Intervals,DurationOfExperiment,'UniformOutput',false);
% get parameters of shuffled intervals
shuffledParameters=cellfun(#(x) fGetParameters(x,nLags),shuffledIntervals,'UniformOutput',false);
shuffledParameters=cell2mat(shuffledParameters);
% get relative deviation
delta=abs((shuffledParameters-observedParams)./observedParams);
% find shuffled Lamps, which are inside alpha range
MaximumDeviation=max(delta,[] ,2);
MinimumDeviation=min(delta,[] ,2);
LampID=find(and(MaximumDeviation<alpha(2),MinimumDeviation>alpha(1)));
% if shuffling of ANY lamp was succesful, save these Intervals
if ~isempty(LampID)
shuffledIntervals=shuffledIntervals(LampID);
shuffledParameters=shuffledParameters(LampID,:);
parsave( LampID,shuffledIntervals,shuffledParameters);
'DONE'
end
end
break % You need to break out of the loop at some point
% otherwise it would run forever....
end