Numerical Methods Guy – Page 21 – Numerical Methods for the STEM Undergraduate

How do I read data from a textfile 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 read data from an external data file. We will use the simplest command to read from a text file, that is, the fgets command.

The MATLAB program link is here and the text file is here.

So let us look at an example. Let’s suppose someone asks you to find the dot product of two vectors: A=[7 11 13 23] and B=[3 5 17 29]. The program for that simply is

A=[7 11 13 23]
B=[3 5 17 29]
n=length(A)
dot_product=0
for i=1:1:n
dot_product=dot_product+A(i)*B(i)
end

What if now the data for the vectors are given in an external text file? How does MATLAB read the data and assign it properly to A and B.

The first thing is to make the text file. Let’s save this data in the file called /blog/vectordata.txt. The text file is here.
7 11 13 23
3 5 17 29

Now how is this data read from the data file.
First you tell MATLAB what the name of the file is
filen=’W:/blog/vectordata.txt’

Now the file needs to be opened by using the fopen command. This also assigns an integer to the file called the filehandler. This integer is automatically assigned by MATLAB and is a unique integer for any open file. The ‘r’ stands for the file being opened for reading. The other choices are ‘w’ for writing and ‘a’ for appending.
fh=fopen(filen,’r’)

Now we need to get the data from the file which is identified through the file identifier variable. The fgets command does this and every time fgets is used, it reads the next line.

A_vector=fgets(fh)

However, this reads the whole line of data as a single string. How do we now get it to be a vector A with the 4 entries. We do this by using the sscanf command that parses the string variable into the format used by sscanf. The format used here is %f which is a floating point format. The other formats for reading numbers include %e for scientific format and %d for integers.
A=sscanf(A_vector,’%f’)

Similarly, one can now read the B vector via fgets command and parse it using the sscanf command.

The MATLAB program link is here and the text file is here.

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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

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MATLAB code for bubble sort

In the previous blog, we spelled out the bubble sort algorithm for putting an array of numbers in an ascending order. In this post, I am posting the matlab program. It is better to download the program as single quotes in the pasted version do not translate properly when pasted into a mfile editor of MATLAB or see the html version for clarity and sample output.

%% PUTTING AN VECTOR OF NUMBERS IN AN ASCENDING ORDER?
% Language : Matlab 2007a
% Authors : Autar Kaw
% Last Revised : November 8, 2009
% Abstract: This program shows you how to put a vector
% of numbers in an ascending order using the bubble sort method
clc
clear all
disp(‘This program shows the bubble sort method’)
disp(‘to put a vector of numbers in an ‘)
disp(‘ascending order’)
disp(‘Matlab 2007a’)
disp(‘Authors : Autar Kaw’)
disp(‘Last Revised : November 8, 2009’)
disp(‘http://nm.mathforcollege.com’)
disp(‘ ‘)
%% INPUTS
% The vector of numbers
disp (‘INPUTS’)
disp(‘Input the vector of numbers’)
A=[18 7 6 15 4 13];
disp(A)
%% SOLUTION
% Number of entries, n
n=length(A);
% making (n-1) passes
for j=1:1:n-1
    % comparing each number with the next and swapping
    for i=1:1:n-1
    if A(i)>A(i+1);
        % temp is a variable where the numbers are kept
        % temporarily for the switch
        temp=A(i);
        A(i)=A(i+1);
        A(i+1)=temp;
    end
    end
end

%% OUTPUT
disp(‘ ‘)
disp (‘OUTPUT’)
disp (‘The ascending matrix is’)
disp(A)

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Bubble sorting

Last week, I was teaching how to randomly pick lotto numbers using MATLAB. The problem was that some of the numbers that were getting picked were identical. We solved this by using comparisons until the current number picked is different from the previously selected numbers. We blogged on this a few months ago. But there is still an aesthetic problem of how the numbers are presented. The numbers are not in an ascending or descending order. This is a good time to show how to do this using the simplest (if not the most efficient) procedure called the bubble sort.

Let’s suppose someone asks you to put [8 7 9 5 4] in an ascending order.

Starting from the first number, you compare the number with the next number, and see if it is greater. If it is, you swap the numbers. You continue to do this with the second number, third number and so on until the second last number. What this does is bubble the largest number to the end.

[8 7 9 5 4 ] -> [7 8 9 5 4] (as 8>7) -> [7 8 9 5 4] (as 8 is not > 9)-> [7 8 5 9 4] (as 9 is >5) -> [7 8 5 4 9] (as 9>4). See how the largest number is at the end.

Now repeat this. [7 8 5 4 9] -> [7 8 5 4 9] (as 7 is not >8] -> [7 5 8 4 9] (as 8>5) -> [7 5 4 8 9] (as 8>4) -> [7 5 4 8 9 ] (as 8 is not >9)

Now repeat this. [ 7 5 4 8 9] -> [5 7 4 8 9] -> [ 5 4 7 8 9] -> [ 5 4 7 8 9] -> [ 5 4 7 8 9]

Now repeat this. [5 4 7 8 9] -> [ 4 5 7 8 9] -> [ 4 5 7 8 9] -> [ 4 5 7 8 9] -> [ 4 5 7 8 9]

It looks like we are done. If n is the number of the numbers in the array, it takes (n-1) swaps within each of the (n-1) repetitions. So we do not have to guess how many swaps it takes or how many repetitions it takes.

To make the bubble sort efficient, we can do the following: 1) Since with each repetition the largest number bubbles up, we may need to do less swaps. For the first repetition, we will do (n-1) swaps, for the next repetition, we do the first (n-2) swaps, and so on. 2) We can also keep track of number of swaps taking place in a repetition. If no swaps take place in a repetition, no more repetitions are needed.

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How do I numerically solve an ODE in MATLAB?

The other day a student came to ask me for help in solving a second order ordinary differential equation using the ode45 routine of MATLAB. To use ode45, one needs to be familiar with how the inputs are required by MATLAB. The understanding of these inputs is important to use ode45 successfully in problems that are more complex than solving a second order ODE.

The ordinary differential equation was
2y”+3y’+5y=7 exp(-x), y(0)=11, dy/dx(0)=13
This has to put in the state variable form by reducing it by using
y’=z
That gives
y’=z with the corresponding initial conditions as y(0)=11
Then
2y”+3y’+5y=7 exp(-x)
reduces to
2z’ + 3z+5y=7exp(-x)
z’ =(7exp(-x)-3z-5y)/2 with the corresponding initial conditions as z(0)=13

So as needed by MATLAB, call y as y(1) and z as y(2)
dy(1)=y(2), y(1) at x=0 is 11
dy(2)=(7exp(-x)-3y(2)-5y(1))/2, y(2) at x=0 is 13

These equations are now put in a MATLAB function we call odestate.m
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=(7*exp(-x)-3*y(2)-5*y(1))/2;

To solve the ODE, the
The inputs are
1) the function odestate
2) The outputs are required between x=0 and x=17,
hence entered as [0 17]
3) The initial conditions are y(0)=11 and dy/dx(0)=13,
hence entered as [11 13]

The outputs are
1) X= array of x values between 0 and 17
2) Y= matrix of 2 columns;
first column is the y(x)
second column is dy/dx(x)
The MATLAB code then is
[X,Y]=ode45(@odestate,[0 17],[11 13]);

Click the links for the MATLAB mfiles for the function odestate.m and the ODE solver odetest.m

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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

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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

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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

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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

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Are software bugs categorised as “that is the way it is”

For a few years, I thought that the shame was only on financial companies to have dragged us through the economic mess. Whether the mess is now affecting our software industry or if it is the new attitude of software companies, remains to be seen. Three different pieces of software that I use for teaching and research in a large university in the Southeast USA, have serious flaws which the companies are taking semi-seriously or as a matter of “life goes on”.

One of them is a finite element program. Running the input file in a new version gives segmentation fault and the company acknowledges that it is a problem. To stop wasting our time and not having to use the features of the new version, we requested that they give us the license for the older version until they fix the problem. It took more than a couple of weeks of reminders (what else our IT group had to do) to get the older version. Then they did not give us the parallel version of the program and we are still waiting for that.

Second is a program that makes interactive quizzes for mathematics courses. This software gives the result as incorrect even for correct answers if the correct answer is a negative number. This makes the program useless for what I want to do. Their take on it – we cannot update it right away. Hey, this is making your program useless to me – wake up. Even after pointing out to them where the potential bug can be (without looking at the program) and which it was, they still did not help me. I even told them how to fix it. Only after much wrangling and waiting for two months, they are promising the update in October. I hope they test it with the test file I sent them; otherwise, I am at square one until December.

Third is a computational package. They updated their symbolic package with a different package and my students now get two different sets of answers using two different versions. The answers are correct but one version gives only one solution while the other version gives multiple solutions. I need the multiple solutions so that students can pick the most appropriate answer. What I heard from them was -“That is the way it is”. Only after much wrangling and calling their reply a “cop out” did they acknowledge it as a problem and gave me an alternate solution. See I am teaching the first programming course to engineers and I cannot teach them to work around the bugs of the software itself. Their confidence is shaken and I have to be extra vigilant now – is it the software or is it the students. Nothing can be taken at face value anymore. And these students are the future industrial users of the software.

Bugs are part of life for any software but when you are making millions of dollars of profit, you have an obligation to work on the bugs that make your software unusable. What I am finding out is the software companies attitude is that they are safe in treating their customer any way they like – they may not be “too big to fail” but they are “too entrenched to fail”. Good day!

_________________________________________________________________________________________________________________________

This post is brought to you by

Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com,
Textbook on Numerical Methods with Applications available from the lulu storefront,
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.

You can watch the numerical methods videos on a mobile device

We are in the process of putting appropriate content of the numerical methods website so that it can be viewed on mobile devices. So far we have checked that it works on the Itouch, Iphone, Blackberry, LG New.

The mobile website is at http://nm.mathforcollege.com/mobile. Let me know what you think about this development.

_________________________________________________________________________________________________________________________

This post is brought to you by

Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com,
Textbook on Numerical Methods with Applications available from the lulu storefront,
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 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 http://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(‘________________________’)

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How do I solve a set of 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://nm.mathforcollege.com/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 http://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/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://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.