I am looking for a way to write fast code and be able to use builtin vector operations (for the sake of readability).
FORTRAN seems to be the good candidate. However, almost all resources I find on the web are about writing code without array expressions, and have only trivial examples of vector operations.
I feel strong need in some good resource which can cover caveats and give some insight into optimizations of code with vector expressions.
Example:
currently I am not even able to predict the behavior of such code:
! a = [0], indices = [1, 1]
a(indices) = a(indices) + 1
After compiling I get a = [2], but it this correct? If I use openmp, will it behave like this?
Personally, I would be very happy to have something like following examples on numpy:
100 numpy excercises
numpy: tips and tricks to work with data
Getting the Best Performance out of NumPy
Your code is not standard conforming:
Fortran 2008 6.5.3.3.2.3:
If a vector subscript has two or more elements with the same value,
an array section with that vector subscript shall not appear in a
variable definition context (16.6.7). NOTE 6.15
Therefore the result of your operation is not defined by the standard.
Other parts of your question appear to be too broad to treat them here. There are many books about scientific programming in Fortran 90 and later.
Also be aware that by vectorization most people in Fortran and C or C++ mean the usage of SIMD instructions simd and not the vectorized expressions from NumPy. These are just array expressions in Fortran.
I have scanned many sources (~20 books and dozens of web pages). Hard luck I missed something really important. The question I posted is indeed incorrect and comes from my initial high expectation about array operations in fortran.
The answer I would expect is: there are no tools to write short, readable code in fortran with automatic parallelization (to be more precise: there are, but those are proprietary libraries).
The list of intrinsic functions available in fortran is quite short
(link), and consists only of functions easily mapped to SIMD ops.
There are lots of functions that one will be missing.
while this could be resolved by separate library with separate implementation for each platform, fortran doesn't provide such. There are commercial options (see this thread)
Brief examples of missing functions:
no built-in array sort or unique. The proposed way is to use this library, which provides single-threaded code (forget threads and CUDA)
cumulative sum / running sum. One trivially can implement it, but the resulting code will never work fine on threads/CUDA/Xeon Phi/whatever comes next.
bincount, numpy.ufunc.at, numpy.ufunc.reduceat (which is very useful in many applications)
In most cases fortran provides 2x speed up even with simple implementations, but the code written will always be one-threaded, while matlab/numpy functions can be reimplemented for GPU or other parallel platform without any effort from user side (which occasionally happened to MATLAB, also see gnumpy, theano and parakeet)
To conclude, this is bad news for me. Fortran developers really care about having fast programs today, not in the future. I also can't lock my code on proprietary software. And I'm still looking for appropriate tool. (Julia is current candidate)
See also:
STL analogue in fortran
where ready-to-use algorithms are asked.
Numerical recipes: the art of parallel programming author implements basic MATLAB-like operations to have more expressive code
I also find useful these notes to see recommended ways of code optimizations (to see there is no place for vector operations)
numpy, fortran, blitz++: a case study
dicussion about implementing unique in fortran, where proprietary tools are recommended.
I am aware that C/C++ is a lower-level language and generates relatively optimized machine code when we compare with any other high-level language. But I guess there is pretty much more than that, which is also evident from the practice.
When I do simple calculations like montecarlo averaging of a Gaussian sample collection or so, I see there is not much of a difference between a C++ implementation or MATLAB implementation, sometimes in fact MATLAB performs a bit better in time.
When I move on to larger scale simulations with thousands of lines of code, slowly the real picture shows up. C++ simulations show superior performance like 100x better in time complexity than an equivalent MATLAB implementation.
The code in C++ most of the times, is pretty much serial and no hi-fi optimization is done explicitly. Whereas, as per my awareness, MATLAB inherently does a lot of optimization. This shows up for example when I try to generate a huge chunk of random samples, where as the equivalent in C++ using some library like IT++/GSL/Boost performs relatively slower (the algorithm used is the same namely mt19937).
My question is simply to know if there is a simpler tradeoff between MATLAB/C++ in performance. Is it just like what people say, "Whenever you can, C/C++ is the better"(The frequently experienced)?. In a different perspective, "What is MATLAB good for, other than comfort?"
By the way, I don't see coding efficiency parameter being significant here, thinking of the same programmer in both cases. And also, I think the other alternatives like python,R are not relevant here. But dependence on the specific libraries we use should be interesting.
[I am a phd student in Coding Theory in communication systems. I do simulations using matlab/C++ all the time, and have reasonable experience of coding few 10K's of lines in both cases]
I have been using Matlab and C++ for about 10 years. For every numerical algorithms implemented for my research, I always start from prototyping with Matlab and then translate the project to C++ to gain a 10x to 100x (I am not kidding) performance improvement. Of course, I am comparing optimized C++ code to the fully vectorized Matlab code. On average, the improvement is about 50x.
There are lot of subtleties behind both of the two programming languages, and the following are some misunderstandings:
Matlab is a script language but C++ is compiled
Matlab uses JIT compiler to translate your script to machine code, you can improve your speed at most by a factor 1.5 to 2 by using the compiler that Matlab provides.
Matlab code might be able to get fully vectorized but you have to optimize your code by hand in C++
Fully vectorized Matlab code can call libraries written in C++/C/Assembly (for example Intel MKL). But plain C++ code can be reasonably vectorized by modern compilers.
Toolboxes and routines that Matlab provides should be very well tuned and should have reasonable performance
No. Other than linear algebra routines, the performance is generally bad.
The reasons why you can gain 10x~100x performance in C++ comparing to vectorized Matlab code:
Calling external libraries (MKL) in Matlab costs time.
Memory in Matlab is dynamically allocated and freed. For example, small matrices multiplication:
A = B*C + D*E + F*G
requires Matlab to create 2 temporary matrices. And in C++, if you allocate your memory before hand, you create NONE. And now imagine you loop that statement for 1000 times. Another solution in C++ is provided by C++11 Rvalue reference. This is the one of the biggest improvement in C++, now C++ code can be as fast as plain C code.
If you want to do parallel processing, Matlab model is multi-process and the C++ way is multi-thread. If you have many small tasks needing to be parallelized, C++ provides linear gain up to many threads but you might have negative performance gain in Matlab.
Vectorization in C++ involves using intrinsics/assembly, and sometimes SIMD vectorization is only possible in C++.
In C++, it is possible for an experienced programmer to completely avoid L2 cache miss and even L1 cache miss, hence pushing CPU to its theoretical throughput limit. Performance of Matlab can lag behind C++ by a factor of 10x due to this reason alone.
In C++, computational intensive instructions sometimes can be grouped according to their latencies (code carefully in assembly or intrinsics) and dependencies (most of time is done automatically by compiler or CPU hardware), such that theoretical IPC (instructions per clock cycle) could be reached and CPU pipelines are filled.
However, development time in C++ is also a factor of 10x comparing to Matlab!
The reasons why you should use Matlab instead of C++:
Data visualization. I think my career can go on without C++ but I won't be able to survive without Matlab just because it can generate beautiful plots!
Low efficiency but mathematically robust build-in routines and toolboxes. Get the correct answer first and then talk about efficiency. People can make subtle mistakes in C++ (for example implicitly convert double to int) and get sort of correct results.
Express your ideas and present your code to your colleagues. Matlab code is much easier to read and much shorter than C++, and Matlab code can be correctly executed without compiler. I just refuse to read other people's C++ code. I don't even use C++ GNU scientific libraries because the code quality is not guaranteed. It is dangerous for a researcher/engineer to use a C++ library as a black box and take the accuracy as granted. Even for commercial C/C++ libraries, I remember Intel compiler had a sign error in its sin() function last year and numerical accuracy problems also occurred in MKL.
Debugging Matlab script with interactive console and workspace is a lot more efficient than C++ debugger. Finding an index calculation bug in Matlab could be done within minutes, but it could take hours in C++ figuring out why the program crashes randomly if boundary check is removed for the sake of speed.
Last but not the least:
Because once Matlab code is vectorized, there is not much left for a programmer to optimize, Matlab code performance is much less sensitive to the quality of the code comparing with C++ code. Therefore it is best to optimize computation algorithms in Matlab, and marginally better algorithms normally have marginally better performance in Matlab. On the other hand, algorithm test in C++ requires decent programmer to write algorithms optimized more or less in the same way, and to make sure the compiler does not optimize the algorithms differently.
My recent experience in C++ and Matlab:
I made several large Matlab data analysis tools in the past year and suffered from the slow speed of Matlab. But I was able to improve my Matlab program speed by 10x through the following techniques:
Run/profile the Matlab script, re-implement critical routines in C/C++ and compile with MEX. Critical routines are mostly likely logically simple but numerically heavy. This improves speed by 5x.
Simplify ".m" files shipped with Matlab tool boxes by commenting all unnecessary safety checks and output parameter computations. Please be reminded that the modified code cannot be distributed with the rest of the user scripts. This improves speed by another 2x (after C/C++ and MEX).
The improved code is ~98% in Matlab and ~2% in C++.
I believe it is possible to improve the speed by another 2x (total 20x) if the entire tool is coded in C++, this is ~100x speed improvement of the computation routines. The hard drive I/O will then dominate the program run time.
Question for Mathworks engineers:
When Matlab code is fully vectorized, one of the performance limiting factor is the matrix indexing operation. For instance, a finite difference operation needs to be performed on Matrix A which has a dimension of 5000x5000:
B = A(:,2:end)-A(:,1:end-1)
The matrix indexing operation makes the Matlab code multiple times slower than the C++ code. Can the matrix indexing performance be improved?
In my experience (several years of Computer Vision and image processing in both languages) there is no simple answer to this question, as Matlab performance depends strongly (and much more than C++ performance) on your coding style.
Generally, Matlab wraps the classic C++ / Fortran based linear algebra libraries. So anything like x = A\b is going to be very fast. Also, Matlab does a good job in choosing the most efficient solver for these types of problems, so for x = A\b Matlab will look at the size of your matrices and chose the appropriate low-level routines.
Matlab also shines in data manipulation of large matrices if you "vectorize" your code, i.e. if you avoid for loops and use index arrays or boolean arrays to access your data. This stuff is highly optimised.
For other routines, some are written in Matlab code, while others point to a C/C++ implementation (e.g. the Delaunay stuff). You can check this yourself by typing edit some_routine.m. This opens the code and you see whether it is all Matlab or just a wrapper for something compiled.
Matlab, I think, is primarily for comfort - but comfort translates to coding time and ultimately money which is why Matlab is used in the industry. Also, it is easy to learn for engineers from other fields than computer science, with little training in programming.
As a PhD Student too, and a 10years long Matlab user, I'm glad to share my POV:
Matlab is a great tool for developing and prototyping algorithms, especially when dealing with GUIs, high-level analysis (Frequency Domain, LS Optimization etc.): fast coding, powerful syntaxis (think about [],{},: etc.).
As soon as your processing chain is more stable and defined and data dimensions grows move to C/C++.
The main Matlab limit rises when considering its language is script-like: as long as you avoid any cycle (using arrayfun, cellfun or other matrix procedures) performances are high since the called subroutine is again in C/C++.
Your question is difficult to answer. In general C++ is faster, but if make use of the well written algorithms of Matlab it can outperform C++. In some cases Matlab can parallelize your code which has to be done manually in many cases for C++. Mathlab can kind of export C++ code.
So my conclusion is, that you have to measure the performance of both programs to get an answer. But then you compare your two implementations and not Matlab and C++ in general.
Matlab does very well with linear algebra and array/matrix operations, since they seem to have been doing some extra optimizations on the underlying operations - if you want to beat Matlab there, you would need a similarly optimized BLAS/LAPACK library.
As an interpreted language, Matlab loses time whenever a Matlab function is called, due to internal overhead, which traditionally meant that Matlab loops were slow. This has been alleviated somewhat in recent years thanks to significant improvement in the JIT compiler (search for "performance" questions on Matlab on SO for examples). As a consequence of the function call overhead, all Matlab functions that have not been implemented in C/C++ behind the scenes (call edit functionName to see whether it's written in Matlab) risks being slower than a C/C++ counterpart.
Finally, Matlab attempts to be user friendly, and may do "unnecessary" input checking that can take time (due to function call overhead). For example, if you know that ismember gets sorted inputs, you can call ismembc directly (the behind-the-scene compiled function), saving quite a bit of time.
I think you can consider the difference in four folds at least.
Compiled vs Interpreted
Strongly-typed vs Dynamically-typed
Performance vs Fast-prototyping
Special strength
For 1-3 can be easily generalized into comparison between two family of programming languages.
For 4, MATLAB is optimized for matrix operations. So if you can vectorize more code in MATLAB, the performance can be drastically boosted. Conversely, if many loops are required, never hesitate to use C++ or create a mex file.
It is a difficult quesion after all.
I saw a 5.5x speed improvement when switching from MATLAB to C++. This was for a robot controller- lots of loops and ode solving. I spent many hours trying to optimize the MATLAB code, hardly any time optimizing the C++ (I'm sure it could have been 10x faster with a little more effort).
However, it was easy to add a GUI for the MATLAB code, so I still use it more often. Like others have said, it was nice to prototype first on MATLAB. That made the implementation on C++ much simpler.
Besides the speed of the final program, you should also take into account the total development time of your code, ie., not only the time to write, but also to debug, etc. Matlab (and its open-source counterpart, Octave) can be good for quick prototyping due to its visualisation capabilities.
If you're using straight C++ (ie. no matrix libraries), it may take you much longer to write C++ code that's equivalent to Matlab code (eg. there might be no point in spending 10 hours writing C++ code that only runs 10 seconds quicker, compared to a Matlab program that took 5 minutes to write).
However, there are dedicated C++ matrix libraries, such as Armadillo, which provide a Matlab-like API. This can be useful for writing performance critical code that can be called from Matlab, or for converting Matlab code into "real" programs.
Some Matlab code uses standard linear algebra fictions with multithreading built into it. So, it appears that they are faster than a sequential C code.
I'm debating whether to use C++ or Python for a largely math-based program.
Both have great math libraries, but which language is generally faster for complex math?
You could also consider a hybrid approach. Python is generally easier and faster to develop in, specially for things like user interface, input/output etc.
C++ should certainly be faster for some math operations (although if your problem can be formulated in terms of vector operations or linear algebra than numpy provides a python interface to very efficient vector manipulations).
Python is easy to extend with Cython, Swig, Boost Python etc. so one strategy is write all the bookkeeping type parts of the program in Python and just do the computational code in C++.
I guess it is safe to say that C++ is faster. Simply because it is a compiled language which means that only your code is running, not an interpreter as with python.
It is possible to write very fast code with python and very slow code with C++ though. So you have to program wisely in any language!
Another advantage is that C++ is type safe, which will help you to program what you actually want.
A disadvantage in some situations is that C++ is type safe, which will result in a design overhead. You have to think (maybe long and hard) about function and class interfaces, for instance.
I like python for many reasons. So don't understand this a plea against python.
It all depends if faster is "faster to execute" or "faster to develop". Overall, python will be quicker for development, c++ faster for execution. For working with integers (arithmetic), it has full precision integers, it has a lot of external tools (numpy, pylab...) My advice would be go python first, if you have performance issue, then switch to cpp (or use external libraries written in cpp from python, in an hybrid approach)
There is no good answer, it all depends on what you want to do in terms of research / calculus
It goes witout saying that C++ is going to be faster for intensive numeric computations. However, there are so many pre-existing libraries out there (written in C/C++/Haskell etc..), with Python wrappers - it's just more convenient to utilise the convenience of Python and let the existing libraries carry the load.
One comprehensive system is http://www.sagemath.org and a fairly interesting link is the components it uses at http://sagemath.org/links-components.html.
A system with numpy/scipy and pandas from my experience is normally sufficient for most things.
Use the one you like better (and you should like python better :)).
In either case, any math-intensive computations should be carried out by existing libraries - which aren't language dependent (usually BLAS / LAPACK are used to perform the actual math).
If you choose to go with python, use numpy
for calculations.
Edit: From your comments, it seems that you are very concerned with the speed of your program. The only way to know for sure how much time is wasted by the high level pythonic code is to profile your program (for example, use ipython with run -p).
In most cases, you will find that the high level stuff takes about 10% of the total running time, and therefore switching from python to C++ will only improve that 10% by some factor, for a total gain of perhaps 5% in running time.
I sincerely doubt that Google and Stanford don't know C++.
"Generally faster" is more than just language. Algorithms can make or break a solution, regardless of what language it's written in. A poor choice written in C++ and be beaten by Java or Python if either makes a better algorithm choice.
For example, an in-memory, single CPU linear algebra library will have its doors blown in by a parallelized version done properly.
An implicit algorithm may actually be slower than an explicit one, despite time step stability restrictions, because the latter doesn't have to invert a matrix. This is often true for hyperbolic partial differential equations.
You shouldn't care about "generally faster". You ought to look deeply into the problem you're trying to solve and the algorithms used to solve it. You'll do better that way than a blind language choice.
I would go with Python running on Java platform. This approach is implemented in DataMelt program. Algorithm that call Java libraries from Python can be faster, since JVM optimizes the code for you.
I'm looking for the best choice of C++ Mathematics library to make easier some operations from LabView blocks.
I need to realize many complex mathematics things on C++ alike: linear regression, peak detection, derivative for the graph and many others alike.
I found there are a lot of libraries for it: http://en.wikipedia.org/wiki/List_of_numerical_libraries#C_and_C.2B.2B
Which library is better to chose for my tasks?
(currently Im thinking about boost BLAS but I never worked with it earlier so maybe this choice is wrong)
Note that there isn't much more to boost uBLAS than basic linear algebra; and even if you consider the larger boost "Math and Numerics" section, it can hardly be considered a complete scientific computing package.
GSL is very good in that it's quite comprehensive. However, it's very much a 'C' library so you need to be prepared to work with raw pointers to array data and function pointer callbacks rather than higher level classes.
(Personally these days I find myself using Python/Numpy/Scipy as much as possible; the scope of Scipy is truly incredible and Numpy arrays are fantastically easy to work with; if there was a LabView/Python/Scipy integration that met any other requirements it'd be the first thing I'd be looking it).
So my current project is mostly in Python, but I'm looking to rewrite the most computationally expensive portions in C++ to try and boost performance. Much of this I can achieve via simple functions loaded from DLL files, but not everything. I have a multidimensional array in Python that I want to perform operations on in C++ (particularly A* pathfinding), but I'm not really sure how to translate them, and constantly sending data one piece at a time into a loaded function seems really inefficient (the array's first two dimensions are in the low hundreds, and the functions will need to deal with scores, if not hundreds, of elements in the array at a time).
My idea was to have a class in C++ that creates its own copy of the array at setup (where performance isn't as much of an issue) and has methods that are performed on the array and return data to the main Python program. However, I'm not sure how to accomplish this, and even if this is the proper way to go about such a thing; that would seem to imply having C++ code running parallel to the main Python program, and intuition tells me that's a bad idea.
I don't know much about integrating C++ and Python beyond how to load simple functions via cTypes in Python, so I'd really appreciate some pointers here. Keep in mind I'm relatively new to C++ at all; most of my programming experience is in Python. What would be the best way to fit the two together in this situation?
First and foremost, when you are working with multidimensional arrays in Python, you should really be using NumPy. Chances are that your program is already fast enough when you let NumPy do the number crunching (use Array arithmetic instead of Python for loops).
If this is not enough, consider writing parts of your program using Cython. Cython also supports NumPy arrays and provides a painless way to write C code using Python-like syntax.
If it really must be C++, I highly recommend using Boost.Python. Bridging Python and C++ has never been this easy. Plus, Boost.Python comes with NumPy support as well (boost::numeric::array).
Take a look at Cython.