[R] Matrix multiplication using apply() or lappy() ?

[Tim Hesterberg]

toby_marks at americancentury.com asked:
>I am trying to divide the columns of a matrix by the first row in the 
>matrix.

Dividing columns of a matrix by a vector is a pretty fundamental
operation, and the query resulted in a large number of suggestions:

x/matrix(v, nrow(x), ncol(x), byrow = TRUE))
sweep(x, 2, v, "/")
x / rep(v, each = nrow(x))
x / outer(rep(1, nrow(x)), v)
x %*% diag(1/v)
t(apply(x, 1, function(x) x/v))
x/rep(v, each=nrow(x))
t(apply(x, 1, "/", v))
library(reshape); iapply(x, 1, "/", v)  # R only
t(t(x)/v)
scale(x, center = FALSE, v)  # not previously suggested


It is unsatisfactory when such a fundamental operation is
done in so many different ways.  
* It makes it hard to read other people's code.  
* Some of these are very inefficient.

I propose to create standard functions and possibly operator forms
for this and similar operators:

	colPlus(x, v)		x %c+% v
	colMinus(x, v)		x %c-% v
	colTimes(x, v)		x %c*% v
	colDivide(x, v)		x %c/% v
	colPower(x, v)		x %c^% v

Goals are:
* more readable code
* generic functions, with methods for objects such as data frames
  and S-PLUS bigdata objects  (this would be for both S-PLUS and R)
* efficiency -- use the fastest of the above methods, or drop to C
  to avoid replicating v.
* allow error checking (that length of v matches number of columns of x)

I'd like feedback (to me, I'll summarize for the list) on:
* the suggestion in general
* are names like "colPlus" OK, or do you have other suggestions?
* create both functions and operators, or just the functions?
* should there be similar operations for rows?  

Note:  similar operations for rows are not usually needed, because
	x * v  # e.g. where v = colMeans(x)
is equivalent to (but faster than)
	x * rep(v, length = length(x))
The advantage would be that
	colTimes(x, v)
could throw an error if length(v) != nrow(x)

Tim Hesterberg

P.S.  Of the suggestions, my preference is
	a / rep(v, each=nrow(a))
It was to support this and similar +-*^ operations that I originally
added the "each" argument to rep.

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| Tim Hesterberg       Research Scientist              |
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