%***************************************************************
%*
%*	tutor.m:  Tutorial for beginning MATLAB users.
%*
%*	Written by:	Kyle D. Dippery
%*			473 Anderson Hall
%*			(606) 257-3893
%*			kdip@engr.uky.edu
%*
%*	Last updated May 20, 1997
%*
%*	Copyright 1997 by Kyle D. Dippery
%*
%*	Reproduction of this document is permitted for
%*	noncommercial use only, provided the entire document,
%*	including this copyright notice, remains intact.
%*
%***************************************************************

clc
echo on

%
%		     WELCOME TO MATLAB!
%

%
%	The purpose of this tutorial is to familiarize the
%	user (that's you) with the basics of MATLAB.
%
%	In the screens to follow, lines preceded by a percent
%	sign ('%') are comment lines, and are ignored by the
%	MATLAB interpreter.  All other lines are actual MATLAB
%	commands, which will be executed before your very eyes.
%
%	Press a key to continue...

pause
clc

%	Probably the first useful thing you need to know is
%	how to enter data from the keyboard.  You can do this
%	by assigning values directly to variables.  For example,
%	to assign the value 5 to the variable 'a', we enter:

a=5

%	That first line ("a=5") is what we entered.  MATLAB
%	then shows us that it understood what we said, by
%	echoing the value of a (5).

%	Press another key...

pause
clc

%	MATLAB doesn't particularly care whether the value
%	we enter is a scalar, vector, or matrix.  The syntax
%	for the assignment is mostly the same, regardless.
%	The only difference for vectors or matrices is that
%	we need square brackets ([]) to tell MATLAB that the
%	input is an array.  So, to enter a row vector, let's
%	call it 'b', we type:

b=[1 3 4 5 8 9]

%	Here we've separated the elements of the array by
%	spaces.  Commas would have worked just as well, but
%	we tend to think commas make the line look a bit more
%	cluttered than it really needs to.

pause
clc

%	Column vectors, like 'bc', are entered as:

bc=[1; 4; 3; 5; 3; 5];

%	Notice the dual use of the semicolon in the last
%	example.  First, it separates the rows of column
%	vectors (or other multi-row arrays).  (Spaces after
%	the semicolons aren't necessary, but we think they
%	help make the line more readable.)
%
%	Second, when a semicolon ends a command it tells
%	MATLAB not to echo the results of the command to
%	the screen.

%	Another key to continue...

pause
clc

%	If we want to look at a variable after it is assigned,
%	we can use the 'disp' command.

disp(bc)

pause
clc

%	Colons have special uses in MATLAB, too - they can
%	be used to build vectors of evenly-spaced numbers:

a2=1:0.5:3.4

%	Notice that the last element of the vector is 3.0, not
%	3.4.  This is because the next element of the specified
%	sequence is 3.5, which is greater than the upper limit
%	(3.4) we assigned.
%
%	Notice also that, in this case, we didn't need the
%	square brackets.  That's because MATLAB expects a
%	vector input when the colon notation is used.  Still,
%	the brackets can be used if there's any doubt; there's
%	nothing wrong with a little redundancy.

pause
clc

%	If the increment (the second number in that last
%	assignment statement) is omitted, it defaults to 1:

a3=0:5

pause
clc

%	Matrices can be entered as a sequence of row vectors,
%	separated by semicolons.

A=[1 3 5 7; 2:2:8; 1 2 4 9]

pause
clc

%	Or as a sequence of column vectors, separated by commas
%	or spaces:

B=[bc,2*bc 3*bc]

pause
clc

%	Complex numbers also receive no special treatment:

C=ones(3,3) + i * A(:,1:3)

pause
clc

%	Some notes about this last command:
%
%		C=ones(3,3) + i * A(:,1:3)
%
%	1.  'i' is implicitly recognized as sqrt(-1).
%	So is 'j'.
%
%	2.  'ones(m,n)', where m and n are positive integers,
%	generates an mxn array of 1's, in this case used for
%	the real part of C.  Some other 'special' matrices can
%	be generated by 'zeros', 'eye', 'rand', 'randn', or
%	'magic'.
%
%	3.  Submatrices can be extracted from matrices by
%	using indices.  In this case, the imaginary part of
%	C is a submatrix of A, consisting of the first three
%	columns of A (the same matrix A we used before, still
%	in memory for us to use.)

pause
clc

%	A bit more about:
%
%		C=ones(3,3) + i * A(:,1:3)
%
%	The first index into an array always indicates the rows
%	to be used, the second index indicates the columns.
%	Indices may be scalars or vectors.  A colon, by itself,
%	means "use 'em all".  Hence, A(:,1:3), A(1:3,1:3), and
%	A([1 2 3],[1 2 3]) would all give the same result (since
%	A, in this particular case, has only three rows).
%
%	4.  Multiplication of a matrix by a scalar is
%	accomplished by the '*'.  Matrices, scalars, and
%	vectors are all added by '+'.

pause
clc

%	Addition and subtraction act the same for scalars,
%	vectors, and matrices.  a+b, where a and b are scalars
%	adds a and b together.
%
%	If a and b are vectors,

a=1:5, b=10:-2:2

pause
clc

%	or matrices, with the same dimensions, then a+b adds each
%	element of a to its corresponding element in b:

a+b

%	Notice that, if an operation is not assigned to a
%	specific variable, it is assigned to the temporary
%	variable, 'ans'.

pause
clc

%	Scalars can be added to (or subtracted from) anything:

ans-3
rand(3,3)+ans(4)

%	See if you can follow what just happened, there...

pause
clc

%	Order of operation is pretty standard - exponents are
%	evaluated first, multiplication and division next,
%	addition and subtraction last; operations are evaluated
%	left to right, except when parentheses are used to group
%	things together.  The usual stuff...

pause
clc

%	Multiplication and division are slightly different:
%	they are assumed to be matrix operations:

A=magic(3)
B=[8 2 1; 2 2 1; 5 3 7]

pause
clc

Mprod=A*B

pause
clc

%	If what we want is an array whose elements are the
%	elements of A times the elements of B, we need to
%	use a 'dot-multiply', or '.*':

Aprod=A.*B

pause
clc

%	This is called 'array multiplication', to distinguish
%	it from 'matrix multiplication'.
%
%	Let's look again at our matrix product, for comparison:

Mprod, Aprod

pause
clc

%	Division with matrices is similar to multiplying
%	one matrix by the inverse of the other:
%
%	A/B is almost A*inv(B) (where inv(B) is the MATLAB
%	command which finds the inverse of B).
%	
%	A\B is almost inv(A)*B.
%
%	(The reason it's "similar to" and not "the same as" is
%	that A and B don't have to be square matrices for the /
%	or \ operations, but do for the inv() operation.)
%
%	For more precise definitions of / and \, try
%	'help /' or 'help slash'.

pause
clc

%	Array division is accomplished by the 'dot-divide'
%	operations, './' and '.\'.
%
%	A./B yields an array whose elements are the elements of
%	A divided BY the elements of B.
%
%	A.\B yields an array whose elements are the elements of
%	A divided INTO the elements of B (or, the elements of B
%	divided BY the elements of A).
%
%	Note that A.\B is the same as B./A, but A\B is NOT the
%	same as B/A.

pause
clc

%	Matrices may be multiplied by scalars without using the
%	'.*', but division requires a bit of care.
%
%	For instance, 2*A and A*2 will both yield

disp(A*2)

%	A/2 gives us an array whose elements are the elements of
%	A divided by 2, but 2/A does _not_ give us an array whose
%	elements are 2 divided by each element of A (unless A
%	happens to be a scalar).

pause
clc

%	Exponents are kinda ugly.  Usually, what you'll probably
%	want is every element of a vector raised to a certain
%	power, or a certain base raised to the power of every
%	element in a vector.  These would be accomplished by the
%	'.^' operator:

disp(a)
disp(a.^3)
disp(3.^a)

%	The '^' operator by itself has more to do with matrix
%	powers, and either the matrix or the exponent, but not
%	both, must be a square matrix.  'help arith' will give
%	more information on this.

pause
clc

%	The '.' means something a bit different when dealing
%	with transposes.
%
%	Normally, a transpose is denoted by a single quote, '.
%	When the matrix is complex, this is actually a complex
%	conjugate ("Hermitian") transpose operator.  A
%	"straight" transpose is denoted by a dot-transpose, .'.
%
%	Note:  for real-valued matrices, there is no difference
%	between a transpose (') and a dot-transpose (.').

pause
clc

%	Some examples, using our matrix C

disp(C)

disp(C')

disp(C.')

pause
clc

%	For an example of why we like array multiplication,
%	let's try to draw a spiral.

t=0:720;		% angle, in degrees, twice around
x=t.*sin(pi/180*t);	% x coordinate
y=t.*cos(pi/180*t);	% y coordinate

%	Notice that mathematical functions can operate on
%	arrays.  sin(pi/180*t) takes the sine of every element of
%	the vector, pi/180*t.  (pi is 3.1415etc., implicitly defined.)
%
%	t*sin(pi/180*t) would try to multiply a 1x721 matrix by
%	another 1x721 matrix, which doesn't work.  Instead,
%	t.*sin(pi/180*t) multiplies the ith element of t by the
%	ith element of sin(pi/180*t), which is what we really
%	want.
%
%	Notice also that the input to the sin and cos functions
%	is converted from degrees to radians.  Trig functions
%	in MATLAB always operate on radians.

pause
clc

%	Notice also how the array operations neatly reduce
%	the need for 'for' loops.
%
%		x=t.*sin(pi/180*t);
%
%	gives the same result as:
%
%		for ii=1:721,
%		    x(ii)=t(ii)*sin(pi/180*t(ii);
%		end
%
%	(We like to use 'ii' and 'jj' instead of 'i' and 'j'
%	for loop counters, because 'i' and 'j' already mean
%	sqrt(-1) to MATLAB, and we'd hate to try to build a
%	complex array out of something, only to find out that
%	i=17.2 or j=150 suddenly, because we used them for
%	something else beforehand...)

pause
clc

%	Now let's look at our spiral.

plot(x,y)

%	This is the simplest method of obtaining a graph.  We
%	can label this graph,

xlabel('X Coordinate')
ylabel('Y Coordinate')
title('Wow, It Worked!')

%	Input to the 'xlabel', 'ylabel', and 'title' commands
%	must be a string argument.  Strings in MATLAB are
%	delimited by single quotation marks (').
%
%	Strings are concatenated (stuffed together) with square
%	brackets.  ['Hi' ' there!'], for instance, yields the
%	string 'Hi there!' (see 'puzzle(2)' for another example).
%	Functions exist for turning numbers into strings, which
%	can then be used in figure titles or labels:

text(0,max(y),['Max y value = ' num2str(max(y))]);
pause
clc

%	If, for some reason, we don't like yellow lines,
%	we could ask for the plot in some other color (we
%	like green, ourselves):

plot(x,y,'g')

%	Notice that all of our nice labels are gone.
%	Successive 'plot' statements generally erase
%	anything that was set by earlier ones.  (This
%	can be changed by playing with the 'hold'
%	function.)

pause
clc

%	Or we could ask it to plot the data as red plusses:

plot(x,y,'r+')

%	For a list of possible linestyles and colors,
%	enter 'help plot' from the command prompt (when
%	you get it back, that is).

pause
clc

%	Multiple plots can be placed in a single window by
%	using 'subplot'.

subplot(211), plot(t,x,'c:')
ylabel('X')
title('A Spiral?')

subplot(212), plot(t,y,'Color',[1 0.5 0],'linestyle','-.')
ylabel('Y')
title('It Doesn''t Look Like a Spiral...')
xlabel('Angle, Degrees')

%	Look carefully at the second 'title' command, above, and
%	compare it to the actual title.  Look again.  There is a
%	difference - where the apostrophe appears in the title,
%	there are two in the command.  This is how you get
%	single apostrophes to appear in MATLAB strings, since
%	one by itself would mean the end of the string.
%
%	Alternate methods of specifying line colors and styles
%	are also illustrated above.
pause
clc

%	Did you notice how nothing happened in the figure window
%	until all the commands for building all of the plots had
%	been executed?  MATLAB doesn't like to update figures
%	until it absolutely has to (who does?), or when it runs
%	out of commands to execute, or when it runs into a
%	'pause' statement (as it did, here).  The 'drawnow'
%	command will force MATLAB to display graphs before it
%	reaches the end of the command stack:

pause

clf
subplot(211), plot(t,x,'c:')
ylabel('X')
title('A Spiral?')
drawnow			% just like this

subplot(212), plot(t,y,'Color',[1 0.5 0],'Marker','.')
ylabel('Y')
title('It Doesn''t Look Like a Spiral...')
xlabel('Angle, Degrees')

pause
clc

%	Or we could look at multiple plots on a single set
%	of axes:

clf
plot(x,y,'g',x,t.*cos(2*pi/180*t),'r--')
title('There''s Something Fishy Here...')
xlabel('X'), ylabel('Y')

pause
clc

%	We can add gridlines:

grid

pause

%	Or turn just some of them on or off:

set(gca,'ygrid','off')
pause

%	Or even zoom in some,

set(gca,'xlim',[340 460])

%	but that's getting a bit fancier than we generally
%	need.  Still, if you want to play with lots of figure
%	or axes properties, you can look into the 'set' and
%	'get' commands, later.  There's lots of fun to be had,
%	in there...

pause
clc

%	Figures can be cleared by 'clf'.  Empty figure windows
%	can be opened by entering 'figure'.  Figure windows
%	can be closed by entering 'close(n)', where n is the
%	number of the window to close.  (The figure number is
%	usually displayed in the window's title bar.)
%
%	'close all' closes all figure windows.

clf

pause
close(1)

pause
clc

%	Hardcopies of plots are obtained through the 'print'
%	command.  'print -deps filename' would print the
%	current figure to filename.eps, in encapsulated
%	PostScript format.  The file could then be printed
%	on a laser printer, or imported into documents, or
%	whatever.  'print', by itself, sends the plot to the
%	default printer.  You may want to be careful of this, if
%	your printer has a page quota, or if you're just trying
%	not to be wasteful, or some such...
%
%	MATLAB also supports formats besides Encapsulated
%	PostScript.  Enter 'help print' to find out about
%	these.

pause
clc

%	We've played with quite a few arrays, so far: a, b,
%	bc, A, B, t, x, y, and maybe one or two more we don't
%	remember.  Right now, they're all still sitting in
%	memory.  What if we've lost track of what we've done?
%	Is there a way to find out what we have in memory?
%
%	Maybe....  Try entering 'who':

who

%	This shows all the variables currently residing in
%	memory.

pause
clc

more on
%	Or we could type 'whos'.  This shows all the variables
%	in memory, along with their sizes and some other neat
%	things about them.  Let's first introduce the 'more'
%	function, though:  this forces screen display to pause
%	each time the screen fills up.  'more on' and 'more off'
%	are used to control this paging routine.
%
%	When 'more' is 'on', the spacebar pages ahead one full
%	screen, 'q' quits the pager (it probably would not be a
%	good idea to press 'q' just now, however...  it likely
%	would also quit the tutorial at this point) and just
%	about any other key moves forward one line.

whos
more off

pause
clc

%	Let's get rid of some of this baggage:

clear Aprod Mprod a a2 a3 ans b bc t x y

%	'clear', by itself, or 'clear all', would get rid of
%	everything.  But I wanted to keep some things...

who

pause
clc

%	What if we only want to know the size of one array?

BSize=size(B)

%	'size' returns a two-element vector, containing the
%	number of rows (1st element) and the number of columns
%	(2nd element) of an array.  'size(ans,1)' will return
%	just the number of rows.  'size(ans,2)' will return
%	just the number of columns.

%	'length' returns the maximum element of the 'size'
%	vector (useful for dealing with vectors)



pause
clc

%	We could use the 'tic' and 'toc' commands to find
%	out how much time it takes to calculate that inverse.

tic;
inv(C)
toc

%	The 'elapsed_time' is shown in seconds.

pause
clc

%	If we just wanted to know what time it is, we could 
%	look at the 'clock' (since some of us don't wear watches):

clock

%	This tells us, in order, the current year, month, day,
%	hour, minute and second (just multiply that '1.0e+03'
%	factor through each element to get the right values).
%
%	(And no, we don't know what's going to happen at the end
%	of the millenium...)

pause
clc

%	Hardcopy of any MATLAB session can be obtained by
%	using the 'diary' function.  If 'diary' is on ('diary
%	on' is the command), then anything that prints on the
%	screen also prints to a file called 'diary'.
%
%	'diary filename' sends all output to the specified file.
%
%	'diary off' turns the diary function off.

pause
clc

%	That's it for this tutorial.  If you want to look
%	at it again, without pressing all those carriage
%	returns, set 'more on', then 'type tutor'.
%
%	To quit MATLAB when you're done (or ready for lunch),
%	type either 'exit' or 'quit'.
%
%	Enjoy!

echo off