nonlinear curve , lsqcurvefit

I am using 'lsqcurvefit' to fit a nonlinear model ( Actualy a fourier series in which I know the frequencies. I want the amplitude of each sin/cosine term). So problem is like this,

suppose I have 'N' grid point and for each grid point I have time series data for which I know three dominant frequencies. Now the model which I want to fit on the time series for each grid is

H=A+B*t + C1*cos(2.pi.f2*t)+ C2*sin(2.pi.f1*t)+ C3*cos(2.pi.f2*t)+
C4*sin(2.pi.f2*t)+ C5*cos(2.pi.f3*t)+ C6*sin(2.pi.f3*t)

As I mentioned, I know the value of f1, f2, f3 for each grid and want to estimate A,B,C1,C2,... for each grid. Here 't' is independent variable.

I want to do this in loop for i=1:N and change the value of 'f' for each loop as I have these values for each grid.

Can you please help me out from this problem.

Here is what I was trying but its not working. Firstly I define a function with some function name say 'FUN' hence

    @FUN((x0,Xdata,f) H=x0(1)+x0(2)*Xdata+x0(3)*cos(2*pi*f1.*Xdata)+x0(4)...
  *sin(2*pi*f1.*Xdata)+x0(5)*cos(2*2*pi*f2.*Xdata)+...
 x0(6)*sin(2*2*pi*f2.*Xdata)+x0(7)*cos(3*2*pi*f3.*Xdata)+...
 x0(8)*sin(3*2*pi*f3.*Xdata);

and

f=[f1,f2,f3]

then using lsqcurvefitting

   [P1,N1,R1,EF1,OP1,L1,J1]=lsqcurvefit(@EWHmodelFunc3,ones(8,1)*0.5,f0,t,EWH);

Please help me out

[Matt J]

Here is what I was trying but its not working.

What are the copy/pasted error messages?

[Matt J]

Your objective function is linear in all of the parameters. Looks like you should really be using lsqlin(). If the lower bound EWH is non-critical, you could even be using mldivide().

Answer 1

[Matt J]

Just some guesses, but you really need to provide copy/pastes of error messages as requested here. Your definition of FUN has the wrong syntax. Looks like it should be

     EWHmodelFunc3 = @FUN((x0,Xdata,f) x0(1)+x0(2)*Xdata+x0(3)*cos(2*pi*f1.*Xdata)+x0(4)...
  *sin(2*pi*f1.*Xdata)+x0(5)*cos(2*2*pi*f2.*Xdata)+...
 x0(6)*sin(2*2*pi*f2.*Xdata)+x0(7)*cos(3*2*pi*f3.*Xdata)+...
 x0(8)*sin(3*2*pi*f3.*Xdata);

Also, the call to lsqcurvefit looks like it should be

   [P1,N1,R1,EF1,OP1,L1,J1]=...
  lsqcurvefit(@(x0,Xdata) EWHmodelFunc3(x0,Xdata,f),ones(8,1)*0.5,f0,t,EWH);

[Saurabh Srivastava]

Dear Matt,

Thanks for your comment. Now quick response to your comments.

Mathematical form of the function which I defined is correct. I understand that you suggested me to add index 'n' in each term of sine/cosine but this will work when I will use single frequency (w) i.e. 1.2pi.w, 2.2pi.w,3.2pi.w and so on... but here frequency is different. Now when I used the code

H=@(x0,Xdata,f)x0(1)+x0(2)*Xdata+x0(3)*cos(2*pi*f(1).*Xdata)+x0(4)...
  *sin(2*pi*f(1).*Xdata)+x0(5)*cos(2*pi*f(2).*Xdata)+...
 x0(6)*sin(2*pi*f(2).*Xdata)+x0(7)*cos(2*pi*f(3).*Xdata)+...
 x0(8)*sin(2*pi*f(3).*Xdata);

f=[0.0139;0.1736;0.0278];
t=1:144;
t=t';
and take random set as predicting variable as 

W=rand(144,1);

[P1,N1,R1,EF1,OP1,L1,J1]=lsqcurvefit(H,ones(8,1)*0.5,f,t,W);

Then I get the following error

Hope this will help you to understand the problem.

[Matt J]

I understand that you suggested me to add index 'n' in each term of sine/cosine but this will work when I will use single frequency (w) i.e. 1.2pi.w, 2.2pi.w,3.2pi.w and so on...

Nope. I didn't suggest that. I copy/pasted the expression for H directly from your posted question, except that I fixed the syntax.

Then I get the following error

See again my original answer. You cannot pass H to lsqcurvefit because H expects 3 arguments. You must wrap H in an additional anonymous function as I demonstrated.

[Saurabh Srivastava]

Dear Matt, Sorry to disturb you again. But alas, I am not able to solve.I have tried to modify the syntax as you suggested as follows where i have defined a function H with argument, (x0, Xdata and f)

H=@(x0,Xdata,f)x0(1)+x0(2)*Xdata+x0(3)*cos(2*pi*f(1).*Xdata)+x0(4)...
  *sin(2*pi*f(1).*Xdata)+x0(5)*cos(2*pi*f(2).*Xdata)+...
 x0(6)*sin(2*pi*f(2).*Xdata)+x0(7)*cos(2*pi*f(3).*Xdata)+...
 x0(8)*sin(2*pi*f(3).*Xdata);

x0 is 8x1 column vector which initialize the parameter which i need to estimate, xData=1:144, EWH=rand(144,1) while f=[0.0139;0.1736;0.0278];

Now Please suggest me how can I wrap H in another fuction and then pass it to lsqcurvefit which you have suggested. i was doing like you suggested.

[P1,N1,R1,EF1,OP1,L1,J1]=lsqcurvefit(@(x0,Xdata)...
H(x0,Xdata,f),ones(8,1)*0.5,f,t,EWH);

Can you tell me where i am doing wrong. it would be nice if you solve by some random example.

Error Msg

Thanks in advance

[Matt J]

I get the feeling you're just putting the lsqcurvefit input arguments in the wrong places. Earlier you said 't' is the independent variable, but here you've called lsqcurvefit with t as the dependent variable. Also, you are now telling lsqcurvefit that 'f' is the independent variable, whereas earlier, you said it was just a set of 3 frequency parameters.

If you look at the documentation, you are calling lsqcurvefit with the 5-argument syntax,

x = lsqcurvefit(fun,x0,xdata,ydata,lb)

and so lsqcurvefit is making the associations,

fun= @(x0,Xdata) H(x0,Xdata,f); %model function

x0= ones(8,1)*0.5; %initial parameter guess

xdata = f;  ydata = t; %data to be fit 

lb=EWH; %lower bounds

lsqcurvefit is iteratively evaluating H(x0,Xdata,f) for different parameter choices and comparing the result element-wise to the 4th input argument, ydata=t. The error message is complaining that H(x0,Xdata,f) does not return an array the same size as ydata=t making the comparison impossible.

There is also a warning saying that the lower bound vector EWH is shorter in length than x0= ones(8,1)*0.5. In other words, you haven't specified a bound on all 8 of your unknown parameters. Therefore, lsqcurvefit is going to assume you want no bounds on all x0(i), i>length(EWH).