Matlab Training Session 3: Control and Flow

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Matlab Training Session 3Control and Flow
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• Course Outline
• Weeks
• Introduction to Matlab and its Interface (Jan. 13
  2009)
• Fundamentals (Operators)
• Fundamentals (Flow)
• Importing Data
• Functions and M-Files
• Plotting (2D and 3D)
• Statistical Tools in Matlab
• Analysis and Data Structures
• Course Website
• http//www.queensu.ca/neurosci/matlab.php

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• Week 3 Lecture Outline
• Fundamentals of Matlab 3
• A. Week 2 Review
• B. Multiple Command Execution
• Breaking up long command instructions
• Entering multiple commands for execution
• Scripts
• C. Control and Flow
• Logical Operators
• Condition Statements
• Loops

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Week 2 Review

• N Dimensional matrices
• A 1 2 4 5 B 5 3 7 9
• 6 3 8 2 1 9 9 8
• Multidimensional matrices can be created by
  concatenating 2-D matrices together
• The cat function concatenates matrices of
  compatible dimensions together
• Usage cat(dimensions, Matrix1, Matrix2)

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Week 2 Review

• Scalar Operations
• Scalar (single value) calculations can be
  performed on matrices and arrays
• A 1 2 4 5 B 1 C 5
• 6 3 8 2 7
• 3
• 3
• Try
• A 10
• A 5
• B / 2

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Week 2 Review

• Matrix Operations
• Matrix to matrix calculations can be performed on
  matrices and arrays
• Addition and Subtraction
• Matrix dimensions must be the same or the
  added/subtracted value must be scalar
• A 1 2 4 5 B 1 C 5 D 2 4
  6 8
• 6 3 8 2 7
  1 3 5 7
• 3
• 3
• Try
• gtgtA B gtgtA C gtgtA D

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Week 2 Review

• Matrix Multiplication
• Built in matrix multiplication in Matlab is
  either
• Algebraic dot product
• Element by element multiplication

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Week 2 Review

• The Dot Product
• A(x1,y1) B(x2,y2) C(x1,y2)

• Element by Element Multiplication
• Element by element multiplication of matrices is
  performed with the . operator
• Matrices must have identical dimensions

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Week 2 Review

• Matrix Division
• Built in matrix division in Matlab is either
• Left or right matrix division
• Element by element division

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Week 2 Review

• Left and Right Division
• Left and Right division utilizes the / and \
  operators
• Left (\) division
• X A\B is a solution to AX B
• Right (/) division
• X B/A is a solution to XA B
• Left division requires A and B have the same
  number of rows
• Right division requires A and B have the same
  number of columns

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Week 2 Review

• Element by Element Division
• Element by element division of matrices is
  performed with the ./ operator
• Matrices must have identical dimensions

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Week 2 Review

• Matrix Exponents
• Built in matrix Exponentiation in Matlab is
  either
• A series of Algebraic dot products
• Element by element exponentiation
• Examples
• A2 A A (Matrix must be square)
• A.2 A . A

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Week 2 Review

• Relational Operators
• Relational operators are used to compare two
  scaler values or matrices of equal dimensions
• Relational Operators
• lt less than
• lt less than or equal to
• gt Greater than
• gt Greater than or equal to
• equal
• not equal

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Week 2 Review

• Relational Operators
• Comparison occurs between pairs of corresponding
  elements
• A 1 or 0 is returned for each comparison
  indicating TRUE or FALSE
• Matrix dimensions must be equal!
• gtgt 5 5
• Ans 1
• gtgt 20 gt 15
• Ans 1

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Week 2 Review

• The Find Function
• The find function is extremely helpful with
  relational operators for finding all matrix
  elements that fit some criteria
• A 1 2 4 5 B 7 C 2 2 2 2
  D 0 2 0 5 0 2
• 6 3 8 2 2
  2 2 2
• The positions of all elements that fit the given
  criteria are returned
• gtgt find(D gt 0)
• The resultant positions can be used as indexes to
  change these elements
• gtgt D(find(Dgt0)) 10 D 10 2
  10 5 10 2

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Week 2 Review

• The Find Function
• A 1 2 4 5 B 7 C 2 2 2 2
  D 0 2 0 5 0 2
• 6 3 8 2 2
  2 2 2
• The find function can also return the row and
  column indexes of of matching elements by
  specifying row and column arguments
• gtgt x,y find(A 5)
• The matching elements will be indexed by (x1,y1),
  (x2,y2),
• gtgt A(x,y) 10
• A 1 2 4 10
• 6 3 8 2

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Matrix Operations

• Embedding Functions
• Functions may be embedded into other functions,
  i.e. the values sent to a function can be the
  result from some other function
• Function embedding can be many levels deep
• Many lines of code can be condensed into one
  single command
• A 1 2 4 5 B 2 C 2 2 2 2
  D 0 2 0 3 0 2
• 6 3 8 2 2 2 2 2
• gtgt D(find(Dgt0))
• Ans 2 3 2

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Matrix Operations

• Embedding Functions
• Functions may be embedded into other functions,
  i.e. the values sent to a function can be the
  result from some other function.
• Function embedding can be many levels deep
• Many lines of code can be condensed into one
  single command
• A 1 2 4 5 B 2 C 2 2 2 2
  D 0 2 0 3 0 2
• 6 3 8 2 2 2 2 2
• gtgt D(find(Dgt0))
• Ans 2 3 2
• gtgtD(D(find(Dgt0)))
• Ans 2 0 0

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Matrix Operations

• Embedding Functions
• Functions may be embedded into other functions,
  i.e. the values sent to a function can be the
  result from some other function.
• Function embedding can be many levels deep
• Many lines of code can be condensed into one
  single command
• A 1 2 4 5 B 2 C 2 2 2 2
  D 0 2 0 3 0 2
• 6 3 8 2 2 2 2 2
• gtgt D(find(Dgt0))
• Ans 2 3 2
• gtgtD(D(find(Dgt0)))
• Ans 2 0 0
• gtgtA(B, D(find(Dgt0)) )
• Ans 3 8 3

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B. Multiple Command Execution
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Programming Tricks

• Entering Long Lines of Code
• If a matlab command contains many calculations,
  embedded functions or long variable names, it may
  be necessary to split the command onto multiple
  lines so that it can be read more easily
• The command tells matlab to continue the
  current command onto the next line

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Programming Tricks

• Entering Long Lines of Code
• If a matlab command contains many calculations,
  embedded functions or long variable names, it may
  be necessary to split the command onto multiple
  lines so that it can be read more easily
• The command tells matlab to continue the
  current command onto the next line
• gtgt long_variable_name1 long_variable_name2
  mean(long_variable_name3)

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Programming Tricks

• Entering Long Lines of Code
• If a matlab command contains many calculations,
  embedded functions or long variable names, it may
  be necessary to split the command onto multiple
  lines so that it can be read more easily
• The command tells matlab to continue the
  current command onto the next line
• gtgt long_variable_name1 long_variable_name2
  mean(long_variable_name3)
• gtgt long_variable_name1 long_variable_name2
• mean(long_variable_name3)

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Programming Tricks

• Entering Multiple Lines Without Running Them
• To enter multiple lines before running any of
  them, use ShiftEnter or ShiftReturn.
• The cursor moves down to the next line, where the
  next line can be written.
• to run all of the lines press Enter or Return .
• This allows the list of commands to be checked
  and edited before they are evaluated by matlab.

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Matlab Scripts

• Entering Multiple Lines Without Running Them
• Matlab can execute sequences of commands stored
  in files
• Files that contain matlab commands have the
  extension .m
• .m files are written and saved in the built in
  matlab m-file editor
• M-files are executed from the M-file editor or
  the command prompt
• M-files can call other M-files
• The location path of the M-file must be set in
  matlab

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Matlab Scripts

• Advantages of M-files
• Easy editing and saving of work
• Undo changes
• Readability/Portability - non executable comments
  can be added using the symbol to make make
  commands easier to understand
• Saving M-files is far more memory efficient than
  saving a workspace

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C. Control and Flow
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Logical Operators

• Logical operators are used to compare two boolean
  values
• A boolean value is a logical representation of
  true or false
• Conventionally 1 and 0 are used to represent true
  and false
• In matlab when boolean comparisons are made, a
  value of false or 0 represents false and any
  positive integer or true represents true

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Logical Operators

• Logical Operators
• AND
• OR
• NOT
• The (AND) operator returns TRUE only if both
  A,B values are TRUE otherwise returns FALSE
• (AND) Truth Table A B Result
• 1
  1 1
• 1
  0 0
• 0
  1 0
• 0
  0 0

A B ?
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Logical Operators

• Logical Operators
• AND
• OR
• NOT
• The (OR) operator returns TRUE if either A, B
  is TRUE, otherwise returns FALSE
• (OR) Truth Table A B Result
• 1
  1 1
• 1
  0 1
• 0
  1 1
• 0
  0 0

A B ?
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Logical Operators

• Logical Operators
• AND
• OR
• NOT
• The (NOT) operator reverses the boolean
  representation
• (NOT) Truth Table A A B B
• 1
  0 1 0
• 0
  1 0 1

A ? B ?
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Logical Operators
Examples A 0 B false C 1 D
8 E true F 0 1 0 2 0 3
0 1 Try gtgtA B gtgtA C gtgtA D
gtgtA E gtgtA F gtgtA B gtgtA C
gtgtA D gtgtA E gtgtA F gtgt
A gtgt B gtgt C gtgt
D gtgt E gtgt F gtgt AC
gtgt C F
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Logical Operators
Examples A 0 B false C 1 D
8 E true F 0 1 0 2 0 3
0 1 gtgtA B 0 gtgtA C 0 gtgtA D
0 gtgtA E 0 gtgtA F 0 0 0 0 gtgtA B
0 gtgtA C 1 0 0 0
0 gtgtA D 1 gtgtA E 1 gtgtA F
0 1 0 1 0 1 0 1
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Logical Operators
Examples A 0 B false C 1 D
8 E true F 0 1 0 2 0 3
0 1 gtgt A 1 gtgt B 1 gtgt C
0 gtgt D 0 gtgt E 0 gtgt F 1 0 1 0
gtgt AC 1 gtgt C F 0 0 0 0
1 0 1 0
0 0 0 0 When performing a
boolean operation with a matrix, an element by
element boolean comparison is made
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Logical Operators

• Order of Precedence
• When performing multiple logical operations
  without separating brackets, the (NOT) operator
  is evaluated first, followed by the (AND)
  operator and (OR) operator
• ABC (AB) C
• ABC A (BC)

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Logical Operators

• Order of Precedence
• When performing multiple logical operations
  without separating brackets, the (NOT) operator
  is evaluated first, followed by the (AND)
  operator and (OR) operator
• ABC (AB) C
• ABC A (BC)
• ABC (A(B)) C
• ABC A ((B)C)

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Control and Flow

• Control flow capability enables matlab to
  function beyond the level of a simple desk
  calculator
• With control flow statements, matlab can be used
  as a complete high-level matrix language
• Flow control in matlab is performed with
  condition statements and loops

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Condition Statements

• It is often necessary to only perform matlab
  operations when certain conditions are met
• Relational and Logical operators are used to
  define specific conditions
• Simple flow control in matlab is performed with
  the If, Else, Elseif and Switch statements

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Condition Statements

• If, Else, and Elseif
• An if statement evaluates a logical expression
  and evaluates a group of commands when the
  logical expression is true
• The list of conditional commands are terminated
  by the end statement
• If the logical expression is false, all the
  conditional commands are skipped
• Execution of the script resumes after the end
  statement
• Basic form
• if logical_expression
• commands
• end

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Condition Statements
Example A 6 B 0 if A gt 6 D 1 2
6 A A 1 end if A B E
mean(B) end
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Condition Statements

• If, Else, and Elseif
• The else statement forces execution of the
  commands below the else statement if the original
  logical expression evaluates to false
• Only one list of commands can be executed
• Basic form
• if logical_expression
• commands 1
• else
• commands 2
• end

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Condition Statements
Example A 6 B 0 if A gt 6
D 1 2 6 A A 1 else D 0
0 0 A A - 1 end
if A B E mean(B) else E 0 end
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Condition Statements

• If, Else, and Elseif
• The elseif statement forces execution of the
  commands below the else statement if the original
  logical expression evaluates to false
• Only one list of commands can be executed
• Basic form
• if logical_expression
• commands 1
• elseif logical_expression_2
• commands 2
• elseif logical_expression_3
• commands 3
• end

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Condition Statements
Example A 6 B 0 if A gt 3
D 1 2 6 A A 1 elseif A gt 2 D
D 1 A A 2 end Both the if and
elseif statements are evaluated
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Condition Statements

• Switch
• The switch statement can act as many elseif
  statements
• Only the one case statement whos value satisfies
  the original expression is evaluated
• Basic form
• switch expression (scalar or string)
• case value 1
• commands 1
• case value 2
• commands 2
• case value n
• commands n
• end

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Condition Statements
Example A 6 B 0 switch
A case 4 D 0 0 0 A A - 1 case 5
B 1 case 6 D 1 2 6 A A
1 end Only case 6 is evaluated
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Loops

• Loops are an important component of flow control
  that enables matlab to repeat multiple statements
  in specific and controllable ways
• Simple repetition in matlab is controlled by two
  types of loops
• For loops
• While loops

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Loops

• For Loops
• The for loop executes a statement or group of
  statements a predetermined number of times
• Basic Form
• for index startincrementend
• statements
• end
• If increment is not specified, an increment
  of 1 is assumed by matlab

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Loops

• For Loops
• Examples
• for i 11100
• x(i) 0
• end
• Assigns 0 to the first 100 elements of vector x
• If x does not exist or has fewer than 100
  elements, additional space will be automatically
  allocated

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Loops

• For Loops
• Loops can be nested in other loops
• A
• for i 1m
• for j 1n
• A(i,j) i j
• end
• end
• Creates an m by n matrix A whose elements are the
  sum of their matrix position

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Loops

• While Loops
• The while loop executes a statement or group of
  statements repeatedly as long as the controlling
  expression is true
• Basic Form
• while expression
• statements
• end

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Loops

• While Loops
• Examples
• A 6 B 15
• while A gt 0 B lt 10
• A A 1
• B B 2
• end
• Iteratively increase A and decrease B until the
  two conditions of the while loop are met
• Be very careful to ensure that your while loop
  will eventually reach its termination condition
  to prevent an infinite loop

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Loops

• While Loops
• Examples
• A 6 B 15
• while A gt 0 B lt 10
• if A lt 0
• A A 1
• elseif B gt 10
• B B 2
• end
• end
• Conditional statements can be nested for specific
  internal control of variables

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Loops

• Breaking out of loops
• The break command instantly terminates a for
  and while loop
• When a break is encountered by matlab, execution
  of the script continues outside and after the
  loop

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Loops

• Breaking out of loops
• Example
• A 6 B 15
• count 1
• while A gt 0 B lt 10
• A A 1
• B B 2
• count count 1
• if count gt 100
• break
• end
• end
• Break out of the loop after 100 repetitions if
  the while condition has not been met

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Getting Help

• Help and Documentation
• Digital
• Accessible Help from the Matlab Start Menu
• Updated online help from the Matlab Mathworks
  website
• http//www.mathworks.com/access/helpdesk/help/tech
  doc/matlab.html
• Matlab command prompt function lookup
• Built in Demos
• Websites
• Hard Copy
• Books, Guides, Reference
• The Student Edition of Matlab pub. Mathworks Inc.