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    Metadata details:
    filename: joint_diag.m
    path of file: ./repos/OSET/external/jade
    
    the code of the file until where you have to start completion: function [ V , D ] =  joint_diag(A,jthresh)
% Joint approximate diagonalization
% 
% Joint approximate of n (complex) matrices of size m*m stored in the
% m*mn matrix A by minimization of a joint diagonality criterion
%
% Usage:  [ V , D ] =  joint_diag(A,jthresh)
%
% Input :
% * the m*nm matrix A is the concatenation of n matrices with size m
%   by m. We denote A = [ A1 A2 .... An ]
% * threshold is an optional small number (typically = 1.0e-8 see the M-file).
%
% Output :
% * V is an m*m unitary matrix.
% * D = V'*A1*V , ... , V'*An*V has the same size as A and is a
%   collection of diagonal matrices if A1, ..., An are exactly jointly
%   unitarily diagonalizable.
%

% The algorithm finds a unitary matrix V such that the matrices

    
function [ V , D ] =  joint_diag(A,jthresh)
% Joint approximate diagonalization
% 
% Joint approximate of n (complex) matrices of size m*m stored in the
% m*mn matrix A by minimization of a joint diagonality criterion
%
% Usage:  [ V , D ] =  joint_diag(A,jthresh)
%
% Input :
% * the m*nm matrix A is the concatenation of n matrices with size m
%   by m. We denote A = [ A1 A2 .... An ]
% * threshold is an optional small number (typically = 1.0e-8 see the M-file).
%
% Output :
% * V is an m*m unitary matrix.
% * D = V'*A1*V , ... , V'*An*V has the same size as A and is a
%   collection of diagonal matrices if A1, ..., An are exactly jointly
%   unitarily diagonalizable.
%

% The algorithm finds a unitary matrix V such that the matrices
% V'*A1*V , ... , V'*An*V are as diagonal as possible, providing a
% kind of `average eigen-structure' shared by the matrices A1 ,...,An.
% If the matrices A1,...,An do have an exact common eigen-structure ie
% a common orthonormal set eigenvectors, then the algorithm finds it.
% The eigenvectors THEN are the column vectors of V and D1, ...,Dn are
% diagonal matrices.
% 
% The algorithm implements a properly extend