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    Metadata details:
    filename: tikhonov.m
    path of file: ./repos/HRTF-Individualization/model/matlabcode/functions/library/regu
    
    the code of the file until where you have to start completion: function [x_lambda,rho,eta] = tikhonov(U,s,V,b,lambda,x_0)
%TIKHONOV Tikhonov regularization.
%
% [x_lambda,rho,eta] = tikhonov(U,s,V,b,lambda,x_0)
% [x_lambda,rho,eta] = tikhonov(U,sm,X,b,lambda,x_0) ,  sm = [sigma,mu]
%
% Computes the Tikhonov regularized solution x_lambda.  If the SVD
% is used, i.e. if U, s, and V are specified, then standard-form
% regularization is applied:
%    min { || A x - b ||^2 + lambda^2 || x - x_0 ||^2 } .
% If, on the other hand, the GSVD is used, i.e. if U, sm, and X are
% specified, then general-form regularization is applied:

    
function [x_lambda,rho,eta] = tikhonov(U,s,V,b,lambda,x_0)
%TIKHONOV Tikhonov regularization.
%
% [x_lambda,rho,eta] = tikhonov(U,s,V,b,lambda,x_0)
% [x_lambda,rho,eta] = tikhonov(U,sm,X,b,lambda,x_0) ,  sm = [sigma,mu]
%
% Computes the Tikhonov regularized solution x_lambda.  If the SVD
% is used, i.e. if U, s, and V are specified, then standard-form
% regularization is applied:
%    min { || A x - b ||^2 + lambda^2 || x - x_0 ||^2 } .
% If, on the other hand, the GSVD is used, i.e. if U, sm, and X are
% specified, then general-form regularization is applied:
%    min { || A x - b ||^2 + lambda^2 || L (x - x_0) ||^2 } .
%
% If x_0 is not specified, then x_0 = 0 is used
%
% Note that x_0 cannot be used if A is underdetermined and L ~= I.
%
% If lambda is a vector, then x_lambda is a matrix such that
%    x_lambda = [ x_lambda(1), x_lambda(2), ... ] .
%
% The solution norm (standard-form case) or seminorm (general-form
% case) and the residual norm are returned in eta and rho.

% Per Christian Hansen, IMM, April 14, 2003.

% Reference: A. N. Tikhonov & V. Y. Arsenin, "Solutions of
% Ill-Posed Problems", Wiley, 1977.

% Initialization.
if (min(lambda)<0)
  error('Illegal regularization parameter lambda')
end