To cite the frab
package in publications please use Hankin (2023). The
frab
package allows one to “add” R tables in a natural way. It also
furnishes an alternative interpretation of named vectors wherein
addition is defined using the (unique) names as the primary key. Support
for multi-dimensional R tables is included. The underlying mathematical
object is the Free Abelian group.
The package has two S4 classes: frab
and sparsetable
. Class frab
is for one-dimensional R tables and is an alternative implementation of
named vectors; class sparsetable
handles multi-way R tables in a
natural way.
frab
Primary construction function frab()
takes a named vector and returns
a frab
object:
suppressMessages(library("frab"))
p <- c(x=1,b=2,a=2,b=3,c=7,x=-1)
frab(p)
#> A frab object with entries
#> a b c
#> 2 5 7
Above, we see from the return value that function frab()
has reordered
the labels of its argument, calculated the value for entry b
[as
],
determined that the entry for x
has vanished [the values cancelling
out], and printed the result using a bespoke show method. It is useful
to think of the input argument as a semi-constructed and generalized
“table” of observations. Thus
p
#> x b a b c x
#> 1 2 2 3 7 -1
Above we see p
might correspond to a story: “look, we have one x
,
two b
s, two a
s, another three b
s, seven c
s…oh hang on that x
was a mistake I had better subtract one now”. However, the package’s
most useful feature is the overloaded definition of addition:
(x <- rfrab())
#> A frab object with entries
#> a b c d g i
#> 3 6 1 5 7 5
(y <- rfrab())
#> A frab object with entries
#> a b c d e f i
#> 4 4 1 1 8 5 2
x+y
#> A frab object with entries
#> a b c d e f g i
#> 7 10 2 6 8 5 7 7
Above we see function rfrab()
used to generate a random frab
object,
corresponding to an R table. It is possible to add x
and y
directly:
xn <- as.namedvector(x)
yn <- as.namedvector(y)
table(c(rep(names(xn),times=xn),rep(names(yn),times=yn)))
#>
#> a b c d e f g i
#> 7 10 2 6 8 5 7 7
but this is extremely inefficient and cannot deal with fractional (or indeed negative) entries.
Class sparsetable
deals with multi-way R tables. Taking three-way R
tables as an example:
(x3 <- rspar())
#> Jan Feb Mar val
#> a a a = 10
#> a c b = 15
#> b a a = 11
#> b a b = 9
#> b a c = 12
#> b b a = 6
#> b b b = 3
#> b b c = 14
#> b c a = 9
#> b c c = 21
#> c c a = 10
Function rspar()
returns a random sparsetable
object. We see that,
of the
possible entries, only 11 are non-zero. We may coerce to a regular R
table:
as.array(x3)
#> , , Mar = a
#>
#> Feb
#> Jan a b c
#> a 10 0 0
#> b 11 6 9
#> c 0 0 10
#>
#> , , Mar = b
#>
#> Feb
#> Jan a b c
#> a 0 0 15
#> b 9 3 0
#> c 0 0 0
#>
#> , , Mar = c
#>
#> Feb
#> Jan a b c
#> a 0 0 0
#> b 12 14 21
#> c 0 0 0
In this case it is hardly worth taking advantage of the sparse
representation (which is largely inherited from the spray
package) but
a larger example might be
rspar(n=4,l=10,d=12)
#> Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec val
#> b c j e f j f a g i a d = 1
#> g a j e c f e c a f g c = 4
#> j b j g h c d c c b b i = 2
#> j j h h a a i f c h g h = 3
The random sparsetable
object shown above would require
floating point numbers in full array form, of which only 4 are nonzero.
Multi-way R tables may be added in the same way as frab
objects:
y3 <- rspar()
x3+y3
#> Jan Feb Mar val
#> a a a = 10
#> a a b = 14
#> a b a = 4
#> a c a = 14
#> a c b = 15
#> b a a = 11
#> b a b = 23
#> b a c = 12
#> b b a = 17
#> b b b = 13
#> b b c = 23
#> b c a = 9
#> b c b = 7
#> b c c = 24
#> c a a = 15
#> c c a = 15
#> c c c = 14
Two-way R tables are something of a special case, having their own print
method. By default, two-dimensional sparsetable
objects are coerced to
a matrix before printing, but otherwise operate in the same way as the
multi-dimensional case discussed above:
(x2 <- rspar2())
#> bar
#> foo A B D E F
#> a 3 20 0 0 9
#> b 0 0 15 0 0
#> c 0 0 0 4 0
#> d 0 0 0 5 22
#> e 0 2 0 11 29
(y2 <- rspar2())
#> bar
#> foo A C D E F
#> a 9 0 25 6 10
#> b 7 0 0 0 1
#> c 0 0 0 11 0
#> d 8 5 0 4 0
#> e 0 3 2 0 0
#> f 0 0 14 0 15
x2+y2
#> bar
#> foo A B C D E F
#> a 12 20 0 25 6 19
#> b 7 0 0 15 0 1
#> c 0 0 0 0 15 0
#> d 8 0 5 0 9 22
#> e 0 2 3 2 11 29
#> f 0 0 0 14 0 15
Above, note how the sizes of the coerced matrices are different
(
for x2
,
for y2
) but the addition method copes, using a bespoke sparse matrix
representation. Also note that the sum has six columns (corresponding
to six distinct column headings) even though x2
and y2
have only
five.
For more detail, see the package vignette
vignette("frab")
R
: the frab
package”, arXiv, https://arxiv.org/abs/2307.13184.R
: introducing the
disordR
package”, arXiv, https://arxiv.org/abs/2210.03856