I am making some spatio-temporal analysis (with MATLAB) on a quite big data set and I am not sure what is the best strategy to adopt in terms of performance for my script.
Actually, the data set is split in 10 yearly arrays of dimension (latitude,longitude,time)=(50,60,8760).
The general structure of my analysis is:
for iterations=1:Big Number
1. Select a specific site of spatial reference (i,j).
2. Do some calculation on the whole time series of site (i,j).
3. Store the result in archive array.
end
My question is:
Is it better (in terms of general performance) to have
1) all data in big yearly (50,60,8760) arrays as global variables loaded for once. At each iteration the script will have to extract one particular "site" (i,j,:) from those arrays for data process.
2) 50*60 distinct files stored in a folder. Each file containing a particular site time series (a vector of dimension (Total time range,1)). The script will then have to open, data process and then close at each iteration a specific file from the folder.
Because your computations are computed on the entire time series, I would suggest storing the data that way in a 3000x8760 vector and doing the computations that way.
Your accesses then will be more cache-friendly.
You can reformat your data using the reshape function:
newdata = reshape(olddata,50*60,8760);
Now, instead of accessing olddata(i,j,:), you need to access newdata(sub2ind([50 60],i,j),:).
After doing some experiments it is clear that the second proposition with 3000 distinct files is much slower than having to manipulate big arrays loaded in workspace. But I didn't try to load all the 3000 files in workspace before computing (A tad to much).
It looks like Reshaping data help's a little bit.
Thanks to all contributors for your suggestions.
Related
New to Julia and programming in general so this is a two part question. Suppose I have a Folder with 3,000 CSV files. Each file is roughly 7,000 x 7. (The number of rows may vary from file to file but the number of columns is constant.) I am trying to read each of these files into an 3000 x N x M tensor or other data structure in julia to compare the outputs by column. (This would mostly involve comparing the sum of the lags in each column vector of each file)
Question 1: What is the most efficient data structure to parse through this data? I would essentially be calculating the max of the sum of the lags of each column for all files. I've been told by a more experienced user that I should be using NamedArrays for this. I was wondering if anyone could provide some insights as to why? Would DataFrames be able to perform similar calculations?
Question 2: Is there an efficient way to read all these files into named arrays? I can read these files into Dataframes with Glob using the following code.
Folder="/Users/Desktop/Data"
Files=glob("*.csv", Folder)
df=DataFrame.(CSV.File.(Files))
But I don't know how to read it into NamedArrays directly. Any insights would be greatly appreciated thanks!
I was trying to collect statistics of a 6D vector and plot a 1D histogram for each coordinate. I get 729000000 different copies of this vector (each 6 dimensional). For this I create an array of zeros of size 729000000x6 before I get any of the actual W's and this seems to be a problem in matlab since it says:
Error using zeros
Requested 729000000x6 (32.6GB) array exceeds maximum array size preference. Creation of arrays
greater than this limit may take a long time and cause MATLAB to become unresponsive. See array
size limit or preference panel for more information.
The reason I did this at first was because it was easy to fill W_history and then just feed it to the histogram plotter:
histogram(W_history(:,d),nbins,'Normalization','probability')
however filling W_history seemed impossible for high number of copies of W. Is there a way to do this in matlab automatically? It feels that there should be and didn't want to re-invent the wheel.
I am sure I could potentially create for each coordinate some array of counters where I count how many times a specific value of the coordinate W falls. However, implementing that and having the checks for in which bin each one should fall seemed inefficient or even unnecessary. Is this really the only solution or what do matlab experts people recommend? Is this re-inventing the wheel? Seems also inefficient if I implement it myself?
Also, I thought I could manually have matlab put thing in memory then bring them back etc (as in store W_history in disk as it fills and then put more back in disk as it fills and eventually somehow plug it in to the histogram plotter), that seemed overwork. I hope I can avoid a solution like this one. It feels a wrong solution since it should be "easy" and high level to use matlab and going down to disk and memory doesn't seem to me what matlab is intended.
Currently through the comment that was given the best solution that I have so far is using histcounts as follow:
for i=2:iter+1
%
W = get_new_W(W)
%
[W_hist_counts_current, edges2] = histcounts(W,edges);
W_hist_counts = W_hist_counts + W_hist_counts_current;
end
however, after this it seems difficult to convert W_hist_counts to pdf/probability or other values since it seems they have to be processed manually. Is there no official way to do this processing without the user having to implement the normalizations again?
I am using Redis to store some information and detect changes in that information over time (for example, think users and locations). What is the value to using a longer or shorter keyname? Using a longer key is clearer, but is there much cost for memory or performance to using longer keyname?
Here are examples:
SET L:123456 "<name> <latitude> <longitude> ..."
HSET U:987654321 loc 123456 time <epoch>
or
SET loc:{123456} "<name> <latitude> <longitude> ..."
HSET user:{U987654321} loc 123456 time <epoch>
It all depends on how you are going to use it.
If every byte counts, for example when you have to pay for each kB transferred to a cloud service, you can calculate the costs. The maths is simple; a byte is a byte 'on the wire'. Inside redis, for larger values it is equally simple. For smaller values, Redis does some memory optimization.
In your HSET example, you split out the members, which only makes sense if you need them separated from eachother most of the time. A better approach -might- be: HSET user:data 987654321 '{"loc": "123456", "time": "2014-01-01T13:00:00"}'. Separate keys/members 'cost' a lot more than longer strings, performance wise. You can even put a whole table or dataset in one member if it's only going to be used as one complete semi-static entity.
Speed and Size: There is a notable difference between keys and values.
Keys:
Shorter is generally more memory efficient as well as speed efficient. If you use a redis Sorted Set you can even use 'numbers' as keys (sorted set 'members' plus 'scores'). I say 'numbers' because a score is technically a float64, but to be used as an ID it has to be between -999999999999999 and 999999999999999 including (that's 15 digits), without any fractional part. This can be really helpful, since Redis does fast and scalable O(log(n)) on-the-fly sorting of Sorted Sets (using skiplists, simplified).
Values:
The MsgPack format (uncompressed) takes up the least space, especially if you store the definitions once and the values many. JSON is a bit less memory efficient, but is ofcourse such a common IPC format that it should not be left out. Raw strings, character separated, fixed length (ugh), whatever your desire, it's possible to use. You can always compress your data before storing it in Redis. So far memory efficiency. When it comes to speed, it's less simple. If you want to use Lua server-side scripting (which you should), you can't do anything with compressed data. JSON and MsgPack can be deserialized, but only 'as a whole'. Which is fine in mosts scenarios. Most flexible is storing separate values (for example as members of a HSET), but this comes at a price as well (most of the time: too high a price). You also can combine all these. What we use most: a prefix of two or three delimiter-separated values, followed by a MsgPack payload.
My general advice is: start with using only HSET's and ZSET's, don't split out data that belongs together, use descriptive PascalCased names for your keys between 10-25 chars, use ':' if you need delimiters in your keys (namespaces), serialize as JSON (for simplicity, but code for easy switching to MsgPack), use Lua scripting (even if you don't know Lua, the subset you use in Redis is tiny).
I wouldn't worry about it too much in the startup phase of your project, you can always change it later on and do some A/B comparisons as soon as you have some interpolatable data.
Hope this helps, TW
Now that Redis v3.2 is almost here, you should consider switching to the new geo hashing functionality: http://redis.io/commands/geoadd
I want to pack a giant DNA sequence with an iOS app (about 3,000,000,000 base pairs). Each base pair can have a value A, C, T or G. Storing each base pair in one bytes would give a file of 3 GB, which is way too much. :)
Now I though of storing each base pair in two bits (four base pairs per octet), which gives a file of 750 MB. 750 MB is still way too much, even when compressed.
Are there any better file formats for efficiently storing giant base pairs on disk? In memory is not a problem as I read in chunks.
I think you'll have to use two bits per base pair, plus implement compression as described in this paper.
"DNA sequences... are not random; they contain
repeating sections, palindromes, and other features that
could be represented by fewer bits than is required to spell
out the complete sequence in binary...
With the proposed algorithm, sequence will be compressed by 75%
irrespective of the number of repeated or non-repeated
patterns within the sequence."
DNA Compression Using Hash Based Data Structure, International Journal of Information Technology and Knowledge Management
July-December 2010, Volume 2, No. 2, pp. 383-386.
Edit: There is a program called GenCompress which claims to compress DNA sequences efficiently:
http://www1.spms.ntu.edu.sg/~chenxin/GenCompress/
Edit: See also this question on BioStar.
If you don't mind having a complex solution, take a look at this paper or this paper or even this one which is more detailed.
But I think you need to specify better what you're dealing with. Some specifics applications can lead do diferent storage. For example, the last paper I cited deals with lossy compression of DNA...
Base pairs always pair up, so you should only have to store one side of the strand. Now, I doubt that this works if there are certain mutations in the DNA (like a di-Thiamine bond) that cause the opposite strand to not be the exact opposite of the stored strand. Beyond that, I don't think you have many options other than to compress it somehow. But, then again, I'm not a bioinformatics guy, so there might be some pretty sophisticated ways to store a bunch of DNA in a small space. Another idea if it's an iOS app is just putting a reader on the device and reading the sequence from a web service.
Use a diff from a reference genome. From the size (3Gbp) that you post, it looks like you want to include a full human sequences. Since sequences don't differ too much from person to person, you should be able to compress massively by storing only a diff.
Could help a lot. Unless your goal is to store the reference sequence itself. Then you're stuck.
consider this, how many different combinations can you get? out of 4 (i think its about 16 )
actg = 1
atcg = 2
atgc = 3 and so on, so that
you can create an array like [1,2,3] then you can go one step further,
check if 1 is follow by 2, convert 12 to a, 13 = b and so on...
if I understand DNA a bit it means that you cannot get a certain value
as a must be match with c, and t with g or something like that which reduces your options,
so basically you can look for a sequence and give it a something you can also convert back...
You want to look into a 3d space-filling curve. A 3d sfc reduces the 3d complexity to a 1d complexity. It's a little bit like n octree or a r-tree. If you can store your full dna in a sfc you can look for similar tiles in the tree although a sfc is most likely to use with lossy compression. Maybe you can use a block-sorting algorithm like the bwt if you know the size of the tiles and then try an entropy compression like a huffman compression or a golomb code?
You can use the tools like MFCompress, Deliminate,Comrad.These tools provides entropy less than 2.That is for storing each symbol it will take less than 2 bits
I am working in a chemistry/biology project. We are building a web-application for fast matching of the user's experimental data with predicted data in a reference database. The reference database will contain up to a million entries. The data for one entry is a list (vector) of tuples containing a float value between 0.0 and 20.0 and an integer value between 1 and 18. For instance (7.2394 , 2) , (7.4011, 1) , (9.9367, 3) , ... etc.
The user will enter a similar list of tuples and the web-app must then return the - let's say - top 50 best matching database entries.
One thing is crucial: the search algorithm must allow for discrepancies between the query data and the reference data because both can contain small errors in the float values (NOT in the integer values). (The query data can contain errors because it is derived from a real-life experiment and the reference data because it is the result of a prediction.)
Edit - Moved text to answer -
How can we get an efficient ranking of 1 query on 1 million records?
You should add a physicist to the project :-) This is a very common problem to compare functions e.g. look here:
http://en.wikipedia.org/wiki/Autocorrelation
http://en.wikipedia.org/wiki/Correlation_function
In the first link you can read: "The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum representing a peptide."
An efficient linear scan of 1 million records of that type should take a fraction of a second on a modern machine; a compiled loop should be able to do it at about memory bandwidth, which would transfer that in a two or three milliseconds.
But, if you really need to optimise this, you could construct a hash table of the integer values, which would divide the job by the number of integer bins. And, if the data is stored sorted by the floats, that improves the locality of matching by those; you know you can stop once you're out of tolerance. Storing the offsets of each of a number of bins would give you a position to start.
I guess I don't see the need for a fancy algorithm yet... describe the problem a bit more, perhaps (you can assume a fairly high level of chemistry and physics knowledge if you like; I'm a physicist by training)?
Ok, given the extra info, I still see no need for anything better than a direct linear search, if there's only 1 million reference vectors and the algorithm is that simple. I just tried it, and even a pure Python implementation of linear scan took only around three seconds. It took several times longer to make up some random data to test with. This does somewhat depend on the rather lunatic level of optimisation in Python's sorting library, but that's the advantage of high level languages.
from cmath import *
import random
r = [(random.uniform(0,20), random.randint(1,18)) for i in range(1000000)]
# this is a decorate-sort-undecorate pattern
# look for matches to (7,9)
# obviously, you can use whatever distance expression you want
zz=[(abs((7-x)+(9-y)),x,y) for x,y in r]
zz.sort()
# return the 50 best matches
[(x,y) for a,x,y in zz[:50]]
Can't you sort the tuples and perform binary search on the sorted array ?
I assume your database is done once for all, and the positions of the entries is not important. You can sort this array so that the tuples are in a given order. When a tuple is entered by the user, you just look in the middle of the sorted array. If the query value is larger of the center value, you repeat the work on the upper half, otherwise on the lower one.
Worst case is log(n)
If you can "map" your reference data to x-y coordinates on a plane there is a nifty technique which allows you to select all points under a given distance/tolerance (using Hilbert curves).
Here is a detailed example.
One approach we are trying ourselves which allows for the discrepancies between query and reference is by binning the float values. We are testing and want to offer the user the choice of different bin sizes. Bin sizes will be 0.1 , 0.2 , 0.3 or 0.4. So binning leaves us with between 50 and 200 bins, each with a corresponding integer value between 0 and 18, where 0 means there was no value within that bin. The reference data can be pre-binned and stored in the database. We can then take the binned query data and compare it with the reference data. One approach could be for all bins, subtract the query integer value from the reference integer value. By summing up all differences we get the similarity score, with the the most similar reference entries resulting in the lowest scores.
Another (simpler) search option we want to offer is where the user only enters the float values. The integer values in both query as reference list can then be set to 1. We then use Hamming distance to compute the difference between the query and the reference binned values. I have previously asked about an efficient algorithm for that search.
This binning is only one way of achieving our goal. I am open to other suggestions. Perhaps we can use Principal Component Analysis (PCA), as described here