Error propagation through a function

Calculates the error propagation through a function NEEDS : Symbolic Math Toolbox

The function takes 4 entries :

1) The function f written with symbolic variables

2) A 1*n matrix of the symbolic variables of the function

3) A 1*n matrix of the values of the variables to evaluate the function at (IMPORTANT : must be in the same order as the variables in 2))

4) A 1*n matrix of the values of the errors of the variables at the point given in 3) (IMPORTANT : must be in the same order as the variables in 2))

It then returns a 1*3 matrix containing the value of the function at this point in the first cell, the absolute error in the second cell and the relative error in the third one (in percentage!!)

See an example below :

syms A B C % We define the symbolic variables

f = 3*A*exp(B-C^2); % We define the function we are looking to propagate the error through

varlist = [A B C]; % The list of variables

vals = [2 4 0.1]; % The list of the values of the variables to evaluate the function at

errs = [0.2 0.1 0.001]; % The errors of the variables at this point

F_and_errors = propagErreur(f, varlist, vals, errs); % Calls the function to evaluate the function at the given point and propagate the error