I have spent the last few days looking for ODE solver in Clojure, and need some help.
Specifically, I was hoping to find one that does the same thing as the popular lsoda() function in the R package deSolve. (originally written in Fortran, I believe)
My search has been for either a Clojure library with these capabilities, or a Clojure library with the ability to call the original Fortran version from inside clojure.
I was hoping someone would already have experience on this topic and would be willing to help.
Thanks in advance!
EDIT: I have very little knowledge of ODEs in general so maybe I am entirely off base. I hope to model planetary orbiting in clojure. In my time with R, I used lsoda() to pass the initial positions and velocities of planets/stars, and ended up with predictions of the planets some amount of time later. Hope this helps explain what I am looking for.
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I have a huge problem. I need to solve a non linear sistem of 3 equations in 3 variables with a C++ function or class. I thought about using Newton-Raphson method to perform the solution. Unlukily I didn't find a source code that can do that for me. There would be someone that knows a program like that? I'm near deciding to build it myself. Thanks
A 3x3 system is not huge; it's actually a very small problem. People routinely solve nonlinear systems of equations with thousands (and more) of variables and constraints.
Given that your system is 3x3 and possibly nasty, a more appropriate choice of method would be a line search method. You get global convergence to a local minimum of the residual this way; it's very easy to make straight Newton's method diverge.
Steepest descent with backtracking line search is the simplest line search method possible. You might try implementing it first.
First, see related questions What good libraries are there for solving a system of non-linear equations in C++? and https://stackoverflow.com/questions/4914967/could-you-explain-how-newton-raphson-for-a-set-of-equations-works-code-inside. Also, try to use boost.
Consider this cozy C++ library
I have a set of problems (sets of equations and inequalities) for which I know that all variables have to be integers, and have finitely many solutions. I know that if I take any random objective function and let an lp or mip solver onto it, it finds a solution, however I want all solutions to the problem, and of course, as efficiently as possible. I don't really care about optimizing anything, but apparently most of the software that deals with it does. Is there any solver that can do that? If so, which one is the best/simplest one, or which one would you recommend? At best one that can be used as a C/C++ library.
There is a nice blog post by Paul Rubin on how to find K best solutions, which can be easily generalized to get all the solutions. As Ali suggested one of the approaches is to use a solution pool. Two other approaches are:
Use an incumbent callback to track and reject solutions.
Use an incumbent callback with solution injection.
See the blog post for details.
IBM ILOG CPLEX has a solution pool feature and it's free for academic purposes.
I guess you can probably get all solution if you set the maximum pool size sufficiently large. I don't know for sure, never tried.
I want to track an object in a video. So i suppose that I could use "Gaussian Mixture Models" in Opencv and C++ . I want to know how to write Gaussian Mixture Models in C++ . Are there any better algorithms for this than GMM?
Sorry to not answer the question directly but:
Reading research papers is a great thing to do, but to be honest, you will get much more knowledge at this point by trying your own ideas on your specific data and getting a better understanding of the problem.
If you know the shapes, it's probably better to use a generalized Hough transform or matched filter for position estimates, combined with a Kalman filter for tracking. These will be relatively easy to implement. Or maybe you can find existing implementations.
Also, I'd prototype your idea in Matlab or Octave instead of C++ if you are not a very good C++ programmer as you'll wind up wasting most of your time with problems in C++ when the problem itself is what you really want to focus on.
As I said in the comment, I'd skip out on using GMM's for now until you get a better understanding of the problem and how you are going to use them. (Unless of course you already have a good idea of how you will use them.)
I've been wanting to write my own multithreaded realtime raytracer in C++, but I don't want to implement all the vector and matrix logic that comes with it. I figured I'd do some research to find a good library for this, but I haven't had much success...
It's important that the implementation is fast, and preferably that it comes with some friendly licensing. I've read that boost has basic algebra, but I couldn't find anything on how good it was regarding its speed.
For the rest, Google gave me Armadillo, which claims to be very fast, and compares itself to certain other libraries that I haven't heard of.
Then I got Seldon, which also claims to be efficient and convenient, although I couldn't find out where exactly they are on the scale.
Lastly I read about Eigen, which I've also seen mentioned here on StackOverflow while searching here.
In the CG lecture at my university, they use HLSL for the algebra (making the students implement/optimise parts of the raytracer), which got me thinking whether or not I could use GLSL for this. Again, I have no idea what option is most efficient, or what the general consensus is on algebra libraries. I was hoping SO could help me out here, so I can get started with some real development :)
PS: I tried linking to sites, but I don't have enough rep yet
I'd recommend writing your own routines. When I wrote my raytracer, I found that most of the algebra used the same small collection of methods. Basically all you need is a vector class that supports addition, subtraction, etc. And from there all you really need is Dot and Cross.
And to be honest using GLSL isn't going to give you much more than that anyways (they only support dot, cross and simple vector math, everything else must be hand coded). I'd also recommend prototyping in C++ then moving to CUDA afterwards. It's rather difficult to debug a GPU code, so you can get it working in the CPU then recode it a bit to work in CUDA.
In reality raytracers are fairly simple. It's making them fast that is hard. It's the acceleration structures that are going to take most of your time and optimization. At least it did for me.
You should take look at http://ompf.org/forum/
This forum treats of realtime raytracing, mostly in C++. It will give you pointers, and sample source.
Most of the time, as every cycle count, people do not rely on external vector math libs: optimizations depend on the compiler you're using, inlining, use of SSE (or kindof) or not, etc.
I recommend "IlmBase" that is part of the OpenEXR package. It's well-written C++, developed by ILM, and widely used by people who professionally write and use graphics software.
For my projects I used glm, maybe it would also suit you.
Note that libraries such as boost::ublas or seldon probably won't suit you, because they're BLAS-oriented (and I assume you're looking for a good 3D-driven linear algebra library).
Also, the dxmath DirectX library is pretty good, although sometimes hard to use, because of it's C-compatible style.
You might look at the source code for POVRAY
I am newbie for integer linear programming.
I plan to use a integer linear programming solver to solve my combinatorial optimization problem.
I am more familiar with C++/object oriented programming on an IDE.
Now I am using NetBeans with Cygwin to write my applications most of time.
May I ask if there is an easy use ILP solver for me?
Or it depends on the problem I want to solve ? I am trying to do some resources mapping optimization. Please let me know if any further information is required.
Thank you very much, Cassie.
If what you want is linear mixed integer programming, then I would point to Coin-OR (and specifically to the module CBC). It's Free software (as speech)
You can either use it with a specific language, or use C++.
Use C++ if you data requires lots of preprocessing, or if you want to put your hands into the solver (choosing pivot points, column generation, adding cuts and so on...).
Use the integrated language if you want to use the solver as a black box (you're just interested in the result and the problem is easy or classic enough to be solved without tweaking).
But in the tags you mention genetic algorithms and graphs algorithms. Maybe you should start by better defing your problem...
For graphs I like a lot Boost::Graph
I have used lp_solve ( http://lpsolve.sourceforge.net/5.5/ ) on a couple of occasions with success. It is mature, feature rich and is extremely well documented with lots of good advice if your linear programming skills are rusty. The integer linear programming is not a just an add on but is strongly emphasized with this package.
Just noticed that you say you are a 'newbie' at this. Well, then I strongly recommend this package since the documentation is full of examples and gentle tutorials. Other packages I have tried tend to assume a lot of the user.
For large problems, you might look at AMPL, which is an optimization interpreter with many backend solvers available. It runs as a separate process; C++ would be used to write out the input data.
Then you could try various state-of-the-art solvers.
Look into GLPK. Comes with a few examples, and works with a subset of AMPL, although IMHO works best when you stick to C/C++ for model setup. Copes with pretty big models too.
Linear Programming from Wikipedia covers a few different algorithms that you could do some digging into to see which may work best for you. Does that help or were you wanting something more specific?