I require a matrix library for C++ AMP that is able to perform basic operations as well as matrix inversion for arbitrarily sized matrices and QR decomposition.
I initially found that there is a BLAS AMP implementation, however I could not find anywhere that stated whether or not BLAS can perform matrix inversion, can anyone enlighten me about its capabilities and/or suggest a more suitable parallel matrix library for AMP? Thanks!
edit: I found a LAPACK AMP library which is capable of matrix inversion (I think), however it's still in development :(
As far as I know, your best bet is the LAPACK library that you already linked to. C++ AMP is still fairly new and doesn't seem to have a large uptake in scientific computing so far.
There are also some other C++ AMP libraries in development that may be of interest to you.
Algorithms
BLAS
FFT
Random Number Generation
Generic Kernels
I have not been able to find any LAPACK libraries for C++ AMP. However, there are some available for OpenCL.
Specifically clMAGMA from the University of Tennessee.
http://icl.cs.utk.edu/magma/software/view.html?id=152
You will need the AMD OpenCL BLAS library to sit under the LAPACK from here:
http://developer.amd.com/tools-and-sdks/heterogeneous-computing/amd-accelerated-parallel-processing-math-libraries/
I think this is your only bet at inverting a matrix with open source libraries on your GPU. Being openCL, this will be platform agnostic (like C++ AMP), unlike CUDA.
-Matt Musto
www.mustotechnologies.com
Related
There has been a post regarding usage of MPI with Armadillo in C++: here
My question is, wether Lapack and OpenBlas did implement MPI support?
I could not anything so far in their documentations.
There seems to be a different library called ScaLAPACK, which uses MPI. Is this library compatible with Armadillo. Is it any different from LAPACK in use?
I need to diagonalise extremely large matrices (over 1TB of memory), therefore I need to spread the memory over multiple nodes on a cluster using MPI, but I don't know how to deal with that using Armadillo.
Do you have any useful tip/reference where I could find how to do that?
Any Blas is single-process. Some Blas implementations do multi-threading. So MPI has nothing to do with this: in an MPI run, each process calls a non-distributed Blas routine.
Scalapack is distributed memory, based on MPI. It is very different from Lapack. Matrix handling is considerably more complicated. Some applications / libraries are able to use Scalapack, but you can not switch out Lapack for Scalapack: support for Scalapack needs to be added explicitly.
Armadillo mentions threading support through OpenMP, and there is no mention of MPI. Therefore, you can not use Armadillo over multiple nodes.
If you want to do distributed eigenvalue calculations, take a look at the PETSc library and the SLEPc package on top of it. Those are written in C, so they can easily (though not entirely idiomatically) be used from C++.
I'm exploring the Armadillo C++ library for linear algebra at the moment. As far as I understood it uses LAPACK/BLAS library for basic matrix operations (e.g. matrix multiplication). As a Windows user I downloaded LAPACK/BLAS from here: http://icl.cs.utk.edu/lapack-for-windows/lapack/#running. The problem is that matrix multiplications are very slow comparing to Matlab or even R. For example, Matlab multiplies two 1000x1000 matrices in ~0.15 seconds on my computer, R needs ~1 second, while C++/Armadillo/LAPACK/BLAS needs more than 10 seconds for that.
So, Matlab is based on highly optimized libraries for linear algebra. My question is if there exists a faster LAPACK/BLAS brary to use from Armadillo? Alternatively, is there a way to extract Matlab linear algebra libraries somehow and use them in C++?
LAPACK doesn't do matrix multiplication. It's BLAS that provides matrix multiplication.
If you have a 64 bit operating system, I recommend to first try a 64 bit version of BLAS. This will get you an immediate doubling of performance.
Secondly, have a look at a high-performance implementation of BLAS, such as OpenBLAS. OpenBLAS uses both vectorisation and parallelisation (ie. multi-core). It is a free (no cost) open source project.
Matlab internally uses the Intel MKL library, which you can also use with the Armadillo library. Intel MKL is closed source, but is free for non-commercial use. Note that OpenBLAS can obtain matrix multiplication performance that is on par or better than Intel MKL.
Note that high performance linear algebra is generally easier to accomplish on Linux and Mac OS X than on Windows.
Adding to what has already been said, you should also use a high level of optimization:
Be sure to use either the O2 or the O3 compiler flag.
Link to the above mentioned high performance (and possibly multi-threaded) BLAS libraries. AFAIK MKL is only freely available for Unix platforms though, if you're using a Linux box like cygwin inside windows, this should be OK then I guess. OpenBLAS is also multi-threaded.
In many libraries, setting the symbol NDEBUG (e.g. passing the compiler flag -DNDEBUG) turns off costly range checking and assertions. Armadillo has its own symbol, called ARMA_NO_DEBUG, which you can either set manually, or you can edit the config.hpp header file (located in the armadillo include directory) and uncomment the corresponding line. I am guessing since you were able to turn on external BLAS usage in armadillo, you should be familiar with this config file anyways...
I did a quick comparison between armadillo/MKL_BLAS and Matlab on my intel core-i7 workstation. For the C++ exe I used -O3, MKL BLAS and had ARMA_NO_DEBUG defined. I multiplied 1000x1000 random matrices 100 times and averaged the multiplication times.
The C++ implementation was roughly 1.5 times faster than matlab.
Hope this helps
is there a way to extract Matlab linear algebra libraries somehow and use them in C++?Yes, for C++ call matlab function, refer to this link: How to Call Matlab Functions from C++
Several C++ lib for linear algebra provide an easy way to link with hightly optimized lib.
look at http://software.intel.com/en-us/articles/intelr-mkl-and-c-template-libraries
You should be able to link Armadillo to the MKL for more performance but it's a commercial package,
What libraries are available for parallel distributed cholesky decomposition of dense matrices in C/C++ in mpi environment?
I've found the ScaLAPACK library, and this might be the solution I'm looking for. It seems that it's a bit fiddly to call though, lots of Fortran <-> C conversions to do, which makes me think that maybe it is not widely used, and therefore maybe there are some other libraries that are used instead?
Alternatively, are there some wrappers for ScaLAPACK that make it relatively not too painful to use in a C or C++ environment, when one is already using MPI, and MPI has already been initialized in the program?
Are these dense or sparse matrices?
Trilinos is a huge library for parallel scientific computation. The sub-package Amesos can link to Scalapack for parallel, direct solution of dense systems and to UMFPACK, SuperLU or MUMPS for sparse systems. Trilinos is mostly in C++, but there are Python bindings if that's your taste. It might be overkill, but it'll get the job done.
Intel MKL might also be a choice, since it calls ScaLAPACK on the inside. Note that Intel supports student use of this library, but in this case you have to use an open source MPI version. Also the Intel forum is very helpful.
Elemental is also an option, written in C++, which is surely a big advantage when you want to integrate with your C/C++ application and the project leader, Jack Poulson is a very friendly and helps a lot.
OpenBLAS, SuperLU and PETSc are also interesting and you may want to read more in my answer.
I have a dense system of equations of type Ax=b to solve in my C++ program, and I was hoping to implement the solution using UBLAS in boost. In some other questions I found that people were using the extension LAPACK, but unfortunately it doesn't seem to be part of my standard boost installation (in Debian at least) and I am not allowed to add more dependencies.
Could someone paste a solution that doesn't use LAPACK or any other libraries?
Unfortunately, you're solving a linear system which either requires LAPACK or writing your own code. If you don't want LAPACK, your only other option is to write your own solver. Such a solver can use uBLAS of course.
If you need the code to do it, you can look at numerical recipes for an example. But, solving dense linear systems is a very rich subject, so it's probably beyond the scope here to address all aspects of it.
Are there free C/C++ libraries taht do the types of functions that matlab does - something complicated i mean, like discrete laplacian, etc? Is the best option to create some kind of interface in matlab and build my own library?
Thanks
Have you looked at Boost.Math?
http://www.boost.org/doc/libs/1_46_1/libs/math/doc/html/index.html
If you are on windows, there is a very easy to use installer by BoostPro:
http://www.boostpro.com/download/
If you want something that was a matlab clone but free, you could use Octave http://www.gnu.org/software/octave/
I haven't used it in a C++ program, but it apparently has a C++ API:
http://octave.sourceforge.net/doxygen/html/index.html
Depending on what you want to do there are various packages available.
Arbitrary Precision
mostly integers: GMP, MPIR (similar codebases, MPIR has VC builds)
floats: MPFR
complex: MPC
Specialist:
Number Theory: Flint
Linear Algebra: Boost Numeric uBLAS
PDEs: libMesh
Computational Fluid Dynamics: OpenFoam
Graph Theory: Boost Graph
General:
TNT (was LAPACK++ (TNT=do everything, LAPACK++=Linear Alg.)
SciMath (Commercial)
GNU Scientific Library
and that's just a few. I haven't repeated ones others have listed like libpari.
Just in case you're wondering, Maple, Mathematica, Matlab etc all use the GNU MP for their arbitrary precision calculations.
PARI could be a good choice, although I am not familiar with using it:
Official Site for PARI
PARI is a C library, and if you want an independent software, they have PARI-GP there.
Below is the description of PARI on the website above:
PARI/GP is a widely used computer
algebra system designed for fast
computations in number theory
(factorizations, algebraic number
theory, elliptic curves...), but also
contains a large number of other
useful functions to compute with
mathematical entities such as
matrices, polynomials, power series,
algebraic numbers etc., and a lot of
transcendental functions. PARI is also
available as a C library to allow for
faster computations.
Hope this could be useful!
P.S. It is said that Octave functions could be called from C++, and that could be an excellent substitution for MATLAB.
Have a look at armadillo for simplifying your handling of matrices. Then for solving PDEs you'll have to do the job yourself, ie. construct explicitly your Laplacian matrix, and solve it the way you want.
There is Intel MKL too (not free though) which adds some value: iterative solvers (GMRES, BCG) and some black-boxes for solving the Laplacian / Poisson equation on simple domains (cubes and spheres).
I use OpenCV for a lot of image processing and matrix manipulation, which is generally what I use matlab for.
http://opencv.willowgarage.com/wiki/
May be overkill depending on what kind of math your trying to do, but it's great for computer vision.
The GNU Scientific Library is a free numerical library for C and C++ programmers.
With the Coder toolbox (requires MATLAB R2011a), you can also turn your MATLAB code into C or C++.
you can use octave runtime:
http://en.wikipedia.org/wiki/GNU_Octave#C.2B.2B_Integration