Matlab tips (29) polynomial fitting plotfit

Preface

MATLAB Learning about image processing is very friendly , You can start from scratch , There are many encapsulated functions that can be called directly for basic image processing , This series of articles is mainly to introduce some of you in MATLAB Some concept functions are commonly used in routine demonstration ！

Polynomial fitting is to use a polynomial expansion to fit all observation points in a small analysis area containing several analysis lattice points , Get the objective analysis field of the observation data . The expansion coefficient is determined by least square fitting . However, the domain polynomial of this method is quasi merge unstable , This is especially true when data is missing , And it will cause the analysis to be discontinuous between the fitting regions .

When analyzing and predicting data , More common fitting methods , The fitting polynomial is obtained by the least square method , Thus, the predicted value of the parameter can be predicted , The example encountered when searching for data , Here to share , This article example simulation MATLAB Version is MATLAB2015b.

One . MATLAB Simulation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： Polynomial fitting 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-28
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% I.  Clear environment variables 
clear all
clc

tic
y=[100.3	101.1	102.1	101.1	101.6	104.4	102.5	102.1	103.9	103.9]; 
x=1:length(y);
A=polyfit(x,y,2)  %2 Secondary phase fitting , This 2 Modifiable    Model coefficients 

Z=polyval(A,x); % forecast y
len=[1:20];
len1=polyval(Z,len); % Predict the trend 

result=[y;Z]% Actual value and predicted value 
error=abs(y-Z);% error 
bfb=error./y% Relative error 
errorsum=sum(error)/length(y)% Average error 
bfbsum=sum(bfb)/length(y)% Average relative error 

figure(1)
plot(x,y,'r-',x,Z,'b-')
legend(' actual value ',' Fit value ')
title(' Comparison between actual value and predicted value ','fontsize',15)
ylabel('Y','fontsize',15)
xlabel('X','fontsize',15)

figure(2)
plot(len,len1,'b-')
legend(' Fit the curve ')
title(' Fitting curve ','fontsize',15)
ylabel('Y','fontsize',15)
xlabel('X','fontsize',15)
toc

Two . Simulation results

A =

   -0.0144    0.5159  100.0167


result =

  100.3000  101.1000  102.1000  101.1000  101.6000  104.4000  102.5000  102.1000  103.9000  103.9000
  100.5182  100.9909  101.4348  101.8500  102.2364  102.5939  102.9227  103.2227  103.4939  103.7364


bfb =

    0.0022    0.0011    0.0065    0.0074    0.0063    0.0173    0.0041    0.0110    0.0039    0.0016


errorsum =

    0.6300


bfbsum =

    0.0061

 Time has passed  2.561846  second .

3、 ... and . Summary

Simulation example of polynomial fitting , It may be used later , Take a note here . Learn one every day MATLAB Little knowledge , Let's learn and make progress together ！