Mapping Operations on Vectors

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• Misc
  • Colloquium this afternoon (2:45, Newton 204)
• Questions?
• Vector Operations
  • Sections 5.5 - 5.6
    • “Element-wise” calculations apply element-by-element to vectors (or several vectors)
    • aka operations that map over vector(s)
    • Dimensions have to be equal (e.g., both 1x5)
      • But multiplication of matrices has different compatibility rules, e.g., 2×3 times 3×2 OK
    • Dot operations, e.g., .*, .^, ./
    • Can do element-wise operations between arrays and scalars
    • Functions on scalars can also be used element-wise on vectors
      • e.g., abs gives absolute value of all numbers in vector
  • Examples
    • Given the vectors [1 2 3 4] and [20 30 40 10]…
      • Calculate their sum
        

        >> v1 = [ 1 2 3 4 ];
        >> v2 = [ 20 30 40 10 ];
        >> sum = v1 + v2
        sum =
            21    32    43    14

      • Divide the sum by 2 (thus calculating the average of each pair of numbers)
        

        >> sum / 2
        ans =
           10.5000   16.0000   21.5000    7.0000
        >> sum ./ 2
        ans =
           10.5000   16.0000   21.5000    7.0000

      • Calculate the geometric mean (square root of product) of each pair
        

        >> products = v1 * v2
        {Error using *
        Inner matrix dimensions must agree.} 
        >> products = v1 .* v2
        products =
            20    60   120    40
        >> sqrt( products )
        ans =
            4.4721    7.7460   10.9545    6.3246
        >> products ^ 0.5
        {Error using ^
        Inputs must be a scalar and a square matrix.
        To compute elementwise POWER, use POWER (.^) instead.} 
        >> products .^ 0.5
        ans =
            4.4721    7.7460   10.9545    6.3246
        >> nthroot( products, 2 )
        ans =
            4.4721    7.7460   10.9545    6.3246

    • How would you round each number in a vector to the nearest integer?
      

      >> numbers = [ 3.6 9.1 5.34 ]
      numbers =
          3.6000    9.1000    5.3400
      >> round( numbers )
      ans =
           4     9     5

    • Modify the volumeCylinder function from Sept. 18 to work on vectors
      

      >> volumeCylinder( [1 2], [2 0.5] )
      {Error using ^
      Inputs must be a scalar and a square matrix.
      To compute elementwise POWER, use POWER (.^) instead.
      Error in volumeCylinder line 4
      volume = pi * radius^2 * height; }
      % Change “volumeCylinder.m” file as follows:
      function [ volume ] = volumeCylinder( radius, height )
      %VOLUMECYLINDER Compute volume of one or more cylinders from radii and
      %heights
      volume = pi * radius.^2 .* height; 
      end
      >> volumeCylinder( [1 2], [2 0.5] )
      ans =
          6.2832    6.2832

• Vector Lab
  • Radian vs degree sine function?
    

    >> sin( pi/2 )
    ans =
         1
    >> sind( 90 )
    ans =
         1

• Next
  • Advanced features of vectors
  • Read sections 5.7 - 5.9 in textbook

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