vignettes/CombinatoricsIterators.Rmd
CombinatoricsIterators.RmdThis document covers working with combinatorial iterators in
RcppAlgos. Combinatorial iterators in
RcppAlgos are memory efficient like traditional iterator
objects. They allow traversal of
combinations/permutations/partitions/compositions/comboGroups one by one
without the necessity for storing all results in memory.
Unlike traditional combinatorial iterators, the iterators in
RcppAlgos offers random access via the [[
operator. This means, we can access the nth lexicographical
order result on demand without having to first iterate over the
previous n - 1 results.
In order to iterate, we must initialize an iterator via
comboIter or permuteIter. The interface is
very similar to comboGeneral and
permuteGeneral.
library(RcppAlgos)
options(width = 90)
## Initialize the iterator
a = comboIter(5, 3)
## Get the first combination
a$nextIter()
#> [1] 1 2 3
## And the next
a$nextIter()
#> [1] 1 2 4
## Set the current iterator to a variable
iter = a$currIter()
i = 1
## Iterate until there are no more
while (!is.null(iter)) {
cat(i, " ", iter, "\n")
iter = a$nextIter()
i = i + 1
}
#> 1 1 2 4
#> 2 1 2 5
#> 3 1 3 4
#> 4 1 3 5
#> 5 1 4 5
#> 6 2 3 4
#> 7 2 3 5
#> 8 2 4 5
#> 9 3 4 5
#> No more results. To see the last result, use the prevIter method(s)
## See the output of comboGeneral for comparison
comboGeneral(5, 3, lower = 2)
#> [,1] [,2] [,3]
#> [1,] 1 2 4
#> [2,] 1 2 5
#> [3,] 1 3 4
#> [4,] 1 3 5
#> [5,] 1 4 5
#> [6,] 2 3 4
#> [7,] 2 3 5
#> [8,] 2 4 5
#> [9,] 3 4 5
## Call the summary method to see information about our iterator
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 11
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] -1Some of the combinatorial iterators in RcppAlgos are
bidirectional iterators. This means that not only can we iterate in a
forward manner (i.e. lexicographically), but we can also iterate
backwards (i.e. Reverse
Lexicographical Order) via the prevIter method(s).
## Using the same iterable from the previous section
a$currIter()
#> No more results. To see the last result, use the prevIter method(s)
#> NULL
## As the comment says, we call the prevIter method to see the last result
a$prevIter()
#> [1] 3 4 5
## Get the previous result
a$prevIter()
#> [1] 2 4 5
## As in the previous example, we set the current iterator to a variable
iter = a$currIter()
## Defined above
print(i)
#> [1] 10
## Iterate until we are at the very beginning. Note that the
## output is exactly the same as above, but in reverse order
while (!is.null(iter)) {
i = i - 1
cat(i, " ", iter, "\n")
iter = a$prevIter()
}
#> 9 2 4 5
#> 8 2 3 5
#> 7 2 3 4
#> 6 1 4 5
#> 5 1 3 5
#> 4 1 3 4
#> 3 1 2 5
#> 2 1 2 4
#> 1 1 2 3
#> Iterator Initialized. To see the first result, use the nextIter method(s)
## Call the summary method to see information about our iterator
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 0
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 10There are four methods which allow for obtaining more than one result
at a time: nextNIter, prevNIter,
nextRemaining, and prevRemaining.
## Reset the iterator
a$startOver()
## Get the next 4 combinations
a$nextNIter(4)
#> [,1] [,2] [,3]
#> [1,] 1 2 3
#> [2,] 1 2 4
#> [3,] 1 2 5
#> [4,] 1 3 4
## Get the summary. Note that the index has been updated
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 4
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 6
## View the current combination
a$currIter()
#> [1] 1 3 4
## Get the remaining combinations with nextRemaining
a$nextRemaining()
#> [,1] [,2] [,3]
#> [1,] 1 3 5
#> [2,] 1 4 5
#> [3,] 2 3 4
#> [4,] 2 3 5
#> [5,] 2 4 5
#> [6,] 3 4 5
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 11
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] -1Now, we look at the opposite direction.
## Get the previous 4 combinations
a$prevNIter(4)
#> [,1] [,2] [,3]
#> [1,] 3 4 5
#> [2,] 2 4 5
#> [3,] 2 3 5
#> [4,] 2 3 4
## Get the summary. Note that the index has been updated
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 7
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 3
## View the current combination
a$currIter()
#> [1] 2 3 4
## Get the remaining previous combinations with prevRemaining
a$prevRemaining()
#> [,1] [,2] [,3]
#> [1,] 1 4 5
#> [2,] 1 3 5
#> [3,] 1 3 4
#> [4,] 1 2 5
#> [5,] 1 2 4
#> [6,] 1 2 3
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 0
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 10As with the bidirectional iterators, with some of the combinatorial
iterators in RcppAlgos, we can jump to the
nth result without the need for iterating over the
first n - 1 results.
## Reset the iterator
a$startOver()
## How many total combinations do we have?
a$summary()$totalResults
#> [1] 10
## Let's get the 3rd combination
a[[3]]
#> [1] 1 2 5
## See the summary. Note that the index has been updated
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 3
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 7
## Let's see the 9th combination
a[[9]]
#> [1] 2 4 5
## What about the first and last combination?
a$front()
#> [1] 1 2 3
a$back()
#> [1] 3 4 5
## Again the index has been updated
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 10
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 0
a$currIter()
#> [1] 3 4 5We can also easily return a random sample of combinations with the
[[ operator by passing a vector of indices. In these cases,
it should be noted that the current index will not be updated.
## Set the current index to the second combination
a[[2]]
#> [1] 1 2 4
set.seed(121)
samp = sample(a$summary()$totalResults, 4)
samp
#> [1] 4 7 10 1
a[[samp]]
#> [,1] [,2] [,3]
#> [1,] 1 3 4
#> [2,] 2 3 4
#> [3,] 3 4 5
#> [4,] 1 2 3
## Note that the current index remains unchanged
a$summary()
#> $description
#> [1] "Combinations of 5 choose 3"
#>
#> $currentIndex
#> [1] 2
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] 8Just as with comboGeneral and
permuteGeneral, we can pass a user defined function to
comboIter and permuteIter.
## Initialize the iterator
b = permuteIter(LETTERS[1:4], 3, FUN = function(p) paste(p, collapse = ""),
FUN.VALUE = "a")
b$nextIter()
#> [1] "ABC"
b$nextNIter(5)
#> [1] "ABD" "ACB" "ACD" "ADB" "ADC"
b$back()
#> [1] "DCB"
b$prevIter()
#> [1] "DCA"
b$prevNIter(5)
#> [1] "DBC" "DBA" "DAC" "DAB" "CDB"
b$nextRemaining()
#> [1] "DAB" "DAC" "DBA" "DBC" "DCA" "DCB"
## Random access
b[[5]]
#> [1] "ADB"
b$prevRemaining()
#> [1] "ACD" "ACB" "ABD" "ABC"
## View the source vector
b$sourceVector()
#> [1] "A" "B" "C" "D"2.5.0
As of version 2.5.0, we no longer rely on
Rcpp as a dependency, which means that we do not utilize
Rcpp modules for exposing C++ classes. This is now carried
out using external pointers (See External
pointers and weak references) along with S4 Classes. We use the slots
of S4 classes for exposing each method so access is carried
out with the “at sign”, @. We have also added the ability
to access each method with the “dollar sign”, $, for
backwards compatibility.
2.5.0+
Our tests show that accessing methods is much more efficient in
2.5.0+ compared to prior versions. In the below tests, we
measure excecution time of calling nextIter multiple times
in different versions. We will use the function
test_nextIter for our testing. If one needs to reproduce,
simply download the 2.4.3 tar here: https://cran.r-project.org/src/contrib/Archive/RcppAlgos/,
change RcppAlgos to RcppAlgos243 in a few
place (e.g. DESCRIPTION, NAMESPACE, etc.), and
rebuild.
test_nextIter <- function(n, m, get_val = FALSE, v = 243) {
a <- if (v == 243) {
RcppAlgos243::comboIter(n, m)
} else {
comboIter(n, m)
}
total <- comboCount(n, m)
if (get_val) {
mat <- matrix(0L, nrow = total, ncol = m)
for (i in 1:total) mat[i, ] <- a$nextIter()
return(mat)
} else {
if (v == 243) {
for (i in 1:total) a$nextIter()
} else {
for (i in 1:total) a@nextIter()
}
invisible(NULL)
}
}2.4.3 Using Rcpp
library(microbenchmark)
## Using R version 4.1.3
comboCount(15, 8)
#> [1] 6435
microbenchmark(v243 = test_nextIter(15, 8))
#> Warning in microbenchmark(v243 = test_nextIter(15, 8)): less accurate nanosecond times to
#> avoid potential integer overflows
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> v243 20.63817 21.75934 23.91622 21.94562 22.30697 200.7697 100
identical(test_nextIter(15, 8, get_val = TRUE),
comboGeneral(15, 8))
#> [1] TRUE
comboCount(25, 10)
#> [1] 3268760
system.time(test_nextIter(25, 10))
#> user system elapsed
#> 11.158 0.053 11.213
Rprof("Version243.out", memory.profiling = TRUE)
test_nextIter(25, 10)
Rprof(NULL)
lapply(summaryRprof("Version243.out", memory = "both"), head)
#> $by.self
#> self.time self.pct total.time total.pct mem.total
#> "as.environment" 3.96 38.37 3.96 38.37 4176.8
#> "$" 3.16 30.62 8.22 79.65 8664.3
#> "test_nextIter" 0.98 9.50 10.32 100.00 10594.2
#> ".External" 0.68 6.59 0.68 6.59 554.4
#> "get" 0.54 5.23 0.54 5.23 483.2
#> "exists" 0.50 4.84 0.50 4.84 530.8
#>
#> $by.total
#> total.time total.pct mem.total self.time self.pct
#> "test_nextIter" 10.32 100 10594.2 0.98 9.5
#> "<Anonymous>" 10.32 100 10594.2 0.00 0.0
#> "block_exec" 10.32 100 10594.2 0.00 0.0
#> "call_block" 10.32 100 10594.2 0.00 0.0
#> "do.call" 10.32 100 10594.2 0.00 0.0
#> "doTryCatch" 10.32 100 10594.2 0.00 0.0
#>
#> $sample.interval
#> [1] 0.02
#>
#> $sampling.time
#> [1] 10.322.8.3 (No Rcpp)
curr_version <- as.integer(gsub("\\.", "", packageVersion("RcppAlgos")))
curr_version
#> [1] 283
microbenchmark(curr_v = test_nextIter(15, 8, v = curr_version))
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> curr_v 2.626214 2.694602 2.806657 2.781789 2.873341 4.065765 100
system.time(test_nextIter(25, 10, v = curr_version))
#> user system elapsed
#> 1.354 0.012 1.366
identical(test_nextIter(15, 8, get_val = TRUE, v = curr_version),
comboGeneral(15, 8))
#> [1] TRUE
Rprof("Version250.out", memory.profiling = TRUE)
test_nextIter(25, 10, v = curr_version)
Rprof(NULL)
lapply(summaryRprof("Version250.out", memory = "both"), head)
#> $by.self
#> self.time self.pct total.time total.pct mem.total
#> ".Call" 0.56 45.90 0.56 45.9 430.3
#> "<Anonymous>" 0.40 32.79 1.22 100.0 909.9
#> "test_nextIter" 0.26 21.31 1.22 100.0 909.9
#>
#> $by.total
#> total.time total.pct mem.total self.time self.pct
#> "<Anonymous>" 1.22 100 909.9 0.40 32.79
#> "test_nextIter" 1.22 100 909.9 0.26 21.31
#> "block_exec" 1.22 100 909.9 0.00 0.00
#> "call_block" 1.22 100 909.9 0.00 0.00
#> "do.call" 1.22 100 909.9 0.00 0.00
#> "doTryCatch" 1.22 100 909.9 0.00 0.00
#>
#> $sample.interval
#> [1] 0.02
#>
#> $sampling.time
#> [1] 1.22It appears that memory is the issue in previous versions. Indeed, if
we look at Memory
statistics from Rprof, and view both files with
memory = "stats" we see that the C funciton,
duplicate, appears to be the main culprit.
## We set index = 1 to ensure we get the very bottom of the stack
### Verison 2.4.3
v243 <- summaryRprof("Version243.out", memory = "stats", index = 1)
v243
#> index: "tryCatch"
#> vsize.small max.vsize.small vsize.large max.vsize.large nodes
#> 1076410 18864400 29382 15160928 20905038
#> max.nodes duplications tot.duplications samples
#> 214708592 18988 9797740 516
## Version 2.5.0
v250 <- summaryRprof("Version250.out", memory = "stats", index = 1)
v250
#> index: "tryCatch"
#> vsize.small max.vsize.small vsize.large max.vsize.large nodes
#> 3320297 25027376 257230 15691032 15623937
#> max.nodes duplications tot.duplications samples
#> 176450792 2 126 61With verison 2.5.0+ there are only 126
tot.duplications whereas with version 2.4.3
there are millions of tot.duplications. In fact, there are
a total of 9797740 duplications with version 2.4.3. This
together with comboCount(25, 10) = 3,268,760 implies that
the C funciton, duplicate, is called about 3 times per
iteration with older versions (i.e. 9797740 / 3268760 ~=
2.9974).
For most partition cases, we have all of the capabilities of the
standard comboIter and permuteIter except for
bidirectionality (i.e. the prevIter methods). For cases
involving standard multisets we also don’t have random access
methods.
## Similar illustration of comboIter(5, 3) at the top
p = partitionsIter(16, 4)
p@nextIter()
#> [1] 1 2 3 10
p@nextIter()
#> [1] 1 2 4 9
iter = p@currIter()
i = 1
while (!is.null(iter)) {
cat(i, " ", iter, "\n")
iter = p@nextIter()
i = i + 1
}
#> 1 1 2 4 9
#> 2 1 2 5 8
#> 3 1 2 6 7
#> 4 1 3 4 8
#> 5 1 3 5 7
#> 6 1 4 5 6
#> 7 2 3 4 7
#> 8 2 3 5 6
#> No more results.
partitionsGeneral(16, 4, lower = 2)
#> [,1] [,2] [,3] [,4]
#> [1,] 1 2 4 9
#> [2,] 1 2 5 8
#> [3,] 1 2 6 7
#> [4,] 1 3 4 8
#> [5,] 1 3 5 7
#> [6,] 1 4 5 6
#> [7,] 2 3 4 7
#> [8,] 2 3 5 6
p@summary()
#> $description
#> [1] "Partitions of 16 into 4 parts"
#>
#> $currentIndex
#> [1] 10
#>
#> $totalResults
#> [1] 9
#>
#> $totalRemaining
#> [1] -1
## Using random access
p[[7]]
#> [1] 1 4 5 6
## No previous iterators
p@prevIter()
#> Error in eval(expr, envir, enclos): no slot of name "prevIter" for this object of class "Partitions"For compositions, the options are limited to a subset of compositions with repetition.
## Similar illustration of comboIter(5, 3) at the top
p = compositionsIter(6, 3, TRUE)
p@nextIter()
#> [1] 1 1 4
p@nextIter()
#> [1] 1 2 3
iter = p@currIter()
i = 1
while (!is.null(iter)) {
cat(i, " ", iter, "\n")
iter = p@nextIter()
i = i + 1
}
#> 1 1 2 3
#> 2 1 3 2
#> 3 1 4 1
#> 4 2 1 3
#> 5 2 2 2
#> 6 2 3 1
#> 7 3 1 2
#> 8 3 2 1
#> 9 4 1 1
#> No more results.
compositionsGeneral(6, 3, TRUE, lower = 2)
#> [,1] [,2] [,3]
#> [1,] 1 2 3
#> [2,] 1 3 2
#> [3,] 1 4 1
#> [4,] 2 1 3
#> [5,] 2 2 2
#> [6,] 2 3 1
#> [7,] 3 1 2
#> [8,] 3 2 1
#> [9,] 4 1 1
p@summary()
#> $description
#> [1] "Compositions with repetition of 6 into 3 parts"
#>
#> $currentIndex
#> [1] 11
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] -1
## Using random access
p[[7]]
#> [1] 2 3 1
## No previous iterators
p@prevIter()
#> Error in eval(expr, envir, enclos): no slot of name "prevIter" for this object of class "Partitions"Now, the combinatorial iterators have all of the features of their
“general” analogs (I.e.
{combo|permute|partitions|compositions}General), which
includes constrained results.
For general constrained cases, these iterators offer huge advantages
over their “general” counterparts. Previously, one had to guess how many
results there would be using the upper parameter as
executing the function with no constraints meant the user could be
waiting for a while or consume a large amount of resources.
Another drawback is that it difficult to start generating from a
particular point. With the “general” functions, if the
lower parameter is used, we have to make a decision in
order to disambiguate the use. Without constraints, using
lower is easy to understand. It simply means to start
generating results starting at a particular lexicographical result,
which we can do efficiently (i.e. no need to generate the first
lower - 1 results). With constraints, it could mean one of
two things:
In RcppAlgos we have always used the first
interpretation. A big downside for the second point is that we don’t
have any fast algorithms for enumerating the total number of results,
which reduces determining the nth result to a brute
force approach.
With iterators, we can generate n results with
nextNIter(n) or calling nextIter() n
times (or some combination of the two). Then, if we want to continue
iterating, we pick up where we left off fetching the (n +
1)th result and beyond (if there are any results left).
This allows us to keep memory low without sacrificing our current
state.
set.seed(55)
s = runif(10, -5, 5)
print(s)
#> [1] 0.478135161 -2.818403214 -4.650360052 2.915492940 0.602420762 -4.257748260
#> [7] -3.684770642 -2.058761222 0.007612633 -4.116755421
## Using comboGeneral to retrieve all results
comboGeneral(s, 5, constraintFun = "mean",
comparisonFun = "<", limitConstraints = -3)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -4.650360 -4.257748 -4.116755 -3.684771 -2.818403214
#> [2,] -4.650360 -4.257748 -4.116755 -3.684771 -2.058761222
#> [3,] -4.650360 -4.257748 -4.116755 -3.684771 0.007612633
#> [4,] -4.650360 -4.257748 -4.116755 -3.684771 0.478135161
#> [5,] -4.650360 -4.257748 -4.116755 -3.684771 0.602420762
#> [6,] -4.650360 -4.257748 -4.116755 -2.818403 -2.058761222
#> [7,] -4.650360 -4.257748 -4.116755 -2.818403 0.007612633
#> [8,] -4.650360 -4.257748 -4.116755 -2.818403 0.478135161
#> [9,] -4.650360 -4.257748 -4.116755 -2.818403 0.602420762
#> [10,] -4.650360 -4.257748 -4.116755 -2.058761 0.007612633
#> [11,] -4.650360 -4.257748 -3.684771 -2.818403 -2.058761222
#> [12,] -4.650360 -4.257748 -3.684771 -2.818403 0.007612633
#> [13,] -4.650360 -4.116755 -3.684771 -2.818403 -2.058761222
#> [14,] -4.650360 -4.116755 -3.684771 -2.818403 0.007612633
#> [15,] -4.257748 -4.116755 -3.684771 -2.818403 -2.058761222
## Using comboIter
a = comboIter(s, 5, constraintFun = "mean",
comparisonFun = "<", limitConstraints = -3)
## See the first result
a@nextIter()
#> [1] -4.650360 -4.257748 -4.116755 -3.684771 -2.818403
## Get the next three
a@nextNIter(3)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -4.65036 -4.257748 -4.116755 -3.684771 -2.058761222
#> [2,] -4.65036 -4.257748 -4.116755 -3.684771 0.007612633
#> [3,] -4.65036 -4.257748 -4.116755 -3.684771 0.478135161
## See the summary... Note the totalResults and totalRemaining
## fields are NA as we are not able to calculate this upfront.
a@summary()
#> $description
#> [1] "Combinations of 10 choose 5 where the mean is < -3"
#>
#> $currentIndex
#> [1] 4
#>
#> $totalResults
#> [1] NA
#>
#> $totalRemaining
#> [1] NA
a@nextNIter(3)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -4.65036 -4.257748 -4.116755 -3.684771 0.602420762
#> [2,] -4.65036 -4.257748 -4.116755 -2.818403 -2.058761222
#> [3,] -4.65036 -4.257748 -4.116755 -2.818403 0.007612633
## Get the rest
a@nextRemaining()
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -4.650360 -4.257748 -4.116755 -2.818403 0.478135161
#> [2,] -4.650360 -4.257748 -4.116755 -2.818403 0.602420762
#> [3,] -4.650360 -4.257748 -4.116755 -2.058761 0.007612633
#> [4,] -4.650360 -4.257748 -3.684771 -2.818403 -2.058761222
#> [5,] -4.650360 -4.257748 -3.684771 -2.818403 0.007612633
#> [6,] -4.650360 -4.116755 -3.684771 -2.818403 -2.058761222
#> [7,] -4.650360 -4.116755 -3.684771 -2.818403 0.007612633
#> [8,] -4.257748 -4.116755 -3.684771 -2.818403 -2.058761222They are very efficient as well. Consider the example below where we
use comboGeneral to generate all results without capping
the output. Again, we are in a situation where we don’t know a
priori how many results we will obtain.
set.seed(77)
s = runif(50, 20, 100)
## Over one trillion results to sift through
comboCount(s, 15)
#> [1] 2.25083e+12
time_all <- system.time({
print(
nrow(
comboGeneral(s, 15,
constraintFun = "mean",
comparisonFun = ">",
limitConstraints = 83)
)
)
})
#> [1] 38935252
time_all
#> user system elapsed
#> 2.014 1.383 3.872
## Over 4 GBs of results
(38935252 * 15 * 8) / 2^30
#> [1] 4.351353Just over 3 seconds isn’t bad, however 4 GBs could put a strain on your computer.
Let’s use iterators instead and only generate ten thousand at a time to keep memory low. We should mention here that the iterators are “smart” in that there is no fear in requesting more results than what is actually left. For example, if in the problem above, we had iterated to the 38th million result and requested 10 million more, we would only obtain 935,252 results.
invisible(gc())
time_iter <- system.time({
a = comboIter(s, 15,
constraintFun = "mean",
comparisonFun = ">",
limitConstraints = 83)
while (!is.null(a@nextNIter(1e4))) {}
print(a@summary())
})
#> No more results.
#>
#> $description
#> [1] "Combinations of 50 choose 15 where the mean is > 83"
#>
#> $currentIndex
#> [1] 38935252
#>
#> $totalResults
#> [1] NA
#>
#> $totalRemaining
#> [1] NA
time_iter
#> user system elapsed
#> 1.637 0.339 1.976
## Only 1 MBs per iteration
(1e4 * 15 * 8) / 2^20
#> [1] 1.144409Wow! Using the iterator approach is not only easier on your RAM, but
faster as well (3.872 / 1.976 ~= 1.9595)! Our
gains came strictly from memory efficiency (From over 4 GBs to just over
1 MB) as the underlying algorithm is exactly the same.
Lastly, using iterators make some problems possible that would
otherwise be intractable because of hardware. For instance, using the
example above, if we changed the limitConstraints from 83
to 81 and tried the first approach your computer will most certainly
become unusable (at least mine did). My memory usage shot up to over 30
GB and R became unresponsive. After a restart, I tried the second
approach and obtained my result in just over 10 seconds barely noticing
any jumps in memory:
## Don't run... consumes a huge chunk of memory
# time_all <- system.time({
# print(
# nrow(
# comboGeneral(s, 15,
# constraintFun = "mean",
# comparisonFun = ">",
# limitConstraints = 81) ## 83 -->> 81
# )
# )
# })
## No problem with iterators
invisible(gc())
system.time({
a = comboIter(s, 15,
constraintFun = "mean",
comparisonFun = ">",
limitConstraints = 81) ## 83 -->> 81
while (!is.null(a@nextNIter(1e4))) {}
print(a@summary())
})
#> No more results.
#>
#> $description
#> [1] "Combinations of 50 choose 15 where the mean is > 81"
#>
#> $currentIndex
#> [1] 271309888
#>
#> $totalResults
#> [1] NA
#>
#> $totalRemaining
#> [1] NA
#> user system elapsed
#> 11.449 2.382 13.833As of version 2.8.2, we can iterate over partitions of
groups with comboGroupsIter.
Just as with partitionsIter, we have all of the
capabilities of the standard comboIter and
permuteIter except for bidirectionality (i.e. the
prevIter methods).
## Similar illustration of comboIter(5, 3) at the top
cg = comboGroupsIter(6, 2, retType = "3Darray")
cg@nextIter()
#> Grp1 Grp2
#> [1,] 1 4
#> [2,] 2 5
#> [3,] 3 6
cg@nextIter()
#> Grp1 Grp2
#> [1,] 1 3
#> [2,] 2 5
#> [3,] 4 6
iter = cg@currIter()
i = 1
while (!is.null(iter)) {
cat("\n ", i, "-------------\n")
print(iter)
iter = cg@nextIter()
i = i + 1
}
#>
#> 1 -------------
#> Grp1 Grp2
#> [1,] 1 3
#> [2,] 2 5
#> [3,] 4 6
#>
#> 2 -------------
#> Grp1 Grp2
#> [1,] 1 3
#> [2,] 2 4
#> [3,] 5 6
#>
#> 3 -------------
#> Grp1 Grp2
#> [1,] 1 3
#> [2,] 2 4
#> [3,] 6 5
#>
#> 4 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 3 5
#> [3,] 4 6
#>
#> 5 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 3 4
#> [3,] 5 6
#>
#> 6 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 3 4
#> [3,] 6 5
#>
#> 7 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 4 3
#> [3,] 5 6
#>
#> 8 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 4 3
#> [3,] 6 5
#>
#> 9 -------------
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 5 3
#> [3,] 6 4
#> No more results.
comboGroups(6, 2, retType = "3Darray", lower = 2)
#> , , Grp1
#>
#> [,1] [,2] [,3]
#> [1,] 1 2 4
#> [2,] 1 2 5
#> [3,] 1 2 6
#> [4,] 1 3 4
#> [5,] 1 3 5
#> [6,] 1 3 6
#> [7,] 1 4 5
#> [8,] 1 4 6
#> [9,] 1 5 6
#>
#> , , Grp2
#>
#> [,1] [,2] [,3]
#> [1,] 3 5 6
#> [2,] 3 4 6
#> [3,] 3 4 5
#> [4,] 2 5 6
#> [5,] 2 4 6
#> [6,] 2 4 5
#> [7,] 2 3 6
#> [8,] 2 3 5
#> [9,] 2 3 4
cg@summary()
#> $description
#> [1] "Partition of v of length 6 into 2 uniform groups"
#>
#> $currentIndex
#> [1] 11
#>
#> $totalResults
#> [1] 10
#>
#> $totalRemaining
#> [1] -1
## Using random access
cg[[7]]
#> Grp1 Grp2
#> [1,] 1 2
#> [2,] 3 4
#> [3,] 6 5
## No previous iterators
cg@prevIter()
#> Error in eval(expr, envir, enclos): no slot of name "prevIter" for this object of class "ComboGroups"