Introduction to Matlab 7 Lesson I

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Introduction to Matlab 7Lesson I

• Marco Lattuada
• Swiss Federal Institute of Technology - ETH
• Institut für Chemie und Bioingenieurwissenschaften
  
• ETH Hönggerberg/ HCI F135 Zürich (Switzerland)
• E-mail lattuada_at_chem.ethz.ch

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How to connect to you folders

• Go to My Computer
• In Tools, click on Map Network Drive
• In the window that appears, type
  \\d.ethz.ch\dfs\users\all\ltnethz usernamegt
• Select option connect with another username
• Enter d\ ltnethz usernamegt
• Enter your E-Mail password.
• Remember do not keep you data on the computer
  you are working on, as they can be deleted!!!!

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Matlab 7.0.4 - 7.8

• What is Matlab?
• Advantages over other choices

Matlab is an interatcive system for numerical
computation

• Quick and easy coding with high level language
• Procedural coding (object-oriented supported)
• Minimal attention required for data
  structure/declaration
• Simple handling of vectors/matrixes
• High quality graphics available
• Full portability of the m-files
• Built-in editing and debugging tools
• Built-in functions (also on internet)

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Matlab 7.0.4 - 7.8

• Disadvantages

• Not optimal for symbolic calculations (choose
  Maple, Mathematica)
• Not as fast as C (C) and Fortran
• Not the best choice for very computationally
  demanding problems

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Matlab Introduction Window
File Structure
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Variables

• Names are case sensitive (Marco ? marco)
• 63 Characters max (1st character must be a
  letter)
• Letters, numerals and sign _ are valid
  characters
• No Spaces in between

Rules
Invalid Examples
Valid Examples
2ndvariable yes first one 1
a 1 speed 1500 BeamOutput_Type1 vQv name
John Smith
No need to specify the variable type
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Variables

• Try to type
• a 2
• b 3
• c ab
• d c/2
• d
• who
• whos
• clear
• who
• myName marco

Why these are arrays??? Every variable is an
array!!!
By pressing w?, the command who is recalled
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Variables

• Where are my results stored?
• a 2
• b 3
• c ab The result is stored in c
• ab The results in stored in ans

By pressing ? or ?, one can recall the previous
commands
By using the symbol at the end of a command,
the execution is performed, but the result is not
shown in the command window
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Vectors

• Row vector gtgt a 1 2 3
• Column vector gtgt b 1 2 3
• Equally spaced vector gtgt c 05100 (or
  0100 or 0100)
• Evenly spaced vector gtgt d linspace(0,100,21)
  
• ( vector linspace(start,end,elements)
  ) ( vector logspace(start,end,elements) )
• generates a vector from 10start to 10end
• Transpose gtgt e d'

If everything is an array, what is a vector ???
You should see
Fast help by gtgt help linspace
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Vector's Arithmetic

• Try to type
• c 2a
• d 2a
• f ac
• g ab
• dot(a,b)
• A ba
• aa
• a2
• a.2
• a.a
• d d./a
• b sqrt(b)
• c exp(c)
• d factorial(d)

Addition/multiplication by constants
Addition of vectors
Dot product of vectors
Your first matrix ? (3,1)(1,3) (3,3)
Error! ? (1,3)(1,3) nothing
Element-by-element operations
Examples of functions returning
element-by-element operations
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Vector's Arithmetic II

• Further examples
• a 1 2 3
• b 1 2 3
• c ab
• d ba

(1,3)x(3,1)(1,1) SCALAR !
(3,1)x(1,3)(3,3) Matrix!
Never forget the rules for matrix multiplication!
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Arrays/Matrices

• Methods of creating matrices
• By coefficients gtgt A 1 2 3 4 5 6 7 8 9
• Matrix of zeros gtgt B zeros(3,2)
• Matrix of ones gtgt C ones(2,3)
• Identity matrix gtgt D eye(3)
• Random matrix gtgt R rand(3,3)
• Normally distr. random matrix gtgt RD randn(3,3)
• Matrix Characteristics
• Size gtgt size(A)
• Length gtgt length(A)

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Accessing Elements

• Vectors (gtgt a 15.2)
• Single element gtgt a(1)
• Multiple elements gtgt a(1 3)
• Range of elements gtgt a(23)
• Last element gtgt a(end)
• Matrices (gtgt A a'a)
• Single element gtgt A(1,3)
• Submatrix gtgt A(23,23)
• Matrix Column gtgt A(2,)
• Matrix Line gtgt A(,3)
• Lines intersected with columns gtgt A(2 3,1 3
  5)

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Arithmetic with Matrices

• Try to type
• B 2A
• C 2A
• D AC
• D D
• C(3,)
• D(,2)
• CD
• DC
• A2
• A.2
• E2.A
• sqrt(A)
• sqrtm(A)
• A(-1)

Addition/multiplication by constants
Addition of matrices
Transpose
Elimination of columns/lines
Product between matrices
Remember product between matrices is usually not
commutative!
Square of matrix Square of matrix's elements Ei,j
2Ai,j Square-root of matrix's
elements Square-root of matrix (try gtgt
(sqrtm(A))2) Inverse of A (equal to gtgt inv(A))
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Matrix Division

• Let us consider the following case
• A, B
• A/B
• A\B

Two square matrices
A divided by B, alternatively mrdevide(A,B)
equivalent to Ainv(B)
alternatively mldevide(A,B) equivalent to
inv(B)A
The two divisions are different, because the
product between matrices is not commutative!
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Other Ways of Creating Matrices

• Matrices in block form
• From matrices to vectors
• From vectors to matrices
• Diagonal matrices
• Meshes
• From one element/column/line

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Operators for Matrices

• Size gtgt size(C)
• Predominant size gtgt length(C)
• Maximum (columns) gtgt max(A)
• Maximum (general) gtgt val,elem max(A)
• Maximum (overall) gtgt max(A())
• Sum of elements gtgt sum(A)
• Mean value gtgt mean(A())
• Determinant gtgt det(A)
• Inverse gtgt inv(A)
• Condition Number gtgt cond(A)
• Norm gtgt norm(A,i)

min(A) -max(-A)
var(A), std(A),
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Exercises

• Compute the approximate value of exp(1)
• Compute the approximate value of exp(2)
• Compute the cross-product of u(1,3,2) ? v(-1,1,2)

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Solution of Linear Algebraic Systems

• Write in matrix notation the following system of
  equations
• Is this system singular?
• How would you solve this system?

Shortcut
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Exercises

• Solve the following system
• Find the inverse matrix of A
• Solve the following system

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Structures in Matlab

• What is a structure?
• Example chemical components (try)
• gtgt comp(1).name 'water'
• gtgt comp(1).Mw 18.02
• gtgt comp(1).density 1
• gtgt comp(2).name 'ethanol'
• gtgt comp(2).Mw 46.06
• gtgt comp(2).density 0.789

Structures are arrays whose names have
dot-separated parts. They can be used to store
information of different kinds together in a
hierarchical structure.
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Loops in Matlab

• General form of for-loops
• Example

for variable expression statements end
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Examples of Loops

• Try the following
• gtgt for i 05100
• i
• end
• gtgt v 0 4 5 11
• gtgt for i v, i, end
• gtgt n 1e6 x rand(n,1)
• gtgt tic s 0 for i 1n, s sx(i)2 end, s,
  toc
• gtgt tic s sum(x.2) s, toc

A technique is a trick that works Giancarlo Rota
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While Loops in Matlab

• General form of while-loops
• Example

while expression statements end
The statement is executed as long as the
expression is true
The statements are executed an indefinite number
of times
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Examples of Loops

• Try the following
• gtgt clear x n 5e4 x(1) 2
• gtgt tic for i 2n, x(i) x(i-1)2i end, toc
• gtgt x1 zeros(1,n) x1(1) 2
• gtgt tic for i 2n, x1(i) x1(i-1)2i end,
  toc
• gtgt v 2linspace(1,n,n)
• gtgt tic x2 cumsum(v) toc

Pre-allocate arrays
Vectorize and use pre-defined functions
20 times faster
129 times faster