% Matlab Lesson I
% A PHYS 451/551  I CSI 451/551
% Kevin Knuth
% 18 Sept 2006



% IDE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Command Window
% Workspace
% Command History
% Current Directory
% Editor



% Matlab stands for Matrix Laboratory
% Matlab is FAST when it comes to matrix computations

% TIME %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% How to measure program run time

tic
toc

% Try this several times
% Sometimes it takes a little longer.
% Your computer is off doing other things!



% NUMERIC VARIABLES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

a = 0.1234567890;
% notice that the variable appears in the Workspace
% notice that it is rounded to the nearest 0.001
% can be changed using 'format'
% note that the variable's PRECISION is NOT reflected in the display

help format

format long
disp(a)

% disp displays the variable
help disp
doc disp

% PRECISION %%%
% search for 'Floating-Point Numbers' in doc
doc

% DATA TYPES %%%
% search for 'Data Types'
doc

% double-precision will usually be sufficient for our needs

% OPERATIONS %%%
b = 123.0;
% Note that the ; suppressed output.

c = a + b

d = a - b;
d

e = a * b;
e = a*b;

f = a/b;

g = a^b;


% SPECIAL NUMBERS %%%

% imaginary i
% UNLESS YOU HAVE DEFINED IT AS AN INTEGER
i

i = 2

sqrt(-1)

i

% e
exp(1)

% pi
pi



% MATRICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% clear the Workspace
clear;

a = [1, 2; 3, 4]
b = [1; 1]
c = a * b

% How fast was that???
tic; c = a*b; toc;


% Let's make a bigger matrix
A = [ 1, 2, 3; 4, 5, 6; 7, 8, 9]

% How do we access the element in the 3rd row and 1st column?
A(3,1)

% How do we access the entire second row?
A(2,:)

% How do we access the entire third column?
A(:,3)


% SPECIAL MATRIX COMMANDS

% identity matrix
I = eye(5)

% ones
W = ones(2,5)

% zeros
Z = zeros(10,1)

% uniformly distributed random numbers between 0 and 1
r = rand(1,10)
% oops long format!
format short
disp(r)

% normally distributed random numbers with mean 0 and var 1
n = randn(1,3000);
disp(n)
% now you can see why we might supress output

% we can estimate its mean and variance
mean(n)

var(n)

stddev = sqrt(var(n))



% an array of counting numbers from 5 to 10
C = 5:10
C = [5:10]

% an array from 5 to 10 stepping by 0.5
D = [5:0.5:10];
disp(D)


% most common error
disp(A)
X = [1 2 3];
Y = A*X
% oops
% look at Workspace
% or type
whos
% A is 3x3, but X is 1x3
% X needs to be 3x1

% transpose
disp(X)
T = X';
disp(T)

Y = A*X'


% inverse
invA = inv(A)
% oops!
% badly conditioned...check its determinant!!!
det(A)

% try this instead
B = round(10*rand(3,3))
% what did this do???
det(B)
inv(B)


% sizes
disp(X)
size(X)
length(X)

disp(T)
size(T)
length(T)

disp(B)
size(B)
length(B)

% what is length doing???
disp(W)
size(W)
length(W)

length(W')



% BASIC FIGURES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;

% Earlier we made an array of consecutive numbers
t = 1:0.01:5;
% this is a lot of numbers!
size(t)

% I often use uppercase variables for counts of things
T = length(t)


% lets make a sine wave
% A sin (2 pi f t)
% we will let amplitude be A = 1
% we will let f = 2 Hz
A = 1.0;
f = 2.0;
y = sin(2.0*pi*f*t);
% WAIT!!!
% t is a long array!!!
% That is OK because sin will evaluate the function at EVERY value of t
% The result is an array y of equal length
size(y)

% we can plot this
figure;
plot(t,y)

% can control the colors
figure;
plot(t,y,'k');

% we can add points and change the line
figure;
plot(t,y,'k:');
hold;
plot(t,y,'r*');


% CLOSE
close
close all



% remember the random numbers
N = randn(1,1000);

% we can make a histogram
figure;
hist(N);




% SAVE AN LOAD THE WORKSPACE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% what directory am I in?
pwd

% how do I change it?
cd 'C:/'

% in functional form
cd('C:/')

% what is in that directory
ls
dir

% save the workspace
save myWorkspace

% or as a function
save('myWorkspace');

% save a two variables
save partOfWorkspace t y N

% clear
clear all

% load the workspace
load partOfWorkspace

% make a plot
figure; hist(N)



% CONTROL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% IF-ELSE-THEN
a = 6;
if a/2 == round(a/2)
    disp('a is even');
else
    disp('a is odd');
end


% FOR LOOPS
for i = 1:10000
    b(i) = 2*i;
end
% note that this is defining and creating the array b as it goes
% we could have defined b first and set it to zero
% LETS TIME THIS...

clear b;
tic;
for i = 1:10000
    b(i) = 2*i;
end
toc;

% OK, now the other way
clear b;
tic;
b = zeros(1,10000);
for i = 1:10000
    b(i) = 2*i;
end
toc;
% This was MUCH FASTER!


% But we could have defined b from the start by:
clear b;
tic;
b = [2:2:20000];
toc;
% CRAZY FAST!!!
% Matrix Laboratory!

% LESSON: Vectorize your Loops


% while loops
keepgoing = 1;
while keepgoing
    keepgoing = keepgoing + 1;
    if keepgoing == 10
        keepgoing = 0;
    end
    disp(keepgoing)
end





% WORKBOOK or NOTEBOOK or WHATEVER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Use the Editor to keep notes of your EXPERIMENTS
% Save your command history
% Save your notes and ideas
% Use the editor to work your way through a complex function

% Commands can be cut-and-pasted from the Editor into the Command Window
% Commands can be cut-and-pasted from the Command History to the Editor

% Save them in an appropriate dictionary
% Name them appropriately
%   YYYYMMDD-NN-Name
%   The above format keeps it in chronological order and allows searching



% M-FILES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% M-Files are how Matlab handles FUNCTIONS or SUBROUTINES

% FORMAT OF AN M-FILE
%   Commented Description - USED BY HELP!

% here is a function to add two numbers
function result = add(a,b)

result = a + b;
return

% Demonstrate SMART INDENT
% Demonstrate COMMENT

% save M-File as add.m
% NOTE THAT THE NAME 'add' MATCHES THE FUNCTION NAME



% THE PATH %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Matlab looks for unrecognized M-file names by searching the PATH
% Demonstration the Path

% save the M-file 'add.m' in one folder

% modify 'add.m' to add pi to a and b: result = a + b + pi;
% save the M-file in a separate folder

% set up the path for the first folder
% show how the first version of 'add.m' runs

% add the second folder
% show how the second version of 'add.m' runs

% show how the first version runs, if it is higher in the path sequence



% YOUR WORK %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Your work should be of professional quality
% Leave your chicken scratchings in your Workbook

% 1. Use a Separate Folder for Each Project
% 2. Common M-Files can be duplicated and put in a Common Folder
% 3. Document ALL Code.  HELP Functionality Should Be Present.
% 4. Abstract Out Stand-Alone Functions.
% 5. Make a habit of Saving your Workspace and Plots during Experiments
% 6. Check Your PATH




% IMPROVING PERFORMANCE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% search for 'Techniques for Improving Performance'
doc

% profile function
% first look at this function
magic(5)

% now where are its bottlenecks?
profile on
plot(magic(35))
profile viewer
p = profile('info');

% You can watch the function call other functions
profile on -history
plot(magic(4));
p = profile('info');

for n = 1:size(p.FunctionHistory,2)
 if p.FunctionHistory(1,n)==0
        str = 'entering function: ';
 else
        str = 'exiting function: ';
 end
 disp([str p.FunctionTable(p.FunctionHistory(2,n)).FunctionName])
end