EGR 106 Week 2 Arrays

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EGR 106 Week 2 Arrays Scripts

• Arrays
• Brief review of some Week 1 ideas
• Construction, addressing, etc
• Script and the editor
• Textbook chapter 2, pages 27-48, chapter 4.1-4.3,
  pages 77-81

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Review from Last Week

• Variables placeholders for numerical data
• equal sign is an assignment operator
• naming restrictions (not pi, etc. )
• can be complex valued ( x 3 7 i )
• Basic math on numbers and variables
• /
• Array Fundamental data unit in Matlab
• all variables are stored as arrays

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• Data values organized into rows and columns
• numeric or alphanumeric entries
• each element has position and value
• Size or dimension number of rows and columns of
  the array (rows by columns)
• Scalar, row vector, column vector, matrix

3 by 4 array
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Array Construction

• Direct specification
• Name followed by an equal sign ( ),
  just like variables
• List values within a pair of brackets ( )
• Enter data one row at a time
• left to right, top to bottom order
• space or comma between the values
• rows separated by semicolons or the enter key

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• For example, for
• use
• b 4,5,3,9 10,4,66,20 18,-3,2,0
• or
• b 4, 5, 3, 9
• 10, 4, 66, 20
• 18, -3, 2, 0

enter
enter
enter
enter
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• Can use math operators as well as numerics as the
  entries
• Note the common format of all entries in the
  response (exp(1) e 2.71828, log10(100) 2,
  2-12 0.00024414) MATLAB scales the exponent
  to the largest entry

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• This scaling is sometimes deceptive

Not really zero
Really zero
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• Special predefined arrays
• A matrix of all zeros
• zeros(R,C) zeros(N)
• A matrix of all ones
• ones(R,C) ones(N)
• A matrix of zeros with ones on the diagonal
• eye(R,C) eye(N)
• A matrix of random numbers (within 0 1 )
• rand(R,C) rand(N)

Square versions
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random on 0, 1
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• Concatenation gluing arrays together
• if a 1 2 3 b 4
  5 6
• Attaching left to right use a comma
• a, b
• Attaching top to bottom use a semicolon
• a b

comma
semicolon
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• Note that sizes must match
• if a 1 2 3
• then
• a, b ?? a b ??
• Size needs for concatenation
• of rows the same for side by side (comma)
• of columns the same for top to bottom
  (semicolon)

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• Evenly spaced vectors colon operator
• first increment maximum
• yields a row vector of equally spaced values
• examples
• 0 2 10 0 2 4 6 8 10
• 1 5 1 2 3 4 5
• 7 -2 -3 7 5 3 1 -1 -3
• 1 2 8 1 3 5 7
• default for increment is 1

Note does not hit 8!!
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• Linspace like the colon operator, but
  definitely gets the last number on the list
• linspace ( start, last, number of values)
• examples
• linspace(0,10,6) 0 2 4 6 8 10
• linspace(0,1,4) 0 0.333 0.667 1
• default for number is 100
• linspace(0,10) 0 0.101 0.202 10

Note increment for 100 points, 99 intervals
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Addressing and Sub-Arrays

• We indicate a particular element within an array
  by its row/column position
• use parentheses after the array name
• e.g.
  yield(2,4)

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• To read a value from an array
• Addressing on the right hand side of

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• To change a value in an array
• Addressing on the left hand side of

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• How about more than one entry?
• can specify a rectangular sub-array
• again, use parenthesis after the array name
• list desired rows, comma, desired columns
• as separate vectors, typically in brackets
• e.g.
• 
  yield(1 2,3 4)

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• Example
• sample(3,2)
• sample (1,24)
• sample (3,4,3,2,1)
• sample (1,3,2,4)

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• Used to read a sub-array ( rhs of )

Note scalar row choice does not need brackets!
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• Used to change a sub-array (lhs of )

Note array on the right needs to be of the
correct size !!!
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• Additional notes
• end specifies the last row or column
• a colon ( ) specifies all of a row or column
• yield(2,)
• yield(end,1)
• use a single index for row and column vectors
• bob 9 7 5 7 2

bob(4)
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• Addressing errors

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Wrong number of elements for the assignment
Wrong dimensions for assignment
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• Other useful methods that do work

Single indexing of matrices counts down columns,
starting at the top left
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Assigning values with too large an index just
grows the array
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Scalars work for sub-array replacement they
just scale up to the right size
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Replacing with a null matrix is the same as
deleting but it only works for entire rows or
columns
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• Rules of the road
• Symbols to use
• brackets to glue elements together to make an
  array (left to right or top to bottom)
• comma (or space) and semicolon (or enter) for
  separating row/column elements
• parentheses after the array name for addressing
• Be careful to match array sizes
• Rows first, then columns in addressing

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Some Useful Array Operators

• Transpose (single quote symbol ' )
• switches rows and columns

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• Size the number of rows and columns
• Length the larger of these two

Array answer
Scalar answer
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• Diag matrix vector operator for diagonal
  elements

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• Reshape
• resize fixed set of elements

Note the set of elements is exactly the
same Note column-wise approach to re-ordering the
values
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Character Arrays

• Rows of the array are strings of alphanumeric
  characters, one array entry per character
• Enter using a single quotation mark ( ' ) at each
  end

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• For multi-row alphanumeric arrays, each row must
  have the same number of characters
• name 'Marty' 'James' 'Bob '
• Use 2 quotation marks in a row to get 1
• 'Mary''s' Mary's (a 1 by 6
  array)
• Also, there are some built-in arrays
• y date y 05-Jan-2004
• (a 1 by 11 array)

Note need 2 spaces
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Scripts Simple Programs

• So far, commands have been typed in the command
  window
• Executed by pressing enter
• Edited using the arrow keys or the history
  window

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Script (m-file) Concept

• A file containing Matlab commands
• Can be re-executed
• Is easily changed/modified or e-mailed to someone
• Commands are executed one by one sequentially
• File is executed by typing its name (without .m)
• Results appear in the command window (or use )
• Can be created using any text editor
• .m extension
• Listed in Current Directory window

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• Matlabs Built-in, Color Editor
• Can create a new file
• or open an existing
• M file (icons or click
• on file name)
• Color used to aid in
• file creation
• (command types,
• typos, etc.)

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• typical Windows menu
• line numbers
• run button or F5
• debug capability

• comment lines
• note use of semicolons
• note use of colors

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• Where Matlab looks for things
• As a variable in the current workspace
• As a built-in function
• As script in the current directory
• can redirect using the buttons marked

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• Down the search path of directories
• Conclusion use unique names

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• How scripts can get data
• From arrays in the current workspace
• From arrays defined in the script
• Using the input command
• Numeric
• x input(' how many? ')
• String
• x input(' name? ', 's')

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• How scripts can show data
• Command of the array name
• Using the display command
• Existing array (a single array only if
  necessary, use !!)
• disp(x) or disp(x y)
• Text
• disp(' The task is done ')

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• Example
• Note that disp shortens the resulting output by
  dropping the array name and removing blank lines

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Sample Scripts
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Sound Arrays (not in the book!)

• Matlab can interface to microphones and speakers
  through the computers sound card (sampled and
  digitized) .e.g. maple

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• Matlab represents sounds using arrays
• (column vectors)
• Tools needed
• Microphone
• Speakers
• and
• 2 Matlab scripts
• init_sound.m
• sound_in.m

Headsets available in ECC
Files available on the egr106 website save them
in your work directory
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• How to use them
• Connect headset (is it muted?)
• Type init_sound at the command prompt (only
  needed once)
• Type sound_in at the prompt to record 1 second of
  sound (waits for your input)
• generates array named data
• Type sound(data,8000) at the prompt to play array
  data
• Can plot data, manipulate data before
  replaying, etc.