Currently i'm trying to implement the time-frequency analysis on the ATI GPU device. Basically, what I need is to run FFTs within the small(256-ish) window moving through the initial array, and store the results of each calculation in a matrix [window_size, analysis_size].
I'm using clFFT library, with the following buffers structure:
data_buffer ~ complex<float>[analysis_size]
out_buffer ~ complex<float>[window_size * (analysis_size-window_size)]
in_buffers ~ overlapped window_size subbuffers within data_buffer, for each calculation
out_buffers ~ window_size subbuffers within out_buffer, for each calculation. No overlapping.
After the writing data(clEnqueueWriteBuffer) to the in_buffer(when all in_buffers should be filled) I simply run in a cycle the desired amount of clfftEnqueueTransforms with in_buffers[i], out_buffers[i] as parameters. After that I read everything from the out_buffer with a single clEnqueueReadBuffer.
All that bothering with subbuffers was supposed to decrease the data transfer overhead, but still...
IPP's implementation of FFT makes the same thing twice faster, which is sort of confusing. What am I doing wrong? Is there any possible optimizations, or maybe fundamental mistakes? Thanks for any help.
My code is available through that link.
Related
So I had to write a program in Matlab to calculate the convolution of two functions, manually. I wrote this simple piece of code that I know is not that optimized probably:
syms recP(x);
recP(x) = rectangularPulse(-1,1,x);
syms triP(x);
triP(x) = triangularPulse(-1,1,x);
t = -10:0.1:10;
s1 = -10:0.1:10;
for i = 1:201
s1(i) = 0;
for j = t
s1(i) = s1(i) + ( recP(j) * triP(t(i)-j) );
end
end
plot(t,s1);
I have a core i7-7700HQ coupled with 32 GB of RAM. Matlab is stored on my HDD and my Windows is on my SSD. The problem is that this simple code is taking I think at least 20 minutes to run. I have it in a section and I don't run the whole code. Matlab is only taking 18% of my CPU and 3 GB of RAM for this task. Which is I think probably enough, I don't know. But I don't think it should take that long.
Am I doing anything wrong? I've searched for how to increase the RAM limit of Matlab, and I found that it is not limited and it takes how much it needs. I don't know if I can increase the CPU usage of it or not.
Is there any solution to how make things a little bit faster? I have like 6 or 7 of these for loops in my homework and it takes forever if I run the whole live script. Thanks in advance for your help.
(Also, it highlights the piece of code that is currently running. It is the for loop, the outer one is highlighted)
Like Ander said, use the symbolic toolbox in matlab as a last resort. Additionally, when trying to speed up matlab code, focus on taking advantage of matlab's vectorized operations. What I mean by this is matlab is very efficient at performing operations like this:
y = x.*z;
where x and z are some Nx1 vectors each and the operator '.*' is called 'dot multiplication'. This is essentially telling matlab to perform multiplication on x1*z1, x[2]*z[2] .... x[n]*z[n] and assign all the values to the corresponding value in the vector y. Additionally, many of the functions in matlab are able to accept vectors as inputs and perform their operations on each element and return an equal size vector with the output at each element. You can check this for any given function by scrolling down in its documentation to the inputs and outputs section and checking what form of array the inputs and outputs can take. For example, rectangularPulse's documentation says it can accept vectors as inputs. Therefore, you can simplify your inner loop to this:
s1(i) = s1(i) + ( rectangularPulse(-1,1,t) * triP(t(i)-t) );
So to summarize:
Avoid the symbolic toolbox in matlab until you have a better handle of what you're doing or you absolutely have to use it.
Use matlab's ability to handle vectors and arrays very well.
Deconstruct any nested loops you write one at a time from the inside out. Usually this dramatically accelerates matlab code especially when you are new to writing it.
See if you can even further simplify the code and get rid of your outer loop as well.
I'm working on a set of Fortran programs that are heavily I/O bound, and so am trying to optimize this. I've read at multiple places that writing entire arrays is faster than individual elements, i.e. WRITE(10)arr is faster than DO i=1,n; WRITE(10) arr(i); ENDDO. But, I'm unclear where my case would fall in this regard. Conceptually, my code is something like:
OPEN(10,FILE='testfile',FORM='UNFORMATTED')
DO i=1,n
[calculations to determine m values stored in array arr]
WRITE(10) m
DO j=1,m
WRITE(10) arr(j)
ENDDO
ENDDO
But m may change each time through the DO i=1,n loop such that writing the whole array arr isn't an option. So, collapsing the DO loop for writing would end up with WRITE(10) arr(1:m), which isn't the same as writing the whole array. Would this still provide a speed-up to writing, what about reading? I could allocate an array of size m after the calculations, assign the values to that array, write it, then deallocate it, but that seems too involved.
I've also seen differing information on implied DO loop writes, i.e. WRITE(10) (arr(j),j=1,m), as to whether they help/hurt on I/O overhead.
I'm running a couple of tests now, and intend to update with my observations. Other suggestions on applicable
Additional details:
The first program creates a large file, the second reads it. And, no, merging the two programs and keeping everything in memory isn't a valid option.
I'm using unformatted I/O and have access to the Portland Group and gfortran compilers. It's my understanding the PG's is generally faster, so that's what I'm using.
The output file is currently ~600 GB, the codes take several hours to run.
The second program (reading in the file) seems especially costly. I've monitored the system and seen that it's mostly CPU-bound, even when I reduce the code to little more than reading the file, indicating that there is very significant CPU overhead on all the I/O calls when each value is read in one-at-a-time.
Compiler flags: -O3 (high optimization) -fastsse (various performance enhancements, optimized for SSE hardware) -Mipa=fast,inline (enables aggressive inter-procedural analysis/optimization on compiler)
UPDATE
I ran the codes with WRITE(10) arr(1:m) and READ(10) arr(1:m). My tests with these agreed, and showed a reduction in runtime of about 30% for the WRITE code, the output file is also slightly less than half the original's size. For the second code, reading in the file, I made the code do basically nothing but read the file to compare pure read time. This reduced the run time by a factor of 30.
If you use normal unformatted (record-oriented) I/O, you also write a record marker before and after the data itself. So you add eight bytes (usually) of overhead to each data item, which can easily (almost) double the data written to disc if your number is a double precision. The runtime overhead mentioned in the other answers is also significant.
The argument above does not apply if you use unformatted stream.
So, use
WRITE (10) m
WRITE (10) arr(1:m)
For gfortran, this is faster than an implied DO loop (i.e. the solution WRITE (10) (arr(i),i=1,m)).
In the suggested solution, an array descriptor is built and passed to the library with a single call. I/O can then be done much more efficiently, in your case taking advantage of the fact that the data is contiguous.
For the implied DO loop, gfortran issues multiple library calls, with much more overhead. This could be optimized, and is subject of a long-standing bug report, PR 35339, but some complicated corner cases and the presence of a viable alternative have kept this from being optimized.
I would also suggest doing I/O in stream access, not because of the rather insignificant saving in space (see above) but because keeping up the leading record marker up to date on writing needs a seek, which is additional effort.
If your data size is very large, above ~ 2^31 bytes, you might run into different behavior with record markers. gfortran uses subrecords in this case (compatible to Intel), but it should just work. I don't know what Portland does in this case.
For reading, of course, you can read m, then allocate an allocatable array, then read the whole array in one READ statement.
The point of avoiding outputting an array by looping over multiple WRITE() operations is to avoid the multiple WRITE() operations. It's not particularly important that the data being output are all the members of the array.
Writing either an array section or a whole array via a single WRITE() operation is a good bet. An implied DO loop cannot be worse than an explicit outer loop, but whether it's any better is a question of compiler implementation. (Though I'd expect the implied-DO to be better than an outer loop.)
I would like to verify whether an element is present in a MATLAB matrix.
At the beginning, I implemented as follows:
if ~isempty(find(matrix(:) == element))
which is obviously slow. Thus, I changed to:
if sum(matrix(:) == element) ~= 0
but this is again slow: I am calling a lot of times the function that contains this instruction, and I lose 14 seconds each time!
Is there a way of further optimize this instruction?
Thanks.
If you just need to know if a value exists in a matrix, using the second argument of find to specify that you just want one value will be slightly faster (25-50%) and even a bit faster than using sum, at least on my machine. An example:
matrix = randi(100,1e4,1e4);
element = 50;
~isempty(find(matrix(:)==element,1))
However, in recent versions of Matlab (I'm using R2014b), nnz is finally faster for this operation, so:
matrix = randi(100,1e4,1e4);
element = 50;
nnz(matrix==element)~=0
On my machine this is about 2.8 times faster than any other approach (including using any, strangely) for the example provided. To my mind, this solution also has the benefit of being the most readable.
In my opinion, there are several things you could try to improve performance:
following your initial idea, i would go for the function any to test is any of the equality tests had a success:
if any(matrix(:) == element)
I tested this on a 1000 by 1000 matrix and it is faster than the solutions you have tested.
I do not think that the unfolding matrix(:) is penalizing since it is equivalent to a reshape and Matlab does this in a smart way where it does not actually allocate and move memory since you are not modifying the temporary object matrix(:)
If your does not change between the calls to the function or changes rarely you could simply use another vector containing all the elements of your matrix, but sorted. This way you could use a more efficient search algorithm O(log(N)) test for the presence of your element.
I personally like the ismember function for this kind of problems. It might not be the fastest but for non critical parts of the code it greatly improves readability and code maintenance (and I prefer to spend one hour coding something that will take day to run than spending one day to code something that will run in one hour (this of course depends on how often you use this program, but it is something one should never forget)
If you can have a sorted copy of the elements of your matrix, you could consider using the undocumented Matlab function ismembc but remember that inputs must be sorted non-sparse non-NaN values.
If performance really is critical you might want to write your own mex file and for this task you could even include some simple parallelization using openmp.
Hope this helps,
Adrien.
I have implemented a MC-Simulation of the 2D Ising model in C99.
Compiling with gcc 4.8.2 on Scientific Linux 6.5.
When I scale up the grid the simulation time increases, as expected.
The implementation simply uses the Metropolis–Hastings algorithm.
I tried to find out a way to speed up the algorithm, but I haven't any good idea ?
Are there some tricks to do so ?
As jimifiki wrote, try to do a profiling session.
In order to improve on the algorithmic side only, you could try the following:
Lookup Table:
When calculating the energy difference for the Metropolis criteria you need to evaluate the exponential exp[-K / T * dE ] where K is your scaling constant (in units of Boltzmann's constant) and dE the energy-difference between the original state and the one after a spin-flip.
Calculating exponentials is expensive
So you simply build a table beforehand where to look up the possible values for the dE. There will be (four choose one plus four choose two plus four choose three plus four choose four) possible combinations for a nearest-neightbour interaction, exploit the problem's symmetry and you get five values fordE: 8, 4, 0, -4, -8. Instead of using the exp-function, use the precalculated table.
Parallelization:
As mentioned before, it is possible to parallelize the algorithm. To preserve the physical correctness, you have to use a so-called checkerboard concept. Consider the two-dimensional grid as a checkerboard and compute only the white cells parallel at once, then the black ones. That should be clear, considering the nearest-neightbour interaction which introduces dependencies of the values.
Use GPGPU:
You can also implement the simulation on a GPGPU, e.g. using CUDA, if you're already working on C99.
Some tips:
- Don't forget to align C99-structs properly.
- Use linear Arrays, not that nested ones. Aligned memory is normally faster to access, if done properly.
- Try to let the compiler do loop-unrolling, etc. (gcc special options, not default on O2)
Some more information:
If you look for an efficient method to calculate the critical point of the system, the method of choice would be finite-size scaling where you simulate at different system-sizes and different temperature, then calculate a value which is system-size independet at the critical point, therefore an intersection point of the corresponding curves (please see the theory to get a detailed explaination)
I hope I was helpful.
Cheers...
It's normal that your simulation times scale at least with the square of the size. Isn't it?
Here some subjestions:
If you are concerned with thermalization issues, try to use parallel tempering. It can be of help.
The Metropolis-Hastings algorithm can be made parallel. You could try to do it.
Check you are not pessimizing the code.
Are your spin arrays of ints? You could put many spins on the same int. It's a lot of work.
Moreover, remember what Donald taught us:
premature optimisation is the root of all evil
Before optimising you should first understand where your program is slow. This is called profiling.
Recently, I implemented parallelisation in my MATLAB program, much to the suggestions offered in Slow xlsread in MATLAB. However, implementing the parallelism has cropped up another problem - non-linearly increasing processing time with increasing scale.
The culprit seems to be the java.util.concurrent.LinkedBlockingQueue method as can be seen from the attached images of profiler and the corresponding condensed graphs.
Problem: How do I remove this non-linearity as my work involves processing more than 1000 sheets in single run - which would take an insanely long time?
Note: The parallelised part of the program involves just reading all the .xls files and storing them in matrices, after which I start the remainder of my program. dlmwrite is used towards the end of the program and optimization on its time is not really required, although could also be suggested.
Culprit:
Code being parallelised:
parfor i = 1:runs
sin = 'Sheet';
sno = num2str(i);
sna = strcat(sin, sno);
data(i, :, :) = xlsread('Processes.xls', sna, '' , 'basic');
end
Doing parallel IO operation is likely to be a problem (could be slower in fact) unless maybe if you keep everything on an SSD. If you are always reading the same file and it's not enormous, you may want to try reading it prior to your loop and just doing your data manipulation in parallel.