Intro to Matlab

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WELCOME
EF 105 Fall 2006 Week 10
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Topics

• Engineering Problem Solving
• Programming Logic
• Intro to MATLAB

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Engineering Problem Solving

• Define the problem clearly
• Work hand examples
• Develop the Algorithm (Steps to follow)
• Document the Algorithm with a FLOWCHART
• Implement the Algorithm (Write computer program)
• Test the Implementation (Run the Program)
• Evaluate the Results

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PROGRAMMING LOGICTop-Down Algorithm Development

• Divide and Conquer
• Break Problem into smaller tasks.
• Define the interaction between tasks.
• Recursively solve the individual tasks.
• Build up the overall solution from the pieces.

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Structured Programming

• Structured Programming
• Combination of
• Sequences
• Selections
• Loops
• Sequences
• Series of operations that are performed in order.
• Selections
• Choose one path from two or more possible paths.
• Loops
• Execute a block of code repeatedly as long as
  some condition is met.

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Basic Flowcharting Elements
Arrows show the flow - cannot diverge but can
converge.
Execution Block
Selection Block
Entry Point
Exit Point
Input/Output Block
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Selection Statements

• Selectively choose one path of execution.
• Based on the evaluation of a test.
• Logical Test outcome is either TRUE or FALSE.

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Loop Structures

• Special case of Selection Statement
• One branch eventually leads back to the original
  selection statement.
• Permits a block of code to be executed repeatedly
  as long as some test condition is satisfied.

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Basic Flowchart Symbols
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Practice Algorithm and Flowchart
Compute a sum of all integers from 1 to 100 and
displays the result

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Algorithm
Step 4 How do we compute the output? (first
solution)

Step 4.1 Start with the current integer 1
Step 4.2 Sum starts with 0
Step 4.3 Add the current integer to Sum
Step 4.4 If the current integer is less than
100, keep on adding the current integer to sum
and increase It by 1(i.e, go back to 4.3).
Step 4.5Otherwise, print out the sum

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Flowchart

Step 4.3 Add the current integer to Sum
Step 4.4 If the current integer is less than
100, go to next integer and keep on adding the
current integer to sum (i.e, go back to 4.3).

Step 4.5Otherwise, print out the sum
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Intro to Matlab
Inside Matlab This is what you should see once
Matlab has loaded. The three most useful areas in
the Matlab window are 1. Right command window
is used for inputting commands 2. Top left
workspace window notes size of matrices used 3.
Bottom left command history window maintains a
sequential list of past commands.
Workspace
Command Window
Command Window
Command Window
Command History
Command History
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Help in MATLAB
The following are three ways to access Matlabs
help files 1. a. From options at top of Matlab
window select Help ? Matlab Help b. Select
Index tab c. Type topic to be searched in
box 2. In Matlab window type a command preceded
by help or 'doc' For example,the following
commands would produce a help file for the plot
command. gtgt help plot or gtgtdoc plot 3. a. Double
click command for which you want help b.
Right-click on command c. Select Help on
Selection
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Creating files in MATLAB
A. To create a new M-file do one of the
following 1. In top left corner of Matlab window
select File ? New ? M-file 2. Select New M-file
shortcut button located at the top left corner of
Matlab screen B. Typing the following clears the
command window gtgt clc C. Typing a semicolon at
the end of a command suppresses output. Note
the difference between typing the following
commands gtgt x00.510 gtgt x00.510
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How/Where to write program

• Go to MATLAB command window
• File-New-M-File
• M-file is an Editor window
• Write your program in M-file
• Save in temp/ or your Disk.
• In command window, Run this file.

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Basic Operators

• addition
• - subtraction
• multiplication
• / right division
• power

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Review Arithmetic Operations and Precedence


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Use Parentheses to Override Operator Precedence

• Normal evaluation of expressions
• Left-to-Right if same level and no parentheses

e.g. 33-8/47-52 27-27-10 257-10
32-10 22

• Use parentheses to override
• e.g. (33-8)/4(7-5)2 (9-8)/422
• 1/44 4.25

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Overview of MatLab Variables

• Variables are names used to hold values that may
  change throughout the program.
• MatLab variables are created when they appear on
  the left of an equal sign.
• gtgt variable expression creates the "variable''
  and assigns to it the value of the expression on
  the right hand side. You do not need to define or
  declare a variable before it is used.
• gtgt x 2 creates a scalar
• The variable is x and indicates a comment

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Hands-On DEMO Expression Evaluation
In MatLab, enter the following gtgt x 1.4 gtgt
numerator x3 - 2x2 x - 6.3 gtgt denominator
x2 0.05005x 3.14 gtgt f numerator /
denominator
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Variable Naming

• Naming Rules
• must begin with a letter, cannot contain blank
  spaces
• can contain any combination of letters, numbers
  and underscore (_)
• must be unique in the first 31 characters
• MatLab is case sensitive name, Name and
  NAME are considered different variables
• Never use a variable with the same name as a
  MatLab command (see next slide)
• Naming convention
• Usually use all_lowercase_letters
• -or- camelNotation ("hump" in middle)

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Reserved Words

• MatLab has some special (reserved) words that you
  may not use as variable names

break case catch catch continue else elseif end for function global if otherwise persistent return switch try while
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Commands involving variables

• who lists the names of defined variables
• whos lists the names and sizes of defined
  variables
• what lists all your m-files stored in memory.
• clear clears all variables, reset the default
  values of special variables.
• clear name clears the variable named
• clc clears the command window
• clf clears the current figure and the graph
  window.

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Scalars and Vectors and Matrices

• In MatLab, a scalar is a variable with one row
  and one column.
• A vector is a matrix with only one row OR only
  one column. The distinction between row and
  column vectors is crucial.
• When working with MatLab you will need to
  understand how to properly perform linear algebra
  using scalars, vectors and matrices. MatLab
  enforces rules on the use of each of these
  variables

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Scalars

• Scalars are the simple variables that we use and
  manipulate in simple algebraic equations.
• To create a scalar you simply introduce it on the
  left hand side of an equal sign.
• gtgt x 1
• gtgt y 2
• gtgt z x y

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Vectors

• A row vector in MATLAB can be created by an
  explicit list, starting with a left bracket,
  entering the values separated by spaces (or
  commas) and closing the vector with a right
  bracket.
• A column vector can be created the same way, and
  the rows are separated by semicolons.
• Example
• gtgt x 0 0.25pi 0.5pi 0.75pi pi
• x
• 0 0.7854 1.5708 2.3562
  3.1416
• gtgt y 0 0.25pi 0.5pi 0.75pi pi
• y
• 0
• 0.7854
• 1.5708
• 2.3562
• 3.1416

x is a row vector. y is a column vector.
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Simple Vector Commands
x startend create row vector x starting with start, counting by one, ending at end
x startincrementend create row vector x starting with start, counting by increment, ending at or before end
linspace(start,end,number) create row vector x starting with start, ending at end, having number elements
length(x) returns the length of vector x
y x' transpose of vector x (row to column, or columnn to row)
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Hands-On DEMO Creating Vectors

• gtgt a 110 leave off semi-colon to see what
  you get each time
• gtgt b 00.11
• gtgt c 7 8 9
• gtgt d 10 11 12
• gtgt length(b)
• gtgt linspace(0,100,21)

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Hands-On DEMO linspace function
Plotting a function using vector math x
linspace(0, 20, 100) define 100 x values (from
0 to 20) y 5exp(-0.3x).sin(x) compute y
vector plot(x,y), xlabel('X'), ylabel('Y'),
title('Vector calc')

• linspace( ) function can be very effective for
  creating the x vector

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Entering Matrices

• A 1 2 3 4 5 6 7 8 9
• OR
• A 1 2 3
• 4 5 6
• 7 8 9
• Must be enclosed in brackets
• Elements must be separated by commas or spaces
• Matrix rows must be separated by semicolons or a
  return
• Matlab is case sensitive

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Matrix Elements

• x -1.3 sqrt(3) (123)4/5
• Output -gt x -1.3000 1.7321 4.8000
• Matrix Manipulation
• x(5) abs(x(1))
• Let r 1 2 3 4 5
• xx xr
• z xx(2,2)
• T xx(2,13) row 2, col. 1-3
• Semicolon at the end of a line means dont print
  to the command window.

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Output Format

• Format short
• 1.3333 0.0000
• Format short e
• 1.3333E000 1.2345E-006
• Format long
• 1.333333333333338 0.000001234500000
• Format long e
• 1.33333333333333E000 1.234500000000003E-006
• Format hex
• 3FF555555555555 3EB4B6231ABFD271
• Defaults to format short.

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Matrix Operations

• Transpose
• A 1 2 3 4 5 6 7 8 9
• C A
• D -1 0 2

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Array Operations(using the period)

• The term array operations refer to
  element-by-element operations.
• Preceding an operator (, /, , ) by a period
  indicates an element-by-element operation.
• The addition and subtraction, matrix and array
  operations are the same and dont need a period
  before these operators.
• Example
• X 1 2 3 Y4 5 6
• W X.Y to mult. X and Y arrays

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Generating Vectors

• Most often used for a time vector.
• time 0.0100.0
• Time 10.00.5100.0
• B_time 100.0-0.550.0
• Variable firstincrementlast

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Useful Matrices

• Empty Matrix
• E
• EE(2 4,)
• Empties rows 2 4 and all columns in rows 2 4.
• Zeros
• Ze zeros(2,3)
• Creates a 2 x 3 matrix consisting all of zeros.
• Ones
• O ones(3,3)
• Creates a 3 x 3 matrix consisting all of ones.
• Eye
• I eye(3,3)
• Creates a 3 x 3 matrix consisting of an identity
  matrix. (Is on diagonal and 0s elsewhere)

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Hands-On DEMO Matrix Operations -
Transposes Transpose (indicated by )new
matrix created by exchanging rows and columns of
original matrix
h 1 2 3h'   (nothing)ans 1      2      3 Switches from row to column vector.
h h'h . h ans 14ans 1 4 9 is matrix multiplication, and so the dimensions must line up correctly. (more on this later). is entry-by-entry multiplication.
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Hands-On DEMO Functions of Vectors

• Most Matlab functions will work equally well with
  both scalars and arrays (of any dimension)

gtgt A1 2 3 4 5 gtgt sin(A) ans 0.8415
0.9093 0.1411 -0.7568 -0.9589 gtgt
sqrt(A) ans 1.0000 1.4142 1.7321
2.0000 2.2361
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Strings of Characters

• MatLab variables may also contain strings, which
  are vectors of individual characters. There is no
  typographical difference in appearance between
  numerical variables and string variables.
• The type of variable (numerical or string) is
  determined when the variable is created.
• gtgt x 5.2 numeric
• gtgt y 'Chewbacca' string

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What are Character Strings? Arrays!

• Example
• C 'Hello' C is a 1x5 character array.
• D 'Hello there' D is a 1x11 character
  array.
• A 43 A is a 1x1 double array.
• T 'How about this character string?'
• size(T)
• ans
• 1 32
• whos What do you observe?
• Name Size Bytes Class
• A 1x1 8 double
  array
• C 1x5 10 char
  array
• D 1x11 22 char
  array
• T 1x32 64 char
  array
• ans 1x2 16 double
  array
• Grand total is 51 elements using 120 bytes

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Hands-On DEMO Strings of Characters

• gtgt h 'Hello'
• gtgt w 'World'
• gtgt h ', ' w called concatenation

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format Examples(MATLAB performs all computations
in double precision)

•   The format command described below switches
  among different display formats.
•   Command      Result                       
  Example format short      5 digit scaled fixed
  point      3.1416 format long       15 digit
  scaled fixed point   3.14159265358979 format
  short e   5 digit floating-point          3.1416e
  00 format long e    15 digit floating-point  
  3.141592653589793e00
• format short g   general purpose           
  5 or 1.25 or 3.0e-12
• format bank       Fixed dollars and
  cents         7.95 format rat        Ratio of
  small integers         355/113   format
  compact Suppresses excess line feeds. format
  loose     Add line feeds.

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Hands-On DEMO Formatting

• p020
• format short e exponential
• p' pow2(p)' pow2(-p)'
• format short g general purpose
• p' pow2(p)' pow2(-p)'

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In-Class Exercise MatLab Calculations

• Do the following in MatLab
• Create a matrix with the form
• 2 3
• 5 1
• Create a row (or "horizontal") vector of 2
  elements, 3 and 4 (inclusive).
• Create a second column (or 'vertical') vector
  with the elements 2 and 1 in that order.
• Type 'whos' to view your variables. It should
  read (for example)
• gtgt whos Name Size Elements Bytes Density
  Complex
• a 2 by 2 4 32
  Full No
• b 1 by 2 2
  16 Full No
• c 2 by 1 2 16 Full No
• Grand total is 14 elements using 112 bytes Here,
  a is the matrix, b is the first vector, and c is
  the second vector.
• Now complete the following exercise
• Multiply your matrix by your first vector, above.
  
• Perform element by element division of your
  resulting vector, divided by your second vector
  transposed. (The result should be a two element
  horizontal vector with 13 as each entry. )
• Type 'clear' to clear all variables from the
  workspace.
• Add your name as comment, print Command Window
  and turn in

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Saving/Loading Data Values

• Be sure you have the correct Current Directory
  set
• clear, clc
• clear workspace and command window to start
• assign and calc a few values
• save file_name
• saves file_name.mat in current directory
• saves all defined variables
• clear load file_name
• brings workspace back

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Hands-On DEMO Saving Workspace

• First make sure your workspace is clear, and that
  your Current Directory is set to "My Documents"
  subfolder with your username (e.g. Djackson)
• Create a few scalars and vectors
• check workspace window for variables
• gtgt save demo -OR- click corresponding button
• look at your folder in My Documents subfolder
• Clear workspace, check Workspace
• then Reload variables, check Workspace

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Scripts

• Scripts allow us to group and save MatLab
  commands for future use
• If we make an error, we can edit statements and
  commands
• Can modify later to solve other related problems
• Script is the MatLab terminology for a program
• NOTE Scripts may use variables already defined
  in the workspace.
• This can lead to unexpected results.
• It is a good idea to clear the workspace (and the
  command window) at the beginning of all scripts.
• clear, clc

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M-files Scripts

• A Script is the simplest example of an M-file.
• When a script-file is invoked, MatLab simply
  executes the commands found in the file.
• Any variables created in the script are added to
  the MatLab Workspace.
• Scripts are particularly useful for automating
  long sequences of command.

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Writing a MATLAB Script (program)

• File ? New ? M-File
• usually start with clear, clc, format compact
• comments after
• for in-class exercises include at least
• Course, date,section (e.g. EF105, Monday 800
  )
• a short title
• your name
• semi-colons to suppress variable initialization
• omit semi-colons to display results
• You can leave off ALL semi-colons to trace a
  program

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Matlab Editor(note "Save and Run" button)
Access to commands
Color keyed text with auto indents
tabbed sheets for other files being edited
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Script Files (filename.m)

• Always check Current Directory Window
• Set to MyDocuments\username
• Running scripts
• from editor window, click "Save and run" button
• -or- just type filename
• -or- type run filename

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Hands-On DEMO Creating our First
Script(factorial)

• File ? New ? M-File
• File ? Save As ... fact_n
• Operates on a variable in "global" workspace
• Variable n must exist in workspace
• Variable fact is created (or over-written)

fact_n Compute n-factorial, n!12...n by
DFJ fact prod(1n) no semi-colon so fact
displays
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Hands-On DEMO Running your Script

• To Run just type
• gtgt n5
• gtgt fact_n
• -OR-
• gtgt n10
• gtgt run fact_n

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Displaying Code and Getting Help

• To list code, use type command
• gtgt type fact_n
• The help command displays first consecutive
  comment lines
• gtgt help fact_n

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MATLAB Exercise 1

• See the Word document for this exercise and
  perform at end of class on your own!!