GCGE — Generalized conjugate gradient eigensolver

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Overview

The package GCGE (Generalized Conjugate Gradient Eigensolver) is a software for solving large scale eigenvalue problems. GCGE is written by C language and constructed with the way of matrix-free and vector-free. So far, the eigensolvers for the matrices which are stored in dense format, compressed row/column sparse format or are supported in MATLAB, Hypre, PETSc, PHG and SLEPc. It is noted that there is no need to copy the built-in matrices and the vectors from these softwares/libraries to the GCGE package.

Software

We can divide GCGE into three levels:

LEVEL1--Basic matrix-vector operations: vector linear combination(y = ax + by), matrix vector multiplication(y = Ax),...
LEVEL2--main algorithms: linear solver(block conjugate gradient method), orthogonalization(block modified Gram-Schmidt method)
LEVEL3--GCG algorithm

download & install

GCGE is a freely-available software package. It is available at https://github.com/Materials-Of-Numerical-Algebra/GCGE .

The license used for the software is the modified MIT license, see:

LICENSE

Like all software, it is copyrighted. It is not trademarked, but we do ask the following:

If you modify the source for these routines we ask that you change the name of the routine and comment the changes made to the original.
We will gladly answer any questions regarding the software. If a modification is done, however, it is the responsibility of the person who modified the routine to provide support.

Configure and install: install_GCGE

GCGE, version 1.0.0

Download: GCGE-main.tar.gz
Documentation

Parallel Solution of Large-scale Sparse Linear Eigenvalue Problems
Ax=λx Ax=λBx

GCG Algorithm

The generalized conjugate gradient algorithm is a type of subspace projection method, which uses the block damping inverse power idea to generate triple blocks [X,P,W], where X saves the current eigenvector approximation, P saves the information from previous iteration step, and W saves vectors from X by the inverse power iteration with some CG steps. We name this method as generalized conjugate gradient algorithm since the structure of triple blocks [X,P,W] is similar to that of conjugate gradient method.

Optimal techniques

GCGE is a currently active project, we are striving to bring new improvements and new algorithms on a regular basis. Here we list the main improvements we have made.
The converged eigenpairs do not participate the subsequent iteration;
The sizes of P and W are set to be blockSize, which is equal to numEigen/5 as default;
The shift is selected dynamically when solving W;
The large scale orthogonalization to V is transformed into the small scale orthogonalization to P and a large scale orthogonalization to W;
A moving mechnism is used when computing large scale eigenvalue problem.