arpack_test

arpack_test, a MATLAB code which calls arpack(), which computes eigenvalues and eigenvectors of large matrices. The arpack() library is accessible in MATLAB via the eigs() command.

1. help eigs
   will print out information about how to use eigs() command inside of MATLAB to interface with ARPACK.
2. Information about the use of the ARPACK execution trace facilities available through "debug.h" is given in arpack_debug.txt
3. Information about the use of the ARPACK operation count and timing statistics available through "stat.h" is given in arpack_stat.txt

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

arpack_test is available in a Fortran90 version and a MATLAB version.

Related Data and Programs:

jacobi_eigenvalue, a MATLAB code which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.

pagerank, a MATLAB code which illustrates the eigenvalue (power method) and surfer (Markov chain) approaches to ranking web pages.

test_eigen, a MATLAB code which defines various eigenvalue test cases.

test_matrix, a MATLAB code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.

web_matrix, a MATLAB code which stores sample matrices describing a web page network. These matrices are typically very sparse, and the examples here are stored using the sparse triplet (ST) format. They can be used to demonstrate pagerank and other graph algorithms.

Reference:

1. Richard Lehoucq, Danny Sorensen, Chao Yang,
   ARPACK User's Guide:
   Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods.
2. Danny Sorensen,
   Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations.

Source Code:

• arpack_test.m, calls all the tests.
• arpack_test.sh, runs all the tests.
• arpack_test.txt, the output file.

• arpack_test01.m, tests EIGS for smallest and largest eigenvalues, with the matrix supplied explicitly.
• arpack_test02.m, tests EIGS for smallest eigenvalues, with the matrix supplied implicitly, by a routine which computes inverse(A)*x.
• ainv_x.m, computes inverse(A)*x for problem 2.