How to use sparta

library(sparta)

Consider two arrays f and g:

dn <- function(x) setNames(lapply(x, paste0, 1:2), toupper(x))
d  <- c(2, 2, 2)
f  <- array(c(5, 4, 0, 7, 0, 9, 0, 0), d, dn(c("x", "y", "z")))
g  <- array(c(7, 6, 0, 6, 0, 0, 9, 0), d, dn(c("y", "z", "w")))

with flat layouts

ftable(f, row.vars = "X")
#>    Y y1    y2   
#>    Z z1 z2 z1 z2
#> X               
#> x1    5  0  0  0
#> x2    4  9  7  0
ftable(g, row.vars = "W")
#>    Y y1    y2   
#>    Z z1 z2 z1 z2
#> W               
#> w1    7  0  6  6
#> w2    0  9  0  0

We can convert these to their equivalent sparta versions as

sf <- as_sparta(f); sg <- as_sparta(g)

Printing the object by the default printing method yields

print.default(sf)
#>   [,1] [,2] [,3] [,4]
#> X    1    2    2    2
#> Y    1    1    2    1
#> Z    1    1    1    2
#> attr(,"vals")
#> [1] 5 4 7 9
#> attr(,"dim_names")
#> attr(,"dim_names")$X
#> [1] "x1" "x2"
#> 
#> attr(,"dim_names")$Y
#> [1] "y1" "y2"
#> 
#> attr(,"dim_names")$Z
#> [1] "z1" "z2"
#> 
#> attr(,"class")
#> [1] "sparta" "matrix"

The columns are the cells in the sparse matrix and the vals attribute are the corresponding values which can be extracted with the vals function. Furthermore, the domain resides in the dim_names attribute, which can also be extracted using the dim_names function. From the output, we see that (x2, y2, z1) has a value of \(2\). Using the sparta print method prettifies things:

print(sf)
#>   X Y Z val
#> 1 1 1 1   5
#> 2 2 1 1   4
#> 3 2 2 1   7
#> 4 2 1 2   9

where row \(i\) corresponds to column \(i\) in the sparse matrix. The product of sf and sg

mfg <- mult(sf, sg); mfg
#>   X Y Z W val
#> 1 2 1 2 2  81
#> 2 2 2 1 1  42
#> 3 1 1 1 1  35
#> 4 2 1 1 1  28

Converting sf into a conditional probability table (CPT) with conditioning variable Z:

sf_cpt <- as_cpt(sf, y = "Z"); sf_cpt
#>   X Y Z   val
#> 1 1 1 1 0.312
#> 2 2 1 1 0.250
#> 3 2 2 1 0.438
#> 4 2 1 2 1.000

Slicing sf on X1 = x1 and dropping the X dimension

slice(sf, s = c(X = "x1"), drop = TRUE)
#>   Y Z val
#> 1 1 1   5

reduces sf to a single non-zero element, whereas the equivalent dense case would result in a (Y,Z) table with one non-zero element and three zero-elements.

Marginalizing (or summing) out Y in sg yields

marg(sg, y = c("Y"))
#>   Z W val
#> 1 2 2   9
#> 2 2 1   6
#> 3 1 1  13

Finally, we mention that a sparse table can be created using the constructor sparta_struct, which can be necessary to use if the corresponding dense table is too large to have in memory.

Functionalities in sparta