User-Defined Functions

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• Misc
  • Write-ups for colloquia “due” any time before end of semester
• Questions?
• User-Defined Functions
  • Section 4.3
    • Create custom function via “new function” or “new script”
    • Save as “.m” with same name as function
    • Use user-defined functions to avoid writing same code over and over
    • Syntax
      

      function [ out1, out2, … ] = functionName( in1, in2, … )
      % help comment(s)
      … body …
      end

    • Remember = in function definition
    • Can create own help comments at beginning of function
    • Local variables
  • Examples
    • Volume of a cylinder (arguments = radius, height; output = volume)
      • Volume = πr²h
        

        function [ volume ] = volumeCylinder( radius, height )
        %VOLUMECYLINDER Compute volume of cylinder from radius and height
        
        volume = pi * radius^2 * height; 
        
        end

      • …and using it…
        

        volumeCylinder( 1, 2 )
        ans =
            6.2832
        help volumeCylinder
         volumeCylinder Compute volume of cylinder from radius and height

    • Rational-number addition (arguments = numerator and denominator of 2 rationals; output = numerator and denominator of sum)
      • a/b + c/d
      • Algorithm
        • Find common denominator as bd
        • Scale a to ad
        • Scale c to cb
        • Add scaled numerators to make n
        • Result is n/gcd(n,bd) and bd/gcd(n,bd)
      • Code that implements this algorithm
        

        function [ n, d ] = add( a, b, c, d )
        %ADD  Add fractions a/b plus c/d
        %   Result is fraction n/d in reduced form
        
        common = b * d;
        scaledA = a * d;
        scaledC = c * b;
        numerator = scaledA + scaledC;
        
        n = numerator / gcd(numerator,b*d);
        d = b * d / gcd(numerator,b*d);
        
        end

      • And some uses
        

        add( 1, 3, 22, 7 )
        ans =
            73
        [n,d] = add( 1, 3, 22, 7 )
        n =
            73
        d =
            21

• Next
  • Vectors
  • Read sections 5.1 - 5.4 in textbook
  • Optionally, second part (from 2:45 on) of “Variables and Simple Arrays” video at http://www.see.ed.ac.uk/teaching/courses/matlab/unit01/variables-arrays.shtml

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