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What is MATLAB ?. MATrix LABratory Originally, it was a front-end to FORTRAN matrix routines developed in the 1970’s @ U. of New Mexico and Stanford Today it is a powerful, interactive mathematics ENVIRONMENT with many powerful capabilities (matrices, symbolic math, analysis)

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what is matlab
What is MATLAB ?
  • MATrix LABratory
    • Originally, it was a front-end to FORTRAN matrix routines developed in the 1970’s @ 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
support materials
Support Materials
  • MATLAB is available @ 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)
  • User’s Guide (comes with student edition)
  • Internet FAQ’s (e.g. www.mathworks.com)
  • MATLAB Primer (Bound copy ~$3.00)
accessing matlab
Accessing Matlab
  • Start Menu.. Programs.. Matlab
  • To exit..
    • >>quit
entering matrices
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
entering matrices contd
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
entering matrices contd1
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.
matrix operations
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
array operations
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
statements expressions variables
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
matrix building functions
Matrix Building Functions
  • Convenient Matrix Building Functions are
    • Eye
    • Zeros
    • Ones
    • Diag
    • Triu
    • Tril
    • Rand
    • Hilb
    • Magic
    • Toeplitz
for while if and relations
For,While, if – and relations
  • MATLAB flow control statements operate like those in most computer languages
  • For
    • x =[]; for i = 1:4, x = [x,i^2],end
    • x =[]; for i = 4:-1:1, x = [x,i^2],end
  • While
    • While relation
    • Statements
    • End
  • If
    • If relation
    • Statements
    • end
relations
Relations
  • < less than
  • > greater than
  • <= less than or equal
  • >= greater than or equal
  • == equal
  • ~= not equal
  • & and
  • | or
  • ~ not
scalar vector functions
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
matrix functions
Matrix Functions
  • Eig chol svd inv lu qr
  • Hess schur rref expm sqrtm poly
  • Det size norm cond rank
command line editing recall
Command Line Editing & Recall
  • Use left & right arrows
  • Backspace & delete keys
  • Home, end, Delete
  • Up/Down arrow keys
submatrices colon notation
Submatrices & Colon Notation
  • To achieve fairly complex data manipulation
  • Colon Notation (generate vectors and reference submatrices
  • Expression 1:5 generates [1 2 3 4 5]
  • Expressions 0.2:0.2:1.2 generates [0.2 0.4 0.6 0.8 1.0 1.2]
  • Expression 5:-1:1 gives [5 4 3 2 1]
  • X= [0.0:0.1:2.0]’;y=sin(x);[x,y] gives a table of sines
  • Colon Notation – used to access submatrices of a matix
    • A(1:4,3), A(:,3), A(1:4,:) , A(:, [2,4])
    • A(:[2,4,5]) = B(:,1:3)
    • A(:[2,4]) = A(:,[2,4])*[1,2:3,4]
m files
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.
function files
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.

function file contd
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
text strings error messages input hardcopy
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
graphics
Graphics
  • Use plot to create linear x,y plots
    • x = -4:0.1:4; y = sin(x); plot (x,y)
    • x = -1.5:0.01:1.5; y = exp(-x.^2); plot (x,y)
    • t = 0:.001:2*pi;x=cos(3*t);y=sin(2*t),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
graphics contd
Graphics (contd.)
  • 3-D mesh plots
    • Use function mesh
      • 3-D perspective of elements of matrix z
      • Mesh (eye(10))
      • xx = -2:.1:2;yy=xx;[x,y] = meshdom(xx,yy);z = exp(-x.^2 - -y.^2);mesh(z)
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