Introductory Programming
Fall 2006

For today, you should have:

1) worked on the two exercises from notes04 


Today:

0) splitting sections?

1) functions

2) eval 2 debriefing

3) update2.m


For next time you should:

1) work on the exercise below

2) prepare for the next evaluation, which will cover vectors


Evaluation 2
------------

Here's the solution we looked at last time:

xnew = x + sigma * (y - x) * dt
ynew = y + (x * (r - z) - y) * dt
znew = z + (x*y - b*z) * dt
x = xnew
y = ynew
z = znew

Here is the most common answer I saw on the evals:

x(n+1) = x(n) + sigma * (y(n) - x(n)) * dt
y(n+1) = y(n) + (x(n) * (r - z(n)) - y(n)) * dt
z(n+1) = z(n) + (x(n)*y(n) - b*z(n)) * dt

This is INCORRECT, because 

1) the variable n is never initialized, and 

2) x, y, and z are scalars, so trying to access the nth 
   element will probably "exceed matrix dimensions"

Remember, if you write something like

x(n+1) = x(n) + ...

you are reading and writing the elements of a matrix.

It is very important to keep track of what is a scalar
and what is a vector, so

    YOU MUST USE CAPITAL LETTERS FOR VECTORS.

That way, when you use a vector, you will know that you
are using a vector, and I will know that you know that
you are using a vector.

Here is a correct version of the program, using vectors
and a loop.  You can download it from wb/ip/code/lorenz_diff.m

sigma = 10; 
b = 8/3;
r = 28;
dt = 0.01;

X(1) = 1;
Y(1) = 2;
Z(1) = 3;

for i = 1:1000
    X(i+1) = X(i) + sigma * (Y(i) - X(i)) * dt;
    Y(i+1) = Y(i) + (X(i) * (r - Z(i)) - Y(i)) * dt;
    Z(i+1) = Z(i) + (X(i)*Y(i) - b*Z(i)) * dt;
end

plot3(X, Y, Z)
    
Anybody know what this is?


update.m
--------

Let's look at another example; you can download it from 
wb/ip/code/update2.m

n = 35;
A(1) = 150;
B(1) = 150;

for i=1:n-1
   fromA = round(0.03 * A(i));
   fromB = round(0.05 * B(i));
   A(i+1) = A(i) - fromA + fromB;
   B(i+1) = B(i) - fromB + fromA;
end

hold on
plot(A, 'ro-')
plot(B, 'bx-')


Notice the before/during/after structure:

1) before the loop, initialize the parameters and the
   initial values of the vectors

2) inside the loop, add the next value to the vectors

3) after the loop, plot or return the accumulated result


Exercise
--------

Write a function named mysum that takes a vector as an
input variable and that returns the sum of the elements
in the vector.

(It's called mysum because MATLAB already has a function
named sum that does the same thing.)

Your function should not print (display) anything, so when
you call it, it should behave like this:

>> X = 1:10;
>> total = mysum(X);
>> total

total = 55