% Script file for Math 305 - lab session 1
%
% Copy into your command window each of the following commands.
% Try to understand the commands as you go.
% Do the exercises, which are variations on what is done; copy
% the commands you make in the three exercises into an email and 
% send it to me at gautier@math.hawaii.edu
% Save your work either using 'Save workspace' in the Edit Menu
% or by copying all your work into a file using Edit and saving % it.
%  Matlab can act as a calculator; operators are: + - * / ^
[5+8,   87*123,  216/4,  10^2]

% Matlab has many standard functions
a=sqrt(10)

a=sin(3*pi)  % this should = 0 but doesn't because matlab uses approximate arithmetic

log(10)		%Natural log

atan(0)         % Arctan          

%  help command - gives you the help page for the command 
help tan

% doc command - gives you a better formated help page
doc tan

% create a vector from 1 to 10 using colon operator

x=1:10

% create a vector from 1 to 10 with increments of 2

x=1:2:10

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EXERCISE 1
% Write as progressions (like in the exemple above) the vectors [1,2.5,4,...,34] and [2, 1.9, 1.8,1.7,...,0]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% length command returns the length of a vector
length(x)

% Entering matrices:

% 1.  separate elements of a row with blanks or commas
x = [16 3 2 13]
xx = [16,3,2,13]

% 2. use semicolon to separate rows
y = [16;5;9;4] 


% 3. The default multiplication operator * is matrix multiplication:
x*y 
y*x

% 4. to force element by element multiplication use .*
x.*x
y.*y

% 5. Enter the matrix:
A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

% 6. What are the dimensions of this matrix?

size(A)		% gives the size in each dimension 

% 7. This matrix is known as a magic square it has some special properties:
% 8. All row sums and column sums are equal:
sum(A)  	% sums the elements in each column of A

% 9. To get the row sums, first transpose the matrix
A'

% note the columns of A are the rows of A' and vice-versa
sum(A')'	% this gives the row sums of A

% 10. to sum the diagonal elements of A 
diag(A)  	% gets the diagonal of A
sum(diag(A)) 	%sums the diagonal elements

% The element in ith row ans jth column is denoted by A(i,j)
X=A
A(2,3)
A(2,3)+A(3,2) 	% sums two elements
A(2,3)=A(2,3)+A(3,2)  % replaces an element
A=X

% You get an error message if you ask for an element
% outside the matrix
A(4,5)

% You can increase the size of the matrix by adding an element
X=A;
X(4,5) = 17

% you can get a row or column by using the : instead a subscript

r1=A(1,:)  	% row 1, all columns

c1=A(:,1)	% column 1, all rows

%Extract a subset of a row
B=[1 2 3 4 5 6; 7 8 9 10 11 12; 13 14 18 16 17 18]
B(2,1:2:size(B,2))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EXERCISE 2 
% Extract the entries in the odd columns of the third row of the matrix B
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% deleting a column
X=A;
X(:,2)=[]  	% deletes the second column

X=A;
X(2,:)=[]  	% deletes the second row

%  Concatination is the process of joining small matrices to make bigger ones.
%  Note: [] is the concatination operator

B=[A A+2; A+10 A]

% This produces an 8x8 matrix

% Matlab provides buit-in functions for generating matrices
  
Z=zeros(2,4)	% 2x4 matrix of zeros

F=5*ones(3,3)	% 3x3 matrix of 5's

% Identity matrix 
eye(3)

% A simple plot

x=1:0.1:10;
y=sin(x*pi/2);
plot(x,y) 

% add another line

z=sin(x*pi/3);
hold on 
plot(x,z,'r-')
hold 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EXERCISE 3
% Plot the function arctan from -10 to 10.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%