What is MATLAB

1
What is MATLAB ?

• MATrix LABratory
• Originally, it was a front-end to FORTRAN matrix
  routines developed in the 1970s _at_ U. of New
  Mexico and Stanford
• Today it is a powerful, interactive mathematics
  ENVIRONMENT with many powerful capabilities
  (matrices, symbolic math, analysis)
• Not unlike a UNIX shell

2
Support Materials

• MATLAB is available _at_ the ECE front desk, and at
  the ODU bookstore
• The only way to master MATLAB is to use it (just
  like any programming language or skill)
• Users Guide (comes with student edition)
• Internet FAQs (e.g. www.mathworks.com)
• MATLAB Primer (Bound copy 3.00)

3
Accessing Matlab

• Start Menu.. Programs.. Matlab
• To exit..
• gtgtquit

4
Entering Matrices

• MATLAB works with essentially one kind of object
  a rectangular numerical MATRIX with possibly
  complex entries
• 1 x 1 interpreted as scalars
• 1 x n or m x 1 interpreted as vectors
• Entered by explicit list of elements, or
• Generated by built-in statements and functions
• Created in M-files
• Loaded from external data files

5
Entering matrices (contd.)

• Example A 1,2,3 4,5,6 7,8,9 or
• A
• 1 2 3
• 4 5 6
• 7 8 9 creates a 3 x 3 matrix and assigns it to
  a variable A.
• , or blank separates the element in a matrix
• Avoid blank spaces while listing a number in
  exponential form (e.g. 2.34e-9)
• Large Matrix best done in M file (easy to edit)
• Built in functions rand, magic, hilb

6
Entering matrices (contd.)

• rand (n) creates a n x n matrix with random
  entries uniformly distributed between 0 and 1
• rand (m x n) will create an m x n matrix
• magic (n) will create a an integral n x n matrix
  which is a magic square
• hilb(n) will create the n x n Hilbert matrix
• Individual matrix and vector entries can be
  referenced with indices (only positive integers)
  within the parentheses
• E.g. A(2,3) refers to entry in second row and
  third column.
• X(3) woild denote third coordinate of a vector x.

7
Matrix Operations

• Addition
• Substraction -
• Multiplication x
• Power
• Transpose
• Left Division \
• Right division /
• E.g. x A\b is the solution of A x b
• x b/A is the solution of x A b

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Array Operations

• Addition substraction Operate entrywise
• Other can be made entrywise by preceding them
  with a period for ,,\,/
• E. g. 1 2 3 4 .1 2 3 4 will yield 1 4 9
  16
• 1 2 3 4.2 will yield 1 4 9 16
• Useful in MATLAB graphics

9
Statements, Expressions Variables

• MATLAB is an expression language CASE SENSITIVE
• Statements are of the form
• Variable expression, or simply
• Expression
• Expressions are composed from operators,
  functions , and variable names.
• Result is a Matrix assigned to the variable for
  future use.
• If variable name and sign are omitted, then a
  variable ans (for answer) is created.
• Statement terminated with a CR, use to continue
  to next line
• Same line use comma to separate statements
• Last character semicolon suppresses the printing
• Who lists all the variables
• Clear clears the variables
• Runaway Display can be stopped by CTRL-C

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Matrix Building Functions

• Convenient Matrix Building Functions are
• Eye
• Zeros
• Ones
• Diag
• Triu
• Tril
• Rand
• Hilb
• Magic
• Toeplitz

11
For,While, if and relations

• MATLAB flow control statements operate like those
  in most computer languages
• For
• x for i 14, x x,i2,end
• x for i 4-11, x x,i2,end
• While
• While relation
• Statements
• End
• If
• If relation
• Statements
• end

12
Relations

• lt less than
• gt greater than
• lt less than or equal
• gt greater than or equal
• equal
• not equal
• and
• or
• not

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Scalar Vector functions

• Scalar
• Sin asin exp abs round
• Cos acos log sqrt floor
• Tan atan rem sign ceil
• Vector
• Max sum median any
• Min prod mean all
• Sort std

14
Matrix Functions

• Eig chol svd inv lu qr
• Hess schur rref expm sqrtm poly
• Det size norm cond rank

15
Command Line Editing Recall

• Use left right arrows
• Backspace delete keys
• Home, end, Delete
• Up/Down arrow keys

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Submatrices Colon Notation

• To achieve fairly complex data manipulation
• Colon Notation (generate vectors and reference
  submatrices
• Expression 15 generates 1 2 3 4 5
• Expressions 0.20.21.2 generates 0.2 0.4 0.6
  0.8 1.0 1.2
• Expression 5-11 gives 5 4 3 2 1
• X 0.00.12.0ysin(x)x,y gives a table of
  sines
• Colon Notation used to access submatrices of a
  matix
• A(14,3), A(,3), A(14,) , A(, 2,4)
• A(2,4,5) B(,13)
• A(2,4) A(,2,4)1,23,4

17
M files

• To execute a sequence of statements
• Script files
• Sequence of normal MATLAB statements
• Variables are global
• Used to enter data into a large matrix
• Entry errors can be easily edited
• Function files
• Provide extensibility to MATLAB
• Create new functions specific to a problem
• Variables are local
• We can however declare them global if so desired.

18
Function files

• Example
• function a randint(m,n)
• a floor (10 rand(m,n)
• Place in a file called randint.m
• first line declares function name,input
  arguments and output arguments
• without this line the file would be a script
  file
• A statement z randint(4,5) will pass 4,5 to m,n
  in the function file with the output result
  passed to variable z.

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Function file (contd.)

• Example 2
• Function mean, stdev stat (x)
• m,n size(x)
• If m 1
• M n
• End
• Mean sum(x)/m
• Stdev sqrt (sum(x.2)/m mean.2)
• to write comment statements

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Text Strings, error messages, inputHardcopy

• Text Strings use single quotes
• Use disp to display text strings
• Use error to display error messages
• Use input to interactively input data
• Use diary to get a hardcopy
• To turn off use diary off

21
Graphics

• Use plot to create linear x,y plots
• x -40.14 y sin(x) plot (x,y)
• x -1.50.011.5 y exp(-x.2) plot (x,y)
• t 0.0012pixcos(3t)ysin(2t),plot(x,y)
• Use shg to see the graphics screen
• Labelling
• Title xlabel ylabel gtext text axis
• Default is auto scaling
• Multiple plots
• Hold
• Linetypes and pointtypes

22
Graphics (contd.)

• 3-D mesh plots
• Use function mesh
• 3-D perspective of elements of matrix z
• Mesh (eye(10))
• xx -2.12yyxxx,y meshdom(xx,yy)z
  exp(-x.2 - -y.2)mesh(z)