DARE Solver

1. Introduction

This library provides a high-performance implementation of the Discrete time Algebraic Riccati Equation (DARE) solver. The DARE solver is used in Adaptive Optics (AO) system of extremely large ground-based telescopes with instruments such as MAVIS. It has significant better application's peformance than other traditional methods. However, the computational cost is also much higher. According to our benchmark on MAVIS specifications, the application has best accuracy when the matrix dimension is more than 20k x 20k. Our high-performance DARE solver exploits advanced linear algebra libraries associated with runtime system, such as Chameleon or DPLASMA, to deploy the DARE algorithm onto shared-memory multicore systems equipped with multiple GPU hardware accelerators.

2. Dependencies

• CMake (>=3.19)
• CUDA (>=11.0)
• Intel MKL (>=2018)
• OpenMPI (>=4.0)
• Chameleon or DPLASMA runtime system

3. Installation

We provide two install scripts for user to download dependencies and compile the dare solver library.

4. Dataset

Input files available at: https://kaust-my.sharepoint.com/:f:/g/personal/ltaiefh_kaust_edu_sa/EgaqEKCdWURBgDq3x2CNsXQBteQs4x0VIdiiHJcY8AVyVA?e=EzETNF

5. Running

The usage is provided by ./ddare --help:

./ddare [options]

Options are:
  --help           Show this help

  --n=X            #samples x #layers. states    (default: 500)
  --ninstr=X       Instrument dimension. measurements (default: 500)
  --nb=X           tile size.            (default: 128)

  --datapath=X     path to the data folder
                   this folder must contain the following files:
                       At.fits
                       BinvRt.fits
                       Btinitial.fits
                       Rt.fits
                       Qt.fits
                   the parameters '--n' and '--ninstr' will be overwritten by the
                   corresponding dimensions of the files

  --threads=X      Number of CPU workers (default: _SC_NPROCESSORS_ONLN)
  --gpus=X         Number of GPU workers (default: 0)
  --sync           Synchronize the execution of all calls (default: async)
  --nooptalgo      Leverage matrix structure in the algorithm (default: optalgo)
  --profile        Profile the execution of all calls (default: no profile)
  --check          Check numerical correctness (default: no check)

The StarPU runtime also needs to be set up. Example:

STARPU_SILENT=0 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 STARPU_CUDA_PIPELINE=4 STARPU_NWORKER_PER_CUDA=4 STARPU_SCHED=prio STARPU_CALIBRATE=1 ./ddare --threads=31 --n=7090 --ninstr=19078 --nb=320 --ib=80 --gpus=1

where n and ninstr are the dimensions of the problem. In this case, the matrices will be generated randomly Or using input matrices (as fits files):

STARPU_SILENT=1 OMP_NUM_THREADS=8 MKL_NUM_THREADS=8 STARPU_CUDA_PIPELINE=2 STARPU_NWORKER_PER_CUDA=12 STARPU_SCHED=$j STARPU_CALIBRATE=1 ./ddare --threads=4 --nb=720 --ib=180 --gpus=1 --datapath=<path/to/data>

Question

For more information and questions please send email to yuxi.hong@kaust.edu.sa and hatem.ltaief@kaust.edu.sa.

Handout