Help!!! Least square fitting

I have a set of values P and D :

P = [175.2582  150.9053  103.9622   69.9965   48.6696]


D = [0   31.3300   61.3200   91.3800  121.4000]

and i want to use the following equation to find a and b

D = a * (P- b)^2 

but I have to satisfy the following conditions

if P <= b then D=a * (P- b)^2 
else D=0

How can i do this and fit the data?

[Walter Roberson]

How does this differ from https://www.mathworks.com/matlabcentral/answers/777947-solving-a-quadratic-equation?s_tid=srchtitle ?

Answer 1

[Matt J]

Using fminspleas from the File Exchange,

P = flip([175.2582  150.9053  103.9622   69.9965   48.6696]).';

D = flip([0   31.3300   61.3200   91.3800  121.4000]).';

funlist={@(b,P) (P<=b).*(P-b).^2};

[b,a]=fminspleas(funlist,P(end), P,D),

b = 230.0623

a = 0.0037

fn=@(P) a*funlist{1}(b,P); %fitted function

plot(P,D,'x',P,fn(P));

[Moza Salem]

Thank you very much !!! without your help I wouldn't be able to get my beam imprint