dbeoap

% Objective: The direct batch generation of desired eigenvectors lying in % the eigenspace Ek of a unitary matrix.

function [UH, p] = dbeoap(k, r, U, P, mtol1)

% Method: Direct Batch Evaluation of optimal eigenvectors by a constrained

% Optimization Algorithm using the notion of Pseudoinverse (DBEOAP).

%

% Input arguments:

% k: the serial number of the eigenspace Ek (numbered starting from 1).

% r: the dimension of the eigenspace Ek.

% U: a matrix whose columns are approximate eigenvectors close to Ek.

% P: the orthogonal projection matrix of the eigenspace Ek.

% mtol1: Multiplying factor of the tolerance. (tol = mtol * eps)

%

% Output argument:

% UH: the desired orthonormal eigenvectors lying in the eigenspace Ek.

% (The matrices U and UH have the same size).

% p: rank of matrix WSQUARE.