Transcript PPT Matlab: – Odu

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
• 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
• Start Menu.. Programs.. Matlab
• To exit..
– >>quit
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.)
• Example A = [1,2,3; 4,5,6; 7,8,9] or
• A=[
– 123
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– 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 (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
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Addition
Substraction
Multiplication
Power
Transpose
Left Division
Right division
– E.g. x = A\b
– x = b/A
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is the solution of A * x = b
is the solution of x * A = b
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
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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
• Convenient Matrix Building Functions are
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Eye
Zeros
Ones
Diag
Triu
Tril
Rand
Hilb
Magic
Toeplitz
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
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< less than
> greater than
<= less than or equal
>= greater than or equal
== equal
~= not equal
& and
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~ not
Scalar & Vector functions
• Scalar
– Sin
– Cos
– Tan
asin exp
acos log
atan rem
abs round
sqrt floor
sign ceil
• Vector
– Max
– Min
– Sort
sum median
prod mean
std
any
all
Matrix Functions
– Eig
– Hess
– Det
chol svd inv lu
qr
schur rref expm sqrtm poly
size norm cond rank
Command Line Editing & Recall
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Use left & right arrows
Backspace & delete keys
Home, end, Delete
Up/Down arrow keys
Submatrices & Colon Notation
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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
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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
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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
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.)
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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
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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
• 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
– Default is auto scaling
• Multiple plots
– Hold
• Linetypes and pointtypes
gtext
text
axis
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)