SuperLU_DIST contains a set of subroutines to solve a sparse linear system A*X=B. It uses Gaussian elimination with static pivoting (GESP). Static pivoting is a technique that combines the numerical stability of partial pivoting with the scalability of Cholesky (no pivoting), to run accurately and efficiently on large numbers of processors.
SuperLU_DIST is a parallel extension to the serial SuperLU library. It is targeted for the distributed memory parallel machines. SuperLU_DIST is implemented in ANSI C, with OpenMP for on-node parallelism and MPI for off-node communications. We are actively developing multi-GPU acceleration capabilities.
- SuperLU_DIST (version 9.1.0)
- Directory structure of the source code
- Installation
- Summary of the environment variables.
- Windows Usage
- Reading sparse matrix files
- REFERENCES
- RELEASE VERSIONS
Created by gh-md-toc
SuperLU_DIST contains a set of subroutines to solve a sparse linear system A*X=B. It uses Gaussian elimination with static pivoting (GESP). Static pivoting is a technique that combines the numerical stability of partial pivoting with the scalability of Cholesky (no pivoting), to run accurately and efficiently on large numbers of processors.
SuperLU_DIST is a parallel extension to the serial SuperLU library. It is targeted for the distributed memory parallel machines. SuperLU_DIST is implemented in ANSI C, with OpenMP for on-node parallelism and MPI for off-node communications. We are actively developing GPU acceleration capabilities.
SuperLU_DIST/README instructions on installation
SuperLU_DIST/CBLAS/ needed BLAS routines in C, not necessarily fast
(NOTE: this version is single threaded. If you use the
library with multiple OpenMP threads, performance
relies on a good multithreaded BLAS implementation.)
SuperLU_DIST/DOC/ the Users' Guide
SuperLU_DIST/FORTRAN/ Fortran90 wrapper functions
SuperLU_DIST/EXAMPLE/ example programs
SuperLU_DIST/INSTALL/ test machine dependent parameters
SuperLU_DIST/SRC/ C source code, to be compiled into libsuperlu_dist.a
SuperLU_DIST/TEST/ testing code
SuperLU_DIST/lib/ contains library archive libsuperlu_dist.a
SuperLU_DIST/Makefile top-level Makefile that does installation and testing
SuperLU_DIST/make.inc compiler, compiler flags, library definitions and C
preprocessor definitions, included in all Makefiles.
(You may need to edit it to suit your system
before compiling the whole package.)
SuperLU_DIST/MAKE_INC/ sample machine-specific make.inc files
There are two ways to install the package. The first method is to use CMake automatic build system. The other method requires users to The procedures are described below.
You will need to create a build tree from which to invoke CMake.
If you have a BLAS library on your machine, you can link with it with the following cmake definition:
-DTPL_BLAS_LIBRARIES="<BLAS library name>"
Otherwise, the CBLAS/ subdirectory contains the part of the C BLAS (single threaded) needed by SuperLU_DIST, but they are not optimized. You can compile and use it with the following cmake definition:
-DTPL_ENABLE_INTERNAL_BLASLIB=ON
The default sparsity ordering is METIS. But, in order to use parallel symbolic factorization function, you need to install ParMETIS parallel ordering package and define the two environment variables: PARMETIS_ROOT and PARMETIS_BUILD_DIR
(Note: ParMETIS library also contains serial METIS library.)
export PARMETIS_ROOT=<Prefix directory of the ParMETIS installation>
export PARMETIS_BUILD_DIR=${PARMETIS_ROOT}/build/Linux-x86_64
In order to use parallel weighted matching HWPM (Heavy Weight Perfect Matching) for numerical pre-pivoting, you need to install CombBLAS and define the environment variable:
export COMBBLAS_ROOT=<Prefix directory of the CombBLAS installation>
export COMBBLAS_BUILD_DIR=${COMBBLAS_ROOT}/_build
Then, install with cmake option:
-DTPL_ENABLE_COMBBLASLIB=ON
By default, LAPACK is not needed. Only in triangular solve routine, we may use LAPACK to explicitly invert the dense diagonal block to improve speed. You can use it with the following cmake option:
-DTPL_ENABLE_LAPACKLIB=ON
You can enable (NVIDIA) GPU with CUDA with the following cmake option:
-DTPL_ENABLE_CUDALIB=TRUE
You can enable (AMD) GPU with HIP with the following cmake option:
-DTPL_ENABLE_HIPLIB=TRUE
Once these needed third-party libraries are in place, the installation can be done as follows at the top level directory:
For a simple installation with default setting, do: (ParMETIS is needed, i.e., TPL_ENABLE_PARMETISLIB=ON)
mkdir build ; cd build;
cmake .. \
-DTPL_PARMETIS_INCLUDE_DIRS="${PARMETIS_ROOT}/include;${PARMETIS_ROOT}/metis/include" \
-DTPL_PARMETIS_LIBRARIES="${PARMETIS_BUILD_DIR}/libparmetis/libparmetis.a;${PARMETIS_BUILD_DIR}/libmetis/libmetis.a" \
For a more sophisticated installation including third-party libraries, do:
cmake .. \
-DTPL_PARMETIS_INCLUDE_DIRS="${PARMETIS_ROOT}/include;${PARMETIS_ROOT}/metis/include" \
-DTPL_PARMETIS_LIBRARIES="${PARMETIS_BUILD_DIR}/libparmetis/libparmetis.a;${PARMETIS_BUILD_DIR}/libmetis/libmetis.a" \
-DTPL_ENABLE_COMBBLASLIB=ON \
-DTPL_COMBBLAS_INCLUDE_DIRS="${COMBBLAS_ROOT}/_install/include;${COMBBLAS_R\
OOT}/Applications/BipartiteMatchings" \
-DTPL_COMBBLAS_LIBRARIES="${COMBBLAS_BUILD_DIR}/libCombBLAS.a" \
-DCMAKE_C_FLAGS="-std=c99 -g -DPRNTlevel=0 -DDEBUGlevel=0" \
-DCMAKE_C_COMPILER=mpicc \
-DCMAKE_CXX_COMPILER=mpicxx \
-DCMAKE_CXX_FLAGS="-std=c++11" \
-DTPL_ENABLE_INTERNAL_BLASLIB=OFF \
-DBUILD_SHARED_LIBS=OFF \
-DCMAKE_INSTALL_PREFIX=.
( see example cmake script: run_cmake_build.sh )
You can disable CombBLAS or LAPACK with the following cmake options:
-DTPL_ENABLE_LAPACKLIB=FALSE
-DTPL_ENABLE_COMBBLASLIB=FALSE
To actually build (compile), type:
make
To install the libraries, type:
make install
To run the installation test, type:
ctest
(The outputs are in file: build/Testing/Temporary/LastTest.log)
or,
ctest -D Experimental
or,
ctest -D Nightly
NOTE:
The parallel execution in ctest is invoked by "mpiexec" command which is
from MPICH environment. If your MPI is not MPICH/mpiexec based, the test
execution may fail. You can pass the definition option "-DMPIEXEC_EXECUTABLE"
to cmake. For example on Cori at NERSC, you will need the following:
-DMPIEXEC_EXECUTABLE=/usr/bin/srun
Or, you can always go to TEST/ directory to perform testing manually.
The following list summarize the commonly used CMake definitions. In each case, the first choice is the default setting. After running 'cmake' installation, a configuration header file is generated in SRC/superlu_dist_config.h, which contains the key CPP definitions used throughout the code.
-TPL_ENABLE_PARMETISLIB=ON | OFF
-DTPL_ENABLE_INTERNAL_BLASLIB=OFF | ON
-DTPL_ENABLE_LAPACKLIB=OFF | ON
-TPL_ENABLE_COMBBLASLIB=OFF | ON
-DTPL_ENABLE_CUDALIB=OFF | ON
-DTPL_ENABLE_HIPLIB=OFF | ON
-Denable_complex16=OFF | ON
-DXSDK_INDEX_SIZE=32 | 64
-DBUILD_SHARED_LIBS= OFF | ON
-DCMAKE_INSTALL_PREFIX=<...>.
-DCMAKE_C_COMPILER=<MPI C compiler>
-DCMAKE_C_FLAGS="..."
-DCMAKE_CXX_COMPILER=<MPI C++ compiler>
-DMAKE_CXX_FLAGS="..."
-DCMAKE_CUDA_FLAGS="..."
-DHIP_HIPCC_FLAGS="..."
-DXSDK_ENABLE_Fortran=OFF | ON
-DCMAKE_Fortran_COMPILER=<MPI F90 compiler>
Before installing the package, please examine the three things dependent on your system setup:
This make include file is referenced inside each of the Makefiles in the various subdirectories. As a result, there is no need to edit the Makefiles in the subdirectories. All information that is machine specific has been defined in this include file.
Sample machine-specific make.inc are provided in the MAKE_INC/ directory for several platforms, such as Cray XT5, Linux, Mac-OS, and CUDA. When you have selected the machine to which you wish to install SuperLU_DIST, copy the appropriate sample include file (if one is present) into make.inc.
For example, if you wish to run SuperLU_DIST on a Cray XT5, you can do
cp MAKE_INC/make.xt5 make.inc
For the systems other than listed above, some porting effort is needed for parallel factorization routines. Please refer to the Users' Guide for detailed instructions on porting.
The following CPP definitions can be set in CFLAGS.
-DXSDK_INDEX_SIZE=64
use 64-bit integers for indexing sparse matrices. (default 32 bit)
-DPRNTlevel=[0,1,2,...]
printing level to show solver's execution details. (default 0)
-DDEBUGlevel=[0,1,2,...]
diagnostic printing level for debugging purpose. (default 0)
The parallel routines in SuperLU_DIST use some BLAS routines on each MPI process. Moreover, if you enable OpenMP with multiple threads, you need to link with a multithreaded BLAS library. Otherwise performance will be poor. A good public domain BLAS library is OpenBLAS (http://www.openblas.net), which has OpenMP support.
If you have a BLAS library your machine, you may define the following in the file make.inc:
BLASDEF = -DUSE_VENDOR_BLAS
BLASLIB = <BLAS library you wish to link with>
The CBLAS/ subdirectory contains the part of the C BLAS (single threaded) needed by SuperLU_DIST package. However, these codes are intended for use only if there is no faster implementation of the BLAS already available on your machine. In this case, you should go to the top-level SuperLU_DIST/ directory and do the following:
-
In make.inc, undefine (comment out) BLASDEF, and define:
BLASLIB = ../lib/libblas$(PLAT).a -
Type:
make blaslibto make the BLAS library from the routines in theCBLAS/ subdirectory.
If you will use Metis or ParMetis for sparsity ordering, you will need to install them yourself. Since ParMetis package already contains the source code for the Metis library, you can just download and compile ParMetis from: http://glaros.dtc.umn.edu/gkhome/metis/parmetis/download
After you have installed it, you should define the following in make.inc:
HAVE_PARMETIS = TRUE
METISLIB = -L<metis directory> -lmetis
PARMETISLIB = -L<parmetis directory> -lparmetis
I_PARMETIS = -I<parmetis directory>/include -I<parmetis directory>/metis/include
You can disable ParMetis with the following line in SRC/superlu_dist_config.h:
#undef HAVE_PARMETIS
Starting Version 6.0, the triangular solve routine can perform explicit inversion on the diagonal blocks, using LAPACK's xTRTRI inversion routine. To use this feature, you should define the following in make.inc:
SLU_HAVE_LAPACK = TRUE
LAPACKLIB = <lapack library you wish to link with>
You can disable LAPACK with the following line in SRC/superlu_dist_config.h:
#undef SLU_HAVE_LAPACK
You can use parallel approximate weight perfect matching (AWPM) algorithm to perform numerical pre-pivoting for stability. The default pre-pivoting is to use MC64 provided internally, which is an exact algorithm, but serial. In order to use AWPM, you will need to install CombBLAS yourself, at the download site: https://people.eecs.berkeley.edu/~aydin/CombBLAS/html/index.html
After you have installed it, you should define the following in make.inc:
HAVE_COMBBLAS = TRUE
COMBBLASLIB = <combblas root>/_build/libCombBLAS.a
I_COMBBLAS=-I<combblas root>/_install/include -I<combblas root>/Applications/BipartiteMatchings
You can disable CombBLAS with the following line in SRC/superlu_dist_config.h:
#undef HAVE_COMBBLAS
In the header file SRC/superlu_FCnames.h, we use macros to determine how C routines should be named so that they are callable by Fortran. (Some vendor-supplied BLAS libraries do not have C interfaces. So the re-naming is needed in order for the SuperLU BLAS calls (in C) to interface with the Fortran-style BLAS.) The possible options for CDEFS are:
-DAdd_: Fortran expects a C routine to have an underscore
postfixed to the name;
(This is set as the default)
-DNoChange: Fortran expects a C routine name to be identical to
that compiled by C;
-DUpCase: Fortran expects a C routine name to be all uppercase.
To use OpenMP parallelism, need to link with an OpenMP library, and set the number of threads you wish to use as follows (bash):
export OMP_NUM_THREADS=<##>
To enable NVIDIA GPU access, need to take the following step: Add the CUDA library location in make.inc:
HAVE_CUDA=TRUE
INCS += -I<CUDA directory>/include
LIBS += -L<CUDA directory>/lib64 -lcublas -lcudart
endif
A Makefile is provided in each subdirectory. The installation can be done completely automatically by simply typing "make" at the top level.
A couple of environment variables affect parallel execution.
export OMP_NUM_THREADS=<...>
export SUPERLU_ACC_OFFLOAD=1 // this enables use of GPU. Default is 1.
Several integer blocking parameters may affect performance. Most of them can be set by the user through environment variables. Oherwise the default values are provided. Various SuperLU routines call an environment inquiry function to obtain these parameters. This function is provided in the file SRC/sp_ienv.c. Please consult that file for detailed description of the meanings.
export NREL=<...> // supernode relaxation parameter
export NSUP=<...> // maximum allowable supernode size, not to exceed 512
export FILL=<...> // estimated fill ratio of nonzeros(L+U)/nonzeros(A)
export MAX_BUFFER_SIZE=<...> // maximum buffer size on GPU for GEMM
Prerequisites: CMake, Visual Studio, Microsoft HPC Pack This has been tested with Visual Studio 2017, without Parmetis, without Fortran, and with OpenMP disabled.
The cmake configuration line used was
'/winsame/contrib-vs2017/cmake-3.9.4-ser/bin/cmake' \
-DCMAKE_INSTALL_PREFIX:PATH=C:/winsame/volatile-vs2017/superlu_dist-master.r147-parcomm \
-DCMAKE_BUILD_TYPE:STRING=Release \
-DCMAKE_COLOR_MAKEFILE:BOOL=FALSE \
-DCMAKE_VERBOSE_MAKEFILE:BOOL=TRUE \
-Denable_openmp:BOOL=FALSE \
-DCMAKE_C_COMPILER:FILEPATH='C:/Program Files (x86)/Microsoft Visual Studio/2017/Professional/VC/Tools/MSVC/14.11.25503/bin/HostX64/x64/cl.exe' \
-DCMAKE_C_FLAGS:STRING='/DWIN32 /D_WINDOWS /W3' \
-DTPL_ENABLE_PARMETISLIB:BOOL=FALSE \
-DXSDK_ENABLE_Fortran=OFF \
-G 'NMake Makefiles JOM' \
C:/path/to/superlu_dist
After configuring, simply do
jom # or nmake
jom install # or nmake install
Libraries will be installed under C:/winsame/volatile-vs2017/superlu_dist-master.r147-parcomm/lib for the above configuration.
If you wish to test:
ctest
The SRC/ directory contains the following routines to read different file formats, they all have the similar calling sequence.
$ ls -l dread*.c
dreadMM.c : Matrix Market, files with suffix .mtx
dreadhb.c : Harrell-Boeing, files with suffix .rua
dreadrb.c : Rutherford-Boeing, files with suffix .rb
dreadtriple.c : triplet, with header
dreadtriple_noheader.c : triplet, no header, which is also readable in Matlab
[1] X.S. Li and J.W. Demmel, "SuperLU_DIST: A Scalable Distributed-Memory
Sparse Direct Solver for Unsymmetric Linear Systems", ACM Trans. on Math.
Software, Vol. 29, No. 2, June 2003, pp. 110-140.
[2] L. Grigori, J. Demmel and X.S. Li, "Parallel Symbolic Factorization
for Sparse LU with Static Pivoting", SIAM J. Sci. Comp., Vol. 29, Issue 3,
1289-1314, 2007.
[3] P. Sao, R. Vuduc and X.S. Li, "A distributed CPU-GPU sparse direct
solver", Proc. of EuroPar-2014 Parallel Processing, August 25-29, 2014.
Porto, Portugal.
[4] P. Sao, X.S. Li, R. Vuduc, “A Communication-Avoiding 3D Factorization
for Sparse Matrices”, Proc. of IPDPS, May 21–25, 2018, Vancouver.
[5] P. Sao, R. Vuduc, X. Li, "Communication-avoiding 3D algorithm for
sparse LU factorization on heterogeneous systems", J. Parallel and
Distributed Computing (JPDC), September 2019.
[6] Y. Liu, M. Jacquelin, P. Ghysels and X.S. Li, “Highly scalable
distributed-memory sparse triangular solution algorithms”, Proc. of
SIAM workshop on Combinatorial Scientific Computing, June 6-8, 2018,
Bergen, Norway.
[7] N. Ding, S. Williams, Y. Liu, X.S. Li, "Leveraging One-Sided
Communication for Sparse Triangular Solvers", Proc. of SIAM Conf. on
Parallel Processing for Scientific Computing. Feb. 12-15, 2020.
[8] A. Azad, A. Buluc, X.S. Li, X. Wang, and J. Langguth,
"A distributed-memory algorithm for computing a heavy-weight perfect matching
on bipartite graphs", SIAM J. Sci. Comput., Vol. 42, No. 4, pp. C143-C168, 2020.
[9] N. Ding, Y. Liu, S. Williams, X.S. Li,
"A Message-Driven, Multi-GPU Parallel Sparse Triangular Solver”,
Proceedings of SIAM Proceedings of ACDA21 conference, 2021.
[10] Y. Liu, N. Ding, P. Sao, S. Williams, X.S. Li,
"Unified Communication Optimization Strategies for Sparse Triangular Solver on CPU and GPU Clusters", Proceedings of SC23, Nov. 2023
[11] X. Li, P. Lin, Y. Liu, P. Sao, “Newly Released Capabilities in Distributed-memory SuperLU Sparse Direct Solver”,
ACM Trans. Math. Software, Volume 49, No. 1, March 2023.
https://dl.acm.org/doi/10.1145/3577197
[12] W. Boukaram, Y. Hong Y, Y. Liu, T. Shi, X.S. Li.
"Batched sparse direct solver design and evaluation in SuperLU_DIST".
International Journal of High Performance Computing Applications. 2024;38(6):585-598.
doi:10.1177/10943420241268200
Xiaoye S. Li, Lawrence Berkeley National Lab, [email protected]
Gustavo Chavez, Lawrence Berkeley National Lab, [email protected]
Jim Demmel, UC Berkeley, [email protected]
Nan Ding, Lawrence Berkeley National Lab, [email protected]
John Gilbert, UC Santa Barbara, [email protected]
Laura Grigori, INRIA, France, [email protected]
Paul Lin, Lawrence Berkeley National Lab, [email protected]
Yang Liu, Lawrence Berkeley National Lab, [email protected]
Piyush Sao, Georgia Institute of Technology, [email protected]
Meiyue Shao, Lawrence Berkeley National Lab, [email protected]
Ichitaro Yamazaki, Univ. of Tennessee, [email protected]
October 15, 2003 Version 2.0
October 1, 2007 Version 2.1
Feburary 20, 2008 Version 2.2
October 15, 2008 Version 2.3
June 9, 2010 Version 2.4
November 23, 2010 Version 2.5
March 31, 2013 Version 3.3
October 1, 2014 Version 4.0
July 15, 2014 Version 4.1
September 25, 2015 Version 4.2
December 31, 2015 Version 4.3
April 8, 2016 Version 5.0.0
May 15, 2016 Version 5.1.0
October 4, 2016 Version 5.1.1
December 31, 2016 Version 5.1.3
September 30, 2017 Version 5.2.0
January 28, 2018 Version 5.3.0
June 1, 2018 Version 5.4.0
September 22, 2018 Version 6.0.0
December 9, 2018 Version 6.1.0
February 8, 2019 Version 6.1.1
November 12, 2019 Version 6.2.0
February 23, 2020 Version 6.3.0
October 23, 2020 Version 6.4.0
May 10, 2021 Version 7.0.0
October 5, 2021 Version 7.1.0
October 18, 2021 Version 7.1.1
December 12, 2021 Version 7.2.0
May 22, 2022 Version 8.0.0
July 5, 2022 Version 8.1.0
October 1, 2022 Version 8.1.1
Novembe 9, 2023 Version 8.2.0
Novembe 17, 2023 Version 8.2.1
May 8, 2024 Version 9.0.0
November 10, 2024 Version 9.1.0