How to fit the data with passing specific point and specific function

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L world
L world on 16 Nov 2021
Commented: Alex Sha on 17 Nov 2021
Please could you me some tips for the below question
To do the fitting, I have searched the polyfit and curve fitting. but i could find the fitting method like below
I would like fit the data by using the specific function like below
y= A (x^2) (x-1)^2 ( I want find A and the function should pass (0,0) and (1,0))
and data is like this:
x=[0 0.166666667 0.333333333 0.5 0.666666667 0.833333333 1]
y=[0 1.09162 1.71904 2.52173 1.20849 2.47433 0]
Therefore, from the data , I would like to get A values from y= A (x^2) (x-1)^2 and data point
And here is constraints that the fiiting function must pass the (0,0) and (1,0)
for example like this:

Accepted Answer

KSSV
KSSV on 16 Nov 2021
Edited: KSSV on 16 Nov 2021
x=[0 0.166666667 0.333333333 0.5 0.666666667 0.833333333 1]' ;
y=[0 1.09162 1.71904 2.52173 1.20849 2.47433 0]' ;
n = 3; % Degree of polynomial to fit
V(:,n+1) = ones(length(x),1); % Vandermonde matrix
for j = n:-1:1
V(:,j) = x.*V(:,j+1);
end
% Constraints
Aeq = x([1 end]).^(n:-1:0);
beq = [y(1) y(end)];
p = lsqlin(V, y,[],[],Aeq,beq);
Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
xnew = linspace(x(1),x(end)) ;
ynew = polyval(p,xnew);
plot(x,y,'.b-')
hold on
% Plot constraints
plot(x([1 end]),y([1 end]),'gx','linewidth',4)
% Plot fitted data
plot(xnew,ynew,'r','linewidth',2)
hold off
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