EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 360+ Courses All in One Bundle
  • Login
Home Data Science Data Science Tutorials Matlab Tutorial Matlab polyfit()
Secondary Sidebar
Matlab Tutorial
  • Advanced
    • MATLAB Class
    • Arrays in MATLAB
    • Matlab find value in array
    • MATLAB Grader
    • Power Spectral Density MATLAB
    • Matlab Textscan
    • String Array in MATLAB
    • MATLAB Random Numbers
    • Matlab Dot
    • MATLAB 2D Array
    • MATLAB? zero padding
    • MATLAB sort matrix
    • MATLAB Plot Function
    • 2D Plots in MATLAB
    • 3D Plots in MATLAB
    • MATLAB Fread
    • Spectrogram MATLAB
    • MATLAB Average
    • MATLAB exponent
    • MATLAB not enough input arguments
    • MATLAB comment
    • MATLAB zpk
    • Scatter Plots in MATLAB
    • MATLAB 3d scatter plot
    • Bar Graph in MATLAB
    • Bar Plot MATLAB
    • Log Plot MATLAB
    • Polar Plot in MATLAB
    • Surface Plot in MATLAB
    • MATLAB Plot Circle
    • Boxplot in MATLAB
    • MATLAB Plot Multiple Lines
    • Linspace MATLAB
    • Histogram in MATLAB
    • Plot Vector MATLAB
    • MATLAB Legend
    • MATLAB Plot Legend
    • MATLAB ezplots
    • Column Vector MATLAB
    • MATLAB Plot Marker
    • MATLAB LineWidth
    • MATLAB Line Style
    • Contour plot in MATLAB
    • MATLAB Sine Wave
    • Reshape in MATLAB
    • Natural Log in MATLAB
    • Random Number Generator in MATLAB
    • Complex Numbers in MATLAB
    • MATLAB Figure
    • Heatmap in MATLAB
    • MATLAB Technical Computing
    • Colors in MATLAB
    • Colormap in MATLAB
    • MATLAB Plot Colors
    • MATLAB fplot()
    • MATLAB Stacked Bar
    • MATLAB sphere()
    • MATLAB cylinder()
    • MATLAB mesh()
    • Pie Chart in MATLAB
    • MATLAB Gradient
    • Grid on MATLAB
    • Repmat in MATLAB
    • dlmread in MATLAB
    • Meshgrid in MATLAB
    • MATLAB Struct
    • MATLAB Cross Product
    • MATLAB colorbar Label
    • MATLAB Save Variable
    • MATLAB Saveas
    • MATLAB Cell Array
    • Polynomial in MATLAB
    • ismember MATLAB
    • Heaviside MATLAB
    • MATLAB rref
    • MATLAB polyfit()
    • MATLAB xlim
    • MATLAB Variance
    • Optimset MATLAB
    • Quiver MATLAB
    • Newton Raphson MATLAB
    • Mat2cell MATLAB
    • Magnitude MATLAB
    • format long MATLAB
    • Dot Product MATLAB
    • Jacobian MATLAB
    • What is Matlab?
    • Convolution MATLAB
    • Moving Average MATLAB
    • Fourier Series MATLAB
    • Gaussian Fit MATLAB
    • Bisection Method MATLAB
    • Laplace Transform MATLAB
    • Fourier Transform MATLAB
    • Signal Processing MATLAB
    • MATLAB Forms
    • Complex Conjugate MATLAB
    • MATLAB Write to File
    • uigetfile MATLAB
    • MATLAB Toolbox
    • MATLAB Errorbar
    • MATLAB Index Exceeds Matrix Dimensions
    • Nyquist MATLAB
    • Impulse Response MATLAB
    • xlsread MATLAB
    • MATLAB xlswrite
    • Matplotlib Scatter
    • MATLAB Import Data
    • MATLAB Export Data
    • MATLAB Read CSV
  • Basic
    • MATLAB Area Under Curve
    • MATLAB not equal
    • MATLAB max
    • MATLAB exist
    • MATLAB Table
    • MATLAB regression
    • MATLAB Lists
    • MATLAB quantile
    • MATLAB Round
    • MATLAB readtable
    • MATLAB disp
    • MATLAB Standard Deviation
    • MATLAB quadprog
    • MATLAB Transpose
    • Introduction to MATLAB
    • Advantages of MATLAB
    • MATLAB Features
    • Taylor Series MATLAB
    • MATLAB Z Transform
    • fsolve in MATLAB
    • MATLAB QR
    • Career in MATLAB
    • Uses Of MATLAB
    • MATLAB Free
    • How to Install MATLAB
    • How to Use MATLAB?
    • MATLAB Version
    • MATLAB Compiler
    • MATLAB Commands
    • MATLAB Block Comment
    • MATLAB? sprintf
    • MATLAB fprintf
    • Data Types in MATLAB
    • MATLAB Integral
    • MATLAB Double Integral
    • MATLAB boolean
    • MATLAB vpa
    • MATLAB Object
    • MATLAB Annotation
    • MATLAB Variables
    • MATLAB Global Variables
    • MATLAB Operators
    • MATLAB Logical Operators
    • MATLAB nan
    • MATLAB Patch
    • MATLAB AND Operator
    • MATLAB OR Operator
    • Vectors in MATLAB
    • What is Simulink in MATLAB
    • MATLAB Interpolation
    • MATLAB Imread
    • fscanf MATLAB
    • Euler Method MATLAB
    • Root Locus MATLAB
    • MATLAB return
    • Bode Plot MATLAB
    • Nargin MATLAB
    • MATLAB Matrix Inverse
    • MATLAB String to Number
    • MATLAB string
    • MATLAB ColorBar
    • MATLAB Surfc
    • MATLAB Concatenate
    • NUMEL MATLAB
    • MATLAB? File Extension
    • MATLAB File
    • MATLAB Smooth
    • MATLAB ones
    • Exponential in MATLAB
    • MATLAB ksdensity
    • MATLAB log
    • MATLAB Append
    • MATLAB hold on
    • MATLAB Magnitude of Vector
    • Heatmap in MATLAB
    • MATLAB xticks
    • MATLAB randn
  • Control Statements
    • IF-Else Statement in MATLAB
    • If Statement in MATLAB
    • Loops in MATLAB
    • For Loop in MATLAB
    • While Loop in MATLAB
    • do while loop in MATLAB
    • Nested Loop in MATLAB
    • Switch Statement in MATLAB
    • Break in MATLAB
  • Functions
    • MATLAB Functions
    • MATLAB user defined function
    • Calling Functions in MATLAB
    • Transfer Functions in MATLAB
    • Anonymous Functions in MATLAB
    • Inline Functions in MATLAB
    • Bessel Functions in MATLAB
    • Mean Function in MATLAB
    • Find Function MATLAB
    • Filter Function in MATLAB
    • IIR Filter MATLAB
    • Piecewise Function in MATLAB
    • Sum Function in MATLAB
    • Simulink MATLAB Function
    • MATLAB Create Function
    • MATLAB Inverse Function
    • MATLAB Count
    • Step Function MATLAB
    • MATLAB limit
    • Fminsearch in MATLAB
    • Covariance in MATLAB
    • Summation in MATLAB
    • Linear Fit MATLAB
    • MATLAB?linear regression
    • MATLAB Derivative
    • MATLAB Derivative of Function
    • MATLAB Comet()
    • Fzero MATLAB
    • xlabel MATLAB
    • Matplotlib Legend
    • Matplotlib Subplots
    • Plot graph MATLAB
    • MATLAB Format
    • MATLAB plot title
    • Multiple Plots in MATLAB
    • MATLAB Indexing
    • Ceil MATLAB
    • Curve Fitting MATLAB
    • MATLAB trapz()
    • MATLAB Normalize
    • MATLAB diff
    • MATLAB sym()
    • MATLAB Syms
    • Absolute Value MATLAB
    • MATLAB Exponential
    • Kalman Filter MATLAB
    • Low Pass Filter MATLAB
    • Bandpass Filter MATLAB
    • MATLAB Unique
    • Trapezoidal Rule MATLAB
    • MATLAB Root Finding
    • MATLAB stem()
    • MATLAB loglog()
    • MATLAB Autocorrelation
    • MATLAB Sort
    • Simplify MATLAB
    • Cumsum MATLAB
    • Eval Function MATLAB
    • Polyval MATLAB
    • MATLAB Colon
    • MATLAB Eigenvalues
    • MATLAB fit
    • Delta Function MATLAB
    • MATLAB Remainder
    • Differentiation in MATLAB
    • Permute MATLAB
    • isempty MATLAB
    • MATLAB text()
    • MATLAB Display Text
    • Varargin in MATLAB
    • MATLAB gca
    • MATLAB fill()
    • MATLAB pcolor()
    • MATLAB min
    • MATLAB xcorr
    • MATLAB? color codes
    • Semilogy MATLAB
    • MATLAB? eye
    • feval MATLAB
    • num2str in MATLAB
    • MATLAB Images
    • MATLAB Image? Segmentation
    • Imagesc MATLAB
    • MATLAB Image Processing
    • MATLAB Image Resize
    • MATLAB Flag
    • MATLAB fopen
    • Strcmp MATLAB
    • MATLAB fwrite
    • MATLAB fft()
    • MATLAB zeros()
    • MATLAB textread
    • Arctan MATLAB
    • MATLAB Scripts
    • Butterworth filter MATLAB
    • MATLAB Findpeaks
    • MATLAB find Index
    • MATLAB Cell
    • MATLAB Unit Step Function
    • MATLAB Backslash
    • MATLAB Mod
    • Size Function in MATLAB
    • Secant MATLAB
  • Matrix
    • Matrix in MATLAB
    • 3D Matrix in MATLAB
    • Transpose Matrix MATLAB
    • Sparse Matrix in MATLAB
    • Matrix Multiplication in MATLAB
    • Identity Matrix in MATLAB
    • MATLAB?writematrix
  • Programs
    • Square Root in MATLAB
    • Square Wave MATLAB
    • Squeeze MATLAB
    • Factorial in MATLAB
    • Cell to String MATLAB
  • Interview Questions
    • MATLAB Interview Questions

Related Courses

MATLAB Certification Course

R Programming Course

All in One Data Science Courses

Matlab polyfit()

By Priya PedamkarPriya Pedamkar

Matlab polyfit()

Introduction of Matlab polyfit()

MATLAB function polyfit() is defined to fit a specific set of data points to a polynomialquickly and easily computing polynomial with the least squares for the given set of data. It generates the coefficients for the elements of the polynomial, which are used for modeling a curve to fit to the given data.

Polyfit() function uses input vector (x) to form Vandermonde matrix (V ) having n+1 columns and r = length(x) rows, which is nothing but results in a linear system.

Syntax of Matlab polyfit()

Syntax of Matlab polyfit() are given below:

Syntax

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

Description

poly = polyfit(x,y,n) It generates the coefficients of the resultant polynomial p(x) with a degree of ‘n’, for the data set in yas the best fit in the view of a least-square. The coefficients in p are assigned to power in descending order and matching length of p to n+1.
[poly,Struct] = polyfit(x,y,n) It results in a structure S which can be used as input to the function polyval() in order to obtain error estimation.
[poly,Struct,mu] = polyfit(x,y,n) It results in a two-element vector having values-centered and scaled.

mu(1) holds a value of the mean of (x), and

All in One Data Science Bundle(360+ Courses, 50+ projects)
Python TutorialMachine LearningAWSArtificial Intelligence
TableauR ProgrammingPowerBIDeep Learning
Price
View Courses
360+ Online Courses | 50+ projects | 1500+ Hours | Verifiable Certificates | Lifetime Access
4.7 (86,584 ratings)

mu(2) ) holds the value of standard of (x).

Using these two values, function polyfit()makes x centered at zero and scaledx to have a unit standard deviation,

 

Input Arguments

  • Query Points: Query points are specified as an input of vector type. If x is non-vector element, then this function polyfit() converts x into a column vector.The data points in x and their corresponding fitted function values contained in the vector y are formed.

Note

If the vector x has recurring data points or if it needs centering and scaling, warning messages may result out.

  • Fitted values at query points: Fitted values as inputs are available at query points being specified with the vector data type. The data points in x and their corresponding fitted function values contained in the vector y are formed. If y is the non-vector element, then this function polyfit() converts y into a column vector.
  • Degree of polynomial fit: Degree of polynomial fit as inputs, are available being specified as any positive integer scalar. In the respective syntax, ‘n’refers to the polynomial power to that of the left-most coefficient in the polynomial ‘p’.

Example of Matlab polyfit()

The below code is designed to generate data points placed equally spaced across a sine curve drawn in a specific interval.

Code:

xdata = linspace(0,5*pi,11);
ydata = sin(xdata);
poly = polyfit(xdata,ydata,7);
xdata1 = linspace(0,4*pi);
ydata1 = polyval(poly,xdata1);
figure
plot(xdata,ydata,'o')
hold on
plot(xdata1,ydata1)
hold off

Output:

Matlab polyfit()-1.1

Use Cases for polyfit() Function

Use cases for polyfit() function are given below:

Fitting  Polynomial to Set of data Points: The below code snippet carry out the fitting process on the polynomial poly of degree 4 towards 5  points.

Code:

xdata = linspace(0,1,6);
ydata = 1./(1+xdata);
poly = polyfit(xdata,ydata,4);
xdata1 = linspace(0,2);
ydata1 = 1./(1+xdata1);
fig1 = polyval(poly,xdata1);
figure
plot(xdata,ydata,'o')
hold on
plot(xdata1,ydata1)
plot(xdata1,fig1,'r--')
legend('ydata','ydata1','fig1')

Output:

Matlab polyfit()-1.2

Fitting the Polynomial function to Error Function: The below code generate a vector having x data points being placed equally in the interval of [0,3.5] and co-efficient are assigned to the polynomial assuming the degree as 6.

Code:

xdata = (0:0.1:3.5)';
ydata = erf(xdata);
poly = polyfit(xdata,ydata,6)
func = polyval(poly,xdata);
T = table(xdata,ydata,func,ydata-func,'VariableNames',{'X','Y','Fit','FitError'})
xdata1 = (0:0.1:5)';
ydata1 = erf(xdata1);
func1 = polyval(poly,xdata1);
figure
plot(xdata,ydata,'o')
hold on
plot(xdata1,ydata1,'-')
plot(xdata1,func1,'r--')
axis([0  5  0  2])
hold off

Output:

Matlab polyfit()-1.3

Improving Numerical Properties using Centering and Scaling: While solving the equation p = V\y, the condition number for V is usually large for higher-order fits and results in a matrix with singular coefficient, as the columns of V (Vandermonde matrix) are powers of the x vector.

In such cases, functions like scaling and centering are helpful to improve the numerical properties associated with the system in order to find a fit that is more reliable. In the below example polyfit() is called on three outputs to fit a polynomial of degree 5 along with the process of centering and scaling. The data is centered for the quarter, at 0, and scaled to have a unit standard deviation.

Code:

quarter = (1725:25:1975)';
data = 1e6*[891 846 938 1250 1272 1344 1550 2232 6142 8370 11450]';
Tab = table(quarter, data)
plot(quarter,data,'o')
[poly,~,mu] = polyfit(Tab.quarter, Tab.data, 5);
func = polyval(poly,quarter,[],mu);
hold on
plot(quarter,func)
hold off

Output:

Matlab polyfit()-1.4

Simple Linear Regression: A simple linear regression model can be used to apply a fitting to a set of discrete two-dimensional data points.

Code:

xdata = 1:60;
ydata = -0.4*xdata + 3*randn(1,60);
poly = polyfit(xdata,ydata,1);
xdata = 1:60;
ydata = -0.4*xdata + 3*randn(1,60);
poly = polyfit(xdata,ydata,1);
func = polyval(poly,xdata);
plot(xdata,ydata,'o',xdata,func,'-')
legend('data','func')

Output:

Output-1.5

Combining Linear Regression and Error Estimation: A linear model can be set fit to a set of specified data points and the results can be plotted including an estimation of a prediction interval of 95%.

A few vectors can be created containing sample data points. The function polyfit can be called to fit a polynomial of degree 1 to the given set of data. Dual outputs can be specified to hold the values of coefficients supporting a linear fit as well as a structure containing error estimation.

Code:

xdata = 1:100;
ydata = -0.3*xdata + 2*randn(1,100);
[poly,Samp] = polyfit(xdata,ydata,1);

/*The error estimation structure is specified as the third input so that the function polyval()computes an estimated standard error. The estimated standard error estimate is stored in the second output variable delta. */

[yaxis_fit,delta] = polyval(poly,xdata,Samp);
plot(xdata,ydata,'bo')
hold on
plot(xdata,yaxis_fit,'r-')
plot(xdata,yaxis_fit+2*delta,'m--',xdata,yaxis_fit-2*delta,'m--')
title('Usage of polyfit and polyval')

Output:

Output-1.6

Additional Note

  • For n number of data points, a polynomial can be fit to that of degree n-1 to passing exactly through the points.
  • With the increase in the degree of the polynomial, a fitting process using polyfit()loses the accuracy resulting in to a poorer fit for the data. In such cases, a low-order polynomial is preferable to use that tends to be smoother between the data points or apply a different technique, based on the requirement.
  • This process of transformation using scaling and centering, add an advantage to the numerical properties of both the polynomial as well as to the fitting algorithm.

Recommended Articles

This is a guide to Matlab polyfit(). Here we also discuss the introduction and use cases for polyfit() function along with examples and its code implementation. you may also have a look at the following articles to learn more –

  1. Matlab zeros()
  2. Matlab Remainder
  3. isempty MATLAB
  4. Permute Matlab
Popular Course in this category
MATLAB Training (3 Courses, 1 Project)
  3 Online Courses |  1 Hands-on Project |  8+ Hours |  Verifiable Certificate of Completion
4.5
Price

View Course

Related Courses

R Programming Training (13 Courses, 20+ Projects)4.9
All in One Data Science Bundle (360+ Courses, 50+ projects)4.8
0 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Database Management
  • Machine Learning
  • All Tutorials
Certification Courses
  • All Courses
  • Data Science Course - All in One Bundle
  • Machine Learning Course
  • Hadoop Certification Training
  • Cloud Computing Training Course
  • R Programming Course
  • AWS Training Course
  • SAS Training Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Data Science Course

SPSS, Data visualization with Python, Matplotlib Library, Seaborn Package

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more