find the required values using Least square fitting curve tool

I have a function f1(r,v,a,q) with all known values (for example f1 = 2,r=3,a=2.5,q = 0.5). I want to estimate the values of r,v,a in a similar function f2(r,v,a,q) (where f2 = 1.5 and q=0.5 is known) using least square curve fitting tool. q always has the same values as within f1.

E = sum(i=1->N)[f2i(qi)-f1i(qi)] this will compute me r,v,a for f2.

could any one help me how to do in matlab? any tutorial or example work would be great help.

thank you

Answer 1

[Prateekshya]

Hello Muhammad,

To estimate the values of parameters r, v, and a in your function using least squares curve fitting in MATLAB, you can use optimization tools like lsqcurvefit from the Optimization Toolbox. Below is a step-by-step guide on how to set this up, along with an example.

• Define Your Functions: You need to have both functions and defined. These should accept parameters r, v, a, and q.
• Set Up the Objective Function: This function will calculate the difference between and for given parameter values and return the sum of squared differences.
• Use lsqcurvefit: This function will help find the parameters that minimize the difference between and .

Here is an example of how you might implement this in MATLAB:

% Define the function f1
f1 = @(r, v, a, q) r .* q + v .* q.^2 + a; % Example function definition

% Known values for f1
r_true = 3;
v_true = 1;
a_true = 2.5;
q_values = linspace(0, 1, 10); % Example q values
f1_values = f1(r_true, v_true, a_true, q_values);

% Define the function f2 with parameters to estimate
f2 = @(params, q) params(1) .* q + params(2) .* q.^2 + params(3);

% Target values for f2
f2_target = 1.5 * ones(size(q_values)); % Example target values

% Objective function for least squares
objective = @(params) f2(params, q_values) - f2_target;

% Initial guess for [r, v, a]
initial_guess = [1, 1, 1];

% Perform least squares curve fitting
options = optimoptions('lsqcurvefit', 'Display', 'iter');
estimated_params = lsqcurvefit(f2, initial_guess, q_values, f1_values, [], [], options);

% Display estimated parameters
disp('Estimated Parameters:');
disp(['r = ', num2str(estimated_params(1))]);
disp(['v = ', num2str(estimated_params(2))]);
disp(['a = ', num2str(estimated_params(3))]);

I hope this helps!