Many students ask me how do I do this or that in MATLAB. So I thought why not have a small series of my next few blogs do that. In this blog, I show you how to conduct spline interpolation.

- The MATLAB program link is here.
- The HTML version of the MATLAB program is here.
- DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES DO NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR. DOWNLOAD THE MATLAB PROGRAM INSTEAD

%% 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

% How do I do spline interpolation?

%% SUMMARY

% Language : Matlab 2008a;

% Authors : Autar Kaw;

% Mfile available at

% http://numericalmethods.eng.usf.edu/blog/interpolate_spline.m;

% Last Revised : June 20, 2009;

% Abstract: This program shows you how to do spline interpolation?

% .

clc

clear all

clf

%% INTRODUCTION

disp(‘ABSTRACT’)

disp(‘ This program shows you how to do spline interpolation?’)

disp(‘ ‘)

disp(‘AUTHOR’)

disp(‘ Autar K Kaw of https://autarkaw.wordpress.com’)

disp(‘ ‘)

disp(‘MFILE SOURCE’)

disp(‘ http://numericalmethods.eng.usf.edu/blog/interpolation_spline.m’)

disp(‘ ‘)

disp(‘LAST REVISED’)

disp(‘ June 20, 2009’)

disp(‘ ‘)

%% INPUTS

% y vs x data to interpolate

% x data

x=[-1 -0.75 -0.5 -0.25 0.25 0.50 0.75 1];

% ydata

y=[-0.5 -0.5 -0.5 -0.5 0.5 0.5 0.5 0.5];

% Where do you want to interpolate at

xin=[-0.8 -0.7 0.7 0.8];

%% DISPLAYING INPUTS

disp(‘INPUTS’)

disp(‘The x data’)

x

disp(‘The y data’)

y

disp(‘The x values where you want to find the interpolated values’)

xin

disp(‘ ‘)

%% THE CODE

% Fitting to spline – it is cubic splines

yin=spline(x,y,xin);

% This is only for plotting the spline interpolants

% Find the number of data points

n=length(x);

xplot=x(1):(x(n)-x(1))/10000:x(n);

yplot=spline(x,y,xplot);

%% DISPLAYING OUTPUTS

disp(‘ ‘)

disp(‘OUTPUTS’)

disp(‘x values at which function is to be interpolated’)

xin

disp(‘y values at the xin values’)

yin

xlabel(‘x’);

ylabel(‘y’);

title(‘y vs x ‘);

plot(x,y,’o’,’MarkerSize’,10,’MarkerEdgeColor’,’b’,’MarkerFaceColor’,’b’)

hold on

plot(xin,yin,’o’,’MarkerSize’,10,’MarkerEdgeColor’,’r’,’MarkerFaceColor’,’r’)

hold on

plot(xplot,yplot,’LineWidth’,2)

legend(‘Points given’,’Points found’,’Spline Curve’,’Location’,’East’)

hold off

disp(‘ ‘)

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy

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Mel

said:Hi, my name is Mel. First of all, thank you very much in advance. And, I hope you could please response if you have any ideas/opinions regarding this mail as I’m a new Matlab user. So, I need your guidance, simple examples since you’re an expert.

Please, I would like to ask your help on how to code using Matlab for two – dimensional heat equation version based on the following one – dimensional heat equation version.

clear all; clc;

%n=number of points, Nstep=time-step

n=100;

Nstep=20;

%L=length of domain, k=heat diffusivity

L=1;

k=0.01;

%define dx and x

dx=2*L/(n-1);

dt=(0.46*dx^2)/k;

x=-L:dx:L;

%initial

for I=2:n-1

if I52

u(I)=0

else

u(I)=1;

end

end

u(1)=0;u(n)=0;

% store profile for computing and display

v=u;

v_initial=u;

title_str=’Heat equation:u_t-\kappa u_{xx}=0′;

%initialization u and v

plot(x,v_initial, ‘-‘,’linewidth’,2);

set(gca, ‘fontsize’,14,’fontweight’,’bold’);

title(title_str);

axis tight;

set(gca,’nextplot’,’replacechildren’);

%time step

for time=1:Nstep

%end points

uxx(1)=v(2)-2*v(1)+v(n)

uxx(n)=v(1)-2*v(2)+v(n-1)

%interior points

for I=2:n-1

uxx(I)=v(I+1)-2*v(I)+v(I-1)

end

%rule

u=v+k*uxx;

%update v

v=u;

%plot

plot(x,v_initial,’-‘,x,u,’linewidth’,2);

picture(time)=getframe;

end

%display movie

disp(‘Playing animation…’);

movie(picture,1);

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nader

said:please help me about “fnplt” i have many data and i intend plot them in a 3-dimensional coordinate(rectangular coordinate). i mus use spline and fnplt

please send me if you have this code in matlab.

king regardly

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said:I am happy to say your post has been accepted for http://www.interestingblogs.info . Your website is now included on our featured websites list.

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rus

said:hello

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agogo

said:hello i need a help how do you do interpolation cubic for image have a grid data and thank you fornyour help

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Sarah Agnalt

said:Is this for natural or clamped cubic spline?

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Autar Kaw

said:If x and y have same length, then the conditions are “not-a-knot’ conditions. That is third derivative is continuous at second and second-last data point. In this case use as spline(x,y)

To use clamped conditions, that is, the first derivative is specified at the end point for first (let us say m1) and last spline (let us say m2), use its as spline(x,[m1 y m2]).

Natural spline is that the second derivative is zero at the two ends.

For more info, see http://www.mathworks.com/help/matlab/ref/spline.html and http://www.cs.tau.ac.il/~turkel/notes/numeng/spline_note.pdf

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