The Art of R Programming

> row(m)

[,1] [,2]

[1,] 1 1

[2,] 2 2

[3,] 3 3

Thecol()function works similarly.

Using this idea, we could replace theforloop inut()with a one-liner:

rtrn$mat <- inmat[row(inmat) <= col(inmat)]

Whenever possible, we should exploit vectorization. Take a look at

line 12, for example:

rtrn$ix <- sum1toi(0:(n-1)) + 1

Sincesum1toi()(which we defined on line 4) is based only on the vector-

ized functions"*"()and"+"(),sum1toi()itself is also vectorized. This allows

us to applysum1toi()to a vector above. Note that we used recycling as well.

We want our"ut"class to include some methods, not just variables. To

this end, we have included three methods:

• Theexpandut()function converts from a compressed matrix to an ordi-
  nary one. Inexpandut(), the key lines are 27 and 28, where we usertrn$ix
  to determine where inutmat$matthejthcolumn of our matrix is stored.
  That data is then copied to thejthcolumn offullmatin line 30. Note the
  use ofrep()to generate the zeros in the lower portion of this column.


• Theprint.ut()function is for printing. This function is quick and easy,
  usingexpandut(). Recall that any call toprint()on an object of type"ut"
  will be dispatched toprint.ut(), as in our test cases earlier.


• The"%mut%"()function is for multiplying two compressed matrices (with-
  out uncompressing them). This function starts in line 39. Since this is
  a binary operation, we take advantage of the fact that R accommodates
  user-defined binary operations, as described in Section 7.12, and imple-
  ment our matrix-multiply function as%mut%.

Let’s look at the details of the"%mut%"()function. First, in line 43,

we allocate space for the product matrix. Note the use of recycling in an

unusual context. The first argument ofmatrix()is required to be a vector

of a length compatible with the number of specified rows and columns, so

the 0 we provide is recycled to a vector of lengthn^2. Of course,rep()could

be used instead, but exploiting recycling makes for a bit shorter, more ele-

gant code.

For both clarity and fast execution, the code here has been written

around the fact that R stores matrices in column-major order. As mentioned

in the comments, our code then makes use of the fact that columniof the

218 Chapter 9