Introduction to MATLAB

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Introduction to MATLAB

• Division of Engineering and Applied Sciences

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What is MATLAB

• High level language for technical computing
• Stands for MATrix LABoratory
• Everything is a matrix - easy to do linear algebra

3
The MATLAB System

• Development Environment
• Mathematical Function Library
• MATLAB language
• Application Programming Language (not discussed
  today)

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Where to get MATLAB

• FAS computing
• Download from http//fas.harvard.edu/computing/sof
  tware/
• You must be on FAS network to use MATLAB
• DEAS IT
• If you are working with a DEAS faculty member
• Mathworks
• Student version is affordable and complete.

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MATLAB Desktop
Menu and toolbar
Workspace
History
Command
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Matrices Vectors

• All (almost) entities in MATLAB are matrices
• Easy to define
• Use , or to separate row elements -- use
  to separate rows
• Order of Matrix -
• mno. of rows, nno. of columns

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Matrices Vectors - II

• Vectors - special case
• n 1 column vector
• m 1 row vector
• Transpose

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Creating Vectors
Create vector with equally spaced intervals gtgt
x00.5pi x 0 0.5000 1.0000 1.5000 2.0000
2.5000 3.0000
Create vector with n equally spaced intervals gtgt
xlinspace(0, pi, 7) x 0 0.5236
1.0472 1.5708 2.0944 2.6180 3.1416
Equal spaced intervals in logarithm space gtgt
xlogspace(1,2,7) x 10.0000 14.6780
21.5443 68.1292 100.0000
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Creating Matrices

• zeroes(m, n) matrix with all zeros
• ones(m, n) matrix with all ones.
• eye(m, n) the identity matrix
• rand(m, n) uniformly distributed random
• randn(m, n) normally distributed random
• magic(m) square matrix whose elements have the
  same sum, along the row, column and diagonal.
• pascal(m) Pascal matrix.

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Matrix operations

• exponentiation
• multiplication
• / division
• \ left division. The operation A\B is
  effectively the same as INV(A)B, although left
  division is calculated differently and is much
  quicker.
• addition
• - subtraction

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Array Operations

• Evaluated element by element
• .' array transpose (non-conjugated transpose)
• . array power
• . array multiplication
• ./ array division
• Very different from Matrix operations

gtgt A1 23 4 gtgt B5 67 8 gtgt AB 19
22 43 50
But gtgt A.B 5 12 21 32
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Indexing Matrices

• Given the matrix
• Then
• A(1,2) 0.6068
• A(3) 0.6068
• A(1,) 0.9501 0.6068 operator

n
A 0.9501 0.6068 0.2311 0.4860
m
1n
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Graphics - 2D Plots

• plot(xdata, ydata, marker_style)
• For example Gives

gtgt x-50.15 gtgt sqrx.2 gtgt pl1plot(x, sqr,
'rs')
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Graphics - Overlay Plots

• Use hold on for overlaying graphs
• So the following Gives

gtgt hold on gtgt cubx.3 gtgt pl2plot(x,
cub,b-o')
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Graphics - Annotation

• Use title, xlabel, ylabel and legend for
  annotation

gtgt title('Demo plot') gtgt xlabel('X Axis') gtgt
ylabel('Y Axis') gtgt legend(pl1, pl2, 'x2',
'x3')
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Graphics - Annotation
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Tabular data
gtgt xlinspace(0, 15, 10) gtgt fidfopen('tabular.tx
t', 'wt') gtgt fprintf(fid, '15s 15s\n', 'x',
'sin(x)') gtgt fprintf(fid,'15.10f 15.10f\n',
x sin(x)) gtgt fclose(fid) gtgt type
tabular.txt x sin(x)
0.0000000000 0.0000000000 1.6666666667
0.9954079578 3.3333333333 -0.1905679629
5.0000000000 -0.9589242747 6.6666666667
0.3741512306
Use fscanf to read data back into Matlab
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Programming MATLAB
Writing an M-File

• function f fact(n) definition
• FACT Factorial. help line
• FACT(N) returns the factorial of N
• usually denoted by N!
• Put simply, FACT(N) is PROD(1N).
• f prod(1n) Function body
• return

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Programming - functions

• Functions have inputs and outputs
• Variables defined in the function isnt defined
  after function completes evaluating

function y myaverage(x) m,n
size(x) if (((m 1) (n 1)) (m 1 n
1)) error('Input must be a
vector') end y sum(x)/length(x)
Actual computation return
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Programming - Scripts

• Scripts have no input and output
• List of commands
• Variables are available on completion
• Simple example

theta -pi0.01pi Computations rho
2 sin(5 theta).2 polar(theta,rho)
Graphics output
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Flow control
If/elseif/else switch/case/otherwise

• Logic control structures
• Iterative structures
• Traditional for loop
• Matlab vector for loop

for while
for i110 for j110 a(i,j)b(i,j)c(i,j)
end end
a b.c
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Workspace

• Matlab remembers old commands
• And variables as well
• Each Function maintains its own scope
• The keyword clear removes all variables from
  workspace
• The keyword who lists the variables

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File I/O

• Matlab has a native file format to save and load
  workspaces. Use keywords load and save.
• In addition MATLAB knows a large number of
  popular formats. Type help fileformats for a
  listing.
• In addition MATLAB supports C style low level
  file I/O. Type help fprintf for more
  information.

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For more assistance

• DEAS Matlab help email
• matlab-fall04_at_deas.harvard.edu
• Mathworks web site
• http//www.mathworks.com