% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program 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
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING. If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.
%
% arhenius.m
%
chisq = 5.99; % chi square value for 95% confidence level with 2 parameters
lnk0 = 1;
E = 100;
ndata = 10;
Tmin = 300;
Tmax = 500;
Tmeas = linspace(Tmin,Tmax,ndata)';
X = [ones(ndata,1) -1./Tmeas];
lnk = X*[lnk0; E];
k = exp(lnk);
measvar= 1e-3;
measstddev = sqrt(measvar);
% set seed for "reproducible" random numbers
randn('seed',0);
%some noisy data points
nexpts = 500;
clear lnkmeas;
for i = 1:nexpts
lnkmeas(:,i) = lnk + measstddev*randn(ndata,1);
end
theta = (inv(X'*X)*X' * lnkmeas)';
Tcenter = -1./Tmeas + 1/mean(Tmeas);
Xcenter = [ones(ndata,1) Tcenter];
thetacenter = (inv(Xcenter'*Xcenter)*Xcenter' * lnkmeas)';
% calculate the elliptical confidence interval and bounding box
npts = 181;
amat = X'*X/measvar;
level = chisq;
[x, y, major, minor, bbox] = ellipse (amat, level, npts);
x = x + lnk0;
y = y + E;
minor(:,1) = minor(:,1) + lnk0;
minor(:,2) = minor(:,2) + E;
major(:,1) = major(:,1) + lnk0;
major(:,2) = major(:,2) + E;
bbox(:,1) = bbox(:,1) + lnk0;
bbox(:,2) = bbox(:,2) + E;
elips = [x, y];
save arrhenius.dat theta bbox elips;
if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (theta(:,1), theta(:,2), '+', bbox(:,1), bbox(:,2), ...
elips(:,1), elips(:,2));
% TITLE
end % PLOTTING
