function [u] = spm_uc_RF(a,df,STAT,R,n)
% corrected critical height threshold at a specified significance level
% FORMAT [u] = spm_uc_RF(a,df,STAT,R,n)
% a     - critical probability - {alpha}
% df    - [df{interest} df{residuals}]
% STAT  - Statisical field
%		'Z' - Gaussian field
%		'T' - T - field
%		'X' - Chi squared field
%		'F' - F - field
% R     - RESEL Count {defining search volume}
% n     - abs(n), number of conjoint SPMs
%
% u     - critical height {corrected}
%
%___________________________________________________________________________
%
% spm_uc returns the corrected critical threshold at a specified significance
% level (a). If n > 1 a conjunction the probability over the n values of the 
% statistic is returned.
%___________________________________________________________________________
% @(#)spm_uc_RF.m	1.4 Karl Friston 04/06/30

if n>0
  Cnj_n = 1;       % Inf on Conjunction Null
else
  Cnj_n = abs(n);  % Inf on Global Null
end

% find approximate value
%---------------------------------------------------------------------------
u     = spm_u((a/sum(R))^(1/Cnj_n),df,STAT);
du    = 1e-6;

% approximate estimate using E{m}
%---------------------------------------------------------------------------
d     = 1;
while abs(d) > 1e-6
	[P P p] = spm_P_RF(1,0,u,df,STAT,R,n);
	[P P q] = spm_P_RF(1,0,u + du,df,STAT,R,n);
        d       = (a - p)/((q - p)/du);
        u       = u + d;
end

% refined estimate using 1 - exp(-E{m})
%---------------------------------------------------------------------------
d     = 1;
while abs(d) > 1e-6
        p       = spm_P_RF(1,0,u,df,STAT,R,n);
	q       = spm_P_RF(1,0,u + du,df,STAT,R,n);
        d       = (a - p)/((q - p)/du);
        u       = u + d;
end