Lesson 1

%Lesson One - 12/24/2010
% Plotting, labeling, concatenation of strings and output to command prompt

%Getting help: You can open the MATLAB documentation by typing 'doc' at
%the command propt. If you want to jump directly to a specifc page of the
%documentation you can type 'doc <function>' where <function> is a valid
%MATLAB function, for example 'doc plot'. Also you can get help at the
%command line by typing 'help plot'.


%clear the variables in the work space. I want to make sure that I can start fresh
clear;

%I am always curious about how long it takes to run a script. 'tic' starts
%the timer, and 'toc' at the end of the file will report out the elapsed
%time.
tic

% There are always many ways of doing any one operation. Knowing your
% options will help you know what is best for each particular application.
% Below we will explore several different ways of doing some actions.

%Creating the time vector with 'linspace'. This function will create a
%linearly space vector from -2 to 3 in 101 steps. see 'doc linspace' for
%more details
t1 = linspace(-2,3,101);

%Create the time vector with the colon operator. see 'help colon' for more
%information. The colon operator is one of the most useful and powerful
%aspects of MATLAB. Learning how to use the colon operatior is essential
%to being a good MATLAB programmer.
%Below creates a vector, starting at -2, incrementing in steps of 0.05 to
%3.
t2 = -2:0.05:3;

%We want to compare the vectors 't1' and 't2' and see if they are identical
%or not.

%First lets look at the size of the vectors. The 'size' command returns
%the length of of each dimension of the vector. Below we will see that the
%vector 't1' is a vector composed of one row and 101 columns

t1_size = size(t1) %A semicolon suppresses output to the command prompt.
t2_size = size(t2);

%The vector 't2_size' vector with two entries. Below we will use indexing
%to select what parts of the vector we want. Indexing is as important as
%the colon operator and we will use it extensively.
t2_size_dim1 = t2_size(1); %first entry in the vector 't2_size'
t2_size_dim2 = t2_size(2); %second entry

%Below is a bit of advanced code. We use the '[' and ']' brackets to
%concatenate a series of strings together and then use the 'disp' or
%display function to output this string to the command prompt.
%Concatenation means to squash things together and is something I use
%everyday in my MATLAB coding. I also used the function 'num2str' or
%number to string to convert the two numbers to strings. Elements must be
%of the same 'type' to be able to be concatenated together.
disp(['t2_size = ',num2str(t2_size_dim1),' x ',num2str(t2_size_dim2)])

%Below is an alternative way of seeing the properties of both t1 and t2
%using the 'whos' command.
whos t1 t2

%type 'whos' at the command prompt now to see the information of all the
%variables in your workspace.


%Ok, we see that the two vectors are the same dimension which is necessary
%for them to be identical. I will show two ways of comparing the contents
%of the two vectors 't1' and t2'

%subtract one vector from the other to find the other to find the
%'distance' between the two vectors at each of the 101 entries.
t_difference = t1-t2;

%Use a logical comparitor '==' to check for equilvalence. A '1' in the
%'t_compare' vector means that the two respective entries are identical and
%a '0' means that they are different.
t_compare = t1==t2;

%Let's visualize these two comparison approaches.

figure(1), %create a figure window with handle of '1'
        stem(t_compare) %create a 'stem' plot of the vector
        xlabel('index number') %add the xlabel to the axis
        ylabel('0= different, 1= identical') %add the y label to the axis
        title('Logical comparison of two ways of creating a time vector') %add a title to the axes



figure(2), %create a figure window with a handle of '2'
        stem(t_difference)
        xlabel('index number')
        ylabel('Distance between the two vectors')
        title('Difference comparison of two ways of creating a time vector')

%Ok, the difference plot is much more informative than the equilvalence
%plot. But note the magnitude of the difference, it's really small.

%Use the 'max' function to find the maximum difference. Note that I first
%take the absolute value of the vector so I can obtain hte true max
%difference.
max_difference = max(abs(t_difference))

%This difference is on the order of magnitude of the precision of your
%computer. Your computer does not have infinite precision in representing
%numbers but must round them off at some point. To understand the floating
%point accuracy of your computer you can use the following command.

float_point_accuracy = eps

%You can see that the max difference of the time vectors is near to the
%machines floating point accuracy so for all but a few advanced application, the
%vectors 't1' and 't2' should be considered identical.

%So what did you learn? Please take a minute to comment on the blog on
%some of the things you learned, what you already knew and any questions or
%topics you would like to discuss in the future.

%-Richard

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