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++.
Related
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
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 am looking into some C++ code which extensively uses boost::multi_array<double>.
The next step is to port the code to use openCL. As I'm quite new to openCL I don't know what I should do with the multi_array. Should I rewrite it into a nested-openCL-vector or nested-c-array.
What would you do?
There are boost like libraries already exist for OpenCL, you may want to look at the following libraries from GPU Vendors
Thurst from NVIDIA: Thrust is a powerful library of parallel algorithms and data structures. Thrust provides a flexible, high-level interface for GPU programming that greatly enhances developer productivity. Using Thrust, C++ developers can write just a few lines of code to perform GPU-accelerated sort, scan, transform, and reduction operations orders of magnitude faster than the latest multi-core CPUs. For example, the thrust::sort algorithm delivers 5x to 100x faster sorting performance than STL and TBB.
AMD offers Math Libraries are software libraries containing FFT and BLAS functions written in OpenCL and designed to run on AMD GPUs for more info look here:
http://developer.amd.com/libraries/appmathlibs/Pages/default.aspx
I need to do multiplication on matrices. I'm looking for a library that can do it fast. I'm using the Visual C++ 2008 compiler and I have a core i7 860 so if the library is optimized for my configuration it's perfect.
FWIW, Eigen 3 uses threads (OpenMP) for matrix products (in reply to above statement about Eigen not using threads).
BLAS is a de facto Fortran standard for all basic linear algebra operations (essentially multiplications of matrices and vectors). There are numerous implementations available. For instance:
ATLAS is free and supposedly self-optimizing. You need to compile it yourself though.
Goto BLAS is maintained by Kazushige Goto at TACC. He is very good at getting the last performance bit out of modern processors. It is only for academic use though.
Intel MKL provides optimised BLAS for Intel processors. It is not free, even for academic use.
Then, you may want to use a C++ wrapper, for instance boost::ublas.
If you program on distributed systems, there are PBLAS and ScaLAPACK which enable the use of message passing for distributed linear algebra operations. On a multicore machine, usually implementations of BLAS (at least Intel MKL) use threads for large enough matrices.
If you want more advanced linear algebra routines (eigenvalues, linear systems, least square, ...), then there is the other de facto Fortran standard LAPACK. To my knowledge, there is nothing to integrate it elegantly with C++ other than calling the bare Fortran routines. You have to write some wrappers to hide the Fortran calls and provide a sound type-checking implementation.
Look into Eigen. It should have all you need.
I have had good experience with Boost's uBLAS. It's a nice option if you're already using Boost.
You can use the GNU Scientific Library(GSL).
Here's a page describing the matrix operations available in the library, including multiplication(gsl_matrix_mul_elements()):
http://www.gnu.org/software/gsl/manual/html_node/Matrix-operations.html
And here are some links to get you started with using GSL with visual studio:
http://gladman.plushost.co.uk/oldsite/computing/gnu_scientific_library.php
http://www.quantcode.com/modules/smartfaq/faq.php?faqid=33
it can't race with scientific libraries, but with visual c++ it is at hand
#include <windows.h>
#include <gdiplus.h>
#pragma comment (lib,"Gdiplus.lib")
using namespace Gdiplus;
int main()
{
ULONG_PTR gpToken = 0;
GdiplusStartup(&gpToken, &GdiplusStartupInput(), NULL);
//lib inited
Matrix A;
A.Translate(10,20);
Matrix B;
B.Rotate(35.0);
A.Multiply(&B);
if (A.IsInvertible())
A.Invert();
if (!A.IsIdentity())
A.RotateAt(120.0, PointF(10,10));
//getting values
REAL elements[6];
A.GetElements(elements);
//lib stopped
GdiplusShutdown(gpToken);
return 0;
}
so with this you can easily take the matrix multiplication obstacle (on Windows)
GdiPlus Matrix Documentation
for more recent version of Visual Studio, you can use ScaLapack + MKL.
A sample of code is provided here , with a tutorial on how to make it run.
http://code.msdn.microsoft.com/Using-ScaLAPACK-on-Windows-d16a5e76#content
There's an option to implement this yourself, perhaps using std::valarray because that may be parallelised using OpenMP: gcc certainly has such a version, MSVC++ probably does too.
Otherwise, the following tricks: one of the matrices should be transposed. Then you have:
AB[i,j] = Sum(k) A[i,k] B^t [j,k]
where you're scanning contiguous memory. If you have 8 cores you can fairly easily divide the set of [i,j] indices into 8, and give each core 1/8 of the total job. To make it even faster you can use vector multiply instructions, most compilers will provide a special function for this. The result won't be as fast as a tuned library but it should be OK.
If you're doing longer calculations such as polynomial evaluation, a threading evaluator which also has thread support (gak, two kind of threads) will do a good job even though it won't do low level tuning. If you really want to do stuff fast, you have to use a properly tuned library like Atlas, but then, you probably wouldn't be running Windows if you were serious about HPC.