gen_form.m

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function x = gen_form(L_p,x_s,A,b,K,M) 
%GEN_FORM Transform a standard-form problem back to the general-form setting. 
% 
% x = gen_form(L_p,x_s,A,b,K,M)    (method 1) 
% x = gen_form(L_p,x_s,x_0)        (method 2) 
% 
% Transforms the standard-form solution x_s back to the required 
% solution to the general-form problem: 
%    x = L_p*x_s + d , 
% where L_p and d depend on the method as follows: 
%    method = 1: L_p = pseudoinverse of L, d  = K*(b - A*L_p*x_s) 
%    method = 2: L_p = A-weighted pseudoinverse of L, d = x_0. 
% 
% Usually, the standard-form problem is generated by means of 
% function std_form. 
% 
% Note that x_s may have more that one column. 
 
% References: L. Elden, "Algorithms for regularization of ill- 
% conditioned least-squares problems", BIT 17 (1977), 134-145. 
% L. Elden, "A weighted pseudoinverse, generalized singular values, 
% and constrained lest squares problems", BIT 22 (1982), 487-502. 
% M. Hanke, "Regularization with differential operators.  An itera- 
% tive approach", J. Numer. Funct. Anal. Optim. 13 (1992), 523-540. 
 
% Per Christian Hansen, IMM, 06/12/93. 
 
% Nargin determines which method. 
if (nargin==6) 
  [p,q] = size(x_s); [Km,Kn] = size(K); 
  if (Km==0) 
    x = L_p*x_s; 
  else 
    x = L_p*x_s + K*(M*(b*ones(1,q) - A*(L_p*x_s))); 
  end 
else 
  x_0 = A; [p,q] = size(x_s); 
  x = L_p*x_s + x_0*ones(1,q); 
end