1. Vectors Lecture 11: Supporting Material Dr Kathryn Merrick Tuesday 7 th April, 2009

3. Overview What is a vector? Creating vectors Accessing vectors Manipulating data in vectors Implicit vectorisation Reference: text book Ch 5

4. A Motivating Experiment:

5. Creating Vectors

6. Listing Elements >> my_vector = [1 4 30 2 6]; or >> my_vector = [1, 4, 30, 2, 6];

7. >> my_vector = [1:10]; or >> my_vector = [1:0.1:10]; or >> my_vector = 1:0.1:10; Using the Colon Operator :

8. Using a Built-in Function >> x = 0:0.1:2*pi; >> my_vector = sin(x); Or >> x = [0:10]; >> my_vector = x*5;

9. Using linspace or logspace linspace(x, y) generates 100 equally spaced points between x and y >> my_vector = linspace(1, 100) linspace(x, y, n) generates n equally spaced points between x and y >> my_vector = linspace(1, 100, 10)

10. Column Vectors >> a = [1; 2; 3; 4; 5] >> a = [1 2 3 4 5]

11. Transposing a Row Vector >> a = [1 2 3 4 5] a = 1 2 3 4 5 >> b = a' b = 1 2 3 4 5

12. Demo 1: Accessing Data in Vectors

13. Accessing One or More Values Accessing Individual Values >> value = my_vector(5); Accessing Multiple Values >> values = my_vector([5 10 15]);

14. Demo 2: Manipulating Vectors

15. Manipulating Vectors: Basic Maths

16. Scalar-Array Maths Example >> x = [0:10]; y = x + 5; Or >> x = [0:10]; y = x * 5;

17. Basic Array Maths Addition >> a = [2 3]; >> b = [4 5]; >> c = a + b c = 6 8 Subtraction >> a = [2 3]; >> b = [4 5]; >> c = a - b c = -2 -2

18. Basic Array Maths Multiplication >> a = [2 3]; >> b = [4 5]; >> c = a.* b c = 8 15 Division >> a = [2 3]; >> b = [4 5]; >> c = a./ b c = 0.5 0.6 Power >> a = [2 3]; >> b = [4 5]; >> c = a.^ b c = 16 243

19. Summary After today’s lecture you should be able to: Create and access data in vectors Manipulate data in vectors using loops or implicit vectorisation