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I need to solve the heat equation for 2D object using C++. I've found many sources explaining the mathematics behind it. I am using the Crank-Nicholson scheme, but given that I need a 1001 x 1001 discretization, the resulting linear system is huge and memory would blow in case of a "traditional" implementation.
Therefore, I am recurring to methods for solving sparse linear systems. I have been looking online and cannot find any source explaining an algorithm to solve this sparse system efficiently. I've found several packages that do solve it (like csparse, eigen, SciPy under-the-hood implementation), but found no theoretical explanation to really code it myself. For the moment I am trying to do "reverse engineering" on the source code of SuperLU.
What I am looking for is an algorithm that you may know to solve sparse linear systems.
Thanks in advance
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The TensorFlow white paper mentions that Eigen is used. Are there public explanations for how Eigen was chosen, and are they motivation for using Eigen in TensorFlow C++ op kernels?
I think that one of the key feature that drove the use of Eigen in the first place is because Eigen features its own highly optimized matrix product kernels whereas all other competitors have to be linked to some BLAS libraries. Moreover, the code of Eigen's product kernel is C++ with easy access to low-level internal kernels, so it was 'easy' for them to tweak and extend it to match their needs. This way Google has been able to develop the Tensor module with high CPU performance in a pure header-only fashion. The support for CUDA and now OpenCL via SyCL came later, those are not intrinsic features of Eigen that drove the initial choice.
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For a more complex project, I need to compute the approximate, relative distances of objects from two images (from stereo-cameras). Practically what this neat tutorial explains: https://chrisjmccormick.wordpress.com/2014/01/10/stereo-vision-tutorial-part-i/ and with a result like that
Think I shouldn't be reinventing the wheel for this project and since speed is very important (realtime from two videostreams) I'm looking for a native library (preferably in C++ where the whole project is written in) for this task.
Does anyone have a suggestion?
Open source would be greatest but not mandatory.
Huge thanks in advance!
try with LIBELAS library (Library for Efficient Large-scale Stereo Matching).
Best!
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are there any examples of solving heat conduction problems in 2D with fourier's law as main equation with finite elements and using either libmesh or deal.II libraries?
The 2D heat equation is the only way to solve heat conduction problems. Lots of examples using finite difference, finite element, and boundary element methods. All require meshes of some kind. Which one do you want to apply?
OK, so now we know you want to solve 2D heat conduction problems using FEA. It's a three step process:
Pre-process (create the mesh for your geometry, apply material properties, boundary conditions, and initial conditions (if transient or non-linear).
Perform the analysis (formulate and solve the matrix equations for node and element unknowns).
Post-process (graphical display of results is best, since pictures are worth thousands of words).
Which solver do you wish to use? Is your objective to write one or just use one? Do you want open source? Must it be written in C++? (Not likely. FORTRAN is by far the most common language for such programs.)
Is yours a large problem? I'm guessing no, but massive parallelization might be of interest to you:
http://www.cas.usf.edu/~cconnor/parallel/2dheat/2dheat.html
FEMHub likes Python, probably because of the nice libraries NumPy and SciPy.
Here's a site that lists open source libraries for Java.
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I have a large 3D matrix and a small 3D matrix which I want to use 3D fft based convolution to find the best match for my small 3D matrix in the larger matrix. Do you have any code in C++ that can do it?
Stackoverflow is no community where one can request a code then gets it done by us, yet we can help you find the necessary resources and information so you are able to do so for yourself (usually questions on how to use libraries and help on specific topics are ok).
Let's come to your question: you already mentioned that you want to use FFT which is by far the best approach - a suitable library would be FFTW, so please take a look at it and keep the following things in mind:
To improve performace try to pad to powers of two which will speed up the process a lot!
Using real FFT and not complex will simplify and speed up this, too.
Usually single precision should be enough to achieve the desired results.
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I am looking for a C++ library, and I am dealing with convex objective and constraint functions.
I am guessing your problem is non-linear. Where i work, we use SNOPT, Ipopt and another proprietary solver (not for sale). We have also tried and heard good things about Knitro.
As long as your problem is convex, all these solvers work well.
They all have their own API, but they all ask for the same information : values, first and second derivatives.
Assuming your problems are nonlinear, you can use free and open-sourced OPT++, available from Sandia Lab. I have used it in one project in C++ and it was easy to use and worked well.
From what I know, the CPLEX solver is the best convex optimization solver. Its the state of the art in LP solvers. Does convex optimization really well. While looking for it, I see that its IBM's software now. You can find it here : http://www-01.ibm.com/software/integration/optimization/cplex/