OpenEuphoria

Re: Dimension of sequences

• Posted by Igor Kachan <kinz at p?terlink?ru> Sep 19, 2007
• 621 views

Fernando Bauer wrote:
> 
> Igor Kachan wrote:
> > 
> > > 'non-rectangular sequence' (NRS) = all sequences that aren't RS.
> > > 'dimension of RS' = maximum depth of the sequence.
> > > 'dimension of NRS' = that is the question!
> > 
> > Let's see the refman.doc file now.
> > 
> > Robert Craig writes:
> > 
> >  "Sequences can be nested to any depth, i.e. you can have sequences within
> >   sequences within sequences and so on to any depth (until you run out of
> >   memory)." 
> > 
> > I see Rob cares just about *maximum* depth here, so his definition
> > of depht, documented in refman.doc, is strongly equivalent to your
> > definition of 'dimension of RS'.
> > Same thing, you just introduce some new term, synonym.
> > 
> > No?
> 
> Ok. We can use "depth" as synonym of "dimension" as you prefer. Then my
> question
> is:
> What is the depth of a NRS? How can I obtain it? For now, I only know the
> depth
> of a RS.

Hello, Fernando!

OK, let's use just that MaxDepth() function by Ricardo,
it seems to work properly not only on 'simple' sequences,
but on any ones, it is recursive, and gives us that
pure maximum maximorum depth of any sequence.

See please:

global function MaxDepth(object o)
    integer n, x
    if atom(o) then
       return 0
    else
       n = 0
	for i = 1 to length(o) do
	    x = MaxDepth(o[i])
	    if x > n then
		n = x
	    end if
	end for
	return n + 1
    end if
end function -- it is function by Ricardo Forno, genfunc.e lib 

? MaxDepth({{{{}}},{},{{},{{{{{{{{{{{{}}}}}}}}}}}}},{{{{{{{{}}}}}}}}})
? MaxDepth({{{{1}}},{1},{{1},{{{{{{{{{{{{1}}}}}}}}}}}}},{{{{{{{{1}}}}}}}}})

 
The maximum depth is 14, all right.
Count please the '{' signs, opening the deepest sequence,
to be sure.
It seems to be a good parameter for description of a sequence.
Now a sequence has its own second dimension, and may be
considered as some 2-dimensional object, which can contain
description of any-dimentional real and unreal objects -
vectors, matrixes, tensors, lists, arrays, trees, books,
images ... etc, etc.
Sequence itself really has two own dimensions - length and depth,
I think now. So attempts to give it some *single* dimension
may be not very productive.

> > Then, I do not think now that the 'rectangular' word is very
> > good for your purpose, maybe, 'regular', as some short
> > for 'regularly nested', is better.
> > 
> Ok. But I think "rectangular" is sligthly more precise than "regular", since
> I could think that the following sequence is regular:
> repeat({1,{1,1}},n) where n is any integer number. And that sequence is NRS.
> Well, this is only a definition problem.

Ricardo names these sequences as 'simple sequences'.

> > > > So what?  What will we do with all these new terms, with
> > > > all these new notions, with all these new concepts?
> > > 
> > > First of all, they facilitate our communication, since we don't have to
> > > say
> > > that whole definition phrase.
> > > Second, the terms RS and NRS can represent types in Euphoria, like vector
> > > or
> > > matrix, and so can be checked.
> > > Some algorithms can function with one and not with other type, etc..
> > 
> > Ok, but for now I do not see some real place for the 'dimension' word
> > here. Length & Depth. These old good words are very clear in 
> > the specific EU context. 
> 
> Ok. But the Depth concept is not so clear as it seems, since nobody defined
> what it is for NRS yet.

OK, now we can calculate that Depth (good, let's name the maximum depth
as Depth) with Ricardo's function.

Regards,
Igor Kachan
kinz at peterlink.ru