cs249 lecture notes, Fall 2001
Week 3, Thursday

Homework 2 due on Monday

Finish Chapter 3 for Monday.  Quiz Monday on Chapter 3.


Homework 1 feedback
-------------------

Out of 4:  1 for each part, one for presentation and discussion.

Write a paper, and include numbers, code, figures, and
MATLAB output as appropriate.

The object of the game is not to provide evidence that
you did what you were told.

It is to explain what you learned from the experiment.

There should be more words than numbers.


Functions revisited
-------------------

Exercise:  write a function that takes two points and computes
the distance between them.

function d = distance (x1, y1, x2, y2)
    d = pythagoras (x1 - x2, y1 - y2);
end

function c = pythagoras (a, b)
    sumSquares = square(a) + square(b);
    c = sqrt (sumSquares);
end

function s = square (x)
    s = x^2;
end


Flow of execution
-----------------

A function call is a detour in the flow of execution

1) evaluate the arguments

2) assign the values of the arguments to the input variables

3) execute the statements in the body of the function 


Root finding
------------

Given some f(x), find x such that f(x) = 0.

For simple f(x), we can find the answer by algebra.

Otherwise, not so easy.

But if we can evaluate f(x) and its derivative, we
can approximate the root.

See diagram page 3-2.

x1 = x0 - f(x0) / f'(x0)


Square roots
------------

The square root of a is the value of x such that

x^2 = a

In other words

f(x) = x^2 - a = 0

f'(x) = 2x

Plugging f(x) and f'(x) into Newton's formula yields

x1 = 1/2 (x0 + a/x0)

And we've already seen how well that works!


for loops
---------

for j = 1:5
    disp (j);
end


strings
-------

So far, only one type of value, numeric.

String values are enclosed in single quotes:

>> t = 'Hello';

Annoyingly, when MATLAB prints a value it doesn't indicate
the type:

t = Hello

Which can be confusing if you have a String that contains
numbers:

>> x = 123
x = 123
>> y = '123'
y = 123
>> x+1
ans = 124
>> y+1
50 51 52

(Note typographical error on page 3-6)


String concatenation
--------------------

The [ ] operator performs string concatenation

>> s = 'Hello, '
>> t = 'World!'
>> [s t]
ans = Hello, World!


Displaying values
-----------------

1) No semi-colon on an assignment

2) disp (expression)

3) fprintf


fprintf (FORMAT STRING, arg1, arg2, arg3...)

Format string contains escape sequences that begin with %

Each sequence prints the next arg in the list.

Sequence controls the format.

Have to have the right number of arguments.

\t prints a tab character
\n prints a newline character


Subfunctions
------------