Re: Dimension of sequences
Fernando Bauer wrote:
>
> Al Getz wrote:
> >
> > Hello again,
> >
>
> Hello Al! Thanks for your comments.
>
> >
> > The game of chess if often referred to as having move sequences that
> > exist on the edge of a multi-dimensional object, so i suppose
> > you could say the same thing about a sequence.
> >
>
> Sorry, I didn't understand this.
>
> > My question would be say you defined the 'dimension' of a sequence
> > as the product of the max of all the inner sequences written out
> > such as 1x2x3 as is sometimes customary with arrays. What would
> > you use this information for in a program?
> >
>
> Examples:
> a)A 2D sequence (a matrix) can represent a system of simultaneous linear
> equations.
> Then, you can use your description (a x b) to find out if the system has
> possibly
> none, one or many solutions.
> b)To know if a sequence represent a square matrix. For example, to know if you
> can calculate its determinant.
>
> > When i did my jpeg decoder program in Euphoria i used sequences
> > like arrays where every level had the same length:
> > s=repeat(0,10)
> > s=repeat(s,4)
> > s=repeat(s,9)
> > s=repeat(s,5)
> > and this builds up a structure similar to a C style array where
> > every level has the same length.
>
> That is what I'm calling rectangular sequence. Perhaps we could call it "array
> sequence".
>
> > The above code creates 5
> > three dimensional 'arrays' that can be accessed by index.
> > I would have no problem calling this a 10x4x9x5 or a 5x9x4x10
> > 'sequence',
>
> Ok, you can call this way, but this isn't the dimension that I was talking
> about.
> This is the number of atoms (after you compute the product).
>
> >but the actual common useage seems to be to use
> > every element, but then again i could easily see an app that
> > although includes a given element, does not in fact use that
> > element in the program, ever, and of course the implication of
> > this is that an element missing altogether (only possible with
> > a sequence) does not necessarily decrease the length because
> > the other sequences at the same level contain more elements:
> > s={
> > {1,2,3,4},
> > {5,6,7}
> > }
> > is still a 2x4 sequence.
> >
>
> If this is true, why *can't* I sum, subtract, multiply, etc, sequences with
> the same description ?
> The information of the structure of the sequence is lost in that
> representation.
> I think if you eliminate an atom of a retangular sequence (array sequence),
> it can't have the same description any longer.
>
> > If you want to get more detailed, you might have to start enumerating
> > every element and returning a sequence that corresponds to that
> > sequence. As with the above, this would be:
> > m={4,3}
> > I guess this would simply be a sequence with the lengths of all
> > first level sequences arranged in the same structure as the
> > original sequence, which would still have to be perused.
> > Again i would have to wonder about how useful this would be unless
> > the sequence isnt that big. For example, "When do i need to know
> > the actual structure of the sequence in full?"
> >
>
> To serialize sequences, which is necessary in several situations: saving and
> restoring sequences to/from files, transmission of sequences via serial
> networks.
>
> > Some applications would be interesting to hear about at this point.
> >
>
> Any application that uses EDS, save and restore the full structures of
> sequences
> to/from the database.
>
> >
> > Al
> >
> > E boa sorte com sua programacao Euphoria!
>
> Obrigado. Para voce tambem!
>
> >
> > My bumper sticker: "I brake for LED's"
> >
>
> Regards,
> Fernando
Hi Fernando,
Ok, since you seem to have shown that there would be some use lets
look a little farther...
First off, i made a mistake when i showed the possible detailed
dimensions for the sequence
s={
{1,2,3,4},
{5,6,7}
}
which should probably be more like this:
m={2,{4,3}}
but does this even really work for all sequences?
Also notice this will get a little hard to read too, almost
as bad as trying to find the individual lengths of the original
sub sequences and if there even are any.
I did a math program a while back that used matrixes too, and what
i did to see if one matrix was compatible with another was to test
for the two dimensions (or only one if needed). For
s={{1,2},{3,4},{5,6}}
the two tests would be
v=length(s)
and
h=length(s[1])
With this info i was able to tell if a multiplication could
be done with either a vector or another matrix, or if the
maxtrix was square, or even if the matrix was really a vector.
Going to one more dimension, you probably have this being application
specific where you know in advance that all the sub sequences are
matixes and you have to test them as any other one, except first
you have to extract the individual matrix:
s={{1,2},{3,4},{5,6}}
MyMatrixes={s,s,s}
for k=1 to length(MyMatrixes) do
Dims=Test(MyMatrixes[k])
end for
Compare two more complex matrixes:
s={1,{2,3},4,5}
t={1,2,{3,4},5}
How do we indicate the dims without repeating almost the
whole sequence?
ms={1,2,1,1}
mt={1,1,2,1}
perhaps?
Then the matrix might be even more complex:
s={1,{2,{3,6}},4,5}
and dims:
m={1,{1,{2}},1,1}
and reading or parsing the dims sequence might be almost as hard
as parsing the original sequence to query its dimensions.
On the other hand, if we do define the dims as the set of
max dims we might end up with something like this:
m={4,{2{1}}}
which is at least a bit simpler than the original sequence.
BTW, by 1x2x3 that doesnt mean multiply all the numbers to get 6,
but rather shows the dimensions in the same way that the dimensions
of C arrays. The numbers dont get multiplied but stay separate:
(1,2,3)
Lastly, you'd have to think about how this is going to be
implemented in the language. During the build of any sequence
the dimension array would have to be maintained and this would
slow down the sequence a bit more too. You'd have to see just
how much effect this would have on the overall speed.
Take care,
Al
E boa sorte com sua programacao Euphoria!
My bumper sticker: "I brake for LED's"
From "Black Knight":
"I can live with losing the good fight,
but i can not live without fighting it".
"Well on second thought, maybe not."
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