Matlab Tutorial

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Matlab Tutorial

• By Nouman Zubair

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Outline

• Introduction to Matlab
• Matlab (matrices and arrays)
• Working with Matlab

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About Matlab

• The name Matlab stands for matrix laboratory.
• Matlab is a high level (matrix/array) language
  for technical computing.
• Matlab is case sensitive language

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Facilitates

• Math and computation
• Data acquisition, data analysis and visualization
• Modeling, simulation and prototyping
• Scientific and engineering graphics
• And many more

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Matlab System

• A Matlab system consist of Five main parts
• Development Environment
• Mathematical function library
• Matlab Language
• Graphics
• Application Program Interface (API)

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Starting Matlab

• On windows platforms double-click on Matlab icon
• On Unix/Linux platforms, type matlab at the
  operating system prompt
• To quit type in windows . Select file followed by
  exit matlab. Or type quit in the operating system
  prompt.

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Matlab (matrices and arrays)

• A variable is a symbolic representation used to
  denote a quantity or expression
• i.e a2
• An array is a collection of variables
• i.e b 2, 3, 4
• A matrix is a rectangular array of numbers.
• i.e c 1 2
• 3 4
• To make it simple. consider matlab store variable
  in form of matrices i.e a single variable as a
  matrix of 1 1
• How will matlab store a set of five variables ?

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Example

• In the command window of matlab type
• a1
• And type
• b2
• Finally type
• cab
• The display value would be
• c3
• Note similarly we can assign different value to
  the variables by using built in math function
  provided by Matlab. i.e d cos(a)

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Entering Matrices

• To enter matrices
• Separate the elements of a row with blanks or
  commas.
• Use a semicolon, , to indicate the end of each
  row
• Surround the entire list of elements with square
  brackets, .
• i.e
• A 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

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Cont

• A
• 16 3 2 13
• 5 10 11 8
• 9 6 7 12
• 4 15 14 1
• known as Durer matrix
• Once a matrices is entered its remember in the
  Matlab workspace and can be referred simply by
  its assigned name.

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Operation on matrices

• sum(x), transpose and diag operation
• Matlab compute along the columns of a matrix
• i.e sum(A)
• gives a row vector containing the sum of the
  matrix columns
• How about rows sum?
• Easiest way is to take a transpose of matrix
  .Transpose Operation is denoted by apostrophe or
  single quote, . i.e A give the transpose (What
  is transpose of a matrix)
• Can you Explain this operation sum(A)
• This operation produce the sum of rows and
  transpose the result in the column format.

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Cont

• diag(A)
• This operation show the element on the main
  diagonal of the matric
• Explain this operation sum(diag(A))
• This produces the sum of matrix element on it
  main diagonal
• How about antidiagonal ?
• fliplr(A) , flips the matrix from left to right
  then

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Cont

• Generating Matrices
• Four built in function for matrices
• zeros() all zeros i.e zzeros(2,4) create 2 4
  matrix whose elements are all zeros
• ones() all ones i.e oones(2,4) create 24
  matrix whose elemenst are all ones
• rand() Uniformally distributed random elements
• Randn() Normally distributed random elements

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Subscripts

• The elements in row I and j of A is denoted by A
  (i,j).
• i.e A(4 , 2 ) stands for fourth row and second
  column element which is 15
• To compute the sum of element in the fourth
  column
• A(1,4) A(2,4) A(3,4) A(4,4)
• The matrix can be considered as one long vector
  array where
• A (n) will represent the n element in position
  of that vector i.e A(8)15 which is also given by
  A(4,2)
• What if we try A(4,5)?
• It is an error as it exceed the matrix dimension
  but on the other hand, If you store a value i.e
  A(4,5 ) 23 the original matrix dimension size is
  increases to accommodate the new entry

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Colon Operator

• Is one of the most important operator
• As spacing operator
• i.e 15 mean increment by 1 upto 5
• 100 -7 50 mean starting at 100 and decrement
  by 7 upto 50
• Subscript expression
• A (1k,j) mean first k elements of the jth column
  of A i.e A (14,4)
• A(,end) where mean all the element and end
  refer to the last row or column
• Explain this operation sum(116)/4?

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Concatenation

• Concatenation is the process of joining small
  matrices to make bigger ones.
• The pair of square brackets, , is the
  concatenation operator
• i.e B A A8 A16 A32
• Results in an 8 8 matrices that is compose of
  sub matrix of A, A8, A16, A32

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Rows, columns deletion

• You can delete rows and columns from matrix using
  just pair of square brackets
• i.e X A assigning a new matrix
• X(,2) this delete the second column
• How would you delete a single element?
• X(n) where n is the element in the vector
  format of the matrix

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Some Linear Algebra

• Matrix matrix multiplication (inner product) is
  achieved by A B
• Matrix .dot product multiplication is achieved by
  A. B
• Inv(A) command gives the inverse of matrix
• Symmetric matrix is when a matrix is added to
  its transpose i.e A A. Also A A produces
  a symmetric matrix
• Try them now

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Cont

• Determinant 0 mean matrix is singular
• i.e d det(A) .. So is it singular try
  ddet(Aa)
• rref(A) gives the Reduced row echelon form
• eig(A) give the eigenvalues

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Some simple commands

• a semicolon avoid command output to be
  displayed i.e t 15 Doesnt display the output
  of the t vector on the command line
• clc command clear the output on the command line
• Whos command shows the variable already created
  and their sizes

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Help topics

• In order to avail the built in help in matlab.
  Type
• gtgt help
• matlab\general -General purpose commands
• matlab\ops Operators and special characters
• matlab\lang -Programming language constructs
• matlab\elmat -Elementary matrices and matrix
  manipulation
• matlab\elfun -Elementary math functions
• matlab\specfun -Specialized math functions
• matlab\matfun -Matrix functions -numerical linear
  algebra
• matlab\datafun -Data analysis and Fourier
  transforms
• matlab\polyfun -Interpolation and polynomials
• matlab\funfun -Function functions and ODE solvers
• matlab\sparfun -Sparse matrices
• matlab\scribe -Annotation and Plot Editing
• matlab\graph2d -Two dimensional graphs
• matlab\graph3d -Three dimensional graphs
• matlab\graphics -Handle Graphics.
• etc...

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M-files

• M-files are text files containing matlab code.
• Files extension is .m
• For example create a matrix in a file i.e b 1
  2 3 4 and save this file as bmatrix.m
• You can simply call this matrix by typing the
  name of the file in the command window of Matlab.
  This will add the matrix b to the variable
  dictionary of matlab that matrix b is now also be
  accessible as simple typing b.

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M-files

• To use personalized folder . You need to change
  the working directory by typing cd \directory
  where directory is the path to the folder where
  you just save an m file
• i.e function zaplusb(a,b)
• Zab
• Save the file as z and run it

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Financial toolbox

• Mean-variance and CVaR-based object oriented
  portfolio optimization
• Cash flow analysis, risk analysis, financial
  time-series modeling, date math and calendar math
• Regression and estimation with missing data
• Basic Black-Scholes, Black and binomial option
  pricing
• Financial times serial analysis
• Technical indicators and financial charts
• And more

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Key features

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• Thank you
• Q A