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

From: Tim Hesterberg <timh_at_insightful.com>
Date: Thu, 07 Sep 2006 09:47:10 -0700

>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:

• 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))

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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