# How do I do spline interpolation in MATLAB?

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://nm.mathforcollege.com/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&#8217;)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/interpolation_spline.m&#8217;)
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://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://nm.mathforcollege.com/videos

## Author: Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

## 7 thoughts on “How do I do spline interpolation in MATLAB?”

1. Mel says:

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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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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3. 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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4. Sarah Agnalt says:

Is this for natural or clamped cubic spline?

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1. 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.

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