function f = fil_fac(s,reg_param,method,s1,V1) 
%FIL_FAC Filter factors for some regularization methods. 
% 
% f = fil_fac(s,reg_param,method) 
% f = fil_fac(sm,reg_param,method)  ,  sm = [sigma,mu] 
% f = fil_fac(s,k,'ttls',s1,V1) 
% 
% Computes all the filter factors corresponding to the 
% singular values in s and the regularization parameter 
% reg_param, for the following methods: 
%    method = 'dsvd' : damped SVD or GSVD 
%    method = 'tsvd' : truncated SVD or GSVD 
%    method = 'Tikh' : Tikhonov regularization 
%    method = 'ttls' : truncated TLS. 
% If sm = [sigma,mu] is specified, then the filter factors 
% for the corresponding generalized methods are computed. 
% 
% If method = 'ttls' then the singular values s1 and the 
% right singular matrix V1 of [A,b] must also be supplied. 
% 
% If method is not specified, 'Tikh' is default. 
 
% Per Christian Hansen, IMM, 12/29/97. 
 
% Initialization. 
[p,ps] = size(s); lr = length(reg_param); 
if (nargin==2), method = 'Tikh'; end 
f = zeros(p,lr); 
 
% Check input data. 
if (min(reg_param) <= 0) 
  error('Regularization parameter must be positive') 
end 
if ((strncmp(method,'tsvd',4) | strncmp(method,'tgsv',4) | ... 
     strncmp(method,'ttls',4)) & max(reg_param) > p) 
  error('Truncation parameter too large') 
end 
 
% Compute the filter factors. 
for j=1:lr 
  if (strncmp(method,'cg',2) | strncmp(method,'nu',2) | strncmp(method,'ls',2)) 
    error('Filter factors for iterative methods are not supported') 
  elseif (strncmp(method,'dsvd',4) | strncmp(method,'dgsv',4)) 
    if (ps==1) 
      f(:,j) = s./(s + reg_param(j)); 
    else 
      f(:,j) = s(:,1)./(s(:,1) + reg_param(j)*s(:,2)); 
    end 
  elseif (strncmp(method,'Tikh',4) | strncmp(method,'tikh',4)) 
    if (ps==1) 
      f(:,j) = (s.^2)./(s.^2 + reg_param(j)^2); 
    else 
      f(:,j) = (s(:,1).^2)./(s(:,1).^2 + reg_param(j)^2*s(:,2).^2); 
    end 
  elseif (strncmp(method,'tsvd',4) | strncmp(method,'tgsv',4)) 
    if (ps==1) 
      f(:,j) = [ones(reg_param(j),1);zeros(p-reg_param(j),1)]; 
    else 
      f(:,j) = [zeros(p-reg_param(j),1);ones(reg_param(j),1)]; 
    end 
  elseif (strncmp(method,'ttls',4)) 
    if (nargin==5) 
      coef = ((V1(p+1,:).^2)')/norm(V1(p+1,reg_param(j)+1:p+1))^2; 
      for i=1:p 
        k = reg_param(j); 
        f(i,j) = s(i)^2*... 
          sum( coef(1:k)./(s1(1:k)+s(i))./(s1(1:k)-s(i)) ); 
        if (f(i,j) < 0), f(i,j) = eps; end 
        if (i > 1) 
          if (f(i-1,j) <= eps & f(i,j) > f(i-1,j)), f(i,j) = f(i-1,j); end 
        end 
      end 
    else 
      error('The SVD of [A,b] must be supplied') 
    end 
  elseif (strncmp(method,'mtsv',4)) 
    error('Filter factors for MTSVD are not supported') 
  else 
    error('Illegal method') 
  end 
end 
