Relations, Databases, and Cell Arrays

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• Questions?
• Relations
  • Summary of videos
    • Set of ordered pairs - binary relation
    • Or ordered triples or n-tuples - n-ary relations
    • But only one size of tuple per set
    • Come from cross product of sets
      • A × B
      • { 1, 2 } × { a, b, c } = { (1,a), (1,b), (1,c), (2,a), (2,b), (2,c) }
  • Example
    • Amazon book = ( title, author, price, star rating, # reviews, # purchases, cover image, … )
    • aka a database—relations are a very good model for computer databases
    • Terminology:
      
  • Lab
    • Handout
    • Loading variables into Matlab from a file
      

      >> load( 'database.mat' );
      >> mathContributions
      mathContributions = 
          'Isaac Newton'         'Calculus'               [1666]
          'Gottfried Leibniz'    'Calculus'               [1675]
          'Kurt Goedel'          'Incompleteness'         [1931]
          'Alan Turing'          'Computability'          [1936]
          'John von Neumann'     'von Neumann Algebra'    [1930]
      >> institutions
      institutions = 
          'Albert Einstein'     'Institute for Ad...'    [1933]    [1955]
          'Albert Einstein'     'Humboldt University'    [1914]    [1932]
          'Isaac Newton'        'Trinity College/...'    [1667]    [1701]
          'John von Neumann'    'Institute for Ad...'    [1933]    [1957]

    • How to represent a relation/database with Matlab data isn’t as simple as it might seem
    • A matrix is the obvious choice, but regular matrices don’t work with data of different types
      • “Type” reflects idea of different kinds of value and things you do with values, e.g., strings vs numbers
        

        >> M = [ 'Isaac Newton', 1667 ]
        M =
        Isaac Newton¿

    • Matlab cell arrays exist to solve this problem, provide arrays of mixed types
      

      >> C = { 'Isaac Newton', 1667 }
      C = 
          'Isaac Newton'    [1667]
      >> C{1}  % content indexing
      ans =
      Isaac Newton
      >> C(1)  % cell indexing
      ans = 
          'Isaac Newton'
      >> C(2)
      ans = 
          [1667]
      >> C{2}
      ans =
              1667
      % Cell arrays generally support the same kinds of indexing and concatenation
      % operations regular matrices do
      >> C2 = { 'abc', 1; 'def', 7 }
      C2 = 
          'abc'    [1]
          'def'    [7]
      >> C2(:,2)
      ans = 
          [1]
          [7]
      >> C2 = [ C2; {'abcd', 17} ]
      C2 = 
          'abc'     [ 1]
          'def'     [ 7]
          'abcd'    [17]

• Next
  • Cell arrays
  • Read sections 15.2 through 15.4 in textbook

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