Vectors, Part 2

Return to List of Lectures

Previous Lecture

• Questions?
  • clc is (probably) safe in a diary. Like many points about programming, this is a good one to just try it and see, using a diary you don’t care about.
• Logical Values and Vectors
  • Sections 1.6 and 2.5
    • Logical operations
      • >, ==, <, >=, ~=, etc.
      • || (or), && (and)
      • xor(a,b) = true if 1 argument is true
      • any, all ask if any or all elements of vector or matrix are true
      • isequal asks if two whole matrices equal, considering dimensions
        • Result is 1 for true, 0 for false
          

          m1 = [1 2 3; 4 5 6]
          m1 =
               1     2     3
               4     5     6
          m2 = m1'
          m2 =
               1     4
               2     5
               3     6
          m1 == m2
          {Error using  == 
          Matrix dimensions must agree.
          } 
          isequal( m1, m2 )
          ans =
               0

      • Comparisons on vectors find all places where comparison holds
        • Results can be used as numbers, e.g., to use sum to count number of places comparison holds
          

          v1 = [1 2 3 4 5]
          v1 =
               1     2     3     4     5
          v1 > 2.5
          ans =
               0     0     1     1     1
          sum( v1 > 2.5 )
          ans =
               3

      • Rotate/transpose matrices
  • Lesson 2
    • Picking out grades by category
      • Algorithm
        • Input: grade and category vectors G and C, desired category k
        • Find A, all occurrences of k in C as logical vector w/ true wherever C = k and False elsewhere
        • Set B = G_n for each n such that A_n = 1
        • Output: B, all grades with category k
      • Example
        • Inputs:
          • G = 10 10 100 8 9 90 10 5
          • C = 1 1 2 1 1 2 3 1
          • k = 2
          • A = 0 0 1 0 0 1 0 0
          • B = 100 90
      • Logical indexing
        

        i = v1 > 2.5
        i =
             0     0     1     1     1
        v1( i )
        ans =
        
             3     4     5
        v1
        v1 =
             1     2     3     4     5

• Next
  • Elementwise multiplication, exponentiation, division
  • Section 2.3
  • Optionally Edinburgh video on “The Dot Operator” at http://www.see.ed.ac.uk/teaching/courses/matlab/unit01/dot-operator.shtml

Next Lecture