Least squares Exponential fit using polyfit

176 Ansichten (letzte 30 Tage)
Rachel Dawn
Rachel Dawn am 21 Mär. 2018
Kommentiert: kainat rasheed am 18 Mai 2022
Let's say I'm given x=[11,60,150,200] and y=[800,500,400,90] These are just random numbers (but imagine the solution is in the form of y=a*exp(b*t)
Now, I want to find what 'a' and 'b' are. This is what I'm thinking to do, but I'm not sure if it's correct:
So, if I take ln of both sides of the above equation, I'll get ln(y)= ln(a) +bx. This is in the form of y=mx+b (linear equation).
x= [10, 55, 120, 180]
y= [750, 550, 300, 100]
yPrime= log(y)%take natural logarithm of y data values
pPrime=polyfit(t,yPrime,1)%
aPrime=pPrime(1)
bPrime=pPrime(2)
so now I found the constants for my above LINEAR equation. To find 'a' and 'b' from 'y=a*exp(b*t)', should I now raise the linear constants I found to e? (e^aPrime = a, e^bPrime= b) ?
Is this how I find 'a' and 'b'?

Akzeptierte Antwort

Star Strider
Star Strider am 21 Mär. 2018
Since you are starting with:
y = a * exp(b * t)
and linearising it yields:
log(y) = log(a) + b*t
however ‘aPrime’ and ‘bPrime’ are reversed with respect to the way polyfit works.
So polyfit returns:
bPrime = pPrime(1)
aPrime = pPrime(2)
you need to transform only ‘aPrime’. So:
a = exp(aPrime)
If you want to plot a line-of-fit, you could either use your originally log-transformed equation with log-transformed variables:
log(y) = aPrime + bPrime*t
or:
yfit = exp(log(aPrime)) * exp(b*t)
with your original data.
In code:
t = [11,60,150,200];
y = [800,500,400,90];
yPrime= log(y)%take natural logarithm of y data values
pPrime=polyfit(t,yPrime,1)%
aPrime=pPrime(2)
bPrime=pPrime(1)
figure(1)
plot(t, log(y), 'p', t, polyval(pPrime, t), '-r')
figure(2)
plot(t, y, 'p', t, exp(aPrime)*exp(t*bPrime), '-r')
figure(3)
semilogy(t, y, 'p', t, exp(aPrime)*exp(t*bPrime), '-r')
  6 Kommentare
Tamir Suliman
Tamir Suliman am 11 Okt. 2021
Bearbeitet: Tamir Suliman am 11 Okt. 2021
didnt you also have to ployfit for log(t) values ?
yPrime= log(y)%take natural logarithm of y data values
tPrime = log(t)
pPrime=polyfit(tPrime,yPrime,1)%
kainat rasheed
kainat rasheed am 18 Mai 2022
can you write code for power function ? i am facing a problem

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (0)

Community Treasure Hunt

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

Start Hunting!

Translated by