How to set curve fitting bound as variabe?

hello i am trying to curve fit a set of data to the equation y=-(c10 + c01/x)*(2/x - 2*x^2) where c01>0 and c01+c10>0, i generated this code from the curve fitting toolbx and have been implementing it in a loop for a number of other data sets, how do i implement the lower bound for c10 > -c01?

please find attached code, thank you

clc
clear
[xData, yData] = prepareCurveData( x1, y1 );
 
% Set up fittype and options.
ft = fittype( '-(c10 + c01/x)*(2/x - 2*x^2)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares','Lower',[0,0] );
names=coeffnames(ft)
opts.Display = 'Off';
opts.StartPoint = [0.421761282626275 0.8002804688888];
 
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
coefficientvalues(1,:)=coeffvalues(fitresult)
txt = ['Sample ',num2str((1))]
t={'c01 = ' num2str(coefficientvalues(1,1)),'c10 = ' num2str(coefficientvalues(1,2))}
 
% Plot fit with data.
hold on
h = plot( fitresult, xData, yData );
legend( h, txt, 'mooney2', 'Location', 'NorthEast', 'Interpreter', 'none' );
text(1.1,2E5,t)
% Label axes
xlabel( '\lambda');
ylabel( '\sigma_{m}');
grid on
 

[Lewis Marshall]

I have also been having a similar issue where my coefficient values are interdependent. If anybody knows how to set this in the bounds in the curve fitting toolbox it would be greatly appreciated.

Answer 1

[Ananya Tewari]

I understand you want to set the curve fitting bounds as a variable. A workaround to satisfy the above condition c01 + c10 > 0 we can consider c10 to be extremely small positive number say 10^-10 and set that as lower bound. This will keep the condition in check while curve fitting. Here is the code for the same.

opts = fitoptions( 'Method', 'NonlinearLeastSquares','Lower',[0, 10^-10] );

[Lewis Marshall]

thank you for getting back to me, unfortuantely this will not work as c10 should ideally be a negative number, it should however be large enough ( close enough to 0) that the sum of c01 and c10 is greater than 0.