CMPS 1371 Introduction to Computing for Engineers

1. CMPS 1371Introduction to Computing for Engineers VECTORS

2. ARRAYS • The real strength of Matlab is in matrix manipulations • Arrays are homogeneous collection of things. • All are the same • Are indexable

3. VECTORS • Our simplest array type is called a vector. • Simple example: ODDS = [ 1 3 5 7 9 11 13 15] • To index a vector, need to know the position within the vector: • First element has position 1 (NOT ZERO!) • ODDS(1) = 1 • Last element: either the length of the array or the special label ‘end’ • ODDS(8) = 15 • ODDS(end) = 15

4. Create a Vector To create a row vector, enclose a list of values in brackets

5. Create a Vector You may use either a space or a comma as a “delimiter” in a row vector

6. Create a Vector Use a semicolon as a delimiter to create a new row

7. Shortcuts • While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command  b= 1:5 or the command b = [1:5] both return a row matrix 

8. Increments The default increment is 1, but if you want to use a different increment put it between the first and final values

9. To calculate spacing • Use linspace number of elements in the array Final value in the array Initial value in the array

10. Basic Functions • Some basic functions: • Consider temp = [1 2 3 4 5] • length(temp) =5 • sum(temp) =15 • mean(temp) =3 • median(temp) =3

11. Calculations • Matrices can be used in many calculations with scalars • There is no confusion when we perform addition and subtraction • Multiplication and division are a little different  • In matrix mathematics the multiplication operator (*) has a very specific meaning regarding Matrix multiplication • We will use (.*) for matrix multiplication • We can use (*) for scalar multiplication

12. Adding Vectors

13. Adding Vectors Addition between arrays is performed on corresponding elements

14. Multiplying Vectors Multiplication between arrays is performed on corresponding elements if the .* operator is used MATLAB interprets * to mean matrix multiplication. The arrays a and b are not the correct size for matrix multiplication in this example

15. Array Operations • Array multiplication .* • Array division ./ • Array exponentiation .^ In each case the size of the arrays must match

16. Changing the Vector • Easy to add elements to the array • Temp = [1 2 3 4]; • Temp(5) = 8;  Temp now has 5 elements 1, 2, 3, 4, 8 • Can also concatenate • fred = [[1,2,3,4] [3,4,5,]] • fred = [fred 4 5 6 7] • Can also remove elements by using the "Null" vector • A = [ 1 2 3 4 5 6 7 ] • A(2) = [ ] – now what is A