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MATLAB CHAPTER 2 Numeric, Cell, and Structure Arrays

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Title: 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
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