Hi experts,
I have a set of data which is in the cartesian coordinates (xOy) but needs to be moved a distance (say xc, yc) and rotate an angle (theta) (still cartesian coordinates) to fitting the theoretical value calculated from ode45 function.
In previous code, I transform data by manual procedure and then use lsqcurvefit to fitting the data, with B and L are optimization variables.
p=lsqcurvefit(@(p,y_exp) pendant_bubble_arc_d(p,y_exp),p0,y_exp,x_exp,lb,ub);
function x_model = pendant_bubble_arc_d(p, y_exp)
sspan = [0 l_exp/L]; y_solver=[];
options = odeset('RelTol',1e-8,'AbsTol',1e-8,'MaxStep',5e-2);
[~, y_solver] = ode45(@(t,y) pendant_bubble_arc_f(t,y,B), sspan, y0, options);
x_model = interp1( y_solver(:,2)*L, y_solver(:,1)*L, y_exp,'spline',2);
The code run successfully and result is correct. However, my PI also needs xc, yc, theta are optimization values for lsqcurvefit function.
And this my idea for the problem:
p0=[0.5, 2, 2.5, 0.8, 1 ];
p= lsqcurvefit(@(p,y_exp) lsq_function(p,y_exp),p0,y_exp,x_exp,lb,ub);
function x_model = lsq_function(p, y_exp)
sspan = [0 l_exp/L]; y_solver=[];
options = odeset('RelTol',1e-8,'AbsTol',1e-8,'MaxStep',5e-2);
[~, y_solver] = ode45(@(t,y) YL_function(t,y,B), sspan, y0, options);
R=[cosd(theta) sind(theta); -sind(theta) cosd(theta)];
y_trans(:,1)=y_solver(:,1)+xc;
y_trans(:,2)=y_solver(:,2)+yc;
x_model = interp1(y_rotate(:,2)*L, y_rotate(:,1)*L, y_exp,'spline',2);
Although the code does not have any error, but it does not return the values I expect. The code just return value slightly change from initial guess (few percents). I just learning this and do not have sufficient knowledge about matlab. So if you have any ideas how I should modify the code, please let me know.
Thank you!
P/s: if the question is unclear, please pointed it and I will explain.
function f=YL_function(s,y,B)
f(3) = 2/B-h-sin(theta)./r;
f(4) = pi*r^.2*sin(theta);
This is function YL_function (also pendant_bubble_arc_f in upper code).
