A Short Introduction to Matlab

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A Short Introduction to Matlab

• Erik Zeitler
• Uppsala Database Laboratory

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Matlab

• MATrix LABoratory
• A high level programming language
• perform numerical computations
• produce graphical output
• Basic data type Matrix
• Very fast matrix manipulation
• Programming control structures are available
• procedures
• loops
• , but these are slow.

Good news You dont need a lot of loops. Use
matrices instead.
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Syntax

• Matlab uses standard infix notation
• gtgt 25
• ans
• 7
• gtgt 9-3
• ans
• 6
• gtgt 1210
• ans
• 120
• gtgt 53
• ans
• 125

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Variable Assignment

• gtgt A214
• gtgt Bsqrt(A)
• gtgt C23i
• C
• 2.0000 3.0000i
• gtgt DABC
• D
• 22.0000 3.0000i

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Matrix creation
gtgt A15 A 1 2 3 4 5 gtgt A1 2 3 4 5 A 1 2 3 4 5
gtgt A127 A 1 3 5 7 gtgt A1 2 3 1 2 3 A 1 2 3 1 2 3
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Matrix creation
gtgt zeros(3,5) ans 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gtgt B1 2 3 B 1 2 3
gtgt ones(3,4) ans 1 1 1 1 1 1 1 1 1 1 1 1 gtgt ABB A 1 2 3 1 2 3
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Matrix Manipulation
A 1 2 3 1 2 3
gtgt A' ans 1 1 2 2 3 3 gtgt A3 ans 0 0 1 0 0 1 gtgt A(3,) 2 3 4 A 1 2 3 1 2 3 2 3 4
gtgt A(,2) ans 2 2 gtgt rot90(A) ans 3 3 2 2 1 1 gtgt A(,4) 44 A 1 2 3 4 1 2 3 4
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Matrix Arithmetics
A 1 2 3 1 2 3
gtgt AA ans 2 4 6 2 4 6 gtgt AA ??? Error using gt mtimes Inner matrix dimensions must agree. gtgt AA ??? Error using gt mtimes Inner matrix dimensions must agree.
gtgt A.A ans 1 4 9 1 4 9 gtgt AA' ans 14 14 14 14 gtgt A'A ans 2 4 6 4 8 12 6 12 18
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Some useful tricks
A 1 2 3 1 2 3
gtgt repmat(A,1,2) ans 1 2 3 1 2 3 1 2 3 1 2 3 gtgt find(A3) ans 5 6
gtgt randperm(4) ans 2 4 3 1 gtgt size(A) ans 2 3
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Some useful tricks
A 1 2 3 1 2 3
gtgt sum(A) ans 2 4 6 gtgt sum(A,2) ans 6 6 gtgt sum(sum(A)) ans 12 gtgt sort(randperm(4)) ans 1 2 3 4
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More tricks
gtgt B1 2 3 4 5 6 B 1 2 3 4 5 6 gtgt std(B) ans 2.1213 2.1213 2.1213
gtgt mean(B) ans 2.5000 3.5000 4.5000 gtgt var(B) ans 4.5000 4.5000 4.5000
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Exercises (to do in pairs)

• Given a (1N) vector A, create a (3N) matrix B
  such that
• the first row in B contains A
• the second row in B contains A backwards
• the third row in B contains the sum of A and A
  backwards
• Given a matrix C, create a sorted vector D which
  contains all of the values in C which are greater
  than 10

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Other useful functions

• princomp(Data)
• Returns the principal components.
• plot(A, B, Symbol)
• where Symbol is one of '' 'o' '' etc
• hold on/off
• grid on/off

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if
if condition statements elseif condition statements else statements end gtgt A0 1 2 gtgt B1 2 3 gtgt if AgtB CA-B elseif BgtA CB-A else CAB end
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for and while
for i vector statements end example j0 for i110 jij end while condition statements end example j0, i1 while ilt10 jij, ii1 end
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for vs. while
j12 a0 for i1size(j) if j(i)1 jj,i else aaj(i) end end j12 a0 while(iltsize(j)) if j(i)1 jj,i else aaj(i) end end
Interrupt execution Ctrl-C
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Functions in Matlab

• Create a function fun
• function Ret1, RetM fun(Arg1, , ArgN)
• statements defining Ret1, , RetM
• end
• This definition must go in a file called fun.m
• Invoking fun from Matlab
• (make sure your cd to the dir where fun.m is)
• gtgt x1, , xM fun(a1, , aN)
• will set the variables x1, , xM.

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traparea.m

• function Area traparea(A,B,H)
• Calculates the area of a trapezoid
• with length A, B of the parallell
• sides and the distance H between the
• sides.
• Area0.5(AB)H
• end

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cylinder.m

• function Vol, Area cylinder(R,H)
• calculates the volume and surface
• area of a cylinder with radius R and
• height H
• Area2piRH
• Vol(AreaR)/2
• end

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Exercise (to do in pairs)

• Write a function subtract_and_scale
• Given this input
• a matrix of dimension NM,
• a vector of size 1M
• Calculate a new matrix, by
• subtracting the vector from each row in the
  matrix,
• multiplying each value in the new matrix by 2
• function NewMatrix subtract_and_scale(Matrix,
  Vector)

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Think vectors!

• Instead of
• nofRows,nofCols size(A)
• for row 1nofRows
• for col 1nofCols
• A(row, col) A(row, col) 1
• end
• end
• Write
• A A 1
• ? More compact and much more efficient

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Think vectors!

• Example (script run.m)
• Xones(500,500)
• Yones(500,500)
• tic start timer
• for i1500
• for j1500
• Val 0
• for k 1500
• Val X(i,k)Y(k,j) Val
• end
• Z(i,j) Val
• end
• end
• toc stop timer and print elapsed time
• tic start timer
• Z XY
• toc stop timer and print elapsed time

gtgt run Elapsed time is 3.47 seconds Elapsed time
is 0.15 seconds
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Learn more

• Pärt-Enander, Sjöberg, Pihl Användning av Matlab
• English version is available too
• For sale at UTH-Gård
• There is an abundance of Matlab tutorials on the
  internet