For Loops

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• Questions?
• For Loops
  • Sections 13.4 - 13.6
    • Replacements for some while loops
      

      i = 0
      while i <= 99
          ...
      end

      • Becomes
        

        for i = 0:1:99
            ...
        end

    • Nested loops = loops within loops
      • Can use either while or for
    • Using loops with arrays
      • Create array before loop to make code run faster
      • But using Matlab array operations instead of loops when possible makes code easier to understand (and faster)
  • Examples
    

    >> % print integers from 1 through 20
    >> for i = 1:20
    >> i
    >> end
    i =
         1
    i =
         2
    ...
    i =
        20
    >> % What happens if you try to increment the loop variable yourself?
    >> % (your increment happens but gets over-written by loop's update)
    >> for i = 1:20
    >> i
    >> i = i + 1
    >> end
    i =
         1
    i =
         2
    i =
         2
    i =
         3
    ...
    i =
        20
    i =
        21
    >> % Print "hello world" 10 times
    >> for i = 1:10
    >> fprintf( 'Hello World\n' );
    >> end
    Hello World
    Hello World
    ...
    Hello World
    >> % add up all the integers from 1 to 20
    >> % Algorithm: for each integer, i, between 1 and 20, add i to
    >> % running total
    >> a = 0;
    >> for i = 1:20
    >> a = a + i;
    >> end
    >> a
    a =
       210
    >> % But you can also do this with Matlab's builtin sum function
    >> sum( 1:20 )
    ans =
       210
    >> % Add all elements of vector v
    >> v = rand( 1, 4 )
    v =
        0.8147    0.9058    0.1270    0.9134
    >> a = 0;
    >> for i = 1:4
    >> a = a + v(i);
    >> end
    >> a
    a =
        2.7609
    >> % or...
    >> % (because for loops really step through any vector)
    >> a = 0;
    >> for x = v
    >> a = a + x;
    >> end
    >> a
    a =
        2.7609

    • Modify book’s multiplication table program to get table size from user
      

      n = input( 'How big do you want your table? ' );
      for x = 1 : n
          for y = 1 : n
              fprintf( '%d ', x * y );
          end
          fprintf( '
      ' );
      end

      • Running original script, and then modified one…
        

        >> % Original:
        >> mtable
        1 2 3 4 5 6 7 8 9 10 11 12 
        2 4 6 8 10 12 14 16 18 20 22 24 
        3 6 9 12 15 18 21 24 27 30 33 36 
        4 8 12 16 20 24 28 32 36 40 44 48 
        5 10 15 20 25 30 35 40 45 50 55 60 
        6 12 18 24 30 36 42 48 54 60 66 72 
        7 14 21 28 35 42 49 56 63 70 77 84 
        8 16 24 32 40 48 56 64 72 80 88 96 
        9 18 27 36 45 54 63 72 81 90 99 108 
        10 20 30 40 50 60 70 80 90 100 110 120 
        11 22 33 44 55 66 77 88 99 110 121 132 
        12 24 36 48 60 72 84 96 108 120 132 144 
        >> % Modifed:
        >> mtable
        How big do you want your table? 1
        1 
        >> mtable
        How big do you want your table? 5
        1 2 3 4 5 
        2 4 6 8 10 
        3 6 9 12 15 
        4 8 12 16 20 
        5 10 15 20 25 

• Animation Project
  • Handout
• Integration Lab
  • Handout
• Next
  • Integration via Riemann sums and the trapezoid rule
  • Watch videos…
    • Simple Riemann Approximation Using Rectangles at https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/simple-riemann-approximation-using-rectangles
    • Generalizing a Left Riemann Sum with Equally Spaced Rectangles at https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles
    • Trapezoidal Approximation of Area under Curve at https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/trapezoidal-approximation-of-area-under-curve

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