Hsseigen

Implementation of the 'divide and conquer' algorithm for Superfast HSS eigensolvers.

• Efficient computation of all eigenvalues of symmetric Hierarchically Semiseparable (HSS) matrices.
• A shared-memory parallel algorithm and the corresponding implementation of the SuperDC eigensolver.
• Optimized the original SuperDC algorithm to reduce the storage requirement from O($N^2$) to O (N) in case of banded matrices.

Keywords

• Symmetric eigenvalue problems.
• Hierarchically semi-separable matrix or HSS matrix.
• Divide-and-conquer.
• Shared memory architecture.

Authors

• Anonymous

Prerequisites

1. Install lapack, blas OR openblas.

$\rightarrow$ On an ubuntu machine sudo apt-get install libblas-dev liblapack-dev liblapacke-dev libatlas-base-dev libopenblas-dev.

$\rightarrow$ Links to install lapack, blas and openblas on other systems.

2. Install intel icpx compiler.

$\rightarrow$ Instructions to install icpx can be found here intel-website.

3. Install GNU make and gcc compiler.

CodeSpaces Support

1. To begin working on the project with all the pre-requsites satisfied, fork the repository and begin working in Code Spaces.

2. After forking the repository, click on the <> Code button.

3. You should see option to create code space on master.

4. Click on the Create code space on master button and you will be redirected to a working environment.

Usage

Compilation

1. In the terminal write the command make for compiling the serial version.

2. In the terminal write the command make PARALLEL=1 for compiling the shared memory version.

3. A binary called Test is created in the root directory of the project.

How to run

1. After compiling the code use ./Test <filename> <matrix_size> <diagblock_size> <Band2HSS(pass 2) or Mat2HSSsym(pass 1)> <bandwidth> to run the code.

2. After compiling the code use ./Test <filename> <matrix_size> <diagblock_size> <Band2HSS(pass 2) or Mat2HSSsym(pass 1)> <bandwidth> <no of processor> to run the code.

Explanation of arguments.

Syntax $~~~~~~~~~~~~~~~~~~~~~~~~~$	Description
<filename>	path to the input file containing hss matrix
<matrix_size>	Size of square hss matrix (can be infered from filename)
<diagblock_size>	Block size to split into hss structure (less than matrix size and typically 8 or 16)
<Band2HSS(pass 2) or Mat2HSSsym(pass 1)>	Whether input matrix is banded (pass 2) or not (pass 1) (can be infered from file name)
<bandwidth>	Half bandwidth of input matrix (can be infered from file name)
<no of processor>	The number of cores you want to run the shared-memory version on.

Drive link to input data:

1. You can download HSS structured test matrices here

Miscellaneous

1. We have tested the project using openblas, lapack, and intel toolchains