Prologue: table()

Suppose we have three tables:

xl <- c("a","a","b","c","d","d","a")
yl <- c("a","a","b","d","d","d","e")
zl <- c("a","a","b","d","d","e","f")
x <- table(xl)
y <- table(yl)
z <- table(zl)

Can we ascribe any meaning to x+y without reference to xl and yl? Well yes, we should simply sum the counts of the various letters. However:

x

## xl
## a b c d 
## 3 1 1 2

y

## yl
## a b d e 
## 2 1 3 1

x+y

## xl
## a b c d 
## 5 2 4 3

The sum is defined in this case. However, close inspection shows that the result is clearly incorrect. Although entries for a and b are correct, the third and fourth entries are not as expected: in this case R idiom simply adds the entries elementwise with no regard to labels. We would expect x+y to respect the fact that we have 5 d entries, even though element d is the fourth entry of x and the third of y. Further:

x

## xl
## a b c d 
## 3 1 1 2

z

## zl
## a b d e f 
## 2 1 2 1 1

x+z

## Error in x + z: non-conformable arrays

Named vectors

A named vector is a vector with a names attribute. Each element of a named vector is associated with a name or label. The names are not necessarily unique. It allows you to assign a name to each element, making it easier to refer to specific values within the vector using their respective names.

Named vectors are a convenient and useful feature of the R programming language (R Core Team 2022). However, given the following two named vectors:

x <- c(a=1,b=2,c=3)
y <- c(c=4,b=1,a=1)

Given that x+y returns a named vector, there are at least two plausible values that it might give, viz:

c(a=5,b=3,c=4)

or

c(a=2,b=3,c=7).

In the first case the elements of x and y are added pairwise, and the names attribute is taken from the first of the addends. In the second, the names are considered to be primary and the value of each name in the sum is the sum of the values of that name of the addends. Note further that there is no good reason why the first answer could not be c(c=5,b=3,a=4), obtained by using the names attribute of y instead of x.

The frab package

The frab package furnishes efficient methods to give a consistent and meaningful way of adding two tables together, using standard R syntax. It uses the names of a named vector as the indexing mechanism. Package idiom is straightforward:

(x <- frab(c(a=1,b=2,d=7)))

## A frab object with entries
## a b d 
## 1 2 7

(y <- frab(c(c=4,b=1,a=-1)))

## A frab object with entries
##  a  b  c 
## -1  1  4

x+y

## A frab object with entries
## b c d 
## 3 4 7

Above, note how y is defined with its entries in non-standard order, but the resulting frab object has its entries ordered alphabetically. In x+y, the entry for a has vanished, as it cancels in the summation. The numeric entries for each letter are summed, accounting for the different names [viz a,b,d and a,b,c respectively]. The result is presented using the frab print method.

Package idiom includes extraction and replacement methods, all of which should work as expected:

x <- frab(c(x=5,d=1,e=2,f=4,a=3,c=3,g=9))
x

## A frab object with entries
## a c d e f g x 
## 3 3 1 2 4 9 5

x>3

## A disord object with hash 8e06d464d006d7ce8c6fa1e5101a1e042bddadf6 and elements
## [1] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
## (in some order)

x<3

## A disord object with hash 8e06d464d006d7ce8c6fa1e5101a1e042bddadf6 and elements
## [1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE
## (in some order)

x[x>3]

## A frab object with entries
## f g x 
## 4 9 5

x[x<3]

## A frab object with entries
## d e 
## 1 2

x[x<3] <- 100
x

## A frab object with entries
##   a   c   d   e   f   g   x 
##   3   3 100 100   4   9   5

Above we see that extraction and replacement methods follow disordR discipline (Hankin 2022). Results are coerced to disord objects if needed. Tables may be added to frab objects:

a <- rfrab()
b <- table(sample(letters[1:8],12,replace=T))
a

## A frab object with entries
## a b c d g i 
## 3 6 1 5 7 5

b

## 
## a b c d e f g 
## 2 2 1 2 2 2 1

a+b

## A frab object with entries
## a b c d e f g i 
## 5 8 2 7 2 2 8 5

Above we see the + operator is defined between a frab and a table, coercing tables to frab objects to give consistent results.

Two dimensional tables

The ideas above have a natural generalization to two-dimensional tables.

(x <- rspar2(9))

##    bar
## foo A  B C D F
##   b 3  0 8 0 2
##   d 5 16 0 0 6
##   f 1  0 0 4 0

(y <- rspar2(9))

##    bar
## foo A C D E F
##   a 0 0 0 9 0
##   b 0 0 0 0 8
##   e 0 0 4 0 0
##   f 7 9 8 0 0

x+y

##    bar
## foo A  B C  D E  F
##   a 0  0 0  0 9  0
##   b 3  0 8  0 0 10
##   d 5 16 0  0 0  6
##   e 0  0 0  4 0  0
##   f 8  0 9 12 0  0

Above, note that the resulting sum is automatically resized to accommodate both addends, and also that entries with nonzero values in both x and y are correctly summed.

A <- matrix(0.95,3,3)
diag(A) <- 1
x <- round(rmvnorm(300,mean=rep(10,3),sigma=A/7))
x[] <- letters[x]
head(x)

##      [,1] [,2] [,3]
## [1,] "i"  "i"  "i" 
## [2,] "j"  "j"  "j" 
## [3,] "j"  "j"  "k" 
## [4,] "j"  "j"  "j" 
## [5,] "j"  "j"  "i" 
## [6,] "j"  "j"  "j"

(sx  <- sparsetable(x))

##            val
##  i i i  =   22
##  i i j  =    2
##  i j i  =    5
##  i j j  =    4
##  j i i  =    2
##  j i j  =    1
##  j j i  =    3
##  j j j  =  223
##  j j k  =    7
##  j k j  =    3
##  j k k  =    1
##  k j j  =    2
##  k j k  =    4
##  k k j  =    1
##  k k k  =   20

(sz <- sparsetable(matrix(sample(letters[9:11],12,replace=TRUE),ncol=3),1001:1004))

##             val
##  i k k  =  1003
##  j j j  =  1004
##  j j k  =  1001
##  k k j  =  1002

sx + sz

##             val
##  i i i  =    22
##  i i j  =     2
##  i j i  =     5
##  i j j  =     4
##  i k k  =  1003
##  j i i  =     2
##  j i j  =     1
##  j j i  =     3
##  j j j  =  1227
##  j j k  =  1008
##  j k j  =     3
##  j k k  =     1
##  k j j  =     2
##  k j k  =     4
##  k k j  =  1003
##  k k k  =    20