CS100A, Fall 1998

1
CS100A, Fall 1998

• Lecture 19, Thursday Nov 05
• Matlab
• Concepts
• Matlab arrays
• Matlab subscripting
• Matlab plotting

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• Arrays (review)
• All data in Matlab is actually an array (or a
  vector) a 1- or 2-dimensional table of numbers.
  
• A single value, called a scalar, is simply an
  array of size 1.
• To construct a 1-D array, list its elements
  surrounded by square brackets.
• y 4 -5 10 0 5.2
• Individual elements are accessed using a
  parenthesized subscript.
• x(3)
• The first element of array x is x(1).
• The number of elements in array x is given by the
  built-in function
• length(x)

3

• Creating Arrays (review)
• An array of evenly-spaced values can be generated
  by
• linspace(minVal, maxVal, nVals)
• Two arrays can be combined with a comma and
  brackets
• x 1 2 3
• y 4 5 6
• x, y (is 1 2 3 4 5 6)
• z x, x, y

4

• Creating Arrays (colon)
• The colon can be used to generate a sequence of
  values. Forms
• lowValue highValue
• lowValue step highValue
• Examples
• 1 10
• 1 2 10
• 1 0.5 10
• 10 1 1
• 0 0.01 0.5
• A sequence of values is an array value.
• a 0 2 16
• b 1 6 / 3
• A sequence of integers can also be used to select
  a segment of an array.
• a(36)

5

• Array Functions
• There are many functions to compute facts about
  arrays.
• min(x), max(x), mean(x), ...
• Array Operations
• Basic operations on arrays are performed
  element-by-element. Example function
  applications
• x 4.2 7.89 2.4 -42.1
• floor(x)
• An operation may involve an array and a scalar.
  The operation is performed on each element of the
  array and the result is an array of these values.
• x / 2

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• Array Operations (cont.)
• Operations may combine two arrays if they have
  exactly the same length.
• x 1 3 5 7
• y 10 20 30 40
• x y
• y - x
• The operations and work as expected.
• For element-by-element multiplication, division,
  and exponentiation, use . , ./ , and . .
• (Explanation The usual operators , / , and
  perform matrix Linear algebra operations
  between arrays. We will not cover that in CS100.)

7

• Multiple Subscripts
• In general, an array of integers can be used as a
  subscript. The result is an array consisting of
  the elements selected by the subscripts in the
  order given.
• a 10 09
• a(3 4 5)
• a(35)
• a(5 4 3)
• a(1 1 7 4 6)
• a(10-11)

8

• Logical Operations Arrays
• 0/1 Arrays
• Logical operations yield 0 (false) or 1 (true).
  When performed on arrays, an array of 0s and 1s
  is the result.
• a 5 8 6 12 9
• b 2 3 6 7 10
• a gt b
• a b
• a gt 5
• rem(a, 3)
• rem(a, 3) 0
• The functions any and all yield 1 if,
  respectively, any or all of the elements in their
  array argument are non-zero.

9

• Selecting Elements with 0/1 Arrays
• If a vector of 0s and 1s is used as a subscript
  of an array of the same length, the result is a
  new array containing only those elements of the
  old array with a 1 subscript.
• This is especially useful when the result of a
  logical expression is used as a subscript to
  select array elements based on some condition.
• a 12 7 21 3 8 14 0 6
• a(0 1 1 0 0 0 1 0)
• b a - 10
• b gt 0
• b( b gt 0 )
• a( rem(a,3) 0 )

10

• Managing the Work Session
• clc Clears the Command window
• clear Removes variables from memory
• help name Searches online help for the
• topic name
• lookfor name Searches the help entries for the
• specified keyword name
• quit Stops Matlab
• who Lists the variables currently in
• memory
• whos Lists the current variables and
• sizes, and indicates whether they
• have imaginary parts

11

• Basic Plotting
• If x and y are two arrays with the same number of
  elements, plot(x,y) draws a plot of x
  (horizontal) vs y (vertical)
• x linspace(0, 4pi, 250)
• y sin(x)
• plot(x,y)
• Normally the graph is scaled so the full range of
  x and y values fill the plot. To have equal
  spacing on the axes, enter
• axis(equal)
• after the plot has been drawn (using straight
  quote marks).
• You can label the axes and title the graph after
  it has been drawn
• xlabel(x axis label)
• ylabel(y axis label)
• title(A Fabulous Graph)

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• Plot Options
• The plot command has an optional third argument
  that can be used to specify the line color and
  style. Examples
• v -100.510
• fv 3pisin(v).2 - v
• plot(v, fv, g) green line
• plot(v, fv, b) blue dotted line
• plot(v, fv, r) red crosses
• plot(v, fv, c--) cyan dashed line
• Use help plot to find other possibilities

13

• Multiple Plots
• Normally each new plot is drawn in a blank
  window, replacing whatever is there. Use hold on
  to retain the previous plot so you can draw a new
  one over it. Use hold off to release the
  previous plot so the next one will appear in a
  blank window. Example
• x linspace(0, 6pi, 1000)
• y sin(x)
• z cos(x)
• plot(x, y, r)
• hold on
• plot(x, z, g)