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Strong scaling

Summary

We compare ChASE with ELPA, the state-of-the-art eigensolver for solving dense Hermitian eigenproblems on both distributed-memory homogeneous and heterogeneous systems. A strong scaling test up to 144 compute nodes have been performed on JUWELS-Booster to compare ChASE-GPU with both ELPA1 and ELPA2 with GPU support.

The eigenproblem that we use for this test is In2O3 115k. For both ChASE and ELPA the number of eigenpairs sought after is set at 1200, representing ~1% of the full spectrum. For ChASE, the size of the external searching space {\sf nex} is fixed as 400.

Data

The expriements require downloading the DFT and BSE matrices at first. Then an environment variable DATA_PATH should be set to the path to store the downloaded matrices.

Software dependencies

Build

The build of both CPU and GPU version ChASE requires

  • a C/C++ compiler (GCC 11.3.0 tested)
  • MPI (OpenMPI 4.1.4 tested)
  • Intel MKL (version 2022.1.0 tested)
  • CMake (version 3.23.1 tested)
  • Boost (version 1.79.0 tested)
  • git (version 2.36.0 tested)
  • CUDA (version 11.7 tested): mandatory only for GPU build

extract data

Extract of useful data from the output of experiments requires

  • grep
  • sed
  • tr

Plot

The plots of results require Python3 (version 3.8.5 tested) with the libraries:

  • matplotlib (version 3.3.2 tested)
  • pandas (version 1.3.2 tested)
  • seaborn (version 0.11.0 tested)
  • numpy (version 1.19.2 tested)

Structure

The structure of this folder is given as follows:

├── ChASE_
│   ├── GPU-v1.2
│   |	├── 4
│   |	|   ├── submit.sh
│   │ 	├── 9
│   |	|   ├── submit.sh
│   │ 	├── ...
│   │ 	├── 144
│   |	|   ├── submit.sh
│   ├── GPU
│   |	├── 4
│   |	|   ├── submit.sh
│   │ 	├── 9
│   |	|   ├── submit.sh
│   │ 	├── ...
│   │ 	├── 144
│   |	|   ├── submit.sh
│   ├── GPU-nccl
│   |	├── 4
│   |	|   ├── submit.sh
│   │ 	├── 9
│   |	|   ├── submit.sh
│   │ 	├── ...
│   │ 	├── 144
│   |	|   ├── submit.sh
│   ├── build.sh
│   ├── data.sh
│   ├── submit.sh
├── elpa_1_2
│   ├── elpa_miniapp
│   ├── 4
│   |   ├── submit.sh
│   ├── 9
│   |   ├── submit.sh
│   ├── ...
│   ├── 144
│   |   ├── submit.sh
│   ├── build.sh
│   ├── data.sh
│   ├── submit.sh
└── README.md

This folder includes two sub-folders ChASE_ and elpa_1_2. As shown by their names, ChASE_ contains the script files for different builds and versions of ChASE.

For elpa_1_2, there is a folder elpa_miniapp, which is an implementation of test app for solving a standard eigenproblem by ELPA. It is used for the benchmark of ELPA1 and ELPA2. The script file build.sh is to build ELPA with GPU support. The version of ELPA is selected as new_release_2022.11.001.rc1. The scripts for submitting jobs and extracting data from output files are also avaiable in this folder.

workflow

Set the data path

Set the path where the downloaded matrices are stored:

export DATA_PATH=/path/store/DFT/Matrices

ChASE v1.2 GPU build and experiments

  1. go into the folder chase/GPU-v1.2
cd chase/GPU-v1.2
  1. build ChASE
./build.sh
  1. launch slurm jobs

For launching slurm jobs, it is required to provide a list of node numbers, which can be a subset of 4,9,16, 25,...144.

Below is an example to submit the jobs with node number 4, 16.

./submit.sh 4,16

ChASE GPU build without NCCL and experiments

  1. go into the folder chase/GPU
cd chase/GPU
  1. build ChASE
./build.sh
  1. launch slurm jobs

For launching slurm jobs, it is required to provide a list of node numbers, which can be a subset of 4,9,16, 25,...144.

Below is an example to submit the jobs with node number 4, 16.

./submit.sh 4,16

ChASE GPU build with NCCL and experiments

  1. go into the folder chase/GPU-nccl
cd chase/GPU-nccl
  1. build ChASE
./build.sh
  1. launch slurm jobs

For launching slurm jobs, it is required to provide a list of node numbers, which can be a subset of 4,9,16, 25,...144.

Below is an example to submit the jobs with node number 4, 16.

./submit.sh 4,16

ELPA GPU build and experiments

  1. go into the folder elpa_1_2
cd elpa_1_2
  1. build ELPA
./build.sh
  1. launch slurm jobs

For launching slurm jobs, it is required to provide a list of node numbers, which can be a subset of 4,9,16, 25,...144.

Below is an example to submit the jobs with node number 4, 16.

./submit.sh 4,16

For each job, both ELPA1 and ELPA2 solvers are tested.

extract data into CSV files

ChASE-v1.2 GPU build

in the folder chase/CPU-v1.2:

./data.sh

ChASE GPU build without NCCL

in the folder chase/GPU:

./data.sh

ChASE GPU build with NCCL

in the folder chase/GPU:

./data.sh

ELPA GPU build

in the folder elpa_1_2:

./data.sh

Plots

All the Python based plot scripts are available in the folder ../../plots. Plots for comparing ChASE with ELPA can be done as

python strong_scaling.py

The Python plot script works even with a subset of points (node numbers).