STARS-H is a high performance parallel open-source package of Software for Testing Accuracy, Reliability and Scalability of Hierarchical computations. It provides a hierarchical matrix market in order to benchmark performance of various libraries for hierarchical matrix compressions and computations (including itself). Why hierarchical matrices? Because such matrices arise in many PDEs and use much less memory, while requiring fewer flops for computations. There are several hierarchical data formats, each one with its own performance and memory footprint. STARS-H intends to provide a standard for assessing accuracy and performance of hierarchical matrix libraries on a given hardware architecture environment. STARS-H currently supports the tile low-rank (TLR) data format for approximation on shared and distributed-memory systems, using MPI, OpenMP and task-based programming models.
The vision of STARS-H is to design, implement and provide a community code for hierarchical matrix generator with support of various data formats for approximation, including, but limited to, TLR, HSS, HODLR, H and H^2. STARS-H aspires to be for the low-rank approximation community what UF Sparse Matrix Collection is for the sparse linear algebra community, by generating hierarchical matrices coming from a variety of synthetic and real-world applications. Furthermore, extracting the performance of the underlying hardware resources (i.e., x86 and GPUs) is in the DNA of STARS-H, since the approximation phase can be time-consuming on large-scale scientific applications.
This project is WIP, with current features limited to:
The only supported data format is Tile Low-Rank (TLR):
- TLR Approximation
- Multiplication of TLR matrix by dense matrix
Programming models (backends):
- OpenMP
- MPI
- Task-based using StarPU (with and without MPI)
Applications in matrix-free form:
- Cauchy matrix
- Electrostatics (1/r)
- Electrodynamics (sin(kr)/r and cos(kr)/r)
- Random synthetic TLR matrix
- Spatial statistics (exponential, square exponential and matern kernels)
- Mesh deformation using radial basis function (gaussian, exponential, inverse quadratic, inverse multi-quadratic, CPTS, and Wendland kernels)
- Acoustic scattering
Low-rank approximation techniques (low-rank engines):
- Ordinary SVD,
- Rank-revealing QR,
- Randomized SVD.
Additional:
- CG method for symmetric positive-definite (SPD) systems.
- Add support for more matrix kernels and applications
- Extend support to hardware accelerators (i.e, GPUs)
- Provide full StarPU support (GPUs and distributed-memory systems)
- Port to other dynamic runtime systems
- Implement additional low-rank routines like ACA.
- Implement additional formats: HODLR/H/HSS/H^2
Installation requires at least CMake of version 3.2.3. To build STARS-H, follow these instructions:
-
Get STARS-H from git repository
git clone git@github.com:ecrc/stars-hor
git clone https://github.com/ecrc/stars-h -
Go into STARS-H folder
cd stars-h -
Get submodules
git submodule update --init -
Create build directory and go there
mkdir build && cd build -
Use CMake to get all the dependencies
cmake .. -DCMAKE_INSTALL_PREFIX=/path/to/install/ -
Build STARS-H
make -j -
Run tests (optional)
make test -
Build local documentation (optional)
make docs -
Install STARS-H
make install -
Add line
export PKG_CONFIG_PATH=/path/to/install/lib/pkgconfig:$PKG_CONFIG_PATHto your .bashrc file.
Now you can use pkg-config executable to collect compiler and linker flags for STARS-H.
The directory examples contains two subfolders: problem and approximation.
The sources in problem show how to generate problems (e.g., spatial statistics,
minimal or dense) and how to create STARSH_problem instance, required for every
step of STARS-H. The examples in approximation are based on problem generations
and have additional steps on approximation of corresponding matrices.
Important notice: the approximation phase does not require the entire dense matrix to be stored, since matrix elements are computed on the fly.
