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Propagation of Uncertainty

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Propagation of Uncertainty

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06 Dec 2007 (Updated )

Returns the propagated uncertainty in a function F imparted to it from its variables

PropError(f,varlist,vals,errs)
function sigma = PropError(f,varlist,vals,errs)
%SIGMA = PROPERROR(F,VARLIST,VALS,ERRS)
%
%Finds the propagated uncertainty in a function f with estimated variables
%"vals" with corresponding uncertainties "errs".
%
%varlist is a row vector of variable names. Enter in the estimated values
%in "vals" and their associated errors in "errs" at positions corresponding 
%to the order you typed in the variables in varlist.
%
%Example using period of a simple harmonic pendulum:
%
%For this example, lets say the pendulum length is 10m with an uncertainty
%of 1mm, and no error in g.
%syms L g
%T = 2*pi*sqrt(L/g)
%type the function T = 2*pi*sqrt(L/g)
%
%PropError(T,[L g],[10 9.81],[0.001 0])
%ans =
%
%    [       6.3437]    '+/-'    [3.1719e-004]
%    'Percent Error'    '+/-'    [     0.0050]
%
%(c) Brad Ridder 2007. Feel free to use this under the BSD guidelines. If
%you wish to add to this program, just leave my name and add yours to it.
n = numel(varlist);
sig = vpa(ones(1,n));
for i = 1:n
    sig(i) = diff(f,varlist(i),1);
end
error1 =sqrt((sum((subs(sig,varlist,vals).^2).*(errs.^2))));
error = double(error1);
sigma = [{subs(f,varlist,vals)} {'+/-'} {error};
         {'Percent Error'} {'+/-'} {abs(100*(error)/subs(f,varlist,vals))}];

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