I use Mathematica for symbolic math calculations. I am planning to switch to another language. Matlab (which I use for standard computation stuff) includes this feature but I am looking at the possibility of using Julia, since it seems to be the future. Yet, there seems to be no symbolic tool available (no mention in official documentation). Apparently the only package available (SymPy) says "Test Failed" in the official website (http://pkg.julialang.org/).
Has anyone been able to do this in Julia?
Now, looking at http://pkg.julialang.org/ one could find more candidates to perform symbolic mathematics in julia:
SymEngine.jl
Julia Wrappers for SymEngine, a fast symbolic manipulation library, written in C++.
Symata.jl
a language for symbolic computations and mathematics, where, for the most part, "mathematics" means what it typically does for a scientist or engineer.
SymPy.jl
Julia interface to SymPy via PyCall
Also:
LinearExpressions.jl
Linear symbolic expressions for the Julia language
SymPy Package works fine, it brings Python's Sympy functionality into Julia via PyCall.
SymPy is a Python library for symbolic mathematics. It aims to
become a full-featured computer algebra system (CAS) while keeping the
code as simple as possible in order to be comprehensible and easily
extensible. SymPy is written entirely in Python and does not require
any external libraries.
Also, consider the Nemo.jl library which they claim is faster than alternatives like SageMath.
Related
I'm a R newbie.
is there a way i can calculate
(x+x^2+x^3)^2
in R?
so i will get the result:
x^6+2 x^5+3 x^4+2 x^3+x^2
I get an Error: object 'x' not found.
Thanks!
R isn't well suited for this. Some interface packages to languages and libraries that are better at this do exist, such as rSymPy, which allows you to access the SymPy Python library for symbolic mathematics (you'll need to install both). In a similar vein, Ryacas links to the yacas algebra system.
Those interfaces are useful if you need symbolic manipulation as part of an R workflow. Otherwise, consider using the original tools. The ones above are open source and freely available, while other free use alternatives also exist, such as the proprietary web based Wolfram Alpha (for limited use).
Over at http://scicomp.stackexchange.com I asked this question about parallel matrix algorithms in IDL. The answers suggest using a multi-threaded LAPACK implementation and suggest some hacks to get IDL to use a specific LAPACK library. I haven't been able to get this to work.
I would ideally like the existing LAPACK DLM to simply be able to use a multi-threaded LAPACK library and it feels like this should be possible but I have not had any success. Alternatively I guess the next simplest step would be to create a new DLM to wrap a matrix inversion call in some C code and ensure this DLM points to the desired implementation. The documentation for creating DLMs is making me cross-eyed though, so any pointers to doing this (if it is required) would also be appreciated.
What platform are you targeting?
Looking at idl_lapack.so with nm on my platform (Mac OS X, IDL 8.2.1) seems to indicate that the LAPACK routines are directly in the .so, so my (albeit limited) understanding is that it would not be simple to swap out (i.e., by setting LD_LIBRARY_PATH).
$ nm idl_lapack.so
...
000000000023d5bb t _dgemm_
000000000023dfcb t _dgemv_
000000000009d9be t _dgeqp3_
000000000009e204 t _dgeqr2_
000000000009e41d t _dgeqrf_
000000000023e714 t _dger_
000000000009e9ad t _dgerfs_
000000000009f4ba t _dgerq2_
000000000009f6e1 t _dgerqf_
Some other possibilities...
My personal library has a directory src/dist_tools/bindings containing routines for automatically creating bindings for a library given "simple" (i.e., not using typedefs) function prototypes. LAPACK would be fairly easy to create bindings for (the hardest part would probably be to build the package you want to use ATLAS, PLAPACK, ScaLAPACK, etc.). The library is free to use, a small consulting contract could be done if you would like it done for you.
The next version of GPULib will contain a GPU implementation of LAPACK, using the MAGMA library. This is effectively a highly parallel option, but only works on CUDA graphics cards. It would also work best if other operations besides the matrix inversion could be done on the GPU to minimize memory transfer. This option costs money.
I would like to convert an ARIMA model developed in R using the forecast library to Java code. Note that I need to implement only the forecasting part. The fitting can be done in R itself. I am going to look at the predict function and translate it to Java code. I was just wondering if anyone else had been in a similar situation before and managed to successfully use a Java library for the same.
Along similar lines, and perhaps this is a more general question without a concrete answer; What is the best way to deal with situations where in model building can be done in Matlab/R but the prediction/forecasting needs to be done in Java/C++? Increasingly, I have been encountering such a situation over and over again. I guess you have to bite the bullet and write the code yourself and this is not generally as hard as writing the fitting/estimation yourself. Any advice on the topic would be helpful.
You write about 'R or Matlab' to 'C++ or Java'. This gives 2 x 2 choices which is too many degrees of freedom for my taste. So allow me to concentrate on C++ as the target.
Let's consider a simpler case: Prototyping in R, and deploying in C++. If and when the R package you use is actually implemented in C or C++, this becomes pretty easy. You "merely" need to disentangle the routine you are after from its other dependencies (header files, defines, data structures, ...) and provide it with the data and parameters needed. I have done that in the past for production systems.
Here, you talk about the forecast package. This happens to depend on the RcppArmadillo package which itself brings the nice Armadillo C++ library to R. So chances are you can in fact re-write this as a self-contained unit.
Armadillo is also interesting when you want to port Matlab to C++ as it is written to help with exactly that task in mind. I have ported some relatively extensive Matlab code to C++ and reaped a substantial speed gain.
I'm not sure whether this is possible in R, but in Matlab you can interact with your Matlab code from Java - see http://www.cs.virginia.edu/~whitehouse/matlab/JavaMatlab.html. This would enable you to leave all the forecasting code in Matlab and have e.g. an interface written in Java.
Alternatively, you might want to have predictive code written in Java so that you can produce a model and then distribute a program that uses the model without having a dependency on Matlab. The Matlab compiler maybe be useful here, but I've never used it.
A final simple way of interacting messily between Matlab and Java would be (on linux) using pseudoterminals where you would have a pty/tty pair to interface Java and Matlab. In this case you would send data from Java to Matlab, and have Matlab return the forecasting results. I expect this would also work in R, but I don't know the syntax.
In general though, reimplementing the code is a decent solution and probably quicker than learning how to interface java+matlab or create Matlab libraries.
Some further information on the answer given by Richante: Matlab has some really nice capabilities for interop with compiled languages such as C/C++, C#, and Java. In your particular case you might find the toolbox Matlab Builder JA to be particularly relevant. It allows you to export your Matlab code directly to Java, meaning you can directly call code that you've constructed during your model-building phase in Matlab from Java.
More information from the Mathworks here.
I am also concerned with converting "R to Java" so will speak to that part.
As Vincent Zooneykind said in his comment - the PMML library in R makes sense for model export in general but "forecast" is not a supported library as of yet.
An alternative is to use something like https://www.opencpu.org/ to make a call to R from your java program. It surfaces the R code on a http server. Can then just call it with parameters as with a normal http call and return what is neede using java.net.HttpUrlConnection or a choice of http libraries available in Java.
Pros: Separation of concerns, no need to re-write the R code
Cons: Invoking an R server in your live process so need to make sure that is handled robustly
I am doing matrix operations on large matrices in my C++ program. I need to verify the results that I get, I used to use WolframAlpha for the task up until now. But my inputs are very large now, and the web interface does NOT accept such large values (textfield is limited).
I am looking for a better solution to quickly cross-check/do math problems.
I know there is Matlab but I have never used it and I don't know if thats what will suffice my needs and how steep the learning curve would be?
Is this the time to make the jump? or there are other solutions?
If you don't mind using python, numpy might be an option.
Apart from the license costs, MATLAB is the state of the art numerical math tool. There is octave as free open source alternative, with a similar syntax. The learning curve is for both tools absolutely smooth!
WolframAlpha is web interface to Wolfram Mathematica. The command syntax is exactly the same. If you have access to Mathematica at your university, it would be most smooth choice for you since you already have experience with WolframAlpha.
You may also try some packages to convert Mathematica commands to MATLAB:
ToMatlab
Mathematica Symbolic Toolbox for MATLAB 2.0
Let us know in more details what is your validation process. How your data look like and what commands have you used in WolframALpha? Then we can help you with MATLAB alternative.
Given my previous questions about the the usage of AMPL.
Are there any other programming/scripting languages that are strictly meant for mathmatical processing?
For example: Matlab (it does deviate a bit from a mathematical structure, but its close enough), Mathematica, and AMPL
R / S+ for statistical computing
Other stat languages: SAS, SPSS, STATA, GAUSS, etc.
Octave, an open source clone of Matlab
Fortress, "a language for high-performance computation that provides abstraction and type safety on par with modern programming language principles."
Maple
Maxima
There's always APL, with its builtin matrix operators. Modern APL even supports .NET.
R, Numpy/scipy for Python, Maple, Yacas, even Fortran.
This may be only of historical significance, but Fortan (The IBM Mathematical Formula Translating System) is especially suited to numeric computation and scientific computing.
OPL (Optimization Programming Language) is one of the most comprehensive modelling languages for Mathematical Programming. You can do Linear Programming (LP), Mixed Integer Programming (MIP), Quadratic Programming (QP), Constraint Programming (CP), MIQP, etc.
IBM-ILOG CPLEX Optimization Studio uses this language.
Maple for symbolic math (similar to Mathematica).
SAS, SPSS, R for statistics.
The Operation Research / Management Science magazine has a yearly survey of Simulation Software, and while I can't find the link I believe they have one yearly survey on optimization packages, such as AMPL you are quoting.
Sage is basically Python with a load of packages and a few language extensions put into a "notebook" interface like that of Mathematica. It has interfaces to all sorts of computer algebra systems. And with Numpy and Scipy (which are included) it's a fine replacement for Matlab. And it's open source and actively developed.
Given your previous question, I assume you are looking for an alternative to commercial mathematics packages. If so, you should try Sage, it is open source and is a unified front end for almost all of the open source mathematics/sci.calc. packages out there (list).
The way it works, is that it uses your web browser as a graphical front end for displaying, editing and evaluating Mathematica style notebooks (it is also possible to just use the command line). All the dirty work, such as selecting the appropriate package for the situation, is done transparently in the background.
Sage uses Python as it's main language / syntax, so it's fairly easy to learn, and if you have old Python scripts, they should work straight out of the box. If I didn't have access to a Mathematica license, I would definitely use this.
Interactive Data Language (IDL) is a proprietary language used in astronomy, medicine and other sciences at least in part because of its built-in array operations and mathematical library.
As this question is still open and well indexed in Google, I would definitively add to the list the Julia language.
Aside the technical aspects that make shine this high level/high performance new language, an important consideration is that the community of developers/users is clearly biased toward mathematicians.