HOW DO I DO THAT IN MATLAB SERIES?

In this series, I am answering questions that students have asked me about MATLAB. Most of the questions relate to a mathematical procedure.

TOPIC
SUMMARY
INTRODUCTION
INPUTS
DISPLAYING INPUTS
THE CODE
DISPLAYING OUTPUTS AND PLOTS

TOPIC

How do I conduct polynomial interpolation for given data.

SUMMARY

Language : Matlab 2010a; Authors : Autar Kaw and Sri Harsha Garapati; Mfile available at Last Revised : January 23, 2012; Abstract: This program shows you how to perform polynomial interpolation in MATLAB

clc
clear all
clf

INTRODUCTION

disp('ABSTRACT')
disp('   This program shows you how to perform polynomial interpolation')

disp(' ')
disp('AUTHOR')
disp('   Autar Kaw and Sri Harsha Garapati of http://autarkaw.wordpress.com')
disp(' ')
disp('MFILE SOURCE')
disp('   http://numericalmethods.eng.usf.edu/blog/interpolation_polynomial_sec002_blog.m')
disp(' ')
disp('LAST REVISED')
disp('   January 23, 2012')
disp(' ')

ABSTRACT
   This program shows you how to perform polynomial interpolation
 
AUTHOR
   Autar Kaw and Sri Harsha Garapati of http://autarkaw.wordpress.com
 
MFILE SOURCE
   http://numericalmethods.eng.usf.edu/blog/interpolation_polynomial_sec002_blog.m
 
LAST REVISED
   January 23, 2012

INPUTS

% Inputs assuming
%    that three points are given

xd  = [1 4 8];   % x data points
yd  = [2 5 7];   % y data points
xval= 4.5;       % predict y at this x value

DISPLAYING INPUTS

disp('  ')
disp('INPUTS')
% Creating a matrix to print input data as a table
data=[xd;yd]';
disp('     X     Y ')
% Printing the input data as a table
disp(data)
% Printing the input value of X at which Y is to be predicted
fprintf('  Predict the value of y when x is %g\n\n',xval)

  
INPUTS
     X     Y 
     1     2
     4     5
     8     7

  Predict the value of y when x is 4.5

THE CODE

% n returns the number of data points
n   =length(xd);
% order of interpolation model
or  =n-1;
% conducting polynomial interpolation
coef=polyfit(xd,yd,or);
% predicting y with the chosen interpolation model
ypre=polyval(coef,xval);

% setting up domain for plotting
xp  =[min(xd):0.1:max(xd)];
 % evaluating over domain xp for plotting the interpolation function
yp  =polyval(coef,xp);

% creating symbolic variable X to display the output function
syms x
% defining the function as a string
fun =char(vpa(coef(1)*(x)+coef(2),5));

DISPLAYING OUTPUTS AND PLOTS

disp('  ')
disp('OUTPUTS')
% printing the predicted value of y
fprintf('  Predicted value of y is %g\n',ypre)
% printing the interpolation function
fprintf('  The interpolation model is:\n  %s\n\n',fun)

disp('  See figure(1)')
% Telling Matlab to name the figure as Figure-1
figure(1)
% Matlab command so that it does hold on to all the plots
hold on
% plotting the data points
plot(xd,yd,'rs','MarkerSize',10)
% plotting the interpolation function
plot(xp,yp,'k-.','LineWidth',2)
% plotting the predicted data point value
plot(xval,ypre,'bo','MarkerSize',10)
% Title of the Plot
title('Interpolation Model for Data Points')
% Legend to distunguish different plots
legend('Given Points','Interpolation Model','Predicted Point',0)
% Labeling the X-axis
xlabel('x')
% Labeling the Y-Axis
ylabel('y')
% Matlab command to exit the hold-on option
hold off

  
OUTPUTS
  Predicted value of y is 5.375
  The interpolation model is:
  1.3571 - 0.071429*x

  See figure(1)