chi2inv_rtb.m

%CHI2INV_RTB Inverse chi-squared function
%
% X = CHI2INV_RTB(P, N) is the inverse chi-squared cdf function of N-degrees of freedom.
%
% Notes::
% - only works for N=2
% - uses a table lookup with around 6 figure accuracy
% - an approximation to chi2inv() from the Statistics & Machine Learning Toolbox
%
% See also chi2inv.

% Copyright (C) 1993-2017, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
% 
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
% 
% RTB is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU Lesser General Public License for more details.
% 
% You should have received a copy of the GNU Leser General Public License
% along with RTB.  If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com

function f = chi2inv_rtb(confidence, n)
 
 assert(n == 2, 'chi2inv_rtb: only valid for 2DOF');
 
 c = linspace(0,1,101);

 % build a lookup table:
 %x = chi2inv(c,2)
 %fprintf('%f ');

 % use the lookup table
 x = [0.000000 0.020101 0.040405 0.060918 0.081644 0.102587 0.123751 0.145141 0.166763 0.188621 0.210721 0.233068 0.255667 0.278524 0.301646 0.325038 0.348707 0.372659 0.396902 0.421442 0.446287 0.471445 0.496923 0.522730 0.548874 0.575364 0.602210 0.629421 0.657008 0.684981 0.713350 0.742127 0.771325 0.800955 0.831031 0.861566 0.892574 0.924071 0.956072 0.988593 1.021651 1.055265 1.089454 1.124238 1.159637 1.195674 1.232372 1.269757 1.307853 1.346689 1.386294 1.426700 1.467938 1.510045 1.553058 1.597015 1.641961 1.687940 1.735001 1.783196 1.832581 1.883217 1.935168 1.988505 2.043302 2.099644 2.157619 2.217325 2.278869 2.342366 2.407946 2.475749 2.545931 2.618667 2.694147 2.772589 2.854233 2.939352 3.028255 3.121295 3.218876 3.321462 3.429597 3.543914 3.665163 3.794240 3.932226 4.080442 4.240527 4.414550 4.605170 4.815891 5.051457 5.318520 5.626821 5.991465 6.437752 7.013116 7.824046 9.210340 Inf];
 
 f = interp1(c, x, confidence);