ADVANCED MATRIX OPERATIONS PART II

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ADVANCED MATRIX OPERATIONS - PART II

• June 1, 99

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ADVANCED SUBSCRIPTING

• You can pick out the elements of an array A using
  another array
• Define
• a1 2 34 5 67 8 9,
• v1 3
• When you see a(,v) read it like this
• all the rows of a but columns defined by v, i.e.
  columns 1 and 3

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Try it!

• Using a and v just defined, try the following
  command
• a(v,) and a(,v)
• Look at what you get. Does it make sense based on
  the definition?

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MAKING AN ARRAY OUT OF A MATRIX

• Using colon by itself strings out all the
  elements of A in a long column vector
• In other words, if you have a 5x5 matrix a, a()
  gives you a 25x1 column vector
• Try a()
• A more interesting effect is observed by the
  following
• A()1120

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Try it!

• Define a 5X5 matrix using rand. Then
• Use a() and see what you get
• More interestingly try this a()125
• The second step above is particularly
  significant. Look at it and see if you see a
  pattern

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The reshape command

• Colon operator took a, say 6x6, matrix and turned
  it into 36x1 array using a().
• reshape can take a 12x1 array and rearrange it as
  2x6 or 3x4, 6x2. The catch is that the rearranged
  matrix and the original must have, naturally, the
  same number of elements
• The question is how does reshape work? See next
  slide

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REARRANGING MATRICES

• It is possible to rearrange a, say, 3x4 matrix
  into a 2x6, 1x12, 4x3 etc. as long as number of
  elements do not change
• Breshape(A,m,n)
• maps A into an m rows, n columns matrix
• 1 2 3 4
• 5 6 7 8
• 9 10 11 12
• 13 14 15 16

1 9 2 10 3 11 4 12 5 13 6 14 7 15 8 16
reshape(A,2,8)
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Working of reshape
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Practical use of reshape

• A popular signal is alternating 1s and -1s
• 1 -1 1 -1 1 -1...1 -1
• How can you create an array like this of length
  1000?
• Hint first create two separate arrays, 1s and
  -1s, then mix them and use reshape

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sum command

• A very powerful command is sum.
• What sum does is to add all the elements of an
  array. For example if a1 2 3 4 5, then
  sum(a)15.
• Now, if a is
• sum(a) sums each column giving a 1x8 array
• sum(a)6 22 8 24 10 26 12 28

1 9 2 10 3 11 4 12 5 13 6 14 7 15 8 16
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EQUATING MATRICES

• It is important that when matrices or arrays are
  equated, the number of rows and columns match on
  both sides
• For example, if a is 3x3
• a()ones(1,10) is invalid because the left hand
  side is 9x1 but the right hand side is 1x10.
• The correct assignment is
• a()ones(1,9)
• Note the use of apostrophe for transposition

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Try it!

• Define a 5x5 matrix using rand. Then set all 25
  elements equal to 7 using an assignment statement

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EMPTY MATRICES

• Statement x defines a zero x zero matrix, an
  empty matrix. This is different from clear x.
• We can use an empty matrix to efficiently remove
  rows and columns from a matrix.
• Do next slide to see how this works
• In a 5x5 matrix, what does this statement do?
• a(, 2 3)

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Removing rows or columns of matrices

• In a 5x5 matrix, what does this statement do?
• a (,2 3)
• How about a ( 2 3,)

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MATRIX MANIPULATION

• Here is a list of interesting operators. Try a
  few
• rot90...............rotates a matrix by 90 dgrees
• fliplr................flip matrix/array left to
  right
• flipud..............flip matrix/array up and
  down
• diag.................extract diagonal

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USEFUL MATLAB FUNCTIONS

• The following functions are quite handy. Try them
  on a random vector of numbers of length 100.
• max(v)............find the maximum of v
• min(v)............find the minimum of v
• mean(v).........find the mean(average) of v
• std(v).............find the standard deviation
• sort(v)............sort v
• sum(v)...........sum of all the elements in v
• prod(v)..........product of elements in v
• hist(v)............histogram of valus in v

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WORKING WITH SOUND

• Lets try out the previous commands on an actual
  sound file.
• From the web page download and save an audio file
  called bond.mat. Place it in a directory MATLAB
  can see and type load bond
• Type sound(m,8000) and test if you hear anything
• Also, plot it using plot(m)

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Homework

• After loading bond, write a code to do the
  following tasks (one line per question! )
• Play bond backwards
• How many samples are in bond?
• Find the peak amplitude and its location
• How many times does the signal amplitude exceed
  0.6 volts
• Set all those amplitudes to 0.6
• Plot your result to verify these changes