Software for Testing Accuracy, Reliability and Scalability of Hierarchical computations

What is STARS-H?

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.

Vision of STARS-H

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.

Current Features of STARS-H

This project is WIP, with current features limited to:

The only supported data format is Tile Low-Rank (TLR):

  1. TLR Approximation
  2. Multiplication of TLR matrix by dense matrix

Programming models (backends):

  1. OpenMP
  2. MPI
  3. Task-based using StarPU (with and without MPI)

Applications in matrix-free form:

  1. Cauchy matrix
  2. Electrostatics (1/r)
  3. Electrodynamics (sin(kr)/r and cos(kr)/r)
  4. Random synthetic TLR matrix
  5. Spatial statistics (exponential, square exponential and matern kernels)

Low-rank approximation techniques (low-rank engines):

  1. Ordinary SVD,
  2. Rank-revealing QR,
  3. Randomized SVD.


  1. CG method for symmetric positive-definite (SPD) systems.


  1. Add support for more matrix kernels and applications
  2. Extend support to hardware accelerators (i.e, GPUs)
  3. Provide full StarPU support (GPUs and distributed-memory systems)
  4. Port to other dynamic runtime systems
  5. Implement additional low-rank routines like ACA.
  6. Implement additional formats: HODLR/H/HSS/H^2