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HiCMA: Hierarchical Computations on Manycore Architectures

The Hierarchical Computations on Manycore Architectures (HiCMA) library aims to redesign existing dense linear algebra libraries to exploit the data sparsity of the matrix operator. Data sparse matrices arise in many scientific problems (e.g., in statistics-based weather forecasting, seismic imaging, and materials science applications) and are characterized by low-rank off-diagonal tile structure. Numerical low-rank approximations have demonstrated attractive theoretical bounds, both in memory footprint and arithmetic complexity. The core idea of HiCMA is to develop fast linear algebra computations operating on the underlying tile low-rank data format, while satisfying a specified numerical accuracy and leveraging performance from massively parallel hardware architectures.

Features of HiCMA 1.0.0

• Matrix-Matrix Multiplication
• Cholesky Factorization/Solve
• Double Precision
• Task-based Programming Models
• Shared and Distributed-Memory Environments
• Support for StarPU Dynamic Runtime Systems
• Testing Suite and Examples
• Support for 3D unstructured mesh deformation of a population of the novel coronaviruses (i.e., SARS-CoV-2)
• LU factorization (hicma_zgetrf) on double complex matrices stored in tile low-rank (TLR) format.

Current Research

• Matrix Inversion
• Schur Complements
• Preconditioners
• Hardware Accelerators
• Support for Multiple Precisions
• Autotuning: Tile Size, Fixed Accuracy and Fixed Ranks
• Support for OpenMP, PaRSEC and Kokkos
• Support for HODLR, H, HSS and H2

External Dependencies

HiCMA depends on the following libraries:

• Chameleon
• HCORE
• STARS-H
• hwloc
• StarPU
• MPI

Installation

Please see INSTALL.md for information about installing and testing.

Dataset

Please see Data.md for information about dataset.

References

1. K. Akbudak, H. Ltaief, A. Mikhalev, and D. E. Keyes, Tile Low Rank Cholesky Factorization for Climate/Weather Modeling Applications on Manycore Architectures, International Supercomputing Conference (ISC17), June 18-22, 2017, Frankfurt, Germany.

2. K. Akbudak, H. Ltaief, A. Mikhalev, A. Charara, and D. E. Keyes, Exploiting Data Sparsity for Large-Scale Matrix Computations, Euro-Par 2018, August 27-31, 2018, Turin, Italy.

3. Q. Cao, Y. Pei, T. Herault, K. Akbudak, A. Mikhalev, G. Bosilca, H. Ltaief, D. E. Keyes, and J. Dongarra, Performance Analysis of Tile Low-Rank Cholesky Factorization Using PaRSEC Instrumentation Tools, 2019 IEEE/ACM International Workshop on Programming and Performance Visualization Tools (ProTools), Denver, CO, USA, 2019, pp. 25-32.

4. Q. Cao, Y. Pei, K. Akbudak, A. Mikhalev, G. Bosilca, H. Ltaief, D. E. Keyes, and J. Dongarra, Extreme-Scale Task-Based Cholesky Factorization Toward Climate and Weather Prediction Applications, The Platform for Advanced Scientific Computing (PASC 2020).

5. N. Al-Harthi, R. Alomairy, K. Akbudak, R. Chen, H. Ltaief, H. Bagci, and D. E. Keyes, Solving Acoustic Boundary Integral Equations Using High Performance Tile Low-Rank LU Factorization, International Supercomputing Conference (ISC 2020). GCS Award Winning Paper at ISC2020