====== Lecture 5: Functions and control flow ======
 
In the following diary, we call functions defined in files of the same name.
These functions are provided in the Lecture table on [[gibson:teaching:fall-2013:math445 | the course website]]
<code>

% How to call the square function, defined in file square.m
square(4)
ans =
    16
square(5)
ans =
    25

% Note that "help square" returns the help string we wrote in the
% the line after the function declaration in square.m
help square
  square takes an argument x and returns its square, s=x*x

% Here's help for the pow(x) function we wrote
help pow
  pow(x,n): return x to the n

% and an example of use
pow(4,3)
ans =
    64

% Our square_cube function has *two* return values.
help square_cube
 [s,c] = square_cube(x): return the square and the cube of x

% If you run it without specifying variables for both return values,
% Matlab drops the second and just gives you the first
square_cube(3)
ans =
     9

% To get both return values, run it like this
[s,c] = square_cube(3) 
s =
     9
c =
    27

% Example run of printtoten function 
printtoten
n =
     1
n =
     2
n =
     3
n =
     4
n =
     5
n =
     6
n =
     7
n =
     8
n =
     9
n =
    10

% Example run of sumtoten function 
sumtoten()
ans =
    55

% Example run of our matvecmult function

A = rand(3,3);
x = rand(3,1);
A
A =
    0.8147    0.9134    0.2785
    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575
x
x =
    0.9649
    0.1576
    0.9706

y = matvecmult(A,x)
y =
    1.2004
    1.5045
    1.0673

y = A*x
y =
    1.2004
    1.5045
    1.0673

% Hooray, our matvecmult(A,x) produces the same result as matlab's A*x!

% You can also execute control flow statements at the matlab command prompt
s=0;
for i=1:10
s = s + i;
end
s
s =
    55

% You can put that all on one line
s = 0; for i=1:10; s = s+ i; end
s
s =
    55
 </code>