You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: l_curve_tikh_svd.m
    path of file: ./repos/MuRAT/Utilities_Matlab/regtu
    
    the code of the file until where you have to start completion: % Parameter Estimation and Inverse Problems, 2nd edition, 2011
% by R. Aster, B. Borchers, C. Thurber
%
% return l curve parematers for Tikhonov Regularization
%
% Routine originally inspired by Per Hansen's l-curve
% program (http://www2.imm.dtu.dk/~pch/Regutools/)
%
% 
% [rho,eta,reg_param] = l_curve_tikh(U,s,d,npoints,[alpha_min, alpha_max]) ) 
% 
% INPUT
%   U       - matrix of data space basis vectors from
    
function [rho,eta,reg_param] = l_curve_tikh_svd(U,s,d,npoints,varargin)
 
% Initialization. 
[m,n] = size(U);
[p] = length(s); 
 
% compute the projection, and residual error introduced by the projection
d_proj = U'*d;
dr = norm(d)^2 - norm(d_proj)^2;

%data projections
d_proj = d_proj(1:p); 

%scale series terms by singular values
d_proj_scale = d_proj./s; 
 
% initialize storage space
eta = zeros(npoints,1);
rho = eta;
reg_param = eta;
s2 = s.^2; 

if size(varargin,2)==0
% set the smallest regularization parameter that will be used
smin_ratio = 16*eps;
reg_param(npoints) = max([s(p),s(1)*smin_ratio]); 

% ratio so that reg_param(1) will be s(1)
ratio = (s(1)/reg_param(npoints))^(1/(npoints-1));
end