Basics of MATLAB (2)

1
Basics of MATLAB (2)
2
Topics

• Do some more matrix operations
• Differentiation and integration
• Plotting graphs
• Some review questions at the end of the class

3
Matrix Operations - Colon Operator

• Try typing in 110
• How about 50-420?
• Subscript expressions involving colons
• A(1k, j) first k elements of the jth column of
  A
• A(k,1j) first j elements of the kth row of A

4
Matrix Operations - Colon Operator

• A(2,24) and A(14,4)
• A(14,4) A(,4) A(,end)
• Colon by itself refers to all the elements in a
  row or column of a matrix
• The keyword end refers to the last row or column
• A(,end) Elements in the last column of A
• Exercise 7

5
Exercise 7

• gtgt A16 3 2 135 10 11 89 6 7 124 5 4 1
• A
• 16 3 2 13
• 5 10 11 8
• 9 6 7 12
• 4 5 4 1
• gtgt Tdiag(A) A(,1) A(2,)'
• T
• 16 16 5
• 10 5 10
• 7 9 11
• 1 4 8

6
Matrix Operations Deleting Rows and Columns

• Delete rows and columns from a matrix using just
  a pair of square brackets
• X A Creating new X matrix
• X(,2) Deleting the 2nd column of X
• will result in
• X 16 2 13
• 5 11 8
• 9 7 12
• 4 14 1 Exercise 8

Before, X
7
Exercise 8

• gtgt A(,3)
• A
• 16 3 13
• 5 10 8
• 9 6 12
• 4 5 1
• gtgt A(2,)
• A
• 16 3 13
• 9 6 12
• 4 5 1
• 
  A(,3) , A(2,)

8
Relational Operations

• lt less than
• lt less than or equal
• gt greater than
• gt greater than or equal
• equal
• not equal

• Ex)
• x1 5 3 7, y0 2 8 7
• kxlty results in k?
• gives a vector with 1 where the relation is true
  and 0 otherwise

9
Differentiation

• Using Symbolic Math Toolbox software to take
  derivatives, (ex f x2 4x 3)
• any variable to be used should be introduced with
  a syms command (creating symbolic expressions)
• syms x
• second, create a new var.(f) that is a function
  of x
• f x2 4x 3
• third, take derivative with the command diff
• diff(f) differentiates f with respect to x

10
Differentiation

• To take the second derivative of f, enter
• diff(f,2)
• Derivatives with several variables, exsin(st)
• Create a symbolic expression
• syms s t
• Creat a function
• gsin(st)
• Take partial derivative wrt t
• diff(g,t)

Exercise 1.
11
Exercise 1.

• syms x
• fexp(x23)/(x3-x3)
• diff(f,x)
• syms x y
• g(x2xy-1)/(y3x3)
• diff(g,y)

12
Exercise 1.

• syms x
• fexp(x23)/(x3-x3)
• diff(f,x)
• (2xexp(x2 3))/(x3 - x 3) - (exp(x2
  3)(3x2 - 1))/(x3 - x 3)2
• syms x y
• g(x2xy-1)/(y3x3)
• diff(g,y)
• x/(y3 x 3) - (3y2(x2 yx - 1))/(y3
  x 3)2

13
Integration

• INT(S,v) is the indefinite integral of S with
  respect to v.
• INT(S,v,a,b) is the definite integral of S with
  respect to v from a to b.

14
Integration

• Exercise 2.

15
Exercise 2

• int((x2x)/(x3),x)
• ans
• int((x2-x1)/(x3),x,0,10)
• ans

16
Exercise 2

• int((x2x)/(x3),x)
• ans
• 6log(x 3) - 2x x2/2
• int((x2-x1)/(x3),x,0,10)
• ans
• 13log(13/3) 10

17
Plotting - example

• Plotting x vs. y,
• where xt, yet (tintegers between 0 and 40)
• t040
• xtyexp(t)
• plot(x,y)

18
Plotting

• Labels, title, legend, and other text objects
  ex) x 0.120 yexp(0.1x) plot (x,y)
• xlabel(time)
• ylabel(response)
• title(time response)
• Saving as a file
• print G\Suhyun\Classes\MATLAB\Programming\a.eps
  -deps
• In jpeg format a.jpg djpeg
• In bmp format a.bmp -dbitmap

Exercise 1.
19
Exercise 1.

• xlinspace(0,2pi,100)
• plot(x,sin(x))
• xlable(x), ylabel(sin(x))
• title(Plot created by Me)

20
Plotting

• Basic 2-D plots (help graph2d)
• plot (xvalues, yvalues, style-option)
• Style option spcifies color, line style, and
  point-marker style

Color style-option Color style-option Line style-option Line style-option Marker style-option Marker style-option
y yellow - solid plus sign
m magenta -- dashed o circle
c cyan dotted asterisk
r red -. dash-dot x x-mark
g green . point
b blue up triangle
w white s square
k black d diamond
21
Plotting

• default blue solid line
• plot(x,y,color line or marker style)
• Examples
• plot(x,y,r) plots y vs. x with a red solid
  line
• plot(x,y,b--) plots y vs. x with a blue dashed
  line
• plot(x,y,) plots y vs. x as unconnected
  points marked by
• Exercise 2.

22
Plotting - fplot

• fplot (function, xmin xmax)
• It takes the function of a single variable and
  the limits of the axes as the input and produces
  a plot of the function
• ex) plot exercise 1 using fplot
• fplot('sin(x)',0 2pi)

23
Overlay Plots

• With two sets of data
• (x1,y1) and (x2,y2) xi and yi are column vectors
• plot(x1,y1,,x2,y2,)
• plots (x1,y1) with a sign, (x2,y2) with a
  dotted line
• gtext(label)
• writes the label at a location clicked with the
  mouse in the graphic window after entering the
  command

Exercises 3,4
24
Data

• 2000 Census
• 4915 obs.
• Census Block Group
• Variables
• Housing Value
• Income
• Unemployment
• Education

25
Exercises 3

• gtgthvdata00(,1)
• gtgt incomedata00(,2)
• gtgt unempdata00(,3)
• gtgt plot(income, hv,'.')
• gtgt xlabel('income')
• gtgt ylabel('housing value')
• gtgt title('housing value on income')

26
Exercises 3
27
Exercise 4

• gtgtplot(hv,edu,'g.',hv,unemp,'')
• gtgt gtext('Education')
• gtgt gtext('Unemployment')
• gtgt xlabel('Housing value')

28
Exercise 4
Plotting tools (plottools)
29
Plotting contour and 3-D

• ezcontour contour plots
• ex) zinline('x2y') ezcontour(z,0,10,0,10)
• ezcontourf filled contours
• ezsurf surface plots in 3-D
• ex) zinline('x2y') ezsurf(z,0,10,0,10)
• (rotation function)
• Exercise 5.

30
Exercise 5

• zinline('xy1/2') ezcontour(z,0,20,0,15)

31
Review Questions

• exp(pi/2i)
• exp(pi/2i)

32
Review Questions

• gtgt A7 -3 5 1-1 2 3 94 5 7 42 6 -2 8
• A
• 7 -3 5 1
• -1 2 3 9
• 4 5 7 4
• 2 6 -2 8
• gtgt A1sort(A,'descend')
• A1
• 7 6 7 9
• 4 5 5 8
• 2 2 3 4
• -1 -3 -2 1

33
Review Questions

• Fxyzinline('(x3y-exp(yz))/(3xz2)','x','y','
  z')
• Fxyz
• Inline function
• Fxyz(x,y,z) (x3y-exp(yz))/(3xz2)
• gtgt Fxyz(2,3,-2)
• ans
• 0.9999