Getting started with Matlab

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Getting started with Matlab

• Numerical Methods
• Appendix B
• http//www.mathworks.com/access/helpdesk/help/tech
  doc/learn_matlab/learn_matlab.html

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What Is MATLAB?

• Math and computation
• Algorithm development
• Data acquisition
• Modeling, simulation, and prototyping
• Data analysis, exploration, and visualization
• Scientific and engineering graphics
• Application development, including graphical user
  interface building

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The MATLAB System

• Development Environment.
• The MATLAB Mathematical Function Library.
• The MATLAB Language.
• a high-level matrix/array language
• Graphics.
• The MATLAB External Interfaces (API).

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MATLAB Online Help

• Desktop Tools and Development Environment
• Mathematics
• Programming
• Graphics
• 3-D Visualization
• Creating Graphical User Interfaces
• External Interfaces/API

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Matrices and Arrays

• To enter Dürer's matrix, simply type in the
  Command Window
• gtgtA 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1
• A
• 16 3 2 13
• 5 10 11 8
• 9 6 7 12
• 4 15 14 1

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sum, transpose, and diag

• sums of the columns of A
• gtgtsum(A)
• ans 34 34 34 34
• gtgtsum(A')'
• ans
• 34
• 34
• 34
• 34
• sum(diag(A))
• ans 34

The transpose operation is denoted by an
apostrophe or single quote, '.
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Subscripts

• gtgtA(1,4) A(2,4) A(3,4) A(4,4)
• ans 34
• gtgtX A
• gtgtX(4,5) 17
• X
• 16 3 2 13 0
• 5 10 11 8 0
• 9 6 7 12 0
• 4 15 14 1 17

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The Colon Operator

• gtgt 110
• ans 1 2 3 4 5 6 7
  8 9 10
• gtgt 100-750
• ans 100 93 86 79 72 65 58
  51
• gtgt 0pi/4pi
• ans 0 0.7854 1.5708 2.3562
  3.1416
• In subscript
• gtgt A(1,14)
• ans 16 3 2 13

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The magic Function

• gtgt B magic(4)
• B
• 16 2 3 13
• 5 11 10 8
• 9 7 6 12
• 4 14 15 1
• To make this B into Dürer's A, swap the two
  middle columns
• A B(,1 3 2 4)

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Expressions

• Variables
• num_students 25
• Numbers
• 3 -99 0.0001 9.6397238 1.60210e-20
  6.02252e23 1i -3.14159j 3e5i
• Operators
• -/
• \ Left division
• Functions
• help elfun
• help specfun
• help elmat

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Working with Matrices
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Generating Matrices

• zeros All zeros
• ones All ones
• rand Uniformly distributed random elements
• randn      Normally distributed random elements

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ones(n,m)

• gtgt ones(3,4)
• ans
• 1 1 1 1
• 1 1 1 1
• 1 1 1 1

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zeros(n,m)

• gtgt zeros(3,4)
• ans
• 0 0 0 0
• 0 0 0 0
• 0 0 0 0

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rand(n,m)

• gtgt rand(3,4)
• ans
• 0.9501 0.4860 0.4565 0.4447
• 0.2311 0.8913 0.0185 0.6154
• 0.6068 0.7621 0.8214 0.7919

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randn(3,4)

• gtgt randn(3,4)
• ans
• -0.4326 0.2877 1.1892 0.1746
• -1.6656 -1.1465 -0.0376 -0.1867
• 0.1253 1.1909 0.3273 0.7258

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Load and Save .mat

• gtgt A 1 2 3
• gtgt B 4 5 6
• gtgt save mydata.mat
• gtgt clear
• gtgt load mydata.mat

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eye(n), eye(size(A))

• gtgt eye(3)
• ans
• 1 0 0
• 0 1 0
• 0 0 1

• gtgt eye(size(A))
• ans
• 1 0 0 0
• 0 1 0 0
• 0 0 1 0

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Load and save ASCII file

• gtgt a magic(4) b ones(2, 4) -5.7 c 8
  6 4 2
• gtgt save -ascii mydata.dat
• gtgt clear
• gtgt load mydata.dat
• gtgt mydata
• mydata
• 16.0000 2.0000 3.0000 13.0000
• 5.0000 11.0000 10.0000 8.0000
• 9.0000 7.0000 6.0000 12.0000
• 4.0000 14.0000 15.0000 1.0000
• -5.7000 -5.7000 -5.7000 -5.7000
• -5.7000 -5.7000 -5.7000 -5.7000
• 8.0000 6.0000 4.0000 2.0000

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Building Tables

• gtgt n (09)'
• pows n n.2 2.n
• pows
• 0 0 1
• 1 1 2
• 2 4 4
• 3 9 8
• 4 16 16
• 5 25 32
• 6 36 64
• 7 49 128
• 8 64 256
• 9 81 512

MATLAB uses a dot, or decimal point, as part of
the notation for multiplicative array operations.
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Multivariate Data

• gtgtD
• 72 134 3.2
• 81 201 3.5
• 69 156 7.1
• 82 148 2.4
• 75 170 1.2
• to obtain the mean and standard deviation of each
  column, use
• gtgtmu mean(D), sigma std(D)
• mu       75.8       161.8         3.48
• sigma     5.6303      25.499 2.2107
• gtgthelp datafun
• gtgthelp stats

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Matlab Graphics
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plot(x,y)

• t05100
• yt.0.34-log10(t)1./t
• plot(t,y)
• title(Plot of y versus t)
• grid

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3D graphics

• x,ymeshgrid(-4.00.24.0,-4.00.24.0)
• z(-20x.2x)(-15y.25.y)
• surfl(x,y,z)
• axis(-4 4 -4 4 -800 0)
• xlabel('x-axis')
• ylabel('y-axis')
• zlabel('z-axis')

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Try yourself, and have fun!