Filter löschen
Filter löschen

Fitting unknowns to a curve with minimized error

5 Ansichten (letzte 30 Tage)
Tiffany
Tiffany am 30 Aug. 2013
I have a series of equations I am trying to fit to a data set (x) separately:
for example:
(a+b*c)*d = x
a*(1+b*c)*d = x
x = 1.9248 3.0137 4.0855 5.0097 5.7226 6.2064 6.4655 6.5108 6.3543 6.0065
c= 0.0200 0.2200 0.4200 0.6200 0.8200 1.0200 1.2200 1.4200 1.6200 1.8200
d = 1.2849 2.2245 3.6431 5.6553 8.3327 11.6542 15.4421 19.2852 22.4525 23.8003
I know c, d and x - they are observations. My unknowns are a and b, and should be constant.
I have tried fsolve and polyfit at the recommendation of others - the polyfit gives a very poor fit. What should I do?
Note: I have asked on SO and this code section was written by Prashant. Another author Emmet suggested a similar strategy using polyfit.
(a+b*c)*d = x
p = polyfit(c, x./d, 1);
a = p(2);
b = p(1);
a*(1+b*c)*d = x
p = polyfit(c, x./d, 1);
a = p(2);
b = p(1) / a;
I'm trying to learn how to fit curves with data instead of curve fitting using the Matlab tool. If someone could show me a general example or use my numbers as an example that I could follow and learn, that would be a brilliant thing :) Thank you for your time.

Akzeptierte Antwort

the cyclist
the cyclist am 30 Aug. 2013
Bearbeitet: the cyclist am 30 Aug. 2013
This doesn't seem like a bad fit to me.
x = [1.9248 3.0137 4.0855 5.0097 5.7226 6.2064 6.4655 6.5108 6.3543 6.0065];
c = [0.0200 0.2200 0.4200 0.6200 0.8200 1.0200 1.2200 1.4200 1.6200 1.8200];
d = [1.2849 2.2245 3.6431 5.6553 8.3327 11.6542 15.4421 19.2852 22.4525 23.8003];
p = polyfit(c,x./d,1);
a = p(2);
b = p(1);
figure
plot(c,x./d,'.',c,a+b*c)
Were you expecting something better than linear?
p_2nd = polyfit(c,x./d,2);
figure
plot(c,x./d,'.',c,p_2nd(1)*c.^2+p_2nd(2)*c+p_2nd(3))
  4 Kommentare
the cyclist
the cyclist am 30 Aug. 2013
polyfit() uses a polynomial to fit. Your code fit a 1st-order polynomial (i.e. straight line). Notice that all I did was fit a 2nd-order polynomial (a parabola).
In other words, you fit
x/d = P0 + P1*c
where I fit
x/d = P0 + P1*c + P2*c^2
So, yes, an extra term, and therefore an extra parameter.
Tiffany
Tiffany am 2 Sep. 2013
Thank you for your explanation :)

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (0)

Kategorien

Mehr zu Get Started with Curve Fitting Toolbox finden Sie in Help Center und File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by