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% % Duke University                                                            %
% % K. P. Trofatter                                                            %
% % kpt2@duke.edu                                                              %
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% zlsq() - construct an invertible linear system with a solution that solves the
% complex least squares problem with L2 regularization for any linear system.
% Use a seperate program to solve the resulting system.
% 
% USAGE:
%   [A_lsq, b_lsq] = zlsq(A, A_adj, b, gamma)
%
% INPUT:
%   [1,1] function | A     | function for multiplication by [m,n] complex A
%   [1,1] function | A_adj | function for adjoint (conjugate transpose) of A
%   [m,1] complex  | b     | data vector
%   [1,1] double   | gamma | regularization weighting factor
%
% OUTPUT:
%   [1,1] function | A_lsq | complex least squares linear operator
%   [n,1] complex  | b_lsq | complex least squares data vector
%
% NOTES:
%   the copmlex least squares cost function to be minimized is:
%     zlsq cost function : f(x) = || b - A x ||^2  +  gamma || x ||^2
%   the gradient of the cost function is
%     grad f = -A' [b - A x] - gamma x
%   therefore the system to solve is
%     A_lsq x_lsq = b_lsq
%     A_lsq = A' A + gamma I
%     b_lsq = A' b

function [A_lsq, b_lsq] = zlsq(A, A_adj, b, gamma)
    
    % build least squares equation
    A_lsq = @(x) A_adj(A(x)) + gamma * x;
    b_lsq = A_adj(b);
    
end


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