Today

1
Todays Class

• Recap
• Homework
• Number Formats
• Text Strings and Vectors
• Arithmetic on vectors
• Creating vectors with colon
• Sums and products
• Drawing Plots
• Booleans and Logical Operators

2
Recap

• Matlab evaluates arithmetic expressions
• 2 different styles infix and function-oriented
• Infix follows typical algebraic rules
• Variables
• Naming similar but different from naming
  files
• Gives names to locations in RAM for calculated
  results
• Assignment Statements
• Format variable expression
• Can use the same variable name on both sides
• Other notational styles prefix, postfix
• Parsing the process of analyzing text

3
Quick Quiz

• Variables X, Y
• Some arithmetic with them

Calculation X Value Y Value
X 8 8 ?
Y 3 8 3
X X Y 2 13 3
X Y - 3 0 3
Y Y X 0 3
Y X 0 0
4
Chapter 3 Homework

• Read Chapters 1 through 3.
• We will cover 1.3 in more detail later
• Do Exercises 3.1, -2, -3, -4, -7, -8, -9
• Answer all of 3.3
• Due at the start of class, Wednesday

5
Storing Numbers in RAM

• Numbers stored in bits binary numbers
• 8 bits byte
• (4 bits nibble, 2 bits ?)
• Number of bits -gt power of 2 -gt number range
• Calculators
• Number of digits -gt power of 10 -gt number range

6
Number Formats

• What about signs, decimal points, exponents?
• Signed integers 1 bit sign, rest magnitude
• 32 bits, 1 bit removed for sign, range is 231
• Floating point numbers
• Part set aside for mantissa (value part)
• Part set aside for exponent (power part)
• In Matlab typical numbers are floating point
• In C, the integer/float distinction MATTERS

7
Text Strings and Vectors

• We create text strings with a pair of quotes
• We create vectors with a pair of braces
• Both are implemented as a sequence of numbers
  with common properties
• One dimension of length
• Example length(Hello) 5
• We can do arithmetic on both, element by element
• We can do other operations that combine all
  elements

8
Arithmetic on vectors

• Add and subtract are always applied pairwise
• 1 2 3 3 gt 4 5 6
• 1 2 3 5 6 7 gt 6 8 10
• Multiply, divide, power may be cross or dot
• In this class, we generally use the dot
• 1 2 3 . 3 gt 3 6 9
• 1 2 3 . 1 2 3 gt 1 4 9
• Always use the dotted version . ./ .

9
Creating vectors with colon

• The colon() function (infix ) creates vectors
• 2 arguments starting value, ending value
• A list of values between that range (increment of
  1)
• 3 arguments starting value, increment, ending
  value
• A list of values incremented as given
• Function form
• colon(1,10) colon(1,.1,2) colon(0,.01,.1)
• Infix form
• 110 1.12 0.01.1

10
Sums and Products

• sum(vector) gt adds up the elements
• prod(vector) gt multiplies elements together
• 5
• ? i
• i1
• How do we write this in Matlab?

11
Taking Sums Apart

• First, is it taking elements from a vector?
• Look at the term indexing the element (i, on
  previous slide)
• If it is subbed to another variable, you have a
  vector
• Refer to the vector in the calculation
• Second, are we doing arithmetic on the index?
• On the previous slide?
• If so, refer to the index variable in the
  calculation

12
Questions?

• Continue..

13
Sum the contents of a Vector

• n
• ? n ai
• i1
• Given a vector named a,
• How do we calculate this in Matlab?

14
Power Series

• n
• ? xi
• i1
• Given a value for x, like 2 or 14,
• How do we calculate this in Matlab?

15
Polynomial Expansion

• n
• ? aixi
• i1
• Given a vector named a, and a value for x,
• How do we calculate this in Matlab?

16
Drawing Plots

• The plot function
• does not return any value, but it has the
  useful side-effect of drawing a graph. italics
  added
• Functions usually return a value to be useful,
  but not always.
• Takes 2 or 3 arguments
• First 2 arguments are 2 vectors
• First are the X axis values
• Second are the corresponding Y axis values
• Try graphing some trig functions
• We need x values gt use the colon function
• Third argument contains a text string with
  options
• Omit it, or try these
• -o . g ro - k

17
Boolean Operations

• The basic ones are for comparison
• List is on page 55 gt gt lt lt
• Mostly identical for C, except for
• Question Are you 21? Say it in Matlab
• Lots of other specialized booleans
• Depends on the programming environment
• Matlab examples
• isletter(x)
• isspace( )
• ispc isunix
• issorted( 1 2 3 4 5 )
• strcmp(abc abd)

18
Logical Operators

• Take boolean inputs yield results (or vectors)
• One type lets us combine Boolean operators
• and () and or ()
• In C, theyre and
• and are operations on numbers
• Example Age between 18 and 35.
• Applied individually to vector entries
• xor operation (why?) in C, uses infix

19
Vector Logic

• Expressing For all values in the vector
• Or For any value in the vector
• First, we apply the test to the vector.
• Then we apply the all() or any() function
• Examples
• Is everyone over 21?
• Is anyone over 21?

20
Chapter 3 Homework

• Read Chapters 1 through 3.
• We will cover 1.3 in more detail later
• Do Exercises 3.1, -2, -3, -4, -7, -8, -9
• Answer all of 3.3
• Due at the start of class, Wednesday

21
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