From help-octave-request at bevo dot che dot wisc dot edu Fri Dec 27 18:56:24 2002
Subject: Re: Newbie question solving lin sys
From: "John B. Thoo" <jb2 at ms dot yuba dot cc dot ca dot us>
To: <zlash at mail dot notwires dot com>
Cc: <help-octave at bevo dot che dot wisc dot edu>
Date: Fri, 27 Dec 2002 16:55:47 -0800

On Friday, December 27, 2002, at 03:51 PM, William Lash wrote:

>> **Three follow-up questions.  (I hope that you don't mind.)
>>
>> 1. What does the dot after the  s  in  s.^[0:11]  mean in the "for" 
>> loop?
>
> In Octave (and Matlab), usually things like multiplication and 
> exponentiation are matrix type operations.  Putting a "." in front
> of the operation makes it do things in an "element by element"
> fashion.  To be honest, I wasn't sure that s.^[0:11] would give me
> a row vector with the elements s^0 through s^11 untill I tried
> it.

I see.  Neat.


>> 2. What in the "for" loop tells Octave to add the terms?
>
> The multiplication of the row vector containing the powers of s
> and the column vector containing the values of x in matrix
> arithmetic give you the sum of the products as above. Think of
> it as S*X where S is 1x12, and X is 12x1.  You could do the same
> using:
> sum(x'.*s.^[0:11])

Oh, right, Octave treats everything as vectors.  (I've played a little 
bit with Maple in the past; this is different here.)  Duh!


>> 3. How do I plot the graph on  [0:11]  without a loss of precision?  I
>> tried this without success:
>>
>> octave:84> gplot [0:11] "x(1) + x(2)*x + x(3)*x**2 + x(4)*x**3 +
>> x(5)*x**4 + x(6)*x**5 + x(7)*x**6 + x(8)*x**7 + x(9)*x**8 + 
>> x(10)*x**9 +
>> x(11)*x**10 + x(12)*x**11"
>>          line 0: undefined function: x
>
> I would probably do something like:
> for s = [0:11]
> z(s+1) = s.^[0:11] * x;
> end
> plot([0:11],z)

That works to give me a polygonal curve that connects the 12 points.  
That's good, but how would I plot the polynomial with more grid points 
(smoother)?  It works reasonably when I do "format long" and then copy & 
paste the coefficients to plot

octave:139> gplot [0:11] "22 + 129.316052352359*x - 
330.008191451222*x**2 + 356.743251568416*x**3 - 211.743557625161*x**4 + 
77.5116682813202*x**5 - 18.4455900615644*x**6 + 2.90919225949428*x**7 - 
0.301909718420775*x**8 + 0.0198178458639753*x**9 - 
0.000745701048375786*x**10 + 0.0000122504808365439*x**11"

but there must be an easier way. :-)

Once again, thanks very much for all your help.

---John.



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