function Basic_intro_to_matlab   %The function name should be the same as the <filename>.m

%end each line of code with a semicolon to supress its output.
%using 3 dots ... at end of a line will tell matlab to continue reading the
%next line below.
%typing 'clc' into the commad window clears the workspace.


%=========================== Structures ===========================%
%Two basic structures of matlab are vectors and matrices, both are examples
%of arrays.

row = [1 2 3 4 5];              %generate a row vector.
column = [1; 2; 3; 4; 5];       %generate a column vector.

squ_matrix = [1 2 3 4 5; ...    %generate a 5x5 matrix.
             6 7 8 9 10; ...
             11 12 13 14 15; ...
             16 17 18 19 20; ...
             21 22 23 24 25];

rect_matrix = [1 2 3 4 5; ...
               6 7 8 9 10];
           
%you can access elements of a vector or matrix directly:
row(1);             %first element of row.
column(3);          %third element of column.
squ_matrix(3,3);    %element which is 3rd column and 3rd row.
rect_matrix(1,1);   %first element of the matrix.

%you can access structures within these variables:
squ_matrix(1,:); %outputs the entire first row.
squ_matrix(:,1); %outputs the entire first column.
           
%=========================== Basic arthmetic ===========================%

a = 1;
b = 2;

add = a + b;
sub = a - b;
multi = a*b;
div = a/b;

%similar rules apply for vectors and matrices
vector_add = row + row;
vector_sub =  column - column;
vector_multi = row*column;
vector_div = row/row;
matrix_multi = squ_matrix*squ_matrix;

%using the element wise operations, using the '.'
vector_div = row./row; %i.e. element 1 of one vector is divded by the element 1 of the second vector.
vector_div = row.^row; %element 1 of vector 1 raised to the power of element 1 of the second vector.
%=======================================================================%

%=========================== Printing outputs ===========================%

%disp(a);            %display 'a'.
%disp([a b]);        %display both a and b by placing them into a row vector.
%fprintf('Addition = %f, Subtraction = %f, Multiplication = %f, Division = %f \n', add ,sub ,multi ,div);

%fprintf is sometimes more useful than using just disp. The %f means, place
%a floating point value of a variable here. They are then defined after the
%string, %n can be used to place an integer n.b rounding! You can also
%specify the precision the numbers are printed to, see internet. 

%========================================================================%

%=========================== Loops ===========================%
%main types of loops. 'for' and 'while'.

for i=1:10               %default is to increment i by 1.
   
    x(i) = i*i;
    
end

for i=1:2:10              %each loop increments i by 2.
   
    y = i*i;
    %disp(y);
    
end

while i<100               %this considers up to and including i=99.
   
    z(i) = i;
    i = i+1;              %need to increment i by 1 otherwise loop will not end.
    
end

%=============================================================%

%=========================== if and else ===========================%

j = 10;
for i=1:20
   
    if i==j               %if i is equal to j, (== is boolean) then...
       x(j) = 100; 
    else                  %if i is not equal to j, then do this.
    x(i) = i;
    end
    
end

%===================================================================%

%=========================== plotting ===========================%
%lots of different ways to plot, see mathworks website.
x = 1:10;
y = x.^2;   %use the . to ensure each ELEMENT is squared, not squared vector.

% figure
% plot(x,y);
% 
% figure
% scatter(x,y);
% 
% [X,Y,Z] = peaks(25);
% 
% figure
% surf(X,Y,Z);

end