Non-linear data fit with multiple constants

I have a non-linear equation with 3 variables I wish to be constants and only 1 variable to be fitted to x,y data.

Using fittype, I have entered the equation and tried to specify b, c & d as constants. However, the options 'problem' only seems to allow single variables to be specified as constants

ft = fittype(@(a, b, c, d,x) a*c*x./(1+c*x) + b*d*x./(1+d*x),'problem','b,c,d');

Error using fittype>iAssertValidVariableNames

The name '[b,c,d]' is not a valid MATLAB variable name.

In the next part I use "fit" to fit the data, and specify the value of the 3 constants and starting point of the fit:

f = fit(p(1:index),q(1:index),ft,'problem',[Qm2 b1 b2],'StartPoint',Qm1);

Is there another way to specify constants in the fittype?

[Torsten]

If b,c and d are known constants, why don't you simply specify them with their numerical values in the fittype function ?

[Lawrence]

I've just learnt to specify them as cell arrays so using curly brackets:

ft = fittype(@(a, b, c, d,x) a*c*x./(1+c*x) + b*d*x./(1+d*x),'problem',{'b','c','d'});

This seems to work. They are variables I want constant for the fit, but they are variable in the rest of the code so can't just put in numerical values.

[Torsten]

Or like this:

xfit = (0:0.1:1).';
yfit = 3*xfit + 0.01*(2*rand(11,1)-1);
b = 4;
fun = @(a,b,x) a/b*x;
ft = fittype( @(a,x) fun(a,b,x));
f = fit(xfit,yfit,ft)

Warning: Start point not provided, choosing random start point.

f = 
     General model:
     f(x) = fun(a,b,x)
     Coefficients (with 95% confidence bounds):
       a =       12.02  (11.99, 12.05)

[Lawrence]

Thanks! That's a neat solution.

Answer 1

[Matt J]

Though your post's title says the fitting problem is nonlinear, it is actually linear when b and d are known, and so has a simple analytical solution. When c is also known the solution is even simpler:

x=p(:); y=q(:);
x=x(1:index); y=y(1:index);
P=c*x./(1+c*x);
Q=(b*d)*x./(1+d*x);


ft = fittype(@(a, b, c, d,x) a*c*x./(1+c*x) + b*d*x./(1+d*x),'problem',{'b','c','d'});

f=cfit(ft,  P\(y(:)-Q))  ; %fit result