[R] %*% in Matrix objects

[Martin Maechler]

>>>>> "Jose" == Jose Quesada <quesada at gmail.com>
>>>>>     on Fri, 26 Jan 2007 05:24:12 +0100 writes:

    Jose> Dear R users,
    Jose> I need to normalize a bunch of row vectors. At a certain point I need to divide a matrix by a vector of norms. I find that the behavior of Matrix objects differs from normal matrix objects.

I believe you are showing evidence for that; though I know it's
still true, and will be less true for the next release of the
Matrix package.

    Jose> Example the following code examples differ only in
    Jose> xnormed changing from normal to Matrix object:

    Jose> x = matrix(1:12,3,4)
    Jose> x = as(x, "CsparseMatrix")

or directly
   
   x <- Matrix(1:12, 3,4, sparse = TRUE)

I hope that you are aware of the fact that it's not efficient at
all to store a dense matrix (it has *no* 0 entry) as a sparse one..

    Jose> xnorms  = sqrt(colSums(x^2))
    Jose> (xnormed = t(x) * (1/xnorms))

    Jose> This produces a "warning: coercing sparse to dense matrix for arithmetic
    Jose> in: t(x) * 1/xnorms." but gets the result (a 4 x 3 matrix)

    Jose> I want to stay in sparse format anyway
    Jose>  (if it helps!) 

what should it help for? Are you talking about a real
application with a proper sparse matrix as opposed to the toy
example here? In that case I agree, and as a matter of fact, the
source code of the Matrix package leading to the above warning
is the following

	      } else {
		  ## FIXME: maybe far from optimal:
		  warning("coercing sparse to dense matrix for arithmetic")
		  callGeneric(as(e1, "dgeMatrix"), e2)
	      }

and your posting is indeed an incentive for the Matrix developers
to improve that part ... ;-)

    Jose> so I tried

    Jose> x = matrix(1:12,3,4)
    Jose> x = as(x, "CsparseMatrix")
    Jose> xnorms  = sqrt(colSums(x^2))
    Jose> xnorms = as(xnorms, "CsparseMatrix")
    Jose> (xnormed = t(x) * (1/xnorms))

    Jose> But now, instead of a warning I get
    Jose> "Error: Matrices must have same dimensions in t(x) * (1/xnorms)"

yes.  And the same happens with traditional matrices -- and well so:
For arithmetic with matrices (traditional or "Matrices"),

    A o B       (o in {"+", "*", "^", ....})   
    -----

does require that matrices A and B are ``conformable'', i.e.,
have exact same dimensions.

Only when one of A or B is *not* a matrix,
then the usual S-language recycling rules are applied,
and that's what you were using in your first example 
(<Matrix> * <numeric>) above.

    Jose> If I transpose the norms, the error dissapears, but the result is 1 x 4 (not 3 x 4 as before).

That would be a bug of *not* giving an error... but I can't see
it. Can you please give an exact example -- as you well gave otherwise; and 
BTW, do you use a sensible sparse matrix such as
 (x <- Matrix(c(0,0,1,0), 3,4))


    Jose> I suspect I'm facing the drop=T as before...
why??

    Jose> Also, it seems that in normal matrix objects %*%
    Jose> behaves the same as *,

not at all!!  If that was the case, the inventors of the S
language would never have introduced '%*%' !

    Jose> but in Matrix objects that is not the case.

    Jose> What am I missing?

I guess several things, see above, notably how basic
matrix+vector - arithmetic is defined to in the S language.

Regards,
Martin Maechler, ETH Zurich