What's the correct order of things in a file? (beginner's question)

[David Collett]

Hi, everyone.

This is only my second post as I'm just starting to learn octave.
I'm not a mathematician, nor a professional. I'm actually  interested  
in algorithmic music composition.

I've been looking at several algorithms for translating the logistic  
map (bifurcation) function onto music parameters.

I went to this Wikipedia site, and saw the mention of Octave (which I  
had never heard of).

http://en.wikipedia.org/wiki/Image:Logistic-burification.png

So, two days ago, I installed Octave (on Mac OS X), and Octave ran.

I decided to copy/paste the Octave lines given on Wikipedia into a  
text file to see if it would run.

Here are the lines in the same order that they appear on Wikipedia's  
site
(Wikipedia refers to each of these 7 blocks as "scripts"):

-----

r_min = 2.5; r_max = 4; # the range of parameter values we study
n = 1000; # the number of parameter values we consider in this range

t_max = 1000; # how many iterations to simulate per parameter value
p_max = 100; # the last p_max iterations are plotted

x0 = 0.1; # we use the same initial value x0 for all parameters.

r = linspace(r_min, r_max, n);
pop = zeros(p_max, n);

for k = 1:n
  x = population(r(k), x0, t_max);
  pop(:, k) = x(t_max-p_max+1:t_max);
end

gset nokey;
plot(r, pop, 'b.');

function x =  population(r, x0, n)
# simulates n iterations of the logistic map with parameter
# r and initial value x0. The results are returned in the
# array x.
  x = zeros(n, 1);
  x(1) = x0;
  for k = 1:n-1
    x(k + 1) = r * x(k) * (1 - x(k));
  end

-----

When I put this in a file and tried to run it, Octave gave several  
error messages about 'population' not being defined, etc.
So, unsure of what else to try, I tried rearranging these blocks  
until one arrangement worked. Here's what I ended up with:

-----

r_min = 2.5; r_max = 4; # the range of parameter values we study
n = 1000; # the number of parameter values we consider in this range

t_max = 1000; # how many iterations to simulate per parameter value
p_max = 100; # the last p_max iterations are plotted

x0 = 0.1; # we use the same initial value x0 for all parameters.

r = linspace(r_min, r_max, n);
pop = zeros(p_max, n);

function x =  population(r, x0, n)
# simulates n iterations of the logistic map with parameter
# r and initial value x0. The results are returned in the
# array x.
  x = zeros(n, 1);
  x(1) = x0;
  for k = 1:n-1
    x(k + 1) = r * x(k) * (1 - x(k));
  endfunction

for k = 1:n
  x = population(r(k), x0, t_max);
  pop(:, k) = x(t_max-p_max+1:t_max);
endfor

gset nokey;
plot(r, pop, 'b.');

-----

I have 3 questions:

1.  Why did the order I have work, but the one that Wikipedia gave  
wouldn't? In other words, why does the function have to be moved up?


2.  In the Wikipedia version, they use for...end, and function...end,
whereas in the Octave manual, I believe it says to use:
for...endfor, and function...endfunction  (which I did).

Can you use either? Are there different "flavors" of Octave that use  
different commands?


3.  Finally, why does Wikipedia refer to their 7 blocks as "scripts"?  
Why not just have all of these lines in a single file, as I have done?


Thanks again for helping a beginner!

David Collett




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