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 integrate a discrete function.

The MATLAB program link is here.

The HTML version of the MATLAB program is here.

_____________________________________________________

%% 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 integrate a discrete function? Three cases of data are

% discussed.

%% SUMMARY

% Language : MATLAB 2008a;

% Authors : Autar Kaw;

% Mfile available at

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

% Last Revised : April 3, 2009;

% Abstract: This program shows you how to integrate a given discrete function.

clc

clear all

%% INTRODUCTION

disp(‘ABSTRACT’)

disp(‘ This program shows you how to integrate’)

disp(‘ a discrete function’)

disp(‘ ‘)

disp(‘AUTHOR’)

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

disp(‘ ‘)

disp(‘MFILE SOURCE’)

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

disp(‘ ‘)

disp(‘LAST REVISED’)

disp(‘ April 3, 2009’)

disp(‘ ‘)

%% CASE 1

%% INPUTS

% Integrate the discrete function y from x=1 to 6.5

% with y vs x data given as (1,2), (2,7), (4,16), (6.5,18)

% Defining the x-array

x=[1 2 4 6.5];

% Defining the y-array

y=[2 7 16 18];

%% DISPLAYING INPUTS

disp(‘____________________________________’)

disp(‘CASE#1’)

disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION MATCH x(1) AND x(LAST)’)

disp(‘ ‘)

disp(‘INPUTS’)

disp(‘The x-data is’)

x

disp(‘The y-data is’)

y

fprintf(‘ Lower limit of integration, a= %g’,x(1))

fprintf(‘\n Upper limit of integration, b= %g’,x(length(x)))

disp(‘ ‘)

%% THE CODE

intvalue=trapz(x,y);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)

fprintf(‘ Value of integral is = %g’,intvalue)

disp(‘ ‘)

disp(‘___________________________________________’)

%% CASE 2

%% INPUTS

% Integrate the discrete function y from x=3 to 6

% with y vs x data given as (1,2), (2,7), (4,16), (6.5,18)

% Defining the x-array

x=[1 2 4 6.5];

% Defining the y-array

y=[2 7 16 18];

% Lower limit of integration, a

a=3;

% Upper limit of integration, b

b=6;

%% DISPLAYING INPUTS

disp(‘CASE#2’)

disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION DO not MATCH x(1) AND x(LAST)’)

disp(‘ ‘)

disp(‘INPUTS’)

disp(‘The x-data is’)

x

disp(‘The y-data is’)

y

fprintf(‘ Lower limit of integration, a= %g’,a)

fprintf(‘\n Upper limit of integration, b= %g’,b)

% Choose how many divisions you want for splining from a to b

n=1000;

fprintf(‘\n Number of subdivisions used for splining = %g’,n)

disp(‘ ‘)

disp(‘ ‘)

%% THE CODE

xx=a:(b-a)/n:b;

% Using spline to approximate the curve from x(1) to x(last)

yy=spline(x,y,xx);

intvalue=trapz(xx,yy);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)

fprintf(‘ Value of integral is = %g’,intvalue)

disp(‘ ‘)

disp(‘___________________________________________’)

%% CASE 3

%% INPUTS

% Integrate the discrete function y from x=1 to 6.5

% with y vs x data given as (1,2), (4,16), (2,7), (6.5,18)

% The x-data is not in ascending order

% Defining the x-array

x=[1 4 2 6.5];

% Defining the y-array

y=[2 16 7 18];

% Lower limit of integration, a

a=3;

% Upper limit of integration, b

b=6;

%% DISPLAYING INPUTS

disp(‘CASE#3’)

disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION DO not MATCH x(1) AND x(LAST) ‘)

disp(‘AND X-DATA IS NOT IN ASCENDING OR DESCENDING ORDER’)

disp(‘ ‘)

disp(‘INPUTS’)

disp(‘The x-data is’)

x

disp(‘The y-data is’)

y

fprintf(‘ Lower limit of integration, a= %g’,a)

fprintf(‘\n Upper limit of integration, b= %g’,b)

% Choose how many divisions you want for splining from a to b

n=1000;

fprintf(‘\n Number of subdivisions used for splining = %g’,n)

disp(‘ ‘)

disp(‘ ‘)

%% THE CODE

[x,so] = sort(x); % so is the sort order

y = y(so); % y data is now in same order as x data

xx=a:(b-a)/n:b;

% Using spline to approximate the curve from x(1) to x(last)

yy=spline(x,y,xx);

intvalue=trapz(xx,yy);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)

fprintf(‘ Value of integral is = %g’,intvalue)

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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The above integration scheme for discrete function is very useful for physicsists. For example, in characterizing the spectrum of x-ray diffraction, which it’s data are always available in discrete forms. Thanks for your explanation.

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sir can u please teach us double integration for discrete function having three matrices x, y,and z.

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