library.sparseig Submodule

Module Summary

Interfaces for the NAG Mark 27.1 sparseig Chapter.

sparseig - Large Scale Eigenproblems

This module provides functions for computing some eigenvalues and eigenvectors of large-scale (sparse) standard and generalized eigenvalue problems. It provides functions for:

solution of symmetric eigenvalue problems;

solution of nonsymmetric eigenvalue problems;

solution of generalized symmetric-definite eigenvalue problems;

solution of generalized nonsymmetric eigenvalue problems;

partial singular value decomposition.

Functions are provided for both real and complex data.

The functions in this module have all been derived from the ARPACK software suite (see Lehoucq et al. (1998)), a collection of Fortran 77 functions designed to solve large scale eigenvalue problems. The interfaces provided in this module have been chosen to combine ease of use with the flexibility of the original ARPACK software. The underlying iterative methods and algorithms remain essentially the same as those in ARPACK and are described fully in Lehoucq et al. (1998).

The algorithms used are based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method. For symmetric matrices, this reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method. These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed.

Functionality Index

Standard or generalized eigenvalue problems for complex matrices

banded matrices

initialize problem and method: complex_band_init()

selected eigenvalues, eigenvectors and/or Schur vectors: complex_band_solve()

general matrices

initialize problem and method: complex_init()

option setting: complex_option()

reverse communication implicitly restarted Arnoldi method: complex_iter()

reverse communication monitoring: complex_monit()

selected eigenvalues, eigenvectors and/or Schur vectors of original problem: complex_proc()

Standard or generalized eigenvalue problems for real nonsymmetric matrices

banded matrices

initialize problem and method: real_band_init()

selected eigenvalues, eigenvectors and/or Schur vectors: real_band_solve()

general matrices

initialize problem and method: real_init()

option setting: real_option()

reverse communication implicitly restarted Arnoldi method: real_iter()

reverse communication monitoring: real_monit()

selected eigenvalues, eigenvectors and/or Schur vectors of original problem: real_proc()

Standard or generalized eigenvalue problems for real symmetric matrices

banded matrices

initialize problem and method: real_symm_band_init()

selected eigenvalues, eigenvectors and/or Schur vectors: real_symm_band_solve()

general matrices

initialize problem and method: real_symm_init()

reverse communication implicitly restarted Arnoldi(Lanczos) method: real_symm_iter()

reverse communication monitoring: real_symm_monit()

selected eigenvalues and eigenvectors and/or Schur vectors of original problem: real_symm_proc()

For full information please refer to the NAG Library document

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/f12/f12intro.html