An open-source (BSD) library for sparse linear algebra and associated algorithms. It is primarily developed by the Numerical Analysis group at STFC Rutherford Appleton Laboratory (hsl@stfc.ac.uk).

For detailed information about the SPRAL packages and API see Fortran documentation or C documentation.

• LSMR - Solves sparse least squares problems using LSMR algorithm.
• RANDOM - Pseudo-random number generator.
• RANDOM_MATRIX - Generates random matrices for testing purposes.
• RUTHERFORD_BOEING - Read and write matrices in Rutherford-Boeing format.
• SCALING - Calculates matrix scalings through a variety of algorithms
• SSIDS - Sparse Symmetric Indefinite Direct Solver.
• SSMFE - Sparse Symmetric Matrix-Free Eigensolver. Uses Jacobi-conjugate preconditioned gradients method.

If the functionality you are looking for is not supported, it may be offered by our proprietary licenced HSL Library (free to academics).

Please note that we require METIS and hwloc to be installed (hwloc should be compiled with CUDA support if building for GPU).

We now support building with the Meson Build system:

meson setup builddir -Dexamples=true -Dtests=true -Dlibblas=openblas -Dliblapack=openblas
meson compile -C builddir
meson install -C builddir

For more options (including how to specify paths to the above libraries) please see meson_options.txt.

Alternatively, you can use a standard autotools-based build system:

./autogen.sh # If compiling from fresh git checkout
mkdir build
cp nvcc_arch_sm.c build/ # If building for GPU
cd build
../configure --with-metis="-L/path/to/metis -lmetis"
make
make install

When using SSIDS please ensure the following environment variables are set:

export OMP_CANCELLATION=TRUE
export OMP_PROC_BIND=TRUE

failure to do so will result in SSIDS failing with Error flag = -53.

SPRAL must be compiled with -fPIC to be able to generate a shared library. The static library libspral.a can be converted to a shared library using one of the following commands:

# Linux
gfortran -fPIC -shared -Wl,--whole-archive libspral.a -Wl,--no-whole-archive -lgomp -lblas -llapack -lhwloc -lmetis -lstdc++ -o libspral.so

# Windows
gfortran -fPIC -shared -Wl,--whole-archive libspral.a -Wl,--no-whole-archive -lgomp -lopenblas -lhwloc -lmetis -lstdc++ -o libspral.dll

# Mac
gfortran -fPIC -shared -Wl,-all_load libspral.a -Wl,-noall_load -lgomp -lopenblas -lhwloc -lmetis -lstdc++ -o libspral.dylib

If you write a paper using software from SPRAL, please cite an appropriate paper (a list can usually be found in the method section of the user documentation). To cite SSIDS, please use the following reference:

J. Hogg, E. Ovtchinnikov, and J. Scott (2016). A sparse symmetric indefinite direct solver for GPU architectures. ACM Transactions on Mathematical Software (TOMS), 42(1), 1-25, https://dx.doi.org/10.1145/275654

In BibTeX, the citation is:

@article{hogg2016sparse,
  title={A sparse symmetric indefinite direct solver for GPU architectures},
  author={Hogg, Jonathan D and Ovtchinnikov, Evgueni and Scott, Jennifer A},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  volume={42},
  number={1},
  pages={1--25},
  year={2016},
  publisher={ACM New York, NY, USA}
}

If no paper is listed, a citation of the SPRAL GitHub website should be used, for example:

SPRAL: an open-source library for sparse linear algebra, Version 2024-05-08, https://github.com/ralna/spral, May 2024.