Lecture 2 Matlab Introduction

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Lecture 2 - Matlab Introduction

• CVEN 302
• August 29, 2001

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Lecture Goals

• Scalar Operations
• Vectors Operations
• Matrix Operations
• Plot Graphics
• Matlab files
• Matlab controls

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Scalar Operations

• Addition - a b
• Subtraction - a - b
• Multiplication - a b
• Right Division - a / b
• Left Division - b \ a
• Exponential - ab

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Order of Precedence of Arithmetic 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.

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Vector

• A vector is defined as a combination of variables
  values to with components of xj , where j 1,n
  values.

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Vectors

• Matlab is designed for vector and matrix
  manipulation some of the basic commands are given
  as

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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.

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Vector element Operations

• Individual addition A B A B
• Individual subtraction A B A - B
• Individual multiplication AB A.B
• Individual division (left) A/B A./B
• Individual division (right) A\B A.\B
• Individual power AB A.B

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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.

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Vector Operations

• Vector product - A is 1 x n vector
• The magnitude of the vector is a dot product of
  the vector.

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Vector Examples
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Matrix

• A matrix is a two dimensional arrays, where the
  matrix B is represented by a m x n

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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

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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.

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Matrix Multiplication Examples
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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.

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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 lt left
• lt right
• p pentagram
• h hexagram

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Plot Commands

• t linspace(0, 2pi) - 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 cosinesine verse t
  with red dots.

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Plot Commands

• Example
• plot(t,y1,-,t,y2,g,t,y3,r-.) - plots all
  3
• axis( 0 2pi -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.

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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

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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.

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Data Files

• Data files can be written in two forms
• Matlab format
• ascii format

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Matlab data format

• MatLab generates a data
• file, which will have
• look like
• filename.mat
• File can be loaded into
• the memory with
• load filename

• t linspace(0, 2pi)
• x cos(t)
• save data1 t x
• clear
• what
• data1.mat
• load data1

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ACSII format

• An ascii file type can be
• created by adding a flag
• on the end of the save
• command
• save filename.dat -ascii

• t linspace(0 2pi)
• x sin(t)
• save data2.dat t x -ascii
• dir
• data2.dat
• clear
• load data2.dat -ascii

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Loading Data Files

• Matlab Files
• load filename
• The file will load the file into
• the same format as it was
• saved.

• ASCII Files
• load filename.dat -ascii
• The file will be loaded as an
• data array and will require
• you to modify to obtained the
• data vectors.

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Data file example

• tlinspace(0,2pi)
• y1 sin(x)
• save data1 t y1
• clear
• (created data1.mat and
• will show up in home
• directory.)
• load data1

• (data1 will have created
• t and y1 vectors.)
• save data2.dat t y1 -ascii
• clear
• (created a ascii file with
• the data)
• load data2 -ascii

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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

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Homework

• Check the Homework files
• create a data file
• input a simple program
• run the program
• plot the results