Fit NonLinearLeastSquares to data and constrain curve to pass through point (0,1)

I have data I need to fit to an equation, which I can do, but I want the equation to pass through point (0,1).

The equation is an exponential y = a*exp(-x/b)+ c*exp(-x/d)+ e

Currently, this is my code:

f3 = fitoptions('Method','NonlinearLeastSquares','Startpoint',[1,100,1,100,1])
newrelax = fittype('q*exp(-x/r)+ s*exp(-x/t)+u','options',f3);
[h,gof] = fit(timeR,stressR,newrelax)
plot(h,timeR,stressR)

Thank you,

-Zach

[Torsten]

Use

y = a*exp(-x/b) + c*exp(-x/d) + (1-(a+c))

as equation.

Answer 1

[Jyotsna Talluri]

You can use a “lsqlin” function from optimization toolbox.

t=coeffvalues(h); 
C=[exp(-x/t(2)) exp(-x/t(4)) ones(size(x))]; 
D=y; 
A = []; % No inequality constraint 
B= []; % No inequality constraint 
%Set the specified points in C and D to find equality constraints Aeq, Beq..By substituting (0,1) they turned out to be 
Aeq =[1 1 1];Beq=[1]; 
l=lsqlin(C,D,A,B,Aeq,Beq);     %generates coefficients of the curve fitted passing through a specified point  
Plot(timeR,C*l); 
 

Refer to the below link

https://www.mathworks.com/help/optim/ug/lsqlin.html

Answer 2

[Matt J]

This answer incorporates Torsten's advice, but I also think you should re-formulate the model to make the exponential terms asymmetric. Otherwise, the solver cannot decide which exponential term belongs to q and which belongs to s.

f3 = fitoptions('Method','NonlinearLeastSquares',...
     'Startpoint',[1,100,1,100,1],'Lower',[-inf,-inf,-inf,0]);

newrelax = fittype('q*exp(-x/r)+ s*exp(-x/(r+d))+(1-(q+s))','options',f3);