PaStiX Handbook  6.2.0
PaStiX: A sparse direct solver

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PaStiX (Parallel Sparse matriX package) is a scientific library that provides a high performance parallel solver for very large sparse linear systems based on direct methods. Numerical algorithms are implemented in single or double precision (real or complex) using LLt, LDLt and LU with static pivoting (for non symmetric matrices having a symmetric pattern). This solver also provides some low-rank compression methods to reduce the memory footprint and/or the time-to-solution.

Get PaStiX

To use last development state of PaStiX, please clone the master branch. Note that PaStiX contains two git submodule for spm and morse_cmake. To get sources please use these commands:

# if git version >= 1.9
  git clone --recursive git@gitlab.inria.fr:solverstack/pastix.git
  cd pastix
# else
  git clone git@gitlab.inria.fr:solverstack/pastix.git
  cd pastix
  git submodule init
  git submodule update

Previous releases of PaStiX are hosted on the gforge.inria.fr for now. Future releases will be available on this gitlab project.

Available Features

  • Features available in shared memory with POSIX threads for multicores architectures.
Seq Static Dyn StarPU PaRSEC
POTRF (Cholesky) FR/LR FR/LR FR/LR FR/LR/GPU FR/LR/GPU
PXTRF (LL^t for complex) FR/LR FR/LR FR/LR FR/LR/GPU FR/LR/GPU
HETRF (LDL^h) FR/LR FR/LR FR/LR FR/LR/GPU FR/LR/GPU
SYTRF (LDL^t) FR/LR FR/LR FR/LR FR/LR/GPU FR/LR/GPU
GETRF (LU) FR/LR FR/LR FR/LR FR/LR/GPU FR/LR/GPU
TRSM FR/LR FR/LR FR/LR FR/LR -
DIAG FR/LR FR/LR FR/LR FR/LR -
  • Features available in hybrid shared/distributed memory with MPI between processes, and POSIX threads within a process.
Seq Static Dyn StarPU PaRSEC
POTRF (Cholesky) FR FR FR FR/GPU FR/GPU
PXTRF (LL^t for complex) FR FR FR FR/GPU FR/GPU
HETRF (LDL^h) FR FR FR FR/GPU FR/GPU
SYTRF (LDL^t) FR FR FR FR/GPU FR/GPU
GETRF (LU) FR FR FR FR/GPU FR/GPU
TRSM FR FR FR FR -
DIAG FR FR FR FR -
  • FR means Full-Rank computations without compression techniques
  • LR means Low-Rank compression technique to reduce the memory footprint and/or the time-to-solution
  • WARNING GPU kernels are not available on compressed supernodes
  • WARNING Low-rank compression and Schur complement are not available with MPI yet.

Documentation

The latest Doxygen documentation is available here.

The main steps and parameters of the solver are described. Some examples are also provided.

Installation

Build and install with CMake

PaStiX can be built using CMake. This installation requires to have some library dependencies already installed on the system:

  • BLAS (MKL, OpenBlas, ...) and CBLAS (sequential version required)
  • LAPACK and LAPACKE (sequential version required, with TMG enabled for testing)
  • HWLOC (highly recommended)
  • SCOTCH (optional)
  • METIS (optional)
  • STARPU runtime support (optional)
  • PARSEC runtime support (optional)
  • CUDA/CuBLAS to enable GPU functionality with runtime support (optional)
  • EZTRACE to enable tracing support (optional)
  • Python and Fortran compiler for wrappers and examples (optional)

For instance, on debian-like systems, dependencies can be installed with the following command:

  sudo apt-get install cmake gcc gfortran libhwloc-dev libscotch-dev libopenblas-dev liblapacke-dev python-numpy

The main options to configure the PaStiX configuration build are:

  • Classic cmake options:
    • CMAKE_BUILD_TYPE: Debug, RelWithDebInfo, Release, MinSizeRel; we recommend to use the Release, or RelWithDebInfo, for performance.
    • CMAKE_INSTALL_PREFIX: Specify the prefix directory to install the library
    • BUILD_SHARED_LIBS=[OFF]: Enable the shared libraries build. This option needs to be enabled for the Python wrapper.
  • Integer type:
    • PASTIX_INT64[=ON]: Enable/disable int64_t for integer arrays.
  • Ordering libraries:
    • Ordering libraries must match the integer type chosen for integer arrays in PaStiX
    • PASTIX_ORDERING_SCOTCH[=ON]: Enable/Disable the support of the Scotch library to compute the ordering.
    • PASTIX_ORDERING_METIS[=OFF]: Enable/Disable the support of the Metis library to compute the ordering. Metis 5.1 is required.
  • External schedulers:
    • PASTIX_WITH_PARSEC[=OFF]: Enable/disable the PaRSEC runtime support. Require to install PaRSEC tag pastix-_releasenumber_ (mymaster for master branch) from the repository https://bitbucket.org/mfaverge/parsec that includes a few patches on top of the original PaRSEC runtime system. PaRSEC needs to be compiled with option -DPARSEC_WITH_DEVEL_HEADERS=ON.
    • PASTIX_WITH_STARPU[=OFF]: Enable/disable the StarPU runtime support. Require to install StarPU 1.3.
  • Distributed memory:
    • PASTIX_WITH_MPI=[OFF]: Enable/disable distributed memory support (See above for details). If used with the PaRSEC library, MPI should be enabled or disabled in both libraries.*
  • External SpM library:
    • PASTIX_WITH_EXTERNAL_SPM=[OFF]: Enable/disable the use of an external SpM library in favor of the internal one.
  • Documentation:
    • BUILD_DOCUMENTATION[=OFF] to enable the Doxygen documentation generation.

Get involved

Reporting an issue

We strongly recommend all users to use the issue tracker to report any problems with the software, or for any feature request. We will try our best to answer them in a short time frame.

Contributions

https://gitlab.inria.fr/solverstack/pastix/blob/master/CONTRIBUTING.md

Authors

The following people contribute or contributed to the development of PaStiX:

  • Mathieu Faverge, PI
  • Pierre Ramet, PI
  • David Goudin
  • Mathias Hastaran
  • Pascal Henon
  • Xavier Lacoste
  • François Pellegrini
  • Grégoire Pichon, Low-rank solver
  • Florent Pruvost, CMake and Spack
  • Theophile Terraz
  • Tony Delarue, MPI implementation

If we forgot your name, please let us know that we can fix that mistake.

Citing PaStiX

Feel free to use the following publications to reference PaStiX:

  • Original paper that initiated PaStiX:
    • Pascal Hénon, Pierre Ramet, Jean Roman. Pascal Hénon, Pierre Ramet, Jean Roman. PaStiX: A High-Performance Parallel Direct Solver for Sparse Symmetric Definite Systems. Parallel Computing, Elsevier, 2002, 28 (2), pp.301–321. INRIA HAL
  • Parallel incomplete factorization implemented in PaStiX:
    • Pascal Hénon, Pierre Ramet, Jean Roman. On finding approximate supernodes for an efficient ILU(k) factorization. Parallel Computing, Elsevier, 2008, 34, pp.345–362. INRIA HAL
  • Reordering strategy for blocking optimization in PaStiX:
    • Grégoire Pichon, Mathieu Faverge, Pierre Ramet, Jean Roman. Reordering Strategy for Blocking Optimization in Sparse Linear Solvers. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, SIAM Journal on Matrix Analysis and Applications, 38 (1), pp.226 - 248. INRIA HAL
  • On the use of low rank approximations in PaStiX:
    • Grégoire Pichon, Eric Darve, Mathieu Faverge, Pierre Ramet, Jean Roman. Sparse supernodal solver using block low-rank compression: Design, performance and analysis. International Journal of Computational Science and Engineering, Inderscience, 2018, 27, pp.255 - 270. 10.1016/J.JOCS.2018.06.007 Inria HAL

Licence

https://gitlab.inria.fr/solverstack/pastix/blob/master/LICENSE