R help - Dec 2014 - ave(x, y, FUN=length) produces character output when x is character

You have written a lot, Mike, as though we did not know it.  You are not the
only one with math and multiple computing languages under your belt. The point
Bert made is that the concept that a matrix IS-A vector is not just an
implementation detail in R... it helps the practitioner keep straight why things
like a[3] is perfectly valid when a is a matrix, and why

a*a
     [,1] [,2]
[1,]    1    9
[2,]    4   16

is true. I understand why you are uncomfortable with it, as I was once, but this
is how R works so you are only impeding your own effectiveness by clinging to
theory on this point.

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Sent from my phone. Please excuse my brevity.

On December 24, 2014 11:15:28 PM PST, Mike Miller <mbmiller+l at
gmail.com> wrote:
>On Wed, 24 Dec 2014, Bert Gunter wrote:
>
>> You are again misinterpreting because you have not read the docs, 
>> although this time I will grant that they are to some extent
>misleading.
>>
>> First of all, a matrix _IS_ a vector:
>>
>>> a <- matrix(1:4, 2,2)
>>> a[3] ## vector indexing works because it is a vector
>> [1] 3
>>
>> In fact, a matrix (or array) is a vector with a "dim"
attribute. This
>> is documented in ?matrix:
>>
>> "is.matrix returns TRUE if x is a vector and has a "dim"
attribute of
>> length 2) and FALSE otherwise."
>
>But a vector has no such attribute, so a matrix is not a vector which
>is 
>why you see this:
>
>> a <- matrix(1:4, 2,2)
>> is.vector(a)
>[1] FALSE
>
>Of course the matrix can be coerced back into a vector just as the
>vector 
>was coerced into a matrix:
>
>> b <- as.vector(a)
>> is.vector(b)
>[1] TRUE
>
>
>> Your confusion arises because, despite its name, is.vector() does not
>
>> actually test whether something "is" a vector (after all
these are
>all 
>> abstractions; what it "is" is contents of memory, implemented
as a
>> linked list or some such).  ?is.vector tells you:
>>
>> "is.vector returns TRUE if x is a vector of the specified mode
having
>> no attributes other than names. It returns FALSE otherwise."
>
>So that means that a vector in R has no attributes other than names.
>
>
>> An array has a "dim" attribute, so is.vector() returns FALSE
on it.
>But 
>> it actually _is_ ("behaves like") a vector (in column major 
>> order,actually).
>
>An array is a vector with additional attributes which cause it to be an
>
>array rather than a vector.  This is why R says FALSE when we query it 
>about an array using is.vector().
>
>
>> Now you may complain that this is confusing and I would agree. Why is
>it 
>> this way? I dunno -- probably due to historical quirks -- evolution
>is 
>> not necessarily orderly. But that's the way it is; that's the
way
>it's 
>> documented; and tutorials will tell you about this (that's how I 
>> learned). So please stop guessing and intuiting and read the docs to 
>> understand how things work.
>
>I don't think it is confusing.  This is the kind of behavior I'm
used
>to 
>from other programs like Octave/MATLAB.  A vector is just an ordered
>list 
>of numbers.  Those numbers can be put into matrices or
>higher-dimensional 
>arrays, but they then become something more than just a vector.  A
>vector 
>like 1:4 becomes a 2x2 matrix when we do matrix(1:4, 2,2) such that the
>
>number 3 which was just the third element before (and still is) is now 
>also the [1,2] element of a matrix.  It didn't have that before, back
>when 
>it was a vector, but now that it has become something more than a
>vector, 
>it has that new property.  We can take that away using as.vector().
>
>In many situations the behavior of the R vector and the same values in
>a 
>matrix format will be very different:
>
>> a <- 1:4
>> b <- matrix(a, 2,2)
>> a %*% a
>      [,1]
>[1,]   30
>> b %*% b
>      [,1] [,2]
>[1,]    7   15
>[2,]   10   22
>> b %*% t(b)
>      [,1] [,2]
>[1,]   10   14
>[2,]   14   20
>> a %*% t(a)
>      [,1] [,2] [,3] [,4]
>[1,]    1    2    3    4
>[2,]    2    4    6    8
>[3,]    3    6    9   12
>[4,]    4    8   12   16
>
>That is not true in ave(), as I showed earlier, because it uses the
>vector 
>ordering of elements in the x matrix or array (what one would get from 
>as.vector()) to form the correspondence with the factor.
>
>I get your idea, but I don't think it is correct to say "a matrix
is a
>vector."  Rather, I would say that there is a standard way in which one
>
>can create a one-to-one correspondence between the elements of a matrix
>of 
>given dimensions and the elements of a vector.  I believe this is
>usually 
>called "fortran indexing," or at least that is what it is called
in
>Octave.  The same thing is done with vectorization and the vec()
>operator 
>in mathematics:
>
>http://en.wikipedia.org/wiki/Vectorization_(mathematics)
>
>But in math as in computing, we wouldn't say that a matrix *is* a
>vector. 
>If vec(A) = v, that does not mean that A = v.  In R, it looks like 
>as.vector() can do what vec() does, and more.
>
>Mike

On Thu, 25 Dec 2014, Jeff Newmiller wrote:
> You have written a lot, Mike, as though we did not know it.  You are not 
> the only one with math and multiple computing languages under your belt.
I'm not assuming that you and Bert don't know things, but I do expect to
have a wider audience -- when I search for things, sometimes I find my 
postings from 10 years ago.  I'm probably not the only one.

> The point Bert made is that the concept that a matrix IS-A vector is not 
> just an implementation detail in R... it helps the practitioner keep 
> straight why things like a[3] is perfectly valid when a is a matrix, and 
> why
>
> a*a
>     [,1] [,2]
> [1,]    1    9
> [2,]    4   16
>
> is true. I understand why you are uncomfortable with it, as I was once, 
> but this is how R works so you are only impeding your own effectiveness 
> by clinging to theory on this point.
Sorry, your concepts aren't helping me and I'm not uncomfortable with
what
R is doing.  In fact, what I wrote earlier is that R seems to be much like 
Octave/MATLAB, which I have used even more than I've used R.  The use of 
what Octave calls "fortran indexing" is an example.  We can refer to 
matrix element a[3] in R or element a(3) in Octave and we're referring to 
the same element.  It's also the third element of vec(a).  That doesn't 
mean that 'a' is a vector.  R says that it is not a vector.  That
doesn't
confuse me.  I can refer to the third element of a matrix even if the 
matrix is not a vector.

I don't understand how your concept helps in understanding a*a.  It's an
element-by-element product (also called Hadamard product).  In Octave it 
would be a.*a.  The matrix product in R is a%*%a and in Octave it is a*a. 
I find nothing confusing about any of this and I don't see how conceiving 
of 'a' as a vector helps at all.

The difference between our concepts is that this makes no sense within 
your framework where you think of a matrix as being a vector:
> a <- matrix(1:4, 2,2)
> is.vector(a)
[1] FALSE

But to me it makes perfect sense because 'a' is a matrix and a matrix is
not a vector.  We might say that it contains a vector, or that the 
elements of the matrix are constructed from the elements of a vector, but 
not that the matrix is a vector.  It is a different class of object:
> class(a)
[1] "matrix"

Mike

On Thu, 25 Dec 2014, Mike Miller wrote:
> On Thu, 25 Dec 2014, Jeff Newmiller wrote:
>
>> You have written a lot, Mike, as though we did not know it.  You are 
>> not the only one with math and multiple computing languages under your 
>> belt.
>
> I'm not assuming that you and Bert don't know things, but I do
expect to
> have a wider audience -- when I search for things, sometimes I find my 
> postings from 10 years ago.  I'm probably not the only one.

To clarify one point:  I write some things to organize my own ideas.  I 
also think I'm not the only one who will want to see it.

I don't believe that I know more about R or programming than you guys do. 
I consider that an extremely remote possibility, at best.  That doesn't 
mean you are right about everything, or about any particular thing.

Mike