PSBLAS library, version 3.9

The PSBLAS library, developed with the aim to facilitate the parallelization of computationally intensive scientific applications, is designed to address parallel implementation of iterative solvers for sparse linear systems through the distributed memory paradigm. It includes routines for multiplying sparse matrices by dense matrices, solving block diagonal systems with triangular diagonal entries, preprocessing sparse matrices, and contains additional routines for dense matrix operations. The current implementation of PSBLAS addresses a distributed memory execution model operating with message passing.

The PSBLAS library version 3 is implemented in the Fortran 2008 programming language, with reuse and/or adaptation of existing Fortran 77 and Fortran 95 software, plus a handful of C routines.

References

The architecture, philosophy and implementation details of the library are contained in the following papers:

• The architecture of the Fortran 2003 sparse BLAS is described in:

  S. Filippone, A. Buttari. Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003, ACM Trans. on Math. Software, vol. 38, No. 4, 2012.

• The ideas are explored further with the paper:

  V. Cardellini, S. Filippone and D. Rouson. Design Patterns for sparse-matrix computations on hybrid CPU/GPU platforms, Scientific Programming, 22(2014), pp.1-19.

• Version 1.0 of the library is described in:

  S. Filippone, M. Colajanni. PSBLAS: A library for parallel linear algebra computation on sparse matrices, ACM Trans. on Math. Software, 26(4), Dec. 2000, pp. 527-550.

• The software infrastructure changes required to accommodate the implementation of the Additive-Schwarz preconditioners available in AMG4PSBLAS are detailed in:

  A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, Extending PSBLAS to build parallel Schwarz preconditioners, Applied Parallel Computing. State of the Art in Scientific Computing: 7th International Workshop, PARA 2004, LNCS 3732, 2006, pp. 593-602.

  A. Buttari, P. D'Ambra, D. Di Serafino, S. Filippone, 2LEV-D2P4: A package of high-performance preconditioners for scientific and engineering applications, Applicable Algebra in Engineering, Communications and Computing, 2007, 18(3), pp. 223-239.

  P. D'Ambra, D. Di Serafino, S. Filippone, MLD2P4: A package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 ACM Transactions on Mathematical Software, 2010, 37(3), 30

PSBLAS is the backbone of the Parallel Sparse Computation Toolkit (PSCToolkit) suite of libraries. See the paper:

D’Ambra, P., Durastante, F., & Filippone, S. (2023). Parallel Sparse Computation Toolkit. Software Impacts, 15, 100463.

Other Software credits

We originally included a modified implementation of some of the Sparker (serial sparse BLAS) material; this has been completely rewritten, way beyond the intention(s) and responsibilities of the original developers. The main reference for the serial sparse BLAS is:

Duff, I., Marrone, M., Radicati, G., and Vittoli, C. Level 3 basic linear algebra subprograms for sparse matrices: a user level interface, ACM Trans. Math. Softw., 23(3), 379-401, 1997.

Installing

To compile and run our software you will need the following prerequisites (see also SERIAL below):

1. A working version of MPI

2. A version of the BLAS; if you don't have a specific version for your platform you may try ATLAS available from http://math-atlas.sourceforge.net/

3. We have had good results with the METIS library, from http://www-users.cs.umn.edu/~karypis/metis/metis/main.html. This is optional; it is used in the util and test/fileread directories but only if you specify --with-metis.

4. If you have the AMD package of Davis, Duff and Amestoy, you can specify --with-amd (see ./configure --help for more details). We use the C interface to AMD.

5. If you have CUDA available, use --enable-cuda to compile CUDA-enabled methods --with-cudadir= to specify the CUDA toolkit location --with-cudacc=XX,YY,ZZ to specify a list of target CCs (compute capabilities) to compile the CUDA code for.

The configure script will generate a Make.inc file suitable for building the library. The script is capable of recognizing the needed libraries with their default names; if they are in unusual places consider adding the paths with --with-libs, or explicitly specifying the names in --with-blas, etc.

[!CAUTION] Please note that a common way for the configure script to fail is to specify inconsistent MPI vs. plain compilers, either directly or indirectly via environment variables; e.g. specifying the Intel compiler with FC=ifort while at the same time having an MPIFC=mpif90 which points to GNU Fortran.

[!TIP] The best way to avoid this situation is (in our opinion) to use the environment modules package (see http://modules.sourceforge.net/), and load the relevant variables with (e.g.)

module load gcc/13.2.0 openmpi/4.1.6

This will delegate to the modules setup to make sure that the version of openmpi in use is the one compiled with the gnu46 compilers. After the configure script has completed you can always tweak the Make.inc file yourself.

After you have Make.inc fixed, run

make

to compile the library; go to the test directory and its subdirectories to get test programs done. If you specify --prefix=/path you can do make install and the libraries will be installed under /path/lib, while the module files will be installed under /path/modules. The regular and experimental C interface header files are under /path/include.

CUDA and GPU support

This version of PSBLAS incorporates into a single package three entities that were previouslty separated:

Library
PSBLAS	the base library
PSBLAS-EXT	a library providing additional storage formats for matrices and vectors
SPGPU	a package of kernels for NVIDIA GPUs originally written by Davide Barbieri and Salvatore Filippone; see the license file cuda/License-spgpu.md

OpenACC

There is a highly experimental version of an OpenACC interface, you can access it by speficifying

--enable-openacc  --with-extraopenacc="-foffload=nvptx-none=-march=sm_70"

where the argument to the extraopenacc option depends on the compiler you are using (the example shown here is relevant for the GNU compiler).

Serial

Configuring with --enable-serial will provide a fake MPI stub library that enables running in pure serial mode; no MPI installation is needed in this case (but note that the fake MPI stubs are only guaranteed to cover what we use internally, it's not a complete replacement).

Integers

We have two kind of integers: IPK for local indices, and LPK for global indices. They can be specified independently at configure time, e.g.

--with-ipk=4 --with-lpk=8

which is asking for 4-bytes local indices, and 8-bytes global indices (this is the default).

Documentation

Further information on installation and configuration can be found in the documentation. See docs/psblas-3.9.pdf; an HTML version of the same document is available in docs/html. Please consult the sample programs, especially

• test/pargen/psb_s_pde2d.F90 test/pargen/psb_d_pde2d.F90
• test/pargen/psb_s_pde2d.F90 test/pargen/psb_d_pde2d.F90

which contain examples for the solution of linear systems obtained by the discretization of a generic second-order differential equation in two:

- a_1 \frac{\partial^2 u}{\partial x^2} 
- a_2 \frac{\partial^2 u}{\partial y^2} 
+ b_1 \frac{\partial u}{\partial x} 
+ b_2 \frac{\partial u}{\partial y} 
+ c u = f

or three

- a_1 \frac{\partial^2 u}{\partial x^2} 
- a_2 \frac{\partial^2 u}{\partial y^2} 
- a_3 \frac{\partial^2 u}{\partial z^2} 
+ b_1 \frac{\partial u}{\partial x} 
+ b_2 \frac{\partial u}{\partial y} 
+ b_3 \frac{\partial u}{\partial z} 
+ c u = f

dimensions on the unit square/cube with Dirichlet boundary conditions.

Utilities

The test/util directory contains some utilities to convert to/from Harwell-Boeing and MatrixMarket file formats.

TODO and bugs

• Improving OpenACC support
• Improving OpenMP support
• Fix all reamining bugs. Bugs? We dont' have any ! 🤓

[!NOTE] To report bugs 🐛 or issues ❓ please use the GitHub issue system.

The PSBLAS team.

Project lead: Salvatore Filippone

Contributors (roughly reverse cronological order):

• Theophane Loloum
• Fabio Durastante
• Dimitri Walther
• Andea Di Iorio
• Stefano Petrilli
• Soren Rasmussen
• Zaak Beekman
• Ambra Abdullahi Hassan
• Pasqua D'Ambra
• Alfredo Buttari
• Daniela di Serafino
• Michele Martone
• Michele Colajanni
• Fabio Cerioni
• Stefano Maiolatesi
• Dario Pascucci

RELATED SOFTWARE

If you are looking for more sophisticated preconditioners, you may be interested in the package AMG4PSBLAS from http://github.com/sfilippone/amg4psblas and the whole PSCTooolkit suite.

Contact: https://github.com/sfilippone/psblas3