Extra Modules

ARPACK

ARPACK is a numerical software library written in FORTRAN 77 for solving large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of large sparse or structured matrices, using the Implicitly Restarted Arnoldi Method (IRAM) or, in the case of symmetric matrices, the corresponding variant of the Lanczos algorithm.

API

template<Number T, template<typename, typename> class S>
internal::convert_to_complex<T> max_eigen(const CSRMatrix<T, Host, S> &A, ARPACKOptions options = ARPACKOptions())

Estimate the maximum eigenvalue in magnitude of a sparse matrix A using the standard algorithm from ARPACK.

See also

ARPACKOptions for all parameters.

Parameters:

  • A – [in] input matrix

  • options – [in] options for ARPACK.

template<Number T, template<typename, typename> class S>
internal::convert_to_complex<T> min_eigen(const CSRMatrix<T, Host, S> &A, ARPACKOptions options = ARPACKOptions())

Estimate the minimum eigenvalue in magnitude of a sparse matrix A using the shift-and-invert algorithm from ARPACK.

See also

ARPACKOptions for all parameters.

Parameters:

  • A – [in] input matrix

  • options – [in] options for ARPACK.

template<Number T, template<typename, typename> class S>
T max_symmetric_eigen(const CSRMatrix<T, Host, S> &A, ARPACKOptions options = ARPACKOptions())

Estimate the maximum eigenvalue in magnitude of a sparse symmetric, real matrix A using the standard algorithm from ARPACK.

See also

ARPACKOptions for all parameters.

Parameters:

  • A – [in] input matrix

  • options – [in] options for ARPACK.

template<Number T, template<typename, typename> class S>
T min_symmetric_eigen(const CSRMatrix<T, Host, S> &A, ARPACKOptions options = ARPACKOptions())

Estimate the minimum eigenvalue in magnitude of a sparse symmetric, matrix A using the shift-and-invert algorithm from ARPACK.

See also

ARPACKOptions for all parameters.

Parameters:

  • A – [in] input matrix

  • options – [in] options for ARPACK.