Introduction to Matlab

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Introduction to Matlab
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Desktop Tools (Matlab v6)

• Command Window
• type commands
• Workspace
• view program variables
• clear to clear
• double click on a variable to see it in the Array
  Editor
• Command History
• view past commands
• save a whole session using diary
• Launch Pad
• access tools, demos and documentation

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Matlab Files (.m)

• Use predefined functions or write your own
  functions
• Reside on the current directory or the search
  path
• add with File/Set Path
• Use the Editor/Debugger to edit, run

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Matrices

• a vector x 1 2 5 1
• x
• 1 2 5 1
• a matrix x 1 2 3 5 1 4 3 2 -1
• x
• 1 2 3
• 5 1 4
• 3 2 -1
• transpose y x. y
• 1
• 2
• 5
• 1

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Matrices

• x(i,j) subscription
• whole row
• whole column

yx(2,3) y 4 yx(3,) y 3 2
-1 yx(,2) y 2 1 2
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Operators (arithmetic)

• addition
• - subtraction
• multiplication
• / division
• power
• complex conjugate transpose

. element-by-element mult ./ element-by-element
div . element-by-element power . transpose
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Operators (relational, logical)

• equal
• not equal
• lt less than
• lt less than or equal
• gt greater than
• gt greater than or equal
• AND
• OR
• NOT

• pi 3.14159265
• j imaginary unit,
• i same as j

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Generating Vectors from functions

• x zeros(1,3)
• x
• 0 0 0
• x ones(1,3)
• x
• 1 1 1
• x rand(1,3)
• x
• 0.9501 0.2311 0.6068

• zeros(M,N) MxN matrix of zeros
• ones(M,N) MxN matrix of ones
• rand(M,N) MxN matrix of uniformly distributed
  random numbers on (0,1)

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Operators

• concatenation
• ( ) subscription

• x zeros(1,3) ones(1,2)
• x
• 0 0 0 1 1
• x 1 3 5 7 9
• x
• 1 3 5 7 9
• y x(2)
• y
• 3
• y x(24)
• y
• 3 5 7

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Matlab Graphics

• x 0pi/1002pi
• y sin(x)
• plot(x,y)
• xlabel('x 02\pi')
• ylabel('Sine of x')
• title('Plot of the Sine Function')

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Multiple Graphs

• t 0pi/1002pi
• y1sin(t)
• y2sin(tpi/2)
• plot(t,y1,t,y2)
• grid on

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Multiple Plots

• t 0pi/1002pi
• y1sin(t)
• y2sin(tpi/2)
• subplot(2,2,1)
• plot(t,y1)
• subplot(2,2,2)
• plot(t,y2)

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Graph Functions (summary)

• plot linear plot
• stem discrete plot
• grid add grid lines
• xlabel add X-axis label
• ylabel add Y-axis label
• title add graph title
• subplot divide figure window
• figure create new figure window
• pause wait for user response

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Math Functions

• Elementary functions (sin, cos, sqrt, abs, exp,
  log10, round)
• type help elfun
• Advanced functions (bessel, beta, gamma, erf)
• type help specfun
• type help elmat

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Functions

• function fmyfunction(x,y)
• fxy
• save it in myfunction.m
• call it with ymyfunction(x,y)

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Flow Control

• if A gt B
• 'greater'
• elseif A lt B
• 'less'
• else
• 'equal'
• end
• for x 110
• r(x) x
• end

• if statement
• switch statement
• for loops
• while loops
• continue statement
• break statement

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Miscellaneous

• Loading data from a file
• load myfile.dat
• Suppressing Output
• x 1 2 5 1

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Getting Help

• Using the Help Browser (.html, .pdf)
• View getstart.pdf, graphg.pdf, using_ml.pdf
• Type
• help
• help function, e.g. help plot
• Running demos
• type demos
• type help demos

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Random Numbers

• xrand(100,1)
• stem(x)
• hist(x,100)

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Coin Tosses

• Simulate the outcomes of 100 fair coin tosses
• xrand(100,1)
• psum(xlt0.5)/100
• p
• 0.5400
• Simulate the outcomes of 1000 fair coin tosses
• xrand(1000,1)
• psum(xlt0.5)/1000
• p
• 0.5110

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Coin Tosses

• Simulate the outcomes of 1000 biased coin tosses
  with pHead0.4
• xrand(1000,1)
• psum(xlt0.4)/1000
• p
• 0.4160

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Sum of Two Dies

• Simulate 10000 observations of the sum of two
  fair dies

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Sum of Two Dies

• Simulate 10000 observations of the sum of two
  fair dies
• x1floor(6rand(10000,1)1)
• x2floor(6rand(10000,1)1)
• yx1x2
• sum(y2)/10000 ans 0.0275 p20.0278
• sum(y3)/10000 ans 0.0554 p30.0556
• sum(y4)/10000 ans 0.0841 p40.0833
• sum(y5)/10000 ans 0.1082 p50.1111
• sum(y6)/10000 ans 0.1397 p60.1389
• sum(y7)/10000 ans 0.1705 p70.1667
• sum(y8)/10000 ans 0.1407 p80.1389
• sum(y9)/10000 ans 0.1095 p90.1111
• sum(y10)/10000 ans 0.0794 p100.0833
• sum(y11)/10000 ans 0.0585 p110.0556
• sum(y12)/10000 ans 0.0265 p120.0278

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Sum of Two Dies

• for i212
• z(i)sum(yi)/10000
• end
• bar(z)

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Bernoulli Trials-Binomial Distribution

• k020
• ybinopdf(k,20,0.5)
• stem(k,y)

Bernoulli 1720 k020 ybinopdf(k,20,0.2) stem(
k,y)
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Combinatorics

• Permutations n objects
• Permutations choose k objects from n
• (hint fill 2 spaces on a bookshelf with books
  chosen from 5 available books)
• Combinations choose k objects from n without
• regard to the order
• (hint make a committee of 2 people chosen from
  a group of 5 people)