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# gen_form

## (PublicToolbox/regutools/gen_form.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    x = gen_form(L_p,x_s,A,b,K,M)

### Help Text

    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.

### Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\gen_form.m

    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, UNI-C, 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

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