Lecture 2 - Matlab Introduction

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Lecture 2 - Matlab Introduction Powered By Docstoc
					Lecture 2 - Matlab Introduction

           CVEN 302
          May 30, 2001
              Lecture Goals
•   Vectors Operations
•   Matrix Operations
•   Plot & Graphics
•   Matlab files
•   Matlab controls
                  Vector
A vector is defined as a combination of
 variables values to with components of xj ,
 where j = 1,…n values.
                                       
                  x  x1 , x2 , x3 ,...
                       x1 
                      x 
                       
                 xT   2
                       x3 
                      
                       
                        Vectors
• Matlab is designed for vector and matrix
  manipulation some of the basic commands
  are given as
                             1 
                             3 
                              
        t   ,3,4,6
             1          t   
                             4 
                             6 
                              
        t  [1
                                         1 
                                          
             4     or t  [1;4;6]    t 4
                                         6 
                                          
             6]
                     Vectors
• t‟ represents the transpose of the vector “t”.
• Individual components can be represented by
        t = [ 4,5,6,9], where t(3) = 6.
• [ ] represent the start and finish of the vector
  and/or matrix. ( ) represent components of the
  vector.
• A period “.” represent an elemental set of
  functions, such as multiplication, division,etc.
       Vector element Operations
• Individual addition             A+B   A+B
•   Individual subtraction        A–B   A-B
•   Individual multiplication     A*B   A.*B
•   Individual division (left)    A/B   A./B
•   Individual division (right)   A\B   A.\B
• Individual power                AB    A.^B
        Hierarchy of the vector
              operations
Precedence
  (1)     - Parenthesis
  (2)     - Exponential from left to right
  (3)     - Multiplication and division from left
            to right.
  (4)     - Addition and subtraction from left to
            right.
          Vector Operations
• Vector product - A is 1 x n vector
           A * A'  1 x n * n x 1  1 x 1
           A'*A  n x 1* 1 x n   n x n 


• The magnitude of the vector is a dot product
  of the vector.
             A * A'  1 x n * n x 1  1 x 1
             A  A * A'
Vector Examples
                  Matrix
• A matrix is a two dimensional arrays, where
  the matrix B is represented by a [ m x n ]

              b1,1  b1,n 
                           
           B    
             bm ,1
                     bm ,n 
                            
          Matrix Operations
• For addition and subtraction, the matrix
  sizes must match up. If you are adding to
  each component of the matrix you can do a
  simple scalar addition.

• Examples: [A] + [B] = [C]
             [A] + 3 = [D]
           Matrix Operation
• Multiplication of matrices will need to
  match up the columns to the row values of
  the following matrix. Scalar multiplication
  will work.
• Division is different. You will either divide
  member by member, where the matrices are
  the same size or you will need to find the
  inverse of the matrix.
Matrix Multiplication Examples
     Graphical Representation
• Matlab has a function known as “plot( ),
  where the values are plotted on an x-y
  plane.
• General format of the graph is given as,
           plot(x,y,‟symbols‟)
• The symbols represent the color, point
  shape, and the line type.
             Plot symbols commands
Colors             Symbols                Lines
y – yellow         . – point           - – solid line
m – mag            o – circle          : – dots
c – cyan           x – xmark           -. – line dot
r – red            + – plus            - - – dashes
g – green          * – star
b – blue           s – square
w – white          d – diamond
k – black          v – triangle down
                   ^ – triangle up
                   < – left
                   < – right
                   p – pentagram
                   h – hexagram
                  Plot Commands
t = linspace(0, 2*pi);   - results in 100 data points
y1 = cos(t);             - cosine of the points
y2 = sin(t);             - sine of the points
y3 = y1.*y2;             - cos(t)*sin(t)
plot(t,y1,‟-‟) ;         - plots cosine verse t with a
                           straight line.
plot(t,y3,‟r:‟)          - plots cosine*sine verse t
                           with red dots.
              Plot Commands
Example:
plot(t,y1,‟-‟,t,y2,‟g*‟,t,y3,‟r-.‟) - plots all 3
axis( [0 2*pi -1.5 1.5]) - adds axes
legend(„cos(t)‟,‟sin(t)‟,‟cos(t)*sin(t)‟) - legend

Note that the [ ] represent an array and ( ) represent a
 function, and „ „ represent the symbols.
         Matlab commands for
          file management
 The files can be written as a script, which can be
 loaded into the memory. From the command line:

• “echo” - causes the file to be echoed to the screen.
• “what” - shows the type of file in the current
  directory.
• “type” - will present show the file contents
                    Matlab Files
There are three types of files:
• Data files
   – Matlab files have their own format for saving data
   – ascii files are standard text files, which can be printed
     out or used in excel files.
• m-files represent the program files.
• function files are functions similar to „sin(x)‟, cos(x), etc.
                Data Files

Data files can be written in two forms:

     • Matlab format
     • ascii format
          Matlab data format
MatLab generates a data   t = linspace(0, 2*pi)
file, which will have     x = cos(t)

look like:                save data1 t x
“filename”.mat            clear
                          what
File can be loaded into
the memory with:          data1.mat

load “filename”           load data1
                ACSII format
An ascii file type can be    t = linspace(0 2*pi)
                             x = sin(t)
created by adding a flag     save data2.dat t x -ascii
on the end of the save       dir
                             data2.dat
command
                             clear
save “filename”.dat -ascii   load data2.dat -ascii
                Loading Data Files
        Matlab Files                      ASCII Files

load “filename”                    load “filename.dat” -ascii

The file will load the file into   The file will be loaded as an
the same format as it was          data array and will require
saved.                             you to modify to obtained the
                                   data vectors.
              Data file example
t=linspace(0,2*pi);      (data1 will have created
y1 = sin(x);              t and y1 vectors.)
save data1 t y1;
clear                    save data2.dat t y1 -ascii
                         clear
(created data1.mat and
 will show up in home    (created a ascii file with
 directory.)             the data)

load data1;              load data2 -ascii
    Data file example continued
(loaded an ascii file into
memory as data2 array)
whos

data2 2X100 double array

t= data2(1,:);
y1= data2(2,:);

: assigns the row to the
vector
                 Homework
• Check the Homework files
  –   create a data file
  –   input a simple program
  –   run the program
  –   plot the results