CS100A, Fall 1998

1
CS100A, Fall 1998

• Lecture 20, Tuesday Nov 10
• More Matlab
• Concepts
• plotting (cont.)
• 2-D arrays
• Control structures while, if, for
• Defining new Matlab functions
• Readings As before. Select from
• Getting Started with Matlab
• Mastering Matlab
• Student Edition of Matlab Users Guide

2

• 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)

3

• 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

4

• 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)

5

• 2-D Arrays
• Matlabs basic data structure is a 2-D array of
  numbers (1-D arrays are a special case of this).
  There are various ways to create 2-D arrays.
  Easiest is to list the rows separated by
  semicolons
• a 1 2 3 4 5 6 7 8 9 10 11 12
• Functions are provided to construct arrays with m
  rows and n columns initialized in various ways.
• ones(m,n) m by n 1s
• zeros(m,n) m by n 0s
• rand(m,n) m by n random
• numbers in the range
• 0.0 to 1.0.
• If A is a 2-D array, size(A) is a 1-D array
  containing the number of rows and columns in A.

6

• 2-D Array Subscripting
• Individual elements of a 2-D array a are accessed
  by listing the row and column numbers in
  parentheses
• a(1,3)
• a(3,1)
• a(2,2)
• Entire rows and columns can be accessed using a
  colon as a wildcard
• a(2, )
• a(, 3)

7

• 2-D Array Subscripting
• The colon operator can be used to access
  arbitrary slices of an array.
• a(23, 12) rows 2-3, cols 1-2
• a(12, 4) rows 1-2, col 4
• a(12, ) rows 1-2, all cols
• It can also be used to change the shape of an
  array by deleting rows, columns, or sub-matrices
  of a matrix.
• a(12, ) removes rows 1-2
• from a

8

• Combining and Transposing 2-D arrays
• If A, B, C, and D are arrays,
• A B or A , B is an array formed by combining
  the columns of A and B with A on the left. A and
  B must have the same number of rows.
• C D is an array formed by stacking the rows
  of C above the rows of D. C and D must have the
  same number of columns.
• If A is an array with m rows and n columns, A
  (A quote-mark) is an array with n rows and m
  columns with A(i,j) A(j,i). The result is
  known as the transpose of A.

9

• Functions and 2-D Arrays
• Functions like sqrt, sin, cos that operate
  element-by-element on 1-D arrays work the same on
  2-D arrays.
• m 10 rand(5,4)
• sqrt(sin(m))
• Functions like sum, prod that produce a scalar
  result from a 1-D array produce a
• 1-D array result when applied to a 2-D array.
  The function is applied to columns of the 2-D
  array.
• a 1 2 3 4 5 6 7 8 9 10 11 12
• sum(a)
• To apply these functions to rows in a 2-D array,
  transpose the array with the quote operator.
• sum(a)

10

• Control Structures in Matlab if
• Like most programming languages, Matlab has loops
  and conditional statements, although these are
  needed far less often because of the available
  array operations. The punctuation differs from
  Java.
• if statement basic form
• if logical expression
• statements
• end
• Example
• if x gt y
• temp x
• x y
• y temp
• end
• Semicolons are optional

11

• Control Structures in Matlab else
• if-else statement basic form if logical
  expression
• statements
• else statements
• end
• Exampleif x gt y
• temp x
• x y
• y temp
• else
• x y
• end

12

• Control Structures in Matlab while
• while statement basic form
• while logical expression
  statements end
• Example while kgt0
• sum sum k
• k k - 1 end

13

• Control Structures in Matlab for
• The colon operator (or any array for that matter)
  can be used to generate index values for a loop.
• Example Create an array with each element
  a(i,j) initialized to ij. We allocate the array
  first to avoid array index out-of-bounds errors.
• a zeros(25, 15)
• for r 1 25
• for c 1 15
• a(r,c) r c
• end
• end
• But In Matlab there are often ways to do matrix
  operations without explicit loops. Dont write
  loops if you dont need them.

14

• Creating New Functions .m Files
• New functions can be defined by storing the
  commands to compute them in a file with a name
  that exactly matches the function name followed
  by .m .
• Function definition syntax
• function output vars function_name ( input
  vars )
• Example File sqr.m.
• function result sqr(x)
• yield the square of the values in x
• result x . x
• All variables are local to the function.
• Comments that immediately follow the function
  definition line are used by help and lookfor
• Functions may be applied to any Matlab data and
  will be applied element-by-element automatically
  if appropriate.