File Exchange

## Power Law, Exponential and Logarithmic Fit

version 1.5.0.0 (20.9 KB) by
Finds and plots the linear fit to some data points when plotted on a log scale.

Updated 22 Aug 2014

logfit(X,Y,graphType), where X is a vector and Y is a vector or a
matrix will plot the data with the axis scaling determined
by graphType as follows: graphType-> xscale, yscale
loglog-> log, log
logx -> log, linear
logy -> linear, log
linear -> linear, linear
A line is then fit to the scaled data in a least squares
sense.
See the 'notes' section below for help choosing a method.
logfit(X,Y), will search through all the possible axis scalings and
finish with the one that incurs the least error (with error
measured as least squares on the linear-linear data.)

Notes:
A power law relationship
[slope, intercept] = logfit(x,y,'loglog');
yApprox = (10^intercept)*x.^(slope);

An exponential relationship
[slope, intercept] = logfit(x,y,'logy');
yApprox = (10^intercept)*(10^slope).^x;

A logarithmic relationship
[slope, intercept] = logfit(x,y,'logx');
yApprox = (intercept)+(slope)*log10(x);

A linear relationship
[slope, intercept] = logfit(x,y,'linear');
yApprox = (intercept)+(slope)*x;

### Cite As

Jonathan C. Lansey (2021). Power Law, Exponential and Logarithmic Fit (https://www.mathworks.com/matlabcentral/fileexchange/29545-power-law-exponential-and-logarithmic-fit), MATLAB Central File Exchange. Retrieved .

Abdullah Al Alhareth

Great, thank you
I have a small question, how can I display the intercept and slope in the plot In the power law

Pim Goedhart

Oriol Bertran

Ivan Rojkov

M. Tilmans

Evan Young

DuRK

Arislan Makhmudov

Athos Garcia

Zhida Li

Nicholas Herrick

Excellent! Thank you.

Ruijia Wang

JJ_unr

jeetesh jain

Sir I want to find the value of a and b so plz suggest the code for this curve

Yetti

@ashley, the b is the slope output. exp(intercept) gives a.

Ashley Skeete

Great stuff. Do you know of a way to input powerlaw data and to determine the b in y = a x^b ?

Nathaniel Howard

Jonathan C. Lansey, you sir are a legend!
Many thanks for this function.
Would the be any way to extend the fitted line to meet x-axis at all?
Its not vital, merely for display purposes.
Many thanks anyway.
Nath

Jørgen Grythe

Perfect, exactly what I needed!

Great!

Budi

very usefull,,

by the way, how to make non linear curve fit using custom equation when plot on log scale?

thx

Franziska

Shea

Just what the Dr. ordered. Thank You.

a

Awesome!

Shatrughan

Saviour !!!!!!!!!!

Matlab2010

Nice.

I use:

% y = a x^b
function [a b] = my_powerLawFit(y, x)

logx=log(x);
logy=log(y);
p=polyfit(logx,logy,1);
b=p(1);
loga=p(2);
a=exp(loga);
end

Manas Hardas

Extremely cool!

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux