For Loops

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• Misc
  • CIT hiring a student web assistant for spring
    • Help develop/maintain college web pages; programming not required but possible if interested
    • Contact Paul Jackson (jackson@geneseo.edu) to apply or for more info
• Questions?
• Derivative Function
  • Solution to Newton’s method extra credit problem
  • e.g., derivative(f) = f′
  • Key idea is for derivative to create an anonymous function from f and return that anonymous function
    

    function fprime = derivative( f )
    %DERIVATIVE numerically differentiates a given function.
    % Works by creating a function that takes an x value at which to calculate
    % the derivative, and that calculates a symmetric difference quotient of
    % the original function around that x value.
    
    tolerance = 1e-10;
    fprime = @(x)( f( x + tolerance ) - f( x - tolerance ) ) / ( 2 * tolerance );
    
    end

  • Call the result on an x value to get value of derivative at that x
    

    >> f = @(x) x^2
    f = 
        @(x)x^2
    >> fprime = derivative( f )
    fprime = 
        @(x)(f(x+tolerance)-f(x-tolerance))/(2*tolerance)
    >> fprime( 3 )
    ans =
        6.0000
    >> fprime( -3 )
    ans =
       -6.0000
    >> fprime( 1.4 )
    ans =
        2.8000
    >> sinPrime = derivative( @sin )
    sinPrime = 
        @(x)(f(x+tolerance)-f(x-tolerance))/(2*tolerance)
    >> sinPrime( 0 )
    ans =
         1

• For (and Other) Loops
  • Summary of sections 12.5 - 12.7
    • for loop repeats fixed number of times
      

      for var = first : last
          body
      end

    • Generally, for iterates through a vector
      

      for var = vector
         body
      end

    • Like while but while repeats until condition (doesn’t) hold
    • Nested loops?
      • One loop in body of another
      • Inner and outer loops
    • tic starts timer, toc stops timer
      • See how long a script takes
      • Demonstrated how pre-allocating arrays can improve time over extending bit by bit
      • In general, array operations will be faster than loops
  • Examples
    

    >> fprintf( 'hello world\n' );
    hello world
    >> %% print 'hello world' 100 times
    >> for i = 1 : 100
    >>     fprintf( 'hello world\n' );
    >> end
    hello world
    hello world
    …
    hello world
    
    >> %% Sum integers from 1 to 100
    >> % Expected result:
    >> 1000 * 1001 / 2
    ans =
          500500
    >> % With "for"
    >> total = 0;
    >> for i = 1 : 1000
    >>     total = total + i;
    >> end
    >> total
    total =
          500500
    
    >> %% Sum without loop
    >> sum( 1 : 1000 )
    ans =
          500500
    
    >> %% Add all the numbers in vector v
    >> v = rand( 1, 10 )
    >> total = 0;
    >> for i = v
    >>     total = total + i;
    >> end
    >> fprintf( 'Computed sum = %f, actual = %f\n', total, sum(v) );
    v =
      Columns 1 through 6
        0.8147    0.9058    0.1270    0.9134    0.6324    0.0975
      Columns 7 through 10
        0.2785    0.5469    0.9575    0.9649
    Computed sum = 6.238553, actual = 6.238553
    
    >> %% Add all the numbers in vector v with indexing
    >> v = rand( 1, 10 )
    >> total = 0;
    >> for i = 1 : 10
    >>     total = total + v(i);
    >> end
    >> fprintf( 'Computed sum = %f, actual = %f\n', total, sum(v) );
    v =
      Columns 1 through 6
        0.1576    0.9706    0.9572    0.4854    0.8003    0.1419
      Columns 7 through 10
        0.4218    0.9157    0.7922    0.9595
    Computed sum = 6.602112, actual = 6.602112
    
    >> %% Add all elements of a matrix
    >> m = rand( 4, 2 )
    >> [ rows columns ] = size( m );
    >> total = 0;
    >> for r = 1 : rows
    >>     for c = 1 : columns
    >>         total = total + m(r,c);
    >>     end
    >> end
    >> fprintf( 'Computed sum = %f, actual = %f\n', total, sum(sum(m)) );
    m =
        0.6557    0.6787
        0.0357    0.7577
        0.8491    0.7431
        0.9340    0.3922
    Computed sum = 5.046410, actual = 5.046410

• Next
  • Pseudocode for integration
  • Come to class Monday with pseudocode ready to discuss

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