simultaneous fitting of two plots with two functions

I have two sets of dependent variable column vectors (y1, y2) for a set of independent variable column vectors (x). I want to fit the (x, y1) plot with the function f1(ca. f1 = (a + (b-a)*(1 + c*x^d))) and the (x, y2) plot with the function f2(ca. f2 = (b-a)*c*x^d)) simultaneously. Could anyone please help?

Many thanks, in advance! Arun

[Kaushik Lakshminarasimhan]

What do you mean by simultaneous? Based on your equations, the transformation from x to y_1 is independent of y_2 and likewise x -> y_2 is independent of y_1. So you can just fit the two functions separately.

[Arun Kumar Bar]

The parameters a, b, c and d are to be same for both the fits. If I fit separately, it will not guarantee same values of the parameters for both the fits. Anyway, thank you.

Answer 1

[Torsten]

Use "lsqcurvefit" with the data set xdata = (x,x),ydata = (y1,y2).

Best wishes

Torsten.

[Arun Kumar Bar]

Hi Torsten, In fact I new that lsqcurvefit would work. But when I do it, it ends with an error: the function values and the ydata are not of same size. Most probably I am messing with the function set-up.

I was trying as follow:

xdata=[x(:1); x(:1)];

ydata=[y1(:1); y2(:1)]; % FYI, all x(:1), y1(:1) and y2(:1) are of same size.

fun=@(x,xdata) f1(x,a,b,c,d); f2(x,a,b,c,d);

x0=[- - - -];

x=lsqcurvefit(fun,xO,xdata, ydata);

Though I am not able to find out, I am definitely making a mess somewhere. Could you please point out?

Thanks and regards, Arun

[Torsten]

xdata=[x(:,1); x(:,1)];
ydata=[y1(:,1); y2(:,1)]; 
fun=@(x,xdata) [f1(xdata(1:numel(xdata)/2),x(1),x(2),x(3),x(4)); f2(xdata(1:numel(xdata)/2),x(1),x(2),x(3),x(4))];
x0=[- - - -];
x=lsqcurvefit(fun,x0,xdata,ydata);

where f1(...),f2(...) must be column vectors each of the same size as xdata(1:numel(xdata)/2).

Best wishes

Torsten.

[Arun Kumar Bar]

Hi Torsten, Thanks a lot for your help! Could you please help me out from the associated following problem?

As I mentioned earlier, for the set of independent vectors x1, there are two sets of vectors, y1 and y2. So essentially, I should be able to fit them separately, ca. (x1 vs y1) and (x1 vs y2) plots. When I use APP in MATLAB, it works fine with the following custom equation:

y=f(x1)=m1+((m2-m1)*(1+(((2*pi*x1*m3)^(1-m4))*sin(m4*pi/2)))/(1+(2*((2*pi*x1*m3)^(1-m4)*sin(m4*pi/2)))+((2*pi*x1*m3)^((2-(2*m4))))))

But, it does not work in CommandWindow when I use the same equation in the function:

fun=@(m,x1) (m(1)+((m(2)-m(1)).*(1+(((2.*pi.*x1.*m(3)).^(1-m(4))).*sin(m(4).*pi/2)))/(1+(2.*((2.*pi.*x1.*m(3)).^(1-m(4)).*sin(m(4).*pi/2)))+((2.*pi.*x1.*m(3)).^((2-(2.*m(4))))))));

The error is a bit surprising to me! Both the x1 and y1 are 24x1 matrices (column vectors). While, the fun is returning a 24x24 matrix, with all identical elements.

Suppose, if I use, m0=[1.1; 17; 1.85; 0.54]; % these are the parameters obtained from the best fit using APP with the above custom equation; fun(m0,x1) returns a 24x24 matrix with all identical elements. Could you please suggest where I am going wrong ?

Kind regards, Arun

[Torsten]

... .*pi/2)))./(1+(2.* ...

instead of

... .*pi/2)))/(1+(2.* ...

Best wishes

Torsten.

[Arun Kumar Bar]

That's great! Thanks a lot, Torsten!

Kind regards, Arun

Answer 2

[Torsten]

xdata=[x(:,1); x(:,1)];
ydata=[y1(:,1); y2(:,1)]; 
fun=@(x,xdata) [f1(xdata(1:numel(xdata)/2),x(1),x(2),x(3),x(4)); f2(xdata(1:numel(xdata)/2),x(1),x(2),x(3),x(4))];
x0=[- - - -];
x=lsqcurvefit(fun,x0,xdata,ydata);

where f1(...),f2(...) must be column vectors each of the same size as x.