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) 1993-2019 Peter I. Corke
%
% This file is part of The Spatial Math Toolbox for MATLAB (SMTB).
% 
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% in the Software without restriction, including without limitation the rights
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% so, subject to the following conditions:
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% The above copyright notice and this permission notice shall be included in all
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% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
% FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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%
% https://github.com/petercorke/robotics-toolbox-matlab

function f = chi2inv_rtb(confidence, n)
 
 assert(n == 2, 'RTB:chi2inv_rtb:badarg', '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);