Function Handles

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• Misc
  • REU Talk
    • REU = research experiences for undergraduates = summer research “internship”
    • Wednesday, March 30, 3:30 PM
    • South 328
    • Walter Gerych re obstructed “mean curvature flow” and cellular automata
    • Up to 2 points homework extra credit for write-ups
• Questions?
• Function Handles
  • Sections 14.3 and 14.4
    • Anonymous functions defined in workspace
    • @ indicates definition, function handle
    • Argument list can be empty or one or more arguments
    • Function handles
      • feval calls a function via a handle with inputs
  • Examples
    • Create an “alias” for the sqrt function
      

      >> sqrt( 4 )
      ans =
           2
      >> s = @sqrt
      s = 
          @sqrt
      >> s
      s = 
          @sqrt
      >> s(4)
      ans =
           2
      >> s(2)
      ans =
          1.4142
      >> s(-2)
      ans =
         0.0000 + 1.4142i
      >> feval( s, 4 )
      ans =
           2
      >> s + 3
      {Undefined operator '+' for input arguments of type 'function_handle'.}
      >> s = 3
      s =
           3
      >> s(4)
      {Index exceeds matrix dimensions.} 
      >> s + 3
      ans =
           6

      • Notice that you don’t need feval to call a handle
      • Also notice that variables that store handles are normal variables, you can reassign numbers to them to make them stop storing a handle
    • Write “sumFirst” function for which sumFirst(f) = f(1) + f(2) + f(3)
      

      function [ y ] = sumFirst( f )
      %SUMFIRST computes y as f(1) + f(2) + f(3)
      y = f( 1 ) + f( 2 ) + f( 3 );
      end

      • Calling sumFirst
      • Always call it with a function handle
      • But handle can refer to a built-in function, an anonymous one made just for that call, or a function you defined
        

        >> % add up square roots of 1, 2, 3
        >> sumFirst( @sqrt )
        ans =
            4.1463
        >> % add up (sqrt(x) + 1) for x = 1, 2, 3
        >> sumFirst( @(x) sqrt(x) + 1 )
        ans =
            7.1463
        >> % add up fib(1), fib(2), fib(3)
        >> sumFirst( @fib )
        ans =
             4

• Newton Lab
  • Derivative function
    • Calculate difference quotient from limit definition with a small but not 0 h
    • Numerically better, use “symmetric difference quotient”
      
    • Several ways to come up with h
      • Use a small value relative to the x values you expect, e.g., h = 10^-10 aka 1e-10 in Matlab
      • Better: calculate a value around 10^-10 times x
      • But the problem with that calculation is that it produces 0 if x = 0
        • So best is to use an if statement to give h a small constant value if x is close to 0, and to calculate h from x if x is not close to 0
• Next
  • Lab day for Newton
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