MATLAB CHAPTER 2 Numeric, Cell, and Structure Arrays

1
MATLAB ??CHAPTER 2 Numeric, Cell, and
Structure Arrays

2
Arrays

• Arrays Collection of numbers
• the basic building block in MATLAB
• addition, subtraction, multiplication, division,
  and exponentiation
• polynomial algebra and root
• Available classes of arrays in MATLAB 7
• numeric arrays contains only numeric values
• cell arrays access data by its location
• structure arrays access data by name

3
Arrays

• Cartesian coordinates x, y, and z
• unit vector i, j, k
• express the vector p xi yj zk
• e.g.
• p 5i 7j 2k
• in MATLAB write in a specific order,
• separate with a space,
• identify the group with brackets
• ? 5 7 2
• vector
• row vector 5 7 2
• column vector

4
Arrays

• Creating Vectors in MATLAB
• MATLAB displays row vectors horizontally and
  column vectors vertically.
• Create a row vector space or commas separate
  elements
• g 3 7 9 3,7,9
• Create a column vector semicolon or Enter
  separate elements, you can use transpose
• g 379 3,7,9 3 (Enter)
• 7 (Enter)
• 9
• Create vectors by appending
• r 2, 4, 20, w 9, -6, 3
• u r, w 2, 4, 20, 9, -6, 3

5
Arrays

• Creating Vectors in MATLAB
• Generate a large vector of regularly spaced
  elements using colon operator ()
• x mqn
• m the first value
• q the increment (default 1)
• n the last value lt n
• x 028 0, 2, 4, 6, 8 x 027 0,
  2, 4, 6
• y -32 -3, -2, -1, 0, 1, 2
• u 10-24 10, 8, 6, 4
• The linspace command, logspace command
• linspace(x1, x2, n) n is number of points
  between x1 and x2
• linspace(5,8,31) 50.18
• logspace(a, b, n) n is number of points between
  10a and 10b
• logspace(-1,1,4) 0.1000, 0.4642, 2.1544,
  10.000

6
Arrays

• Two-Dimensional Arrays
• An array can have multiple rows, multiple
  columns, or both
• called a matrix
• .
• Creating Matrices
• Space or commas separate elements in different
  columns
• Semicolons separate elements in different rows
• You can also create a matrix from row or column
  vectors
• ltexample (a 1,3,5, b7,9,11) gt

7
Arrays

• Array Addressing
• The row number is always listed first
• The colon operator selects individual elements,
  rows, columns, or subarrays of arrays
• v( ) represents all the row or column elements
  of the vector v.
• v(2 5) represents the second through fifth
  elements
• A( , 3) denotes all the elements in the third
  column of the matrix A

C B(23, 13)
The general indexes of two dimensional array
8
Arrays

• The empty or null array
• contains no elements,
• Rows and columns can be deleted by setting the
  selected row or column equal to the null array.
• A(3, ) deletes the third row in A
• A(, 24) deletes the second through
  fourth columns In A
• A(1 4, ) deletes the first and fourth
  rows of A
• lt Other examples gt

A(1,5) 3
B A(,5-11)
9
Arrays

• Some Useful Array Functions

10
Arrays

• Magnitude, Length, and Absolute Value of a Vector
• length the number of elements in the vector.
• magnitude
• absolute value The absolute value of a vector x
  is a vector whose elements are the absolute
  values of the elements of x.
• ltexamplegt
• x 2, -4, 5
• length 3, magnitude 6.7082, absolute value
  2, 4, 5
• The Array Editor
• A graphical interface for working with arrays.
• To open the Array Editor from the Workspace
  Browser, double-click on the variable you want to
  open.

11
Multidimensional Arrays

• MATLAB supports multidimensional arrays
• The first two dimensions are the row and column,
  as with a matrix.
• The higher dimensions are called pages.
• ltexamplegt
• Want to create a three dimensional array whose
  first page is
• and whose second page is
• gtgtA 4, 6, 15, 8, 03, 9, 2
• gtgtA( , , 2) 6, 2, 90, 3, 14, 7, 5

12
Multidimensional Arrays

• cat command

C cat(3, A, B) produces a three-dimensional
array
ltexamplegt
gtgt A 1 23 4 gtgt B 5 67 8 gtgt C
cat(3, A, B) concatenating the arrays
A, B along the dimension three. C(,,1)
1 2 3 4 C(,,2)
5 6 7 8 gtgt d
size(c) d 2 2 2
13
Element-by-Element Operations

• Element-by-element operations

14
Element-by-Element Operations
ltexample1gt
ltexample2gt
gtgtx 00.015 gtgty sin(x2) ??? Error using
gt Matrix must be square. gtgtysin(x.2) gtgtplo
t(x,y)
gtgt x 1 2 3 gtgt y 4 5 6 gtgt x.y ans
1 32 729 gtgty.2 ans 16 25
36 gtgt2.x y ans 2 4 8 16 32 64 cf)
gt 21 2 3 4 5 6 21 22 23 24 25 26
15
Matrix Operations

• Matrix Multiplication
• Use the operator to perform matrix
  multiplication in MATLAB
• ltexamplegt
• gtgtA 6, -2,10,34,7
• gtgtB 9,8-5,12
• gtgtAB
• ans
• 64 24
• 75 116
• 1 116
• Special Matrices

16
Matrix Operations

• Matrix Division
• Right and left operators, / and \
• Chapter 6 covers matrix division and matrix
  inverse.
• Matrix Exponentiation
• must be a square matrix
• to find A2, type A2
• Special products

17
Polynomial Operations Using Arrays

• Type help polyfun for more information
• We will use following notation
• Polynomial Addition and Subtrction
• add the arrays that describe their coefficients
• if the polynomials are of different degrees, add
  zeros to the coefficient array of the
  leower-degree polynomial.
• ltexamplegt
• coefficient array is f9, -5, 3, 7 and g 6,
  -1, 2
• g 0 g 0, 6, -1, 2
• h fg 9, 1, 2, 9

18
Polynomial Operations Using Arrays

• Polynomial Multiplication and Division
• Multiply polynomials use conv function (it
  stands for convolve)
• synthetic division use deconv function (it
  stands for deconvolve)
• Polynomial functions

gtgtf 9, -5, 3, 7 gtgtg 6, -1, 2 gtgtproduct
conv(f, g) product 54 -39 41 29
-1 14 gtgtquotient, remainder
deconv(f,g) quotient 1.5 -0.5833
remainder 0 0 -0.5833 8.1667
19
Polynomial Operations Using Arrays

• Plotting Polynomials
• The polyval(a,x) function is very useful for
  poltting polynomials.
• ltexamplegt
• plot the polynomial

20
Cell Arrays

• Cell array an array in which each element is a
  bin, or cell which can contain an array.
• examples
• B 2, 4, 6,-93, 5 72, 10
• H 2, 4, 8, 6, -8, 3 26, 9, 2, 5
  1, 4, 5, 7, 5, 2
• J H1, 1 H1, 2 H(2, 2

21
Cell Arrays

• Cell array functions

22
Cell Arrays

• Cell Array Function Examples

23
Structure Arrays

• Structure arrays composed of structures.
• enables you to store dissimilar arrays together
• accessed using namefields
• Creating Structures
• using assignment statements
• using the struct function
• dot notation (.) to specify and to access the
  fields
• ltexamplegt

student.name John Smith student.SSN
392-77-1786 student.email smithj_at_myschool.ed
u student.tests 67, 75, 84 student(2).name
Mary Jones student(2).SSN
431-56-9832 student(2).email
jonsm_at_myschool.edu student(2).tests 84, 78,
93
24
Structure Arrays

• Structure functions

25
Structure Arrays

• Structure Function Examples