Introduction to MATLAB

1
Introduction to MATLAB

• Ethan Katz-Bassett
• ethan_at_cs
• November, 2007

2
What is MATLAB?

• MATrix LABoratory
• Numerical computing environment
• Mathematical functions
• Visualizations
• Programming language

3
What is MATLAB good for?

• Easy matrix manipulation/ data exploration
• Implementation of numerical algorithms
• Plotting of functions/data
• User interfaces??
• Interfacing with programs in other languages?

4
Some things Ive used it for

• Plotting graphs
• Plotting geographic data on maps
• Writing various numerical algorithms
• Solving linear programs
• Defining and solving semidefinite programs on
  lots of variables
• K-means and other clustering

5
MATLAB in the Department

• /projects/matlab/bin/matlab
• Includes many toolboxes (signal processing,
  optimization, statistics, ), but not all
• Limited number of licenses
• /projects/matlab/etc/lmstat -A
• MATLAB compiler (mcc)?
• Licenses for Mac betas available (at least last
  January). See Mac-users archives
• Some people have Windows copies
• Licenses available for purchase-- 100 plus

6
Ways to use it

• Interactive interpreter in Command Window
• Writing functions/ scripts as .m files
• Passing scripts from the Linux shell

7
MATLAB Language

• diary('ethan/matlab_tutorial/diary.txt')
• diary on
• Looks clean, like math
• Dynamically typed
• Assign without declaring type, type can change
• Semicolons suppress output

8
Vectors/ matrices I

• gtgt B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
  16
• B 1 2 3 4
• 5 6 7 8
• 9 10 11 12
• 13 14 15 16
• gtgt B(2,3)
• ans 7
• gtgt B(3,)
• ans 9 10 11 12
• gtgt B(24, 34)
• ans 7 8 11 12 15 16
• gtgt zeros(1,4) gtgt ones(2,2)

9
Vectors/ matrices II

• gtgt A 14
• A 1 2 3 4
• gtgt A
• ans 1
• 2
• 3
• 4
• gtgt C repmat(A,3,2)
• C 1 2 3 4 1 2 3 4
• 1 2 3 4 1 2 3 4
• 1 2 3 4 1 2 3 4

10
Vectors/ matrices III

• gtgt Dsum(B)
• D 28 32 36 40
• gtgt power(B(12,34),2)
• ans 9 16
• 49 64
• gtgt EAB (concatenation)
• gtgt B(2,)
• B 1 2 3 4
• 9 10 11 12
• 13 14 15 16
• gtgt (13)(46) VS gtgt (13).(46)

11
Vectors/ matrices continued

• What MATLAB is optimized for
• Everything is a matrix! (sort of)
• Multi-variate data
• Most functions work on matrices (more on this
  later)

12
Loading and saving

• save/load to save/load workspace or
  variables/structures in .mat binary formatsave
  filenamesave(filename,var1,var2,)load
  filenameload filename X Y Z
• dlmwrite/dlmread to write/read matrix to/from
  delimited ASCII filedlmwrite(filename,M,D)Md
  lmread(filename,D)

13
Graphing

• gtgt x 0pi/20 2pi
• gtgt y sin(x)
• gtgt plot(x,y,b-x) blue line, Xs
• gtgt hold keep lines
• gtgt z cos(x)
• gtgt plot(x,z,r) dotted red, s
• gtgt hold release lines
• gtgt dataimportdata(data_unsorted.txt)
• gtgt plot(sort(data),(1128)/128) cdf

14
Control flow I

• if any(Bgt5) NOT if Bgt5
• true
• else
• false
• end
• for bB iterate over columns
• 2b
• End

15
You know those for loops I showed?

• Never use them!
• Or at least avoid when possible.
• MATLAB meant for matrices-- vectorize code
• P
• for aA slow
• P P (agt0)
• end
• P2 Agt0 fast

16

• Original code
• numAss 0 num assigned
• numAssCorr 0 and should be
• for I1numel(Actual)
• if Assigned(i) 1
• numAss numAss 1
• if Actual(i) 1
• numAssCorr numAccCorr 1
• end end end
• precision numAssCorr/numAss

17

• Original code
• numAss 0 num assigned
• numAssCorr 0 and should be
• for I1numel(Actual)
• if Assigned(i) 1
• numAss numAss 1
• if Actual(i) 1
• numAssCorr numAccCorr 1
• end end end
• precision numAssCorr/numAss
• Vectorized code
• numAss sum(Assigned)
• numAssCorr sum( Assigned Actual )
• precision numAssCorr/numAss

18

• In m num of clusterings
• n num points to be clustered, ngtgtm
• E m X n set of clusterings, where
  E(i,j)cluster of point j in cluster i
• Out C n X n similarity matrix, where C(j,k)
  number of i with E(i,j)E(i,k)
• Naïve code (or, non-MATLAB code)
• C zeros(n,n)
• for i 1m
• for j 1n
• for k 1n
• C(j,k) C(j,k) (E(i,j)E(i,k))
• endendend
• Can reorder for loops without affecting
  performance

19

• In m num of clusterings
• n num points to be clustered, ngtgtm
• E m X n set of clusterings, where
  E(i,j)cluster of point j in cluster i
• Out C n X n similarity matrix, where C(j,k)
  number of i with E(i,j)E(i,k)
• Vectorize, try 1-- do all comparisons for one
  point at once
• C should hoist allocation
• for clustersE get clusters for
  one point
• rep repmat(clusters,1,n) replicate
  clusters
• C C sum(repE) compare to other
  points
• end
• Much better (3.3x faster on 20x1000)! Can we
  improve?

20

• In m num of clusterings
• n num points to be clustered, ngtgtm
• E m X n set of clusterings, where
  E(i,j)cluster of point j in cluster i
• Out C n X n similarity matrix, where C(j,k)
  number of i with E(i,j)E(i,k)
• Vectorize, try 2-- ngtgtm, so iterate over m, not n
• C zeros(n,n)
• for clusteringE get one clustering
• rep repmat(clustering,1,n) create copies
  of
• clustering
• C C (reprep) compare within
  clustering
• end
• Turned out to be slower on 20x1000, but consider
  changes like this.

21
Scripts and Functions

• Save as .m files (and make sure in path)
• See ethan/matlab_tutorial/ensemble1-3.m
• _____
• function C,time ensemble2( m, n, E )
• tic
• code from earlier slide
• timetoc
• _______
• C2,t2ensemble2( 20, 1000, Ensemble)

22
Scripting MATLAB from Linux Shell

• 2 options Ive used
• 1) /projects/matlab/bin/matlab -nojvm -nodesktop
  -nosplash -nodisplay lt myscript.m
• .m file specifies input and output
  values/filenames
• 2) /projects/matlab/bin/matlab -nojvm -nodesktop
  -nosplash -nodisplay -r "A33dlmwrite('test.txt
  ',A,' ')quit"

23
Scripting MATLAB from Shell, II

• ensemble2_wrap.m
• Dims load(dims.txt')
• E load(ensemble.txt)
• Censemble2(Dims(1),Dims(2), E)
• dlmwrite(similarity2.txt,C,' ')
• quit
• __________________________________
• ethan/matlab_tutorial /projects/matlab/bin/matla
  b -nojvm -nodesktop -nosplash -nodisplay lt
  ensemble2_wrap.m

24
Scripting MATLAB from Shell, III

• ensemble2_wrap2.m
• function ensemble2_wrap2(dimsfn, ensfn,
  outfn)
• Dims load(dimsfn)
• Eload(ensfn)
• Censemble2(Dims(1),Dims(2),E)
• dlmwrite(outfn,C,' ')
• _____________________________________
• ethan/matlab_tutorial /projects/matlab/bin/matl
  ab -nojvm -nodesktop -nosplash -nodisplay -r
  "ensemble2_wrap2('dims.txt','ensemble.txt','simila
  rity2.txt')quit"

25
Weirdness and limitations

• One-based indexing hard coded
• Parentheses used for calling a function AND for
  indexing an array
• No namespace resolution, so same code on
  different machines (w different path variables)
  can produce different results
• Many functions have different behavior for
  matrices vs vectors (so base case broken)
• No references
• Limits data structures (linked list)
• All functions call by value

26
MATLAB Functions

• Tons implemented
• Sometimes hard to find what you need
• But great documentation once you do
• help functionname
• http//www.mathworks.com/access/helpdesk/help/help
  desk.html
• Many additional found online