MATLAB: Automating Changing Partial Derivatives

symbolic

I'm trying to create a program to automate Kline-McClintock Uncertainty analysis'.
My only problem with my current script is in the %% Declaring Variables section. I don't know how I can define a variable, which was symbolic, to equal a number so that I can evaluate the partials. I want to do this in a way that I can put it into a for loop and it will work for any number of variables. My only thought is to edit the script by scanf within itself.
clear all; close all; clc;
%%Declare Stuff
Variables = 'M t L h1 h2 g D rho';
Eq = '((h1-h2)*2*g*D*rho^2*t^2*(pi/4*D^2)^2)/(L*M^2)';
Conversion = 1;
string.Units = '';
string.Eq = ' for f';
%       Example  =  Var Value       Var Error       % Var    Unit
%------------------------------------------------------------------
Variable_Values  = [2.95            0.005       ;   % M      Kg
                    30.07           0.1         ;   % t      sec
                    360E-3          1E-3        ;   % L      m
                    29.5E-2         0.5E-2      ;   % h1     m
                    11E-2           0.5E-2      ;   % h2     m
                    9.81            0.002       ;   % g      m/s^2
                    8.6E-3          0.3E-3      ;   % D      m
                    999             1          ];   % rho    kg/m^3
%%Gogo Matlab
index = 0;
string.old = [];
for i = 1:length(Variables)
    if ~isspace(Variables(i)) && i ~= length(Variables)
        string.new = sprintf('%c',Variables(i));
        string.old = strcat(string.old,string.new);
    elseif i == length(Variables)
        index = index + 1;
        string.new = sprintf('%c',Variables(i));
        string.old = strcat(string.old,string.new);    
        Symbolic_Variables(index) = sym(string.old);
        string.old = [];
    else
        index = index + 1;
        Symbolic_Variables(index) = sym(string.old);
        string.old = [];
    end
end
%%Finding Partials
% Display Initial Equation
string.Initial_Eq = sprintf('Initial Equation%s:\n%s\n',string.Eq,char(Eq));
disp(string.Initial_Eq)
% Calculate and Display Partials
for i = 1:length(Symbolic_Variables)
    string.Partial = sprintf('Partial wrt %s:', ...
        char(Symbolic_Variables(i)));
    Partial(i) = diff(Eq,Symbolic_Variables(i));
    if Partial(i) ~= 0
        disp(string.Partial)
        disp(Partial(i))
    end
end
%%Declaring Variables
M        = Variable_Values(1,1);
t        = Variable_Values(2,1);
L        = Variable_Values(3,1);
h1       = Variable_Values(4,1);
h2       = Variable_Values(5,1);
g        = Variable_Values(6,1);
D        = Variable_Values(7,1);
rho      = Variable_Values(8,1);
%%Computing Uncertainty
uncertainty = 0;
for i = 1:length(Symbolic_Variables)
    uncertainty = (eval(Partial(i))*Variable_Values(i,2))^2 + uncertainty;
end
uncertainty = sqrt(uncertainty)*Conversion;
%%Display Answer
string.Answer = sprintf('The uncertainty is %.4f%s%s',uncertainty,...
    string.Units,string.Eq);
disp(string.Answer)

Best Answer

If you have a symbolic expression and you wish to substitute a particular numeric value for a symbol, use subs(). If you are need a double-precision number as the result, use double() on the symbolic number that results from the subs().
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