I am optimizing a rather messy likelihood function in Matlab, where I need to run about 1,000 separate runs of the optimization algorithm (fmincon) at different initial points, where there are something like 32 free parameters.
Unfortunately I can not both parallelize the 1,000 runs of the optimization algorithm, and the computation of the finite difference gradient simultaneously. I must choose one.
Does anyone know if its more efficient to parallelize the outer loop and have each optimization run on its own core, or the calculation of the finite-difference gradient computation?
Thanks!
This is impossible to answer exactly without knowing anything about your code and or hardware.
If you have more than 32 cores, then some of them will have nothing to do during parallel gradient computation. In this case, running the 1000 simulations in parallel might be faster.
On the other hand, computing the gradients in parallel might enable your CPU(s) to use their caches more efficiently, in that there will be fewer cache misses. You may have a look at Why does the order of the loops affect performance when iterating over a 2D array? or What is “cache-friendly” code?.
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I'm writing simulation with MATLAB where I used CUDA acceleration.
Suppose we have vector x and y, matrix A and scalar variables dt,dx,a,b,c.
What I found out was that by putting x,y,A into gpuArray() before running the iteration and built-in functions, the iteration could be accelerated significantly.
However, when I tried to put variables like dt,dx,a,b,c into the gpuArray(), the program would be significantly slowed down, by a factor of over 30%. (Time increased from 7s to 11s).
Why it was not a good idea to put all the variables into the gpuArray()?
(Short comment, those scalars were multiplied together with x,y,A, and was never used during the iteration alone.)
GPU hardware is optimised for working on relatively large amounts of data. You only really see the benefit of GPU computing when you can feed the many processing cores lots of data to keep them busy. Typically this means you need operations working on thousands or millions of elements.
The overheads of launching operations on the GPU dwarf the computation time when you're dealing with scalar quantities, so it is no surprise that they are slower than on the CPU. (This is not peculiar to MATLAB & gpuArray).
I have three big 3D arrays of the same size [41*141*12403], named in the Matlab code below alpha, beta and ni. From them I need to calculate another 3D array with the same size, which is obtained elementwise from the original matrices through a calculation that combines an infinite sum and definite integral calculations, using the value of each element. It therefore seems inevitible to have to use several nested loops to make this calculation. The code is already running now for several hours(!) and it is still in the first iteration of the outer loop (which needs to be performed 41 times!! According to my calculation, in this way the program will have to run more than two years!!!). I don't know how to optimize the code. Please help me !!
the code I use:
z_len=size(KELDYSH_PARAM_r_z_t,1); % 41 rows
r_len=size(KELDYSH_PARAM_r_z_t,2); % 141 columns
t_len=size(KELDYSH_PARAM_r_z_t,3); % 12403 slices
sumRes=zeros(z_len,r_len,t_len);
for z_ind=1:z_len
z_ind % in order to track the advancement of the calculation
for r_ind=1:r_len
for t_ind=1:t_len
sumCurrent=0;
sumPrevious=inf;
s=0;
while abs(sumPrevious-sumCurrent)>1e-6
kapa=kapa_0+s; %some scalar
x_of_w=(beta(z_ind,r_ind,t_ind).*(kapa-ni...
(z_ind,r_ind,t_ind))).^0.5;
sumPrevious=sumCurrent;
sumCurrent=sumCurrent+exp(-alpha(z_ind,r_ind,t_ind).* ...
(kapa-ni(z_ind,r_ind,t_ind))).*(x_of_w.^(2*abs(m)+1)/2).* ...
w_m_integral(x_of_w,m);
s=s+1;
end
sumRes(z_ind,r_ind,t_ind)=sumCurrent;
end
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function res=w_m_integral(x_of_w,m)
res=quad(#integrandFun,0,1,1e-6);
function y=integrandFun(t)
y=exp(-x_of_w^2*t).*t.^(abs(m))./((1-t).^0.5);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Option 1 - more vectorising
It's a pretty complex model you're working with and not all the terms are explained, but some parts can still be further vectorised. Your alpha, beta and ni matrices are presumably static and precomputed? Your s value is a scalar and kapa could be either, so you can probably precompute the x_of_w matrix all in one go too. This would give you a very slight speedup all on its own, though you'd be spending memory to get it - 71 million points is doable these days but will call for an awful lot of hardware. Doing it once for each of your 41 rows would reduce the burden neatly.
That leaves the integral itself. The quad function doesn't accept vector inputs - it would be a nightmare wouldn't it? - and neither does integral, which Mathworks are recommending you use instead. But if your integration limits are the same in each case then why not do the integral the old-fashioned way? Compute a matrix for the value of the integrand at 1, compute another matrix for the value of the integrand at 0 and then take the difference.
Then you can write a single loop that computes the integral for the whole input space then tests the convergence for all the matrix elements. Make a mask that notes the ones that have not converged and recalculate those with the increased s. Repeat until all have converged (or you hit a threshold for iterations).
Option 2 - parallelise it
It used to be the case that matlab was much faster with vectorised operations than loops. I can't find a source for it now but I think I've read that it's become a lot faster recently with for loops too, so depending on the resources you have available you might get better results by parallelising the code you currently have. That's going to need a bit of refactoring too - the big problems are overheads while copying in data to the workers (which you can fix by chopping the inputs up into chunks and just feeding the relevant one in) and the parfor loop not allowing you to use certain variables, usually ones which cover the whole space. Again chopping them up helps.
But if you have a 2 year runtime you will need a factor of at least 100 I'm guessing, so that means a cluster! If you're at a university or somewhere where you might be able to get a few days on a 500-core cluster then go for that...
If you can write the integral in a closed form then it might be amenable to GPU computation. Those things can do certain classes of computation very fast but you have to be able to parallelise the job and reduce the actual computation to something basic comprised mainly of addition and multiplication. The CUDA libraries have done a lot of the legwork and matlab has an interface to them so have a read about those.
Option 3 - reduce the scope
Finally, if neither of the above two results in sufficient speedups, then you may have to reduce the scope of your calculation. Trim the input space as much as you can and perhaps accept a lower convergence threshold. If you know how many iterations you tend to need inside the innermost while loop (the one with the s counter in it) then it might turn out that reducing the convergence criterion reduces the number of iterations you need, which could speed it up. The profiler can help see where you're spending your time.
The bottom line though is that 71 million points are going to take some time to compute. You can optimise the computation only so far, the odds are that for a problem of this size you will have to throw hardware at it.
Can we improve performance by calculating some parts of CPU's parfor or spmd blocks using gpuArray of GPU functions? Is this a rational way to improve performance or there are limitations in this procedure? I read somewhere that we can use this procedure when we have some GPU units. Is this the only way that we can use GPU computing besides CPU parallel loops?
It is possible that using gpuArray within a parfor loop or spmd block can give you a performance benefit, but really it depends on several factors:
How many GPUs you have on your system
What type of GPUs you have (some are better than others at dealing with being "oversubscribed" - i.e. where there are multiple processes using the same GPU)
How many workers you run
How much GPU memory you need for your alogrithm
How well suited the problem is to the GPU in the first place.
So, if you had two high-powered GPUs in your machine and ran two workers in a parallel pool on a problem that could keep a single GPU fully occupied - you'd expect to see good speedup. You might still get decent speedup if you ran 4 workers.
One thing that I would recommend is: if possible, try to avoid transferring gpuArray data from client to workers, as this is slower than usual data transfers (the gpuArray is first gathered to the CPU and then reconstituted on the worker).
If I assume that a problem is a candidate for parallization e.g. matrix multiplication or some other problem and I use an Intel i7 haswell dualcore, is there some way I can compare a parallel execution to a sequential version of the same program or will matlab optimize a program to my architecture (dualcore, quadcore..)? I would like to know the speedup from adding more processors from a good benchmark parallell program.
Unfortunately there is no such thing as a benchmark parallel program. If you measure a speedup for a benchmark algorithm that does not mean that all the algorithms will benefit from parallelization
Since your target architecture has only 2 cores you might be better off avoiding parallelization at all and let Matlab and the operative system to optimize the execution. Anyway, here are the steps I followed.
Determine if your problem is apt for parallelization by calculating the theoretical speedup. Some problems like matrix multiplication or Gauss elimination are well studied. Since I assume your problem is more complicated than that, try to decompose your algorithm into simple blocks and determine, block-wise, the advantages of parallelization.
If you find that several parts of your algorithms could profit from parallelization, study those part separately.
Obtain statistical information of the runtime of your sequential algorithm. That is, run your program X number of times under similar conditions (and similar inputs) and average the running time.
Obtain statistical information of the runtime of your parallel algorithm.
Measure with the profiler. Many people recommends to use function like tic or toc. The profiler will give you a more accurate picture of your running times, as well as detailed information per function. See the documentation for detailed information on how to use the profiler.
Don't make the mistake of not taking into account the time Matlab takes to open the pool of workers (I assume you are working with the Parallel Computing Toolbox). Depending on your number of workers, the pool takes more/less time and in some occasions it could be up to 1 minute (2011b)!
You can try "Run and time" feature on MATLAB.
Or simply put some tic and toc to the first and end of your code, respectively.
Matlab provides a number of timing functions to help you assess the performance of your code: go read the documentation here and select the function that you deem most appropriate in your case! In particular, be aware of the difference between tic toc and the cputime function.
I need to run several independent analyses on the same data set.
Specifically, I need to run bunches of 100 glm (generalized linear models) analyses and was thinking to take advantage of my video card (GTX580).
As I have access to Matlab and the Parallel Computing Toolbox (and I'm not good with C++), I decided to give it a try.
I understand that a single GLM is not ideal for parallel computing, but as I need to run 100-200 in parallel, I thought that using parfor could be a solution.
My problem is that it is not clear to me which approach I should follow. I wrote a gpuArray version of the matlab function glmfit, but using parfor doesn't have any advantage over a standard "for" loop.
Has this anything to do with the matlabpool setting? It is not even clear to me how to set this to "see" the GPU card. By default, it is set to the number of cores in the CPU (4 in my case), if I'm not wrong.
Am I completely wrong on the approach?
Any suggestion would be highly appreciated.
Edit
Thanks. I'm aware of GPUmat and Jacket, and I could start writing in C without too much effort, but I'm testing the GPU computing possibilities for a department where everybody uses Matlab or R. The final goal would be a cluster based on C2050 and the Matlab Distribution Server (or at least this was the first project).
Reading the ADs from Mathworks I was under the impression that parallel computing was possible even without C skills. It is impossible to ask the researchers in my department to learn C, so I'm guessing that GPUmat and Jacket are the better solutions, even if the limitations are quite big and the support to several commonly used routines like glm is non-existent.
How can they be interfaced with a cluster? Do they work with some job distribution system?
I would recommend you try either GPUMat (free) or AccelerEyes Jacket (buy, but has free trial) rather than the Parallel Computing Toolbox. The toolbox doesn't have as much functionality.
To get the most performance, you may want to learn some C (no need for C++) and code in raw CUDA yourself. Many of these high level tools may not be smart enough about how they manage memory transfers (you could lose all your computational benefits from needlessly shuffling data across the PCI-E bus).
Parfor will help you for utilizing multiple GPUs, but not a single GPU. The thing is that a single GPU can do only one thing at a time, so parfor on a single GPU or for on a single GPU will achieve the exact same effect (as you are seeing).
Jacket tends to be more efficient as it can combine multiple operations and run them more efficiently and has more features, but most departments already have parallel computing toolbox and not jacket so that can be an issue. You can try the demo to check.
No experience with gpumat.
The parallel computing toolbox is getting better, what you need is some large matrix operations. GPUs are good at doing the same thing multiple times, so you need to either combine your code somehow into one operation or make each operation big enough. We are talking a need for ~10000 things in parallel at least, although it's not a set of 1e4 matrices but rather a large matrix with at least 1e4 elements.
I do find that with the parallel computing toolbox you still need quite a bit of inline CUDA code to be effective (it's still pretty limited). It does better allow you to inline kernels and transform matlab code into kernels though, something that