The Numerical Methods Guy

How do I display the data of an array in MATLAB?

Autar Kaw — Wed, 08 Jul 2009 20:18:40 +0000

When I give a MATLAB project, I ask my students that the command window can only show output from disp and frprintf statements. All other statement outputs need to be suppressed. This is done to get an aesthetically pleasing report. So what is a student supposed to do when you may have y vs x data and one needs to show it as an ouput, especially when the number of y vs x data points can change.

For example we may have

x=[1 4 5 7 ]

y=[12 23 34 100]

How do I display this with just disp and fprintf statements?

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 display arrays in MATLAB?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw and Jeremy Baker;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/displaying_arrays.m;
% Last Revised : July 8, 2009;
% Abstract: This program shows you how to display arrays in MATLAB
clc
clear all

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to display arrays’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com and Jeremy Baker’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/displaying_arrays.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   July 8, 2009′)
disp(’ ‘)

%% INPUTS
% Input x and y arrays, for example as y vs x data
x=[1 4 5   7 ];
y=[12 23 34 100];
%% DISPLAYING INPUTS METHOD 1
disp(’INPUTS – Method 1′)
n=length(x);
fprintf(’The number of data points is %g \n’,n)
disp(’________________________’)
disp(’ x-values    y values ‘)
disp(’________________________’)
for i=1:1:n
fprintf(’      %g          %g \n’,x(i), y(i)’)
end
disp(’________________________’)

%% DISPLAYING INPUTS METHOD 2
% Suggested by guest blogger Jeremy Baker
disp(’ ‘)
disp(’INPUTS – Method 2′)
n=length(x);
fprintf(’The number of data points is %g \n’,n)
disp(’________________________’)
disp(’ x y ‘)
disp(’________________________’)
dataval=[x;y]‘;
disp(dataval)
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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Posted in MATLAB programming, Numerical Methods Tagged: arrays, display, matlab

Poems on Numerical Methods

Autar Kaw — Sat, 04 Jul 2009 17:32:58 +0000

In Summer 2009, I gave a HW assignment of writing a poem to my mostly right-brained students. The results were great; I think they think they are poets and they know it. The poems were all compiled and can be viewed at http://numericalmethods.eng.usf.edu/EML3041/homework/poems2009summer.html.

So happy reading and let me know what you think. I selected 14 poems out of the 60 or so submitted and am polling the class to select the best three. The top three poem writers will get prizes including a dollar to get the 89c Chicken Burritto at Taco Bell for “thinking outside the bun” or the biggie fries at Wendy’s for thinking “square rather than round”.

_____________________________________________

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Posted in Numerical Methods Tagged: Numerical Methods, poems

How do I do spline interpolation in MATLAB?

Autar Kaw — Sat, 20 Jun 2009 18:13:33 +0000

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 http://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(’ ‘)

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Posted in Interpolation, matlab

How do I do polynomial interpolation in MATLAB

Autar Kaw — Thu, 11 Jun 2009 12:27:22 +0000

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 do polynomial 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 polynomial interpolation?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/interpolate_polynomial.m;
% Last Revised : June 10, 2009;
% Abstract: This program shows you how to do polynomial interpolation?
% .
clc
clear all
clf

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to do polynomial interpolation?’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/interpolation_polynomial.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   June 10, 2009′)
disp(’ ‘)

%% INPUTS
% y vs x data to interpolate
% x data
x=[-1 -0.6 -0.2 0.2 0.6 1];
% ydata
y=[0.0385 0.1000 0.5000 0.5000 0.1000 0.0385];
% 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
% Find the number of data points
n=length(x);
% Fitting to polynomial of order m=n-1
m=n-1
% pp consists of the coefficients of the polynomial
% pp(1)*x^m+pp(2)*x^m+…….+pp(m)
% pp(1) is coefficient of x^m
% pp(2) is coefficient of x^(m-1)
% and so on
pp=polyfit(x,y,m);
% Getting the values at xin
yin=polyval(pp,xin);
% This is only for plotting the interpolating polynomial
xplot=x(1):(x(n)-x(1))/10000:x(n);
yplot=polyval(pp,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
disp(’These are the coefficients of the polynomial interpolant’)
disp(’pp(1) is coefficient of x^m, pp(2) is coefficient of x^(m-1) and so on’)
fprintf(’Order of polynomial m =%g’,m)
pp
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’,'k’,'MarkerFaceColor’,'k’)
hold on
plot(xplot,yplot,’LineWidth’,2)
legend(’Points given’,'Points found’,'Polynomial Curve’)
hold off
disp(’ ‘)

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Posted in Interpolation, matlab, Numerical Methods

How do I solve a boundary value ODE?

Autar Kaw — Mon, 25 May 2009 20:30:10 +0000

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 solve a boundary value ordinary differential equation.

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 solve a boundary value ordinary differential equation?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/ode_boundaryvalue.m;
% Last Revised : May 26, 2009;
% Abstract: This program shows you how to solve an
% boundary value ordinary differential equation.
clc
clear all

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to solve’)
disp(’   a boundary value ordinary differential equation’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/ode_boundaryvalue.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   May 26, 2009′)
disp(’ ‘)

%% INPUTS
% Solve the ordinary differential equation
% y”-0.0000002y=0.000000075*x*(75-x)
% Define x as a symbol
syms x
%The ODE
ode_eqn=’D2y-0.000002*y=0.000000075*x*(75-x)’;
% The initial conditions
iv_1=’y(0)=0′;
iv_2=’y(75)=0′;
% The value at which y is sought at
xval=37.5;
%% DISPLAYING INPUTS

disp(’INPUTS’)
func=[' The ODE to be solved is ' ode_eqn];
disp(func)
iv_explain=[' The boundary conditions are ' iv_1 ' ' iv_2];
disp(iv_explain)
fprintf(’ The value of y is sought at x=%g’,xval)
disp(’ ‘)

%% THE CODE

% Finding the solution of the ordinary differential equation
soln=dsolve(ode_eqn,iv_1,iv_2,’x');
% vpa below uses variable-precision arithmetic (VPA) to compute each
% element of soln to 5 decimal digits of accuracy
soln=vpa(soln,5);

%% DISPLAYING OUTPUTS
disp(’ ‘)
disp(’OUTPUTS’)
output=[' The solution to the ODE is ' char(soln)];
disp(output)
value=subs(soln,x,xval);
fprintf(’ The value of y at x=%g is %g’,xval,value)
disp(’ ‘)

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Posted in matlab, Numerical Methods, Ordinary Differential Equations Tagged: matlab, Ordinary Differential Equations

How do I solve an initial value ODE in MATLAB?

Autar Kaw — Thu, 14 May 2009 16:15:46 +0000

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 solve an initial value ordinary differential equation.

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 solve an initial value ordinary differential equation?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/ode_initial.m;
% Last Revised : May 14, 2009;
% Abstract: This program shows you how to solve an
% initial value ordinary differential equation.
clc
clear all

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to solve’)
disp(’   an initial value ordinary differential equation’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/ode_initial.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   May 14, 2009′)
disp(’ ‘)

%% INPUTS
% Solve the ordinary differential equation 3y”+5y’+7y=11exp(-x)
% Define x as a symbol
syms x
%The ODE
ode_eqn=’3*D2y+5*Dy+7*y=11*exp(-13*x)’;
% The initial conditions
iv_1=’Dy(0)=17′;
iv_2=’y(0)=19′;
% The value at which y is sought at
xval=23.0;
%% DISPLAYING INPUTS

disp(’INPUTS’)
func=[' The ODE to be solved is ' ode_eqn];
disp(func)
iv_explain=[' The initial conditions are ' iv_1 ' ' iv_2];
disp(iv_explain)
fprintf(’ The value of y is sought at x=%g’,xval)
disp(’ ‘)

%% THE CODE

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Posted in matlab, MATLAB programming, Ordinary Differential Equations Tagged: matlab, Ordinary Differential Equations

How do I solve a nonlinear equation that needs to be setup in MATLAB?

Autar Kaw — Fri, 17 Apr 2009 17:14:24 +0000

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 solve a nonlinear equation that needs to be set up.

For example to find the depth ‘x’ to which a ball is floating in water is based on the following cubic equation
4*R^3*S=3*x^2*(R-x/3)
where
R= radius of ball
S= specific gravity of ball
So how do we set this up if S and R are input values?

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 solve a nonlinear equation if I need to set it up?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/integration.m;
% Last Revised : March 28, 2009;
% Abstract: This program shows you how to solve a nonlinear equation
% that needs to set up as opposed that is just given to you.
clc
clear all

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to solve’)
disp(’   a nonlinear equation that needs to be setup’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/nonlinearequation.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   April 17, 2009′)
disp(’ ‘)

%% INPUTS
% Solve the nonlinear equation where you need to set up the equation
% For example to find the depth ‘x’ to which a ball is floating in water
% is based on the following cubic equation
% 4*R^3*S=3*x^2*(R-x/3)
% R= radius of ball
% S= specific gravity of ball
% So how do we set this up if S and R are input values

S=0.6
R=0.055
%% DISPLAYING INPUTS
disp(’INPUTS’)
func=[' The equation to be solved is 4*R^3*S=3*x^2*(R-x/3)'];
disp(func)
disp(’ ‘)

%% THE CODE
% Define x as a symbol
syms x
% Setting up the equation
C1=4*R^3*S
C2=3
f=[num2str(C1) '-3*x^2*(' num2str(R) '-x/3)']
% Finding the solution of the nonlinear equation
soln=solve(f,x);
solnvalue=double(soln);

%% DISPLAYING OUTPUTS

disp(’OUTPUTS’)
for i=1:1:length(solnvalue)
fprintf(’\nThe solution# %g is %g’,i,solnvalue(i))
end
disp(’ ‘)

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Posted in MATLAB programming, nonlinear equations, Numerical Methods Tagged: matlab, nonlinear equations

How do I solve a nonlinear equation in MATLAB?

Autar Kaw — Sat, 11 Apr 2009 17:02:04 +0000

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 solve a nonlinear equation.

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 solve a nonlinear equation?

%% SUMMARY

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to solve’)
disp(’   a nonlinear equation’)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/nonlinearequation.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   April 11, 2009′)
disp(’ ‘)

%% INPUTS
% Solve the nonlinear equation x^3-15*x^2+47*x-33=0
% Define x as a symbol
syms x
% Assigning the fleft hand side o the equation f(x)=0
f=x^3-15*x^2+47*x-33;
%% DISPLAYING INPUTS

disp(’INPUTS’)
func=[' The equation to be solved is ' char(f), '=0'];
disp(func)
disp(’ ‘)

%% THE CODE

% Finding the solution of the nonlinear equation
soln=solve(f,x);
solnvalue=double(soln);

%% DISPLAYING OUTPUTS

disp(’OUTPUTS’)
for i=1:1:length(solnvalue)
fprintf(’\nThe solution# %g is %g’,i,solnvalue(i))
end
disp(’ ‘)

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Posted in matlab, MATLAB programming, nonlinear equations Tagged: matlab, nonlinear equation

How do I integrate a discrete function in MATLAB?

Autar Kaw — Sat, 04 Apr 2009 00:31:12 +0000

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 http://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(’ ‘)

____________________________________________________________

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Posted in Integration, MATLAB programming Tagged: Integration, matlab

How do I integrate a continuous function in MATLAB

Autar Kaw — Sat, 28 Mar 2009 19:29:02 +0000

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 continuous 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 continuous function?

%% SUMMARY

%% INTRODUCTION

disp(’ABSTRACT’)
disp(’   This program shows you how to integrate’)
disp(’   a given function ‘)
disp(’ ‘)
disp(’AUTHOR’)
disp(’   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(’ ‘)
disp(’MFILE SOURCE’)
disp(’   http://numericalmethods.eng.usf.edu/blog/integration.m’)
disp(’ ‘)
disp(’LAST REVISED’)
disp(’   March 29, 2009′)
disp(’ ‘)

%% INPUTS

% Integrate exp(x)*sin(3*x) from x=2.0 to 8.7
% Define x as a symbol
syms x
% Assigning the function to be differentiated
y=exp(x)*sin(3*x);
% Assigning the lower limit
a=2.0;
% Assigning the upper limit
b=8.7;

%% DISPLAYING INPUTS

disp(’INPUTS’)
func=[' The function is to be integrated is ' char(y)];
disp(func)
fprintf(’ Lower limit of integration, a= %g’,a)
fprintf(’\n Upper limit of integration, b= %g’,b)
disp(’ ‘)
disp(’ ‘)

%% THE CODE

% Finding the integral using the int command
% Argument 1 is the function to be integrated
% Argument 2 is the variable with respect to which the
% function is to be integrated – the dummy variable
% Argument 3 is the lower limit of integration
% Argument 4 is the upper imit of integration
intvalue=int(y,x,a,b);
intvalue=double(intvalue);

%% DISPLAYING OUTPUTS

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

_________________________________________________________

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Posted in Integration, MATLAB programming, Numerical Methods Tagged: Integration, matlab