The continue statement in MATLAB

The continue statement in MATLAB is used to pass control to the next iteration in for and while statements.  Let’s suppose someone wants to find and print the value of k^2-50 for all integers in [-10,10] domain.  The mfile for that is given below.

% For integers k=-10,-9,….,9,10,
% the function k^2-50 will take positive as
% well as negative values. 
%For example, for k=-9, k^2-50=31; for k=1,
% k^2-50=-49; for k=8, k^2-50=14.
% The loop below will calculate values of k^2-50 for
% all values of requested k.
for k=-10:1:10
    val=k^2-50;
fprintf(‘\n k=%g  val=%g’,k,val)
end

___________________________________________________________

Let’s suppose now you are asked to calculate and print value of k^2-50 for all integers in [-10,10] domain but only if (k^2-50) is positive.

% The loop below will calculate and print values of k^2-50
% for all values of the requested k
% for which k^2-50 is positive.
for k=-10:1:10
    if (k^2-50<0)
        continue;
    end
    val=k^2-50;
    fprintf(‘\n k=%g  val=%g’,k,val)
end

____________________________________________________________

Can you do what you did above using the while statement.  Yes, the MATLAB code is given below.

% Equivalent in while
% The loop below will calculate values of k^2-50
% for all values of the requested k for which k^2-50 is positive.
k=-10;
while (k<=10)
    if (k^2-50>0)
        val=k^2-50;
        fprintf(‘\n k=%g  val=%g’,k,val)
    end
k=k+1;
end

_______________________________________________________

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

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

The break statement in MATLAB

The break statement in MATLAB is used to break out of a loop – a for or while statement, that is, it terminates the execution of the loop.  Let’s suppose someone wants to find the value of k^2-50 for all integers in [-10,10] domain.  The mfile for that is given below.

% For integers k=-10,-9,….,9,10,
% the function k^2-50 will take positive as
% well as negative values. 
%For example, for k=-9, k^2-50=31; for k=1,
% k^2-50=-49; for k=8, k^2-50=14.
% The loop below will calculate values of k^2-50 for all values of requested k.
for k=-10:1:10
    val=k^2-50;
end

___________________________________________________________

Let’s suppose now you are asked to calculate value of k^2-50 for all integers in [-10,10] domain but only until k^2-50 becomes negative.

% The loop below will calculate values of k^2-50
% for all values of the requested k
% until it turns negative
for k=-10:1:10
    if (k^2-50<0)
        break;
    end
    val=k^2-50;
    fprintf(‘\n k=%g  val=%g’,k,val)
end

____________________________________________________________

Can you do what you did above using the while statement.  Yes, the MATLAB code is given below.

% Equivalent in while
% The loop below will calculate values of k^2-50
% for all values of the requested k until it turns negative
k=-10;
while (k<=10) & (k^2-50>0)
    val=k^2-50;
    fprintf(‘\n k=%g  val=%g’,k,val)
    k=k+1;
end

_______________________________________________________

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

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

How do I solve simultaneous linear equations given in equation form?

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 simultaneous linear equations given in equation form.

  • 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 set of simultaneous linear equations
% given in equation form?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://nm.mathforcollege.com/blog/sle_equations.m;
% Last Revised : August 22, 2009;
% Abstract: This program shows you how to solve a set of
%     simultaneous linear equations given in equation form?
%           .
clc
clear all
clf

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to solve a’)
disp(‘   set of simultaneous linear equations given in equation form’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/sle_equations.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   August 22, 2009’)
disp(‘ ‘)

%% INPUTS
% Enter the equations
eqn1=’12*a+23*b+39*c=29′;
eqn2=’13*a+17*b+19*c=37′;
eqn3=’21*a+23*b+29*c=59’;
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘________________________’)
disp(‘Equations’)
disp(‘________________________’)
disp(eqn1)
disp(eqn2)
disp(eqn3)

%% THE CODE
% The solution
X=solve(eqn1,eqn2,eqn3);
% Assigning the output
a=double(X.a);
b=double(X.b);
c=double(X.c);
%% DISPLAYING OUTPUTS
disp(‘  ‘)
disp(‘OUTPUTS’)
disp(‘________________________’)
disp(‘Solution Vector’)
disp(‘________________________’)
fprintf(‘\nValue of a= %g’,a)
fprintf(‘\nValue of b= %g’,b)
fprintf(‘\nValue of c= %g’,c)
disp(‘  ‘)
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 and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

How do I solve a set of simultaneous linear equations given in matrix form?

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 simultaneous linear equations given in matrix form.

  • 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 set of simultaneous linear equations?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/sle.m;
% Last Revised : August 12, 2009;
% Abstract: This program shows you how to solve a set of simultaneous linear
% equations?
%           .
clc
clear all
clf

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to solve a’)
disp(‘   set of simultaneous linear equations’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/sle.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   August 12, 2009’)
disp(‘ ‘)

%% INPUTS
% Enter the coefficient matrix of the equation [A][X]=[C]
A=[12  23  39; 13  17  19; 21  23  29];
% Enter the right hand side vector
C=[29;   37;  59];
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘________________________’)
disp(‘Coefficient Matrix’)
disp(‘________________________’)
dataval=[A];
disp(dataval)
disp(‘________________________’)
disp(‘Right hand side vector’)
disp(‘________________________’)
dataval=[C];
disp(dataval)
disp(‘________________________’)

%% THE CODE
% The solution
X=A\C;

%% DISPLAYING OUTPUTS
disp(‘  ‘)
disp(‘OUTPUTS’)
disp(‘________________________’)
disp(‘Solution Vector’)
disp(‘________________________’)
dataval=[X];
disp(dataval)
disp(‘________________________’)

his 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

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

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 and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

How do I do polynomial 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 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://nm.mathforcollege.com/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 https://autarkaw.wordpress.com&#8217;)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/interpolation_polynomial.m&#8217;)
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(‘  ‘)

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 and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

How do I solve a boundary value ODE 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 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://nm.mathforcollege.com/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 https://autarkaw.wordpress.com&#8217;)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/ode_boundaryvalue.m&#8217;)
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(‘  ‘)

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 and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.