How to Add Two R Tables.

The frab package: how to add R tables

Overview

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.

The package in use

One-dimensional R tables: class 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 bs, two as, another three bs, seven cs…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.

Multi-way R tables

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

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.

Further information

For more detail, see the package vignette

vignette("frab")

References

• R. K. S. Hankin 2023. “The free Abelian group in R: the frab package”, arXiv, https://arxiv.org/abs/2307.13184.
• R. K. S. Hankin 2022. “Disordered vectors in R: introducing the disordR package”, arXiv, https://arxiv.org/abs/2210.03856