Review

1
Lecture 2
2
Review

• Matrix construction the concatenation operator
• 1 2 3 gt 1 2 3 and 1,2,3 gt 1 2 3
• 123 gt
• 1
• 2
• 3
• Mix-and-match is OK 1 2 3 4 gt
• 1 2
• 3 4

3
The colon operator

• 15 gt 1 2 3 4 5
• 125 gt 1 3 5
• 5 -1 1 gt 5 4 3 2 1

4
Matrix indexing

• q(i, j) gt entry in row i, column j of matrix q.
• q(1 2, 3) gt entries in rows 1 and 2, column 3.
• Logical indexing If q 13, then q(false
  true true)gt 2 3
• end can be used in indexing, too
• q(1end) gt 1 2 3
• q(1end-1) gt 1 2

5
Quiz

• If we type
• gt m round(5rand(1,40)), we get
• m 4 4 3 2 2 and so on, a 1
  x 40 array of small numbers
• Write an expression (using m) to produce a list
  of 0s and 1s like
• 1 0 0 1
• where a 1 means that m(i) is the same as
  m(i1).
• Hint a b tells (0/1) whether a and b are
  equal.

6
Types

• Everything in matlab has a TYPE you can see it
  in the upper left corner, when you click on
  workspace
• Integers whole numbers like 1, 27, -982
• double double-precision floating-point numbers
  (i.e., things like 7.488, or 3.1415)
• boolean true or false (stored as 1 or 0)

7
Types (II)

• character a, t, W, /, etc. stored as
  small integers (0 to 255, more or less a 32).
• uint8 unsigned 8-bit integer. A number thats
  stored using 8 bits (one byte of memory), and can
  range from 0 to 255. These come up a lot in
  images.

8
Types(III)

• Compound types MATRICES
• Matrices have elements, all of the same type. So
  1 2 3 is a matrix of integers, while a b
  c is a matrix of characters
• 1 x n character matrices are called strings,
  and they print out oddly
• gta b c
• ans abc

9
Types (IV)

• Shorthand for creating character arrays
• abc is the same as a b c

10
Types (V)

• Complex numbers i and j both denote sqrt(-1).
• You can write u 3 4i

11
Brief digression on complex arithm.

• 3 2i
• 4 3i
• ----------
• 7 i

12
More complex arithmetic

• 3 2i
• 4 3i
• ----------
• (-3i)(2i) (-3i)3 4 (2i) (43)
• -6i2 -9i 8i 12
• -6(-1) -i 12
• 6 -i 12
• 18-i

13
One last bit of complex arith

• For a complex number z a bi, the length or
  modulus is defined to be
• z sqrt( a2 b2 )
• So 1 2i sqrt(12 22) sqrt(5).

14
Geometry and complex nums

• We plot complex numbers on the plane by plotting
  a bi at the point (a,b)

1i
20.5i
15
Matrix indexing

• Give subscripts, as before.
• Subscripts can be matrices, too.

16
Matrix indexing

• Matlab has another way to refer to elements, with
  just one index. In the 2 x 3 matrix m
• 1 8 5
• 4 0 9
• the indices are
• 1 3 5
• 2 4 6
• so that m(1) 1, and m(3) 8, and m(6) 9.
• Weird, but amazingly useful.

17
Some useful procedures and idioms

• rand(n) an n x n matrix of random numbers
  between 0 and 1
• ones(n) and n x n matrix of ones.
• zeros(n) zeros
• rand(n, k) an n x k matrix of randoms
• ones(n, k) and n x k matrix of ones, etc.
• Idiom many procs have two forms like this.

18
Multi-dimensional arrays

• You can let m ones(3,4,5) to get a 3x4x5 array.
  
• We wont use this for a while yet.

19
Idioms

• m rand(3,5)
• u size(m)
• ans 3 5
• u(1)
• ans 3
• Simpler
• u size(m, 1)
• ans 3

20
Operations on types

• You can check whether something is a logical, or
  a float, or an int or a uint8, with builtin
  procedures like
• isint(), isfloat(), isuint8()
• Rarely needed.
• You can convert, too double(X), round(Y),
  uint8(Z)

21
Figures

• figure(1) does two things
• If theres a figure named 1, brings it to front
• If not, creates one and brings it to front
• A figure is a window in which to draw stuff.
• Figures all get numbers (1, 2, )
• gcf (get current figure) gets the number of the
  currently active figure.

22
Figures(II)

• figure(gcf) gt creates a figure if there is none
  brings current figure forward to be visible.
• Possibly the most-used line of matlab.

23
Some examples
24
Revised model for matlab
a 4
b 4 5 6
z 1 2i
25
Operations

• Assigning a value to a variable (b 2)
• Write down the name and value on current sheet of
  paper
• c 3 5 b
• Grab a postit, do computations on it,
• Copy answer to pad, next to c
• When you need the value for b, look on the pad

26
Using a procedure

• q 3
• b increment(q)
• Evaluate the argument of the procedure (in this
  case, look up q.
• Tear off a new sheet of paper, covering the old
  one write down the value of the argument next to
  the name of the argument
• Do all the procedures work.
• Write the return value on a postit.
• Throw away this worksheet
• Copy postit value to b.

27
Example procedure

• function y increment(x)
• y x1
• In this case, weve evaluated the argument q
  (its 3) we write, on NEW sheet
• x 3
• We do the procedure steps assign y 31, so y
  4.
• We copy this value onto a postitthrow away the
  worksheet
• and assign the post-it value b.
• At this point, x has no meaning!