Lanczos diagonalization. More...
#include <lanczos_base.h>
Detailed Description
template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>
class o2scl_linalg::lanczos< vec_t, mat_t >
This class approximates the largest eigenvalues of a symmetric matrix.
The vector and matrix types can be any type which provides access via operator[] or operator(), given a suitable vector allocation type.
The tridiagonalization routine was rewritten from the EISPACK routines imtql1.f (but uses gsl_hypot() instead of pythag.f).
- Idea for Future:
- The function eigen_tdiag() automatically sorts the eigenvalues, which may not be necessary.
- Idea for Future:
- Do something better than the simple matrix-vector product. For example, use dgemm() and allow user to specify column or row-major.
- Idea for Future:
- Rework memory allocation to perform as needed.
Definition at line 59 of file lanczos_base.h.
Public Member Functions | |
| int | eigenvalues (size_t size, mat_t &mat, size_t n_iter, vec_t &eigen, vec_t &diag, vec_t &off_diag) |
Approximate the largest eigenvalues of a symmetric matrix mat using the Lanczos method. More... | |
| int | eigen_tdiag (size_t n, vec_t &diag, vec_t &off_diag) |
| In-place diagonalization of a tridiagonal matrix. More... | |
Public Attributes | |
| size_t | td_iter |
| Number of iterations for finding the eigenvalues of the tridiagonal matrix (default 30) | |
| size_t | td_lasteval |
| The index for the last eigenvalue not determined if tridiagonalization fails. | |
Protected Member Functions | |
| void | product (size_t n, mat_t &a, vec_t &w, vec_t &prod) |
| Simple matrix-vector product. More... | |
Member Function Documentation
◆ eigen_tdiag()
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inline |
On input, the vectors diag and off_diag should both be vectors of size n. The diagonal entries stored in diag, and the 
off-diagonal entries should be stored in off_diag, starting with off_diag[1]. The value in off_diag[0] is unused. The vector off_diag is destroyed by the computation.
This uses an implict QL method from the EISPACK routine imtql1. The value of ierr from the original Fortran routine is stored in td_lasteval.
Definition at line 168 of file lanczos_base.h.
◆ eigenvalues()
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inline |
Given a square matrix mat with size size, this function applies n_iter iterations of the Lanczos algorithm to produce n_iter approximate eigenvalues stored in eigen. As a by-product, this function also partially tridiagonalizes the matrix placing the result in diag and off_diag. Before calling this function, space must have already been allocated for eigen, diag, and off_diag. All three of these arrays must have at least enough space for n_iter elements.
Choosing /c n_iter = size will produce all of the exact eigenvalues and the corresponding tridiagonal matrix, but this may be slower than diagonalizing the matrix directly.
Definition at line 95 of file lanczos_base.h.
◆ product()
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inlineprotected |
It is assumed that memory is already allocated for prod.
Definition at line 305 of file lanczos_base.h.
The documentation for this class was generated from the following file:
- /home/awsteiner/wcs/o2scl/src/linalg/lanczos_base.h