I'm facing a little problem. I'm translating a program from matlab/octave to C++. This progam is dealing with some matrix manipulation. I want to reproduce this : in matlab/octave we can define a matrix like :
matrix = zeros(10,25,360);
and I get a matrix with 10 rows, 25 columns and a "depth" of 360. I want to reproduce the same thing in C++ using Eigen.
Thank you in advance for your help.
There are unsupported Modules for Eigen which let you define tensors. With those modules you can translate your problem into C++.
The current Eigen tensor module is extremely limited feature wise. You can't even add the coefficients of 2 tensors together! I have been using the tensor code in this fork of Eigen instead. It adds support for coefficient wise operations, convolutions, contractions, and recently morphing primitives such as slicing. Moreover it can take advantage of GPUs to speed things up which was the big selling point for me.
There is a pending pull request so hopefully it will make its way into the main Eigen code base soon.
Related
At present I have a system Ax = b such that A is a tridiagonal matrix. Using Eigen, I can already solve this system using the line:
x = A.colPivHouseholderQr().solve(b);
However, since A is a tridiagonal matrix this works rather slowly compared to say in MATLAB, since the program is mostly likely computing the solution for all values rather than just on the three diagonals. Can Eigen solve this system faster? This is probably quite a dumb questions but I'm fairly new to C++ and I only started using Eigen a few days ago so there's a lot to take in at the moment! Thanks in advance.
The best you can do is to implement the Thomas algorithm yourself. Nothing can beat the speed of that. The algorithm is so simple, that nor Eigen nor BLAS will beat your hand-written code. In case you have to solve a series of matrices, the procedure is very well vectorizable.
https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
If you want to stick with standard libraries, the BLAS DGTSV (double precision) or SGTSV (single precision) is probably the best solution.
I implemented a program on the GPU (CUDA) which only uses the host (in C++) to start new kernels. During the calculation on the device I need SVD and solving systems of 3x3 (dense) matrices, fixed size.
I've got my own SVD and solver implementation but it is not numerical stable (thus not usable). Due to me being rather new with C++ and CUDA I would prefer to use a library instead. (numerical stuff is very tricky)
Now I have trouble finding that library:
cuSOLVER is not callable from the device
cuLA is not callable form the device (and abandoned so it seems)
Eigen looks promising (should be callable from device?) but it is unclear what the status is on CUDA support (it says experimental). I find people saying it works, others got compile errors?
Preferable I would also being able to do general matrix operations with the library (transpose, inversion, sum, multiply, ...) as my own implementations will likely be less efficient and numerically stable for those.
Any ideas on how to achieve this?
UPDATE:
Seems like Eigen supports basic functions like *,+, transpose and even eigenvalues but SVD, inverse ect is not yet supported. This is at the time of writing.
According to the website, a subset of features works for fixed size matrices (3x3 in your case) from Eigen 3.3. The current stable release is 3.2.6 while 3.3 is in alpha. I don't know if specifically SVD is supported in CUDA. I would recommend trying a small MCVE to see if it works (as well as the other functions you require), and if so, implementing it in your project.
I'm having a similar problem; want to generate random vectors within a kernel function which requires performing cholesky/eigenvalue decompositions of NxN (N<=5) covariance matrices. Since, as you noted, the MAGMA and CULA libraries are not available from the device, and there seems to be no cuSOLVER device API yet, I've resorted to implementing these myself following algorithms outlined in, for example, Numerical Recipes in C. As for solving linear systems, I'd suggest checking out the cuBLAS (level 2 functions), as it provides some basic functionality. If you want to invert matrices, I'd suggest cublasmatinvBatched(). I haven't used it myself, will give it a try during the weekend, but from the description it sounds promising. Hope others will chime into this thread with better solutions...
I need to convert my MATLAB code to C++, which include linear equations in the form xA=0.
I know that Eigen can deal linear equations Ax=b. I am asking: is there a way to solve a system of linear equations xA=b, using Eigen for C++ (Visual Studio 2010), with A being a sparse matrix? If not, what library can I use?
Thank you for any help.
x*A = b
is equivalent to
A.transpose() * z = b.transpose();
x = z.transpose()
which can be solved for x.
Note, that storage operations are cheap in comparison to the solving of the linear system.
A is sparse and the sparsity remains the same for the transpose operation.
Often, transposition is just a flag and a change in the addressing of the elements. From my first glance into the doc this does not apply to Eigen. But, from what I told you before, this does not matter so much.
I need to solve some large (N~1e6) Laplacian matrices that arise in the study of resistor networks. The rest of the network analysis is being handled with boost graph and I would like to stay in C++ if possible. I know there are lots and lots of C++ matrix libraries but no one seems to be a clear leader in speed or usability. Also, the many questions on the subject, here and elsewhere seem to rapidly devolve into laundry lists which are of limited utility. In an attempt to help myself and others, I will try to keep the question concise and answerable:
What is the best library that can effectively handle the following requirements?
Matrix type: Symmetric Diagonal Dominant/Laplacian
Size: Very large (N~1e6), no dynamic resizing needed
Sparsity: Extreme (maximum 5 nonzero terms per row/column)
Operations needed: Solve for x in A*x=b and mat/vec multiply
Language: C++ (C ok)
Priority: Speed and simplicity to code. I would really rather avoid having to learn a whole new framework for this one problem or have to manually write too much helper code.
Extra love to answers with a minimal working example...
If you want to write your own solver, in terms of simplicity, it's hard to beat Gauss-Seidel iteration. The update step is one line, and it can be parallelized easily. Successive over-relaxation (SOR) is only slightly more complicated and converges much faster.
Conjugate gradient is also straightforward to code, and should converge much faster than the other iterative methods. The important thing to note is that you don't need to form the full matrix A, just compute matrix-vector products A*b. Once that's working, you can improve the convergance rate again by adding a preconditioner like SSOR (Symmetric SOR).
Probably the fastest solution method that's reasonable to write yourself is a Fourier-based solver. It essentially involves taking an FFT of the right-hand side, multiplying each value by a function of its coordinate, and taking the inverse FFT. You can use an FFT library like FFTW, or roll your own.
A good reference for all of these is A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles.
Eigen is quite nice to use and one of the fastest libraries I know:
http://eigen.tuxfamily.org/dox/group__TutorialSparse.html
There is a lot of related post, you could have look.
I would recommend C++ and Boost::ublas as used in UMFPACK and BOOST's uBLAS Sparse Matrix
I am writting a program in Visual Studio using MFC dialog based application.
I have 5 matrix in my program where I have to add two of them and multiply other 2 of them and then subtract the result of multiplication from the summed value to get the 5th matrix.
Some time I have to square the summed matrix also so it is quite laborious to write the full code...
So one way is to write the code straight forward in C++ using array...But if I want to multiply two matrices or sum them directly as can be done in MatLab, is it possible in C++?
If yes then how?
Boost has a good library for linear algebra: Boost.uBLAS.
It includes a convenient matrix class, as well as built in matrix arithmetic operations.
Eigen is very powerful and highly optimized. It supports both dynamic matrices (size unknown at compile time) and statically sized matrices. Take a look at the tutorial.
What's a good C++ library for matrix operations
I recommend the gmtl (generic math template library).