CS99 Fall 2002
Lecture 13
11/15/2002
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(0) Announcements
    + Prelim 2 -- follow instructions in e-mail and on News
      (reasons for doing this?)
    + Reminder about Final Project: due 12/6
    + missing work issue
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(1) Overview
    + a bit more function syntax
    + varying returns and inputs
    + subfunctions
    + function functions
    + function advice
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(2) Inputs and Returns

    + can have as many inputs and returns as you want
      - may even have zero of either or both
      - MATLAB actually allows a call to a function with fewer inputs and 
        returns than required by the function, though you may run 
        into trouble with too few inputs
    + can have different amounts of inputs and returns
    + NOTE: returns and outputs are different! 



    =================
    1 input, 1 return
    =================

      function v=y(x)
         v = x+1; <-----------------------no semicolon gives output, too!

      >> y(1:2)

      ans =



    ========================
    multiple input, 1 return
    ========================

    function v=y(x1,x2)
        v=x1+x2;
   
    >> y(1,2)

    ans =










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    ================================
    multiple inputs, multiple return
    ================================

    function [v,w] = y(x1,x2)
       v = x1+x2;
       w = x1.*x2;

    >> y(1,2)      % assumes you mean just the FIRST output
  
    ans = 

    >> z = y(1,2)  % assumes you mean just the FIRST output
 
    z = 

    >> [a b] = y(1,2) % now you get multiple outputs
 
    a =

    b = 

    =========
    no return
    =========

    function y(x1,x2)
       x1+x2

     >> y(1,2)

    ans = 

    But did ans really get assigned? Which ans got assigned?

    function y() % could also say "function y"
       disp('hi');
 
    >> y  % you must enter with no "()"

    ans = 

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(3) Subfunctions:

    + can put other functions in a function M-File
    + these functions are written below the first function
    + the first function is usually the name of the M-File and is visible to
      other functions in the same path
    + the other functions are called SUBFUNCTIONS
      - they are NOT visible to "outside functions"
      - they are strictly visible to the first function and other functions
        in the same M-File

    example)

    function x = blah(a,b)                         
    x = blah2(a,b);                            >> blah(1:2,2:3)
                                               >> blah2(1:2,2:3) 
    function y = blah2(a,b)
    % subfunction of blah
    y = 2.*a+b
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(4) Function function:
    + function with an input argument the name(s) of other function(s)
       ex) ezplot('cos(x)')
           ezplot plots function without having you to figure out other inputs
    + usually input names are strings


     function demofunfun
     % DEMOFUNFUN demonstration of function functions
  
     disp('Starting demo of function functions...');
     name = input('Enter the name of a function as a STRING: ');
     % example: user enters $'cos'$
     plotf(name,linspace(-10,10,10000));
  
     function plotf(name,x)
     % evaluate the function with name $name$ with input $x$
     % $feval$ evaluates a function with given inputs
     y = feval(name,x);
  
     % could also use less efficient $eval(string)$ which
     % evaluates $string$ as a script command
     % now do something interesting with the values
     plot(x,y);
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(5) Recursion:
    + function calls itself
      (Yes, MATLAB and other languages can do that!)

    example)
     function result = rsum(n)
       if n==1
          result = 1;
       else
          result = n + rsum(n-1);
       end
  
     % Actually this case handled much quicker by MATLAB itself
     % sum(1:n)
     % could also do loop
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(6) Reminders/Advice

    + How to know when to use a function?
      - verb/action in problem statement
      - task (or related group of tasks) that gets repeated often
    + How to write?
      - decide on inputs, returns, tasks
      - test individually with dummy inputs

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