Re: continued fraction expansion

[Henry F. Mollet]

Thanks for explaining what the problem was after I've downloaded rat.m for
practice and tried it.
Henry
octave:6> x=rand
x = 0.31647
octave:7> rat(x)
usage: [n,d] = rat(x,tol)
error: evaluating if command near line 33, column 3
error: called from `rat' in file `/Users/mollet/CandO/rat.m'
octave:7> [n,d]=rat(x)
n =   632
d =   1997
octave:8> [n,d]=rat(x, 0.0000001)
n =   632
d =   1997





on 5/27/04 4:42 PM, Paul Kienzle at address@hidden wrote:

> octave-forge (http://octave.sf.net) has rat.  It doesn't print out the
> continued fraction, but only returns the fractional form.
> 
> Please patch it so that it prints out continued fraction if no
> output arguments are requested.  I would suggest
> returning the continued fraction vector (or matrix if
> multiple values) if one output argument is requested.
> 
> That behaviour is incompatible (though not with the
> documentation), but seems more useful than returning
> a string.
> 
> Other options are creating yet another function (ratv?)
> or adding another argument 'vector'  if you want to
> return the vector rather than a string.  None of these
> appeal to me much.
> 
> Paul Kienzle
> address@hidden
> 
> On May 27, 2004, at 4:46 AM, Bart Vandewoestyne wrote:
> 
>> Hello all,
>> 
>> During some experimental work, i came across a little problem where
>> I would need to get the digits of a continued fraction expansion of
>> a real x, up to a certain tolerance.  In Matlab, i can do this as:
>> 
>>>> x = rand
>> 
>> x =
>> 
>>     0.6068
>> 
>>>> rat(x)
>> 
>> ans =
>> 
>> 1 + 1/(-3 + 1/(2 + 1/(5 + 1/(4 + 1/(14)))))
>> 
>>>> rat(x, 0.0000001)
>> 
>> ans =
>> 
>> 1 + 1/(-3 + 1/(2 + 1/(5 + 1/(4 + 1/(14 + 1/(2))))))
>> 
>> 
>> The problem is that I don't need the result as a string, rather i need
>> it as a vector, so in the above two cases this would be something like:
>> 
>>>> rat(x)
>> 
>> ans =
>> 
>> [1 -3 2 5 4 14]
>> 
>>>> rat(x, 0.0000001)
>> 
>> ans =
>> 
>> [1 -3 2 5 4 14 2]
>> 
>> 
>> Does anybody know of an implementation for this?  Or will I have to
>> look
>> at how the Matlab script builds the string and try to adapt it to my
>> own
>> needs?
>> 
>> Thanks,
>> Bart
>> 
>> PS: the algorithm that calculates the continued fraction expansion up
>> to
>> a certain number n of digits is easy and can be found at
>> http://mathworld.wolfram.com/ContinuedFraction.html.  I've implemented
>> it as:
>> 
>> function a = continued_fraction(x, n)
>> 
>> a = zeros(n,1);
>> 
>> r = x;
>> a(1) = floor(x);
>> for i=2:n,
>>   r = 1./(r-a(i-1));
>>   a(i) = floor(r);
>> end
>> 
>> My problem is that i don't want to be able to calculate for n digits,
>> but i want to calculate up to a certain *tolerance* like in the Matlab
>> rat command...
>> 
>> -- 
>> !!!!!!!!!!!!!!!!!!! email change !!!!!!!!!!!!!!!!!!!!
>> My email address is now address@hidden
>> Please update your addressbook!
>> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>> 
>> 
>> 
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> 
> 
> 
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