I want to create a multidimensional array A in Matlab of dimension NxMxG with N,M,G very large (e.g. 10^6).
Then I need to access Ain a loop as
for g=1:G
Atemp=A(:,:,g);
%etc etc
end
What is more convenient in terms of speed and memory between storing the values of A in a multidimensional array or in a cell array?
If you always loop on slices in the same way, and process them one at a time, as your bit of code seem to suggest, then the performance should be roughly equivalent.
If you really intend to store 1e6x1e6x1e6 double's, Matlab is definitely probably not your tool. However, if slices are sparse, then it's probably a bit more efficient to store them as a cell array, so Matlab does not have to search the full 3D space when "cutting" the slice, and Atemp=A{g}; simply copies a sparse matrix.
If you are working on full (nonsparse) slices then probably you should load/save your slice to disk and use instead a function/support class which loads from file: Atemp=A(g);. Mind that text loading takes up much more time than loading a binary file: so choose your file format carefully!
If you use numbers, a multidimensional array is the right thing to use. A cell array also allows other types, so is less optimised for numbers only. Because you are using very large arrays, maybe a sparse matrix may be appropriate for you.
First, note that neither pick will let you handle 10^18 values. You don't have exabytes of storage, let alone memory.
If you will ONLY ever use it as Atemp = A(:,:,g); with N and M always the same size for all g, having it multi-dimensional or cell shouldn't change anything meaningful as far as performance goes. N-D will be probably a bit faster, but nothing significant.
Obviously, if you ever want to have computation with different sizes of N, M depending on g, you need to pick cell array. And if you want to have computation with say Atemp = squeeze(A(:,g,:)); N-D array is clear choice here.
So, choice most likely depends if you prefer doing A(:,:,g) or A{g};, which depends on your meaning of data. Say if you have weather data and currently only care about what happens at specific height (not what happens between the layers), A(:,:,g) is clearly more sensible. It is possible you will require inter-layer calculations at some point. But if you have instead g meaning different measurement sites gathering data, A{g} should be used to pick the site. You will likely have some sites larger or smaller eventually.
Related
I want to use pyfft to repeatedly compute the discrete Fourier transform of a subset of rows for a two-dimensional array. I do not know in advance which rows I need to transform, that depends on the output from the previous round. I do know that doing it for all rows is wasteful.
It is my understanding that a 'plan' in FFTW3 is associated with the type of transform (c2c, r2c, etc) and the input/output length, which is always a vector in the 1D case. In pyfftw it looks like a 'plan' is associated to the type of transform and the input/output shape, so my interpretation is that it uses the same FFTW3 plan for every row.
My question is: is it possible to use the same FFTW3 plan for some of the rows, without creating separate pyfftw.FFTW objects for all possible combinations of rows?
On a different note, I am wondering how pyfftw uses multiple cores: does it use multiple cores for each row (this appears natural in view of FFTW3 documentation) or does it farm out different rows to different cores (which was my initial assumption)?
If you can create a numpy array from a view, you can plan for it with pyFFTW - all valid numpy arrays should work just fine.
This means several things:
Your array needs to have regular strides, but those strides can be arbitrary.
ND arrays are planned as ND transforms, with the selected axes being used.
You can probably do something cunning with stride tricks and it will probably work (but might not do what you expect if you do something too nefarious like overlapping rows and then use threads).
One solution that I've used quite a bit is to copy the rows that you want to transform into an interim array, and transforming that. You might well find that's the fastest option (particularly when you can allow for getting the byte offset correct).
Obviously, this doesn't work if you always have a different number of rows. You might still find that if you plan for the largest number of rows that are transformed and then copy in a subset you still do faster than otherwise.
The problem you're going to come up against, even if you go down to the C level, is that the planning overhead might well dominate if you're changing your transform sizes often.
You could also try pyfftw.interfaces.numpy_fft which is normally faster that numpy and has the ability to cache repeated transform sizes.
I recently discovered an strange behavour of MATLAB cell arrays that was not happening before.
If I create a cell array with
a=cell(1,4)
its size is 32 bytes.
If then I put something inside, e.g.
a{2}='abcd'
its size becomes 144 bytes. But if I remove this content by putting
a{2}=[]
the size becomes 132 bytes and so on. What is the problem?
Simply put, the Matlab cell array needs some internal data structures to keep track of what is stored within.
As it seems, Matlab allocates memory as needed, and thus extends the storage needed by the cell array as you insert data.
Removing the data doesn't mean that matlab can return the now unused memory to the OS or internal memory pool -- that might either be something that is impossible with the internal storage structure, or something that would be unwise with respect to performance, because cell arrays from which data is removed are (speaking over all use cases of cell arrays) be structures that get updated often, so that "prematurely" returning memory just to acquire it back again a few instructions later would be pretty CPU-intense.
As a general note: Matlab has pretty terrible storage approaches for nearly everything but matrices and sparse matrices (vectors of course being special cases of matrices). That's because it's not Matlab's job to be e.g. a string parser etc.
If memory becomes a problem, it might be worth considering implementing the math core of your problem in Matlab and doing the rest in other, more generally usable programming languages and somehow interfacing your Matlab code with that -- I haven't tried that myself, but Mathworks has a Matlab engine for python, and I'd take writing python for things like storing arbitrary data over using Matlab every day; with that engine, you can call Matlab to do your dirty math work, and use python to do your everyday scripting/programming work.
Notice that my bottom line here is that Matlab has great Math routines and impressive documentation, but if you want to actually develop software, using a general purpose tool/language is much more likely to be satisfying quickly.
I'd even go as far as saying that it's probably worth your time to learn python, just to be able to circumvent having to deal with things that Matlab wasn't designed for (and cell arrays are a prime example of what Matlab is really complicated about and what's extremely easy in python).
You use
a{2}=[]
to 'kill' the data in that field. In reality you actually do access the data, that is you leave a non-empty cell entry with an empty double array. (Thanks to matlab for representing empty cells as empty doubles...)
but if you use (no curly braces, but parentheses):
a(2) = cell(1,1)
then the cell array size is back to "empty" = 32 bytes.
I would like to know whether there is a way to reduce the amount of memory used by the following piece of code in Matlab:
n=3;
T=100;
r=T*2;
b=80;
BS=1000
bsuppostmp_=cell(1,BS);
bslowpostmp_=cell(1,BS);
bsuppnegtmp_=cell(1,BS);
bslownegtmp_=cell(1,BS);
for w=1:BS
bsuppostmp_{w}= randi([0,1],n*T,2^(n-1),r,b);
bslowpostmp_{w}=randi([0,3],n*T,2^(n-1),r,b);
bsuppnegtmp_{w}=randi([0,4],n*T,2^(n-1),r,b);
bslownegtmp_{w}=randi([0,2],n*T,2^(n-1),r,b);
end
I have decided to use cells of matrices because after this loop I need to call separately each single matrix in another loop.
If I run this code I get the message error "Your system has run out of application memory".
Do you know a more efficient (in terms of memory) way to store each single matrix?
Let's refer the page about Strategies for Efficient Use of Memory:
Because simple numeric arrays (comprising one mxArray) have the least overhead, you should use them wherever possible. When data is too complex to store in a simple array (or matrix), you can use other data structures.
Cell arrays are comprised of separate mxArrays for each element. As a result, cell arrays with many small elements have a large overhead.
I doubt that the overhead for cell array is really large ...
Let me give a possible explanation. What if Matlab cannot use the swap file in case of storing the 4D arrays into a cell array? When storing large numeric arrays, there is no out-of-memory error because Matlab uses the swap file for caching each variable when the used memory becomes too big. Whereas if each 4D array is stored in a super cell array, Matlab sees it as a single variable and cannot fragment it part in the RAM and part in the swap file. Ok I don't work at Mathworks so I don't know if I'm right or not, it's just an idea about this topic so I would be glad to know what is the real reason.
So my advice is the same as other comments: try to free matrices as soon as you've done with them. There is not so many possibilities to store many dense arrays: one big array (NOT recommended here, will reach out-of-memory sooner because Matlab makes it contiguous), cell array or struct array (and if I correctly understand the documentation, the overhead can be equivalent). In all cases, the data amount over all 4D arrays is really large, so the best thing to do is to care about keeping the memory constantly as low as possible by discarding some data once they are used and keep in memory only the results of computation (in case they take lower memory usage ...).
I am simulating a set of differential equations in Matlab, for which I will save a struct of at least 400 x 80 000 x 24 doubles.
What in your opinion is the easiest way to control memory load? Memory mapping or a parallel process for memory checking, data writing and clearing? The program is single thread, but potentially will be re-written for a parallel computing.
Problem statement
Here are two problems, I think you are facing one of these:
Your data is really a block of mxnxz
Your data is not really a block of mxnxz
Solution for 1
If your data is really a block form, it is likely the best solution to store your data in a matrix.
Solution for 2
If your data is not a nice block, there are some choices to be made.
If your data is nearly a nice block, (for example mx(0.99~1.01)nxz, still consider using a matrix. Think about padding the gaps with zeros or NaN values.
If your data is very much not a block, (for example mx(0.01~100)nxz, consider using a more flexible data structure.
On flexible data structure usage
The trick to using data in a flexible way, is to try to identify the big matrices (that may vary in size) and let those be regular matrices. In your case the data is about 400 x 80000 x 24, hence you will definitely want the 80000 to be the dimension of a simple storage structure. The 24 and 400 are quite small so we don't care whether they are flexible or not.
Conclusion
The most efficient data structure that is not very flexible is a matrix of 400x80000x24
The most flexible data structure that is still fairly efficient is a cell array of 400x24, that contains vectors of approximately 80000x1
The most efficient data structure that is still fairly flexible is a cell array of 1x24 that contains matrices of approximately 400x80000. As 24 is small you could even use a struct for this in a meaningfull way, but usually a cell array will make more sense.
I have an m x n matrix of integers and where n is a fairly big number m and n ~1000. I want to iterate through all of these and perform a some operations, like accessing a particular cell and assigning a value of a particular cells.
However, at least in my implementation, this is rather inefficient as I have two for loops with Matrix(a,b) = Matrix(a,b+1) or something along these lines. Is there any other way to do this seeing as my current implementation takes a long time to traverse through about 100,000 cells and perform some operations.
Thank you
In matlab, it's almost always possible to avoid loops.
If you want to do Matrix(a,b)=Matrix(a,b+1), you should just do Matrix2=Matrix(:,2:end);
If you are more precise about what you do inside the loop, I can help you more.
Matlab uses column major ordering of matrixes in memory (unlike C). Are you sure you are iterating the indexes in the correct order? If not, try switching them and see if performance improves..
If you can't get rid of the for loops, one possibility would be to rewrite the expensive operations in C and create a MEX file as described here.