Sample Partitions of a Vector into Groups — comboGroupsSample • RcppAlgos

Generate a specific (lexicographically) or random sample of partitions of groups.
Produce results in parallel using the Parallel or nThreads arguments.
GMP support allows for exploration where the number of results is large.

Usage

comboGroupsSample(v, numGroups = NULL, grpSizes = NULL, retType = "matrix",
                  n = NULL, sampleVec = NULL, seed = NULL, Parallel = FALSE,
                  nThreads = NULL, namedSample = FALSE)

Arguments

v: Source vector. If v is a positive integer, it will be converted to the sequence 1:v. If v is a negative integer, it will be converted to the sequence v:-1. All atomic types are supported (See is.atomic).
numGroups: An Integer. The number of groups that the vector will be partitioned into. The default is NULL. If provided and grpSize is NULL, it must divide the length of v (if v is a vector) or v (if v is a scalar).
grpSizes: A vector of whole numbers representing the size of each group. The default is NULL. If provided, the sum of the elements must total the length of v (if v is a vector) or v (if v is a scalar).
retType: A string, "3Darray" or "matrix", that determines the shape of the output. The default is "matrix". Note, "3Darray" can only be used when the size of each group is uniform. When the size of each group varies, the return output will always be a matrix.
n: Number of results to return. The default is NULL.
sampleVec: A vector of numbers representing the lexicographical partition of groups to return. Accepts vectors of class bigz as well as vectors of characters
seed: Random seed initialization. The default is NULL. N.B. If the gmp library is needed, this parameter must be set in order to have reproducible results (E.g set.seed() has no effect in these cases).
Parallel: Logical value indicating whether results should be generated in parallel. The default is FALSE. If TRUE and nThreads = NULL, the number of threads used is equal to the minimum of one minus the number of threads available on your system and the number of results requested (e.g. if user has 16 threads and only needs 5 results, 5 threads will be used (i.e. min(16 - 1, 5) = 5)). If nThreads is not NULL, it will be given preference (e.g. if user has 8 threads with Parallel = TRUE and nThreads = 4, only 4 threads will be spawned). If your system is single-threaded, the arguments Parallel and nThreads are ignored.
nThreads: Specific number of threads to be used. The default is NULL. See Parallel.
namedSample: Logical flag. If TRUE, rownames corresponding to the lexicographical result, will be added to the returned matrix. The default is FALSE.

Details

These algorithms rely on efficiently generating the \(n^{th}\) lexicographical result.

Value

By default, a matrix is returned with column names corresponding to the associated group. If retType = "3Darray", a 3D array is returned.

References

Lexicographical order

Author

Joseph Wood

Examples

## generate 10 random partitions of groups of equal size
comboGroupsSample(10, 2, n = 10, seed = 123)
#>       Grp1 Grp1 Grp1 Grp1 Grp1 Grp2 Grp2 Grp2 Grp2 Grp2
#>  [1,]    1    2    4    7    8    3    5    6    9   10
#>  [2,]    1    3    5    8    9    2    4    6    7   10
#>  [3,]    1    2    6    8   10    3    4    5    7    9
#>  [4,]    1    2    3    6    9    4    5    7    8   10
#>  [5,]    1    3    4    7    9    2    5    6    8   10
#>  [6,]    1    2    5    7    9    3    4    6    8   10
#>  [7,]    1    2    6    8    9    3    4    5    7   10
#>  [8,]    1    5    7    8    9    2    3    4    6   10
#>  [9,]    1    2    5    7   10    3    4    6    8    9
#> [10,]    1    4    5    9   10    2    3    6    7    8

## generate 10 random partitions of groups of varying sizes
comboGroupsSample(10, grpSizes = 1:4, n = 10, seed = 123)
#>       Grp1 Grp2 Grp2 Grp3 Grp3 Grp3 Grp4 Grp4 Grp4 Grp4
#>  [1,]    2    8   10    1    6    7    3    4    5    9
#>  [2,]    2    9   10    4    5    6    1    3    7    8
#>  [3,]    9    2    4    3    7   10    1    5    6    8
#>  [4,]    7    8    9    1    2    5    3    4    6   10
#>  [5,]   10    6    9    2    5    7    1    3    4    8
#>  [6,]    3    2    9    1    6    8    4    5    7   10
#>  [7,]    2    4    6    3    7   10    1    5    8    9
#>  [8,]    8    2   10    3    6    9    1    4    5    7
#>  [9,]    3    5    9    1    6    8    2    4    7   10
#> [10,]   10    2    3    4    5    8    1    6    7    9

## using sampleVec to generate specific results
comboGroupsSample(15, 5, sampleVec = c(1, 100, 1e3, 1e6))
#>      Grp1 Grp1 Grp1 Grp2 Grp2 Grp2 Grp3 Grp3 Grp3 Grp4 Grp4 Grp4 Grp5 Grp5 Grp5
#> [1,]    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15
#> [2,]    1    2    3    4    5    6    7    9   12    8   14   15   10   11   13
#> [3,]    1    2    3    4    5    9    6   10   13    7   14   15    8   11   12
#> [4,]    1    8   10    2   12   15    3    5   13    4   11   14    6    7    9

all.equal(comboGroupsSample(10, 5,
            sampleVec = 1:comboGroupsCount(10, 5)),
         comboGroups(10, 5))
#> [1] TRUE

## Examples with enormous number of total results
num = comboGroupsCount(100, 20)
gmp::log2.bigz(num)
#> [1] 325.5498
## [1] 325.5498

first = gmp::urand.bigz(n = 1, size = 325, seed = 123)
#> Seed initialisation
mySamp = do.call(c, lapply(0:10, function(x) gmp::add.bigz(first, x)))

class(mySamp)
#> [1] "bigz"
## [1] "bigz"

## using the sampling function
cbgSamp = comboGroupsSample(100, 20, sampleVec = mySamp)

## using the standard function
cbgGeneral = comboGroups(100, 20,
                         lower = first,
                         upper = gmp::add.bigz(first, 10))

identical(cbgSamp, cbgGeneral)
#> [1] TRUE
## [1] TRUE

if (FALSE) { # \dontrun{
## Using Parallel
system.time(comboGroupsSample(1000, 20, n = 80, seed = 10, Parallel = TRUE))
} # }