eighs Interface

public interface eighs

Description

Computes the leading eigenpairs of a symmetric operator $A$ using the Lanczos iterative process. Given a square linear operator $A$, it finds the leading eigvalues and eigvectors such that:

$$Ax = \lambda x$$

The subspace $X$ is constructed via Lanczos factorization, resulting in a symmetric tridiagonal matrix $T$. The eigenvalues of $A$ are approximated by those of $T$ and the eigenvectors are computed accordingly.

References

• Lanczos, C. (1950). "An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators". United States Governm. Press Office.

Syntax

    call eighs(A, X, eigvals, residuals, info [, kdim] [,tolerance])

Arguments

A : Linear operator derived from abstract_sym_linop_rsp, abstract_sym_linop_rdp, abstract_hermitian_linop_csp or abstract_hermitian_linop_cdp whose leading eigenpairs need to be computed. It is an intent(in) argument.

X : Array of abstract_vectors with the same type and kind as A. On exit, it contains the leading eigenvectors of A. Note that the dimension of X fixes the number of eigenpairs computed.

eigvals : Rank-1 array of real numbers. On exit, it contains the leading eigenvalues of A. It is an intent(out) argument.

residuals : Rank-1 array of real numbers. On exit, it contains the residuals associated with each eigenpairs. It is an intent(out) argument.

info : integer Information flag.

kdim (optional) : integer, maximum dimension of the Krylov subspace used to approximate the leading eigenpairs. It is an intent(in) argument. By default, kdim = 4*size(X).

tolerance (optional) : real tolerance below which an eigenpair is considered as being converged. It is an intent(in) agument. By default, tolerance = rtol_sp or tolerance = rtol_dp.

Module Procedures