I was wondering, does the MatLab compiler automatically change several calls to a function on the same object to one call ?
i. e.
someVector=zeros(length(someOtherVector),1);
for i=1:length(someOtherVector)
...
end
"Optimized"
aSize=length(someOtherVector);
someVector=zeros(aSize,1);
for i=1:aSize
...
end
By-question: How is this optimization technique formally called ? I understand, for instance, the JVM does this kind of stuff.
The MATLAB JIT Compiler makes plenty of optimizations, but I'm pretty sure it doesn't do the optimization you're suggesting.
To see why, imagine that you'd written your own function called length which returned a random integer whatever its input, and put it on the path so that it shadowed the built-in length. Then your second version would not only not be an optimized version of the first, it would actually have different effects.
Indeed, if you really wanted to mess around, you could implement length so that it wrote a new file called length and put that ahead of itself on the path, so that it would have entirely different effects the next time around.
MATLAB is quite a flexible language, which has a lot of advantages, but that makes it less possible to perform the sort of static analysis on MATLAB code that these sort of JIT optimizations would require. Java is much easier to statically analyse, so the JVM can perform more optimizations.
Related
Blocks and functions in Modelica have some similarities and differences. In blocks, output variables are most likely expressed in terms of input variables using equations, whereas in functions output variables are expressed in terms of input variables using assignments. Given a relationship y = f(u) that can be expressed using both notions, I am interested in knowing which notion shall you favour in which situation?
Personally,
Blocks can be better integrated in block diagrams using input/output connectors
Equations in blocks can be most likely better treated by compilers for symbolic manipulation, optimization, and evaluating analytical derivatives required for Jacobian evaluation. So I guess blocks are likely less sensitive to numerical errors in some boundary cases. For functions, derivatives are likely to be evaluated using finite difference methods, if they are not explicitly provided.
on the other hand a set of assignments in a function will be most likely treated as a single equation. The same set of assignments if expressed in terms of a larger set of equations in a block will result in a model of larger size probably leading to a decrease in runtime performance
although a block with an algorithmic section is kind of equivalent to a function with the same assignments set, the syntax of a function call is favored in couple of situations
One can establish hierarchies of blocks types and do all of sort of things of object oriented modelings. Functions are kind of limited. It is not possible to extend from a non-abstract function that contains an algorithm section. But it is possible to have (an) abstract function(s) that act(s) as (an) interface(s) out of which implemented functions can be established etc.
Some of the above arguments are dependent on the way a specific simulation environment treats a block or a function. These might be low-level details not necessarily known.
The list in your "question" is already a pretty good summary. Still there are some additional things that should be considered:
Regarding the differentiation of functions, the developer at least needs to define how often the assignments can be differentiated (here is a nice read on this), as e.g. Dymola will not do it automatically. Alternatively the differentiated function can be specified manually (here). By the way, a partial derivative can be defined as well, see Language Specification, Sec. 12.7.2.
When it is necessary to invert a function, it can be necessary to define it manually. This is described in the Language Specification, Sec. 12.8.
Also it could be important that code from a function can be inlined, which should overcome some of the issues mentioned above, see Language Specification, Sec. 18.3.
Generally I would go for blocks whenever there is no very strong reason for a function. Some that come to my mind are the need for procedural execution, or for-loops.
This is just my two cents - more opinions welcome...
You might be interested in the opposite: calling a block as if it was a function:
https://github.com/modelica/ModelicaSpecification/issues/1512
The advantage of using function syntax is that you don't need to declare + connect components:
Block b;
equation
connect(x, b.in1);
connect(y, b.in2);
connect(z, b.out1);
vs
z = Block(x, y);
Of course right now, this syntax does not exist yet. And you really want to use blocks when you can. Algorithmic blocks might as well be functions as they are shorter and easier to write and will introduce fewer trajectories in your result-file (good unless you want to debug what happens inside the function call I guess).
I am working on reducing dimentionality of a set of (Boolean) vectors with both the number and dimentionality of vectors tending to be of the order of 10^5-10^6 using autoencoders. Hence even though speed is not of essence (it is supposed to be a pre-computation for a clustering algorithm) but obviously one would expect that the computations take a reasonable amount of time. Seeing how the library itself was written in c++ would it be a good idea to stick to it or to code in Java (Since the rest of the code is written in Java)? Or would it not matter at all?
That question is difficult to answer. It depends on:
How computationally demanding will be your code? If the hard part is done by the library and your code is only to generate the input and post-process the output, Java would be a valid choice. Compare it to Matlab: The language is very slow but the built-in algorithms are super-fast.
How skilled are you (or your team, or your future students) in Java and C++. Consider learning C++ takes a lot of time. If you have only a small scaled project, it could be easier to buy a bigger machine or wait two days instead of one, to get the results.
Have you legacy code in one of the languages you want to couple or maybe re-use?
Overall, I would advice you to set up a benchmark example in whatever language you like more. Then give it a try. If the speed is ok, stick to it. If you wait to long, think about alternatives (new hardware, parallel execution, different language).
so I have the following Integral that i need to do numerically:
Int[Exp(0.5*(aCosx + bSinx + cCos2x + dSin2x))] x=0..2Pi
The problem is that the output at any given value of x can be extremely large, e^2000, so larger than I can deal with in double precision.
I havn't had much luck googling for the following, how do you deal with large numbers in fortran, not high precision, i dont care if i know it to beyond double precision, and at the end i'll just be taking the log, but i just need to be able to handle the large numbers untill i can take the log..
Are there integration packes that have the ability to handle arbitrarily large numbers? Mathematica clearly can.. so there must be something like this out there.
Cheers
This is probably an extended comment rather than an answer but here goes anyway ...
As you've already observed Fortran isn't equipped, out of the box, with the facility for handling such large numbers as e^2000. I think you have 3 options.
Use mathematics to reduce your problem to one which does (or a number of related ones which do) fall within the numerical range that your Fortran compiler can compute.
Use Mathematica or one of the other computer algebra systems (eg Maple, SAGE, Maxima). All (I think) of these can be integrated into a Fortran program (with varying degrees of difficulty and integration).
Use a library for high-precision (often called either arbitray-precision or multiple-precision too) arithmetic. Your favourite search engine will turn up a number of these for you, some written in Fortran (and therefore easy to integrate), some written in C/C++ or other languages (and therefore slightly harder to integrate). You might start your search at Lawrence Berkeley or the GNU bignum library.
(Yes I know that I wrote that you have 3 options, but your question suggests that you aren't ready to consider this yet) You could write your own high-/arbitrary-/multiple-precision functions. Fortran provides everything you need to construct such a library, there is a lot of work already done in the field to learn from, and it might be something of interest to you.
In practice it generally makes sense to apply as much mathematics as possible to a problem before resorting to a computer, that process can not only assist in solving the problem but guide your selection or construction of a program to solve what's left of the problem.
I agree with High Peformance Mark that the best option here numerically is to use analytics to scale or simplify the result first.
I will mention that if you do want to brute force it, gfortran (as of 4.6, with the libquadmath library) has support for quadruple precision reals, which you can use by selecting the appropriate kind. As long as your answers (and the intermediate results!) don't get too much bigger than what you're describing, that may work, but it will generally be much slower than double precision.
This requires looking deeper at the problem you are trying to solve and the behavior of the underlying mathematics. To add to the good advice already provided by Mark and Jonathan, consider expanding the exponential and trig functions into Taylor series and truncating to the desired level of precision.
Also, take a step back and ask why you are trying to accomplish by calculating this value. As an example, I recently had to debug why I was getting outlandish results from a property correlation which was calculating vapor pressure of a fluid to see if condensation was occurring. I spent a long time trying to understand what was wrong with the temperature being fed into the correlation until I realized the case causing the error was a simulation of vapor detonation. The problem was not in the numerics but in the logic of checking for condensation during a literal explosion; physically, a condensation check made no sense. The real problem was the code was asking an unnecessary question; it already had the answer.
I highly recommend Forman Acton's Numerical Methods That (Usually) Work and Real Computing Made Real. Both focus on problems like this and suggest techniques to tame ill-mannered computations.
I have built an standalone Matlab application. I was expecting it to be faster than running the application from the Matlab environent but it is indeed a bit slower (1.3 seg per iteration vs 1.5 seg per iteration)
I am not counting the init time required by MCR but the execution of my code.
Is that the expected performance or should I be obtaining a performance improvement?
I haven't found any settings on the deployment tool that could help to reduce execution time.
Thanks in advance
Applications built with MATLAB Compiler should execute at pretty much exactly the same speed as within MATLAB.
MATLAB Compiler does not convert your MATLAB code into machine code in the same way as a C compiler does for C. What it does is to archive and encrypt your MATLAB code (note, it properly encrypts it, not just pcodes it as a comment suggests), create a thin executable wrapper and package them together, possibly also with MATLAB Compiler Runtime (MCR). MCR is very similar to MATLAB itself, without a graphical user interface, and is freely redistibutable.
When you run the executable, it dearchives and decrypts your MATLAB code and runs it against the MCR. It should run exactly the same, both in terms of results and speed.
Very old versions of MATLAB Compiler (pre-version 4.0) worked in a different way, converting a subset of the MATLAB language into C code, and compiling this. This provided a potentially significant speed-up, but only a subset of the language was supported and results, unless you were careful, could sometimes be different. Similar functionality is now available in the separate MATLAB Coder product.
There are a few small things you can do to improve performance: for example, within deploytool you can specify which toolboxes your application uses. deploytool uses a dependency checker to package up all MATLAB functionality that it thinks your code might possibly depend on, but it can't always tell exactly, as the functions your code needs might change at runtime. It therefore errs on the side of caution and includes more than necessary. By specifying only the toolboxes you know to be necessary, you can speed things up a little (it also speeds up the build process quite a bit).
Matlab Coder is a recently released MathWorks product. My understanding is that it is a Matlab-to-C compiler with the biggest advantage over previous solutions being that the resulting program does not need to be linked against a Matlab shared library.
Can someone with access to this product confirm the above? What are the dependencies of the translated programs and what kind of performance are we talking about? Also I would really like to see some example outputs, to know if the resulting C programs can be understood and improved without access to the Matlab source.
If done right this could be very powerful, allowing rapid prototyping in Matlab and instantaneous conversion to C when things are getting serious. I kind of whish it doesn't work well so that Python+Numpy+Scipy.weave is still superior ^^.
MATLAB Coder can allocate memory using malloc, so you can generate C code from MATLAB functions that operate on dynamically sized data. You can also choose the option of static allocation with a maximum size for variables.
RE: using BLAS for matrix multiplication – while the generated C code doesn’t automatically include any processor/platform specific optimizations, there is a feature called Target Function Library, which that allows users to write their own implementation of primitive operations (such as matrix multiplication), and include them in the generated code. You can hook up BLAS libraries to MATLAB Coder via that method. There’s also an ability to include optimized processor specific calls for larger functions through custom code integration and conditional compilation that lets you specify one set of code to use for code generation, and another set for simulation (for example, an optimized FIR function for an Texas Instruments DSP and functionally equivalent code for simulation that can execute on your PC written in C or in MATLAB).
Hope this is helpful --
Arvind Ananthan; Product Manager for MATLAB Coder; MathWorks
I am using Matlab Coder with Real Time Workshop (RTW) in order to generate self standind standard C code.
First of all you are asked to use a Matlab subset called "Embedded Matlab" you can find the doc about it on the web
You also have to avoid any dynamic exploitation of variables and you can't obviously generate c code for plots or figures.
The code it generates could be a mess to understand but it works.
you should actually not try to understand it. In a certain way it is as you would try to understand the assembler your compiler generates from a C code you wrote, quite pointless.
another thing you should take care of is to declare persistent big data types (vectors, big arryes, etc.) otherwise they will be allocated into your stack...
good luck!