simulataneous Curve fitting

Hi,

I am using matlab to fit a family of curves. I want to have one term in the curve with a different coeeficentfor each curve in the family.

 For example say I have 3 curves. Then I want to have a term in my curve such that one of my curves has 1*a, the second curve has 2*a, and the third curve has 3*a where a is the same for all 3 curves

This would require matlab to find "a" simultaneously for all 3 curves and i was wondering how to do that in matlab. I have the curve fitting toolbox but it doesn;t seem to support this simultaneous fitting. Thank you.

[Andreas Goser]

I am not so strong in this area to craft an "answer", but a comment is, that I suppose this is doable with Optimization Toolbox.

[Friedrich]

Could you give us a more specific example? Sounds like it can be achieved with MATLAB itself or maybe Curve Fitting Toolbox can help here.

[Syd]

basically the curves that I am using have a known relationship to me. They all differ by a distance of 1(I know I haven't explained what this distance represents but don;t think that will affect anything). I want to force this relationship to show up in the curves so that each curve has a term whose coeeficent is representative of its distance

Answer 1

[Friedrich]

Hi,

EDIT again full post to match better:

%some x values
x = 1:0.1:10;

%some y values, normally you don't know how they are created, so add some
%noise
y_1 = log(x) + 1*3 + rand(size(x))/10;
y_2 = 2*log(x) + 2*3 + rand(size(x))/10;
y_3 = 0.5*log(x) + 3*3 + rand(size(x))/10;

% so looking for a fit like c_1*log(x) + 1*a for the first one, c_2*log(x) + 2*a for
% the second one and c_3*log(x)+ 3*a for the third one
%so 4 unknown c_1,c_2,c_3 and a which is the same for all the functions

X = [ log(x)', zeros(size(x))', zeros(size(x))', ones(size(x))' ;
      zeros(size(x))', log(x)',zeros(size(x))', 2*ones(size(x))' ;
      zeros(size(x))', zeros(size(x))', log(x)',3*ones(size(x))' ];

Y = [ y_1';
      y_2';
      y_3'];

out = X\Y;

%plot data
hold on
scatter(x,y_1,'*')
scatter(x,y_2,'+')
scatter(x,y_3,'o')

plot(x,out(1)*log(x) + out(4)*1,'b')
plot(x,out(2)*log(x) + out(4)*2,'g')
plot(x,out(3)*log(x) + out(4)*3,'r')

hold off

[Syd]

well let me clarify a little more what I want (I'm new to matlab so I apologize for not being so knowledgeable)

The equations that I want to do the fitting with are:

y= a log x + b

y= c log x + 2* b

y= d log x + 3 *b

the only value that I want to be the same is b. The other coeeficients can vary.

Also, I'm using simulation data so I'm looking for a best fit; it will not be an exact fit.

Thanks for your help!!

[Friedrich]

That whats my above approach does. Use log(x) instead of x.^2 and you should be done. And use your x and y values of course.

[Syd]

thanks again!!

[Syd]

also, I've added a follow up if u get a chance to look at it http://mathworks.com/matlabcentral/answers/13527-simulataneous-curve-fitting-follow-up thanks!

Answer 2

[Fangjun Jiang]

Subtract your first curve with 1a, second curve with 2a and third curve with 3a and then do the curve fitting?

[Syd]

could you explain a little more? thanks so much!