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.
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!
