index: Indexing vectors

In rindex: Indexing for R

Description

Indexing allows to extract small fractions of large vectors very quickly.

Usage

 index(x, uni = NULL, batch = NULL, verbose = FALSE)
 ## S3 method for class 'index'
c(...)
 indexAddTree(obj, batch = NULL)
 indexDelTree(obj)
 indexAutobatch(n, batch = 64)

Arguments

x	a vector (currently only character)
uni	set to TRUE or FALSE to save checking for duplicates (default NULL for checking)
batch	set to preferred batch size to influence RAM – speed – trade-off (default NULL for indexAutobatch)
verbose	set to TRUE to report timing of index creation (default FALSE)
n	number of elements to build a tree on
obj	an object of class ‘index’
...	objects of class ‘index’

Details

Basic functions	creating, modifying and removing indices
index	create an index object and build a tree
c.index	concatenate index objects (currently not tuned)
indexAutobatch	calculates the optimal index resolution (size of a leaf) given number of elements and desired batch size (default 64)
indexAddTree	build or rebuild tree (Calloc)
indexDelTree	remove tree (Free)
rm	removing index object removes tree at next garbage collection gc
Index information	information, printing and retrieving all values
indexNodes	returns number of tree nodes
indexBytes	returns indes size in bytes
print.index	prints index info and optionally tree
str.index	removes class and calls NextMethod("str")
length.index	identical to length of original vector
names.index	currently forbidden
names<-.index	currently forbidden
Basic access	information, printing and retrieving all values
sort.index	identical to sort of original vector, but much faster
order.index	identical to order of original vector, but much faster
[.index	index[] returns original vector, subsetting works identical to susetting original vector [ (via NextMethod)
[<-.index	currently forbidden
is.na.index	identical to is.na of original vector, but much faster
Low level search	low level search functions return positions in index order (sorted)
indexFind	finding exact values in index
indexFindlike	finding values in index that begin like search value (character indices only)
Mid level search	mid level search functions return positions in index order (sorted)
indexFindInterval	finding a sequence of exact or approximate values
indexMatch	finding positions of vector of search values
High level search	high level search functions return positions in original order (unsorted)
indexEQ	index EQual value
indexNE	index NotEqual value
indexLT	index LowerThan value
indexGT	index GreaterThan value
indexLE	index LowerEqual value
indexGE	index GreaterEqual value
High level operators	high level operators return logical vectors in original order (unsorted)
==.index	index EQual value
!=.index	index NotEqual value
<.index	index LowerThan value
>.index	index GreaterThan value
<=.index	index LowerEqual value
>=.index	index GreaterEqual value
match	high level matching
match.index	use this to match in an index instead of match
match.rindex	use this to match in an rindex instead of match

Value

An object of class ‘index’, i.e. a list with components

val	sorted vector of values
pos	integer vector of original positions of sorted values
n	number of values (including NAs)
nNA	number of NAs
batch	resolution of tree
uni	logical flagging the index as unique (TRUE) or non-unique (FALSE)
tree	external pointer to C-tree

Theory

Linear search has O(n) time complexity. By using an index tree, search time can be reduced to O(log(n)). An index that can be used with any R-vector x of length n needs to store the original values together with the original positions, i.e. list(val=x, pos=order(x)), thus requires – strongly simplified – 2*n RAM. If we store this information in a binary tree, each value pair {val,pos} is stored in its own node together with two pointers, the memory requirements are – strongly simplified – 4*n RAM. The b-tree stores more than one value and two pointers in one node and thus minimizes the number of nodes that need to be read (from disk). However, used in RAM, b-trees increase the search time because they impurify logarithmic search across nodes with linear search within nodes. By contrast, the t-tree is optimized for RAM: it stores only two pointers but many sorted values within each node: for branching only min and max values need to be searched, linear search is only required at the final leaf node. However, realizing a t-tree within R's memory model requires additional overhead for the SEXPREC data structures. We avoid that by defining a static read only tree (and save implementation of insert and delete operations). The b*tree and t*tree versions of the mentioned indices reduce the size of the search nodes by storing the data itself in the leafnodes only. This leads to some redundant storage but speeds up search. Some implementations connect the leafnodes by extra pointers to speed up linear search. If we take this principle to the extreme, we can save these extra pointers and merge all leave nodes into one single big leaf. By doing so we loose the ability to update the index, but we gain a static read-only tree structure that supports very fast linear search as well as logarithmic search.

           .
         /   \
       .       .
     /   \   /   \   C-tree
   _________________  R-val
   _________________  R-pos
  

We implement this efficiently by storing the sorted values vector together with the order positions as standard R (SEXPREC) objects and add a pure C tree that is built from pointered struct nodes. The leaf nodes do use integer addressing instead of pointers to identify the associated part of the SEXPREC vector (pointers can't be used because the R garbage collector may move the vector). The topnode is linked into R using an external pointer. The tree itself can be removed explicitely from memory using indexDelTree. If the index object containing the external pointer is deleted, the tree will be freed from memory at the next garbage collection through its finalization method. If the index object does not contain a valid external pointer to the tree – e.g. when loading an index object from disk – the tree will be quickly transparently rebuild or can be build explicitely via indexAddTree.

Benefits

• much faster access to small fractions of large vectors (or few rownames of long data.frames)

• index allows and handles duplicated values

• index allows and handles NAs (unique version of index can still have more than one NA)

• index sort order is identical to (implemented via) order with na.last=TRUE.

• sorted values and original positions are stored simply as standard R vectors

• values in original sequence can be retrieved via [ from the index (original vector not required, thus no duplication of values)

• several vector methods give expected results (length, is.na, sort, order, [, Comparison operators)

• the tree needs minimum RAM due to lean C structs (index is close to 2*n)

• the tree resolution can be user-defined (RAM – speed – trade-off)

• the tree will not consume disk space when the index is saved

• the tree is build up transparently when needed the first time (e.g. after loading the index from disk)

• the tree is build up very quickly because the main work – the sorting – needs not to be repeated

• the tree is removed transparently from the garbage collector when the index is deleted

• this type of tree should perfectly complement the new disk vectors (packages ff and R.huge)

Limitations

• currently indexing is only available for character vectors (not logical, integer, real, complex)

• currently indices cannot be stored as columns of data frames

• functions that want to retrieve the index values in original order need to call indexname[] if the complete vector is needed

• building the index is rather slow (as slow as sorting in R is, building the tree is very fast)

• like all indices the index will reduce performance if a large fraction of the vector is accessed.

• not all methods have been maximally tuned via C-code (e.g. c.index).

Open questions

• Will R core officially export C entry points to UTF-8 resistant strcmp (STRCOLL) and strncmp (nothing yet)?

• Shall we make order() generic to allow dispatch of order.index like we have already dispatch of sort.index?

• Can we call the evaluator from C in order to make <>=comparisons independent of atomic mode (UTF-8 etc.) or will this kill to much performance?

• Can we call the evaluator from C for [-accessing the vector elements in order to generalize the index to ff or R.huge or will this kill to much performance?

Note

For each FOOindexFOO related to the ‘index’ class a function FOOrindexFOO exists related to the ‘rindex’ class. The ‘rindex’ class is a pure R-prototype and is kept for regression-testing using binregtest from package regtest. The regression tests are in dontshow sections in the examples of this help. If you run example(index) the regression tests will (unavoidably) trigger warnings.

Author(s)

Jens Oehlschl<e4>gel

References

Tobin J. Lehman, Michael J. Carey (1986) A Study of Index Structures for Main Memory Database Management Systems. Proceedings of the 12th International Conference on Very Large Data Bases, 294 – 303.
Pfaff, Ben (2004). An Introduction to Binary Search Trees and Balanced Trees, Libavl Binary Search Tree Library. Free Software Foundation, Inc.

See Also

order, sort , match

Examples

  #library(rindex)
  x <- sample(c(rep("c", 5), paste("d", 1:5, sep=""), c(letters[c(1,2,5,6)], NA)))

  cat("\n")
  cat("creating an index from atomic vector\n")
  i <- index(x)
  i
  cat("creating an index by combining indices\n")
  i2 <- c(i,i)
  i2
  cat("if the index (or index$tree) is removed, the C-tree is removed at the next garbage collection\n")
  cat("the index tree can also removed and created explicitely\n")
  i <- indexDelTree(i)
  i
  i <- indexAddTree(i, batch=3)
  print(i, tree=TRUE)
  indexNodes(i)
  indexBytes(i)

  cat("\n")
  cat("extracting the original vector\n")
  i[]
  cat("subsetting works as expected\n")
  i[1:3]
  cat("accessing the sorted data is much faster\n")
  sort(i)[1:3]
  cat("accessing the ordering is also much faster (order.index is not dispatched since order is not yet generic)\n")
  order.index(i)[1:3]

  identical(is.na(i),is.na(x))
  identical(length(i),length(x))

  cat("\n")
  cat("LOW LEVEL SEARCH returns position in SORTED VECTOR\n")
  cat("low level search for position of lowest instance of value in the index\n")
  indexFind(i, "c")
  cat("low level search for position of highest instance of value in the index\n")
  indexFind(i, "c", findlow=FALSE)
  cat("low level search for position of lowest instance beginning like search value\n")
  indexFindlike(i,"d")
  cat("low level search for position of highest instance beginning like search value\n")
  indexFindlike(i,"d",findlow=FALSE)

  cat("\n")
  cat("MID LEVEL SEARCH also returns position in SORTED VECTOR\n")
  cat("mid level search for a set of values\n")
  indexMatch(i,c("c","f"), findlow=TRUE)  # giving parameter findlow= suppresses the warning issued on non-unique indices
  sort(i)[indexMatch(i,c("c","f"), findlow=TRUE)]
  i[indexMatch(i,c("c","f"), findlow=TRUE, what="pos")]
  indexMatch(i,c("c","f"), findlow=TRUE, what="val")
  indexMatch(i,c("c","f"), findlow=TRUE, what="pos")
  indexMatch(i,c("c","f"), findlow=FALSE, what="pos")

  cat("mid level search for interval of values\n")
  indexFindInterval(i,"b","f")
  cat("by default the searched endpoints are included\n")
  sort(i)[indexFindInterval(i,"b","f")]
  cat("but they can be excluded\n")
  sort(i)[indexFindInterval(i,"b","f",high.include=FALSE)]
  cat("by default the searched endpoints need not to be present\n")
  sort(i)[indexFindInterval(i,"a1","e1")]
  cat("but this can be required\n")
  sort(i)[indexFindInterval(i,"a1","e1",low.exact=TRUE)]
  cat("each of the searched endpoints can be defined via indexFindlike\n")
  sort(i)[indexFindInterval(i,"c","d",FUN=indexFindlike)]


  cat("\n")
  cat("HIGH LEVEL SEARCH returns POSITION(s) IN ORIGINAL VECTOR but in SEQUENCE OF INDEX\n")
  indexEQ(i,"d3")
  indexNE(i,"d3")
  indexLT(i,"d3")
  indexLE(i,"d3")
  indexGT(i,"d3")
  indexGE(i,"d3")
  cat("searching for several values returns a list\n")
  indexEQ(i,c("b","c","z",NA))
  indexEQ(i,c("b","c","z",NA), what="val")


  cat("\n")
  cat("HIGH LEVEL OPERATORS returns TRUE/FALSE AT ORIGINAL VECTOR POSITIONS\n")
  i=="d3"
  i!="d3"
  i<"d3"
  i<="d3"
  i>"d3"
  i>="d3"

  cat("HIGH LEVEL match.index and  behave as expected\n")
  match(c("b","c","z",NA), x)
  match.index(c("b","c","z",NA), i)



## Not run: 

   cat("function timefactor helps with timing\n")

   n <-  1000000
   x <- sample(1:n)
   names(x) <- paste("a", x, sep="")
   d <- data.frame(x=as.vector(x), row.names=names(x))

   nsub  <- 100
   i <- sample(1:n, nsub)
   ni <- names(x)[i]

   ind <- index(names(x), verbose=TRUE)
   ind

   # test vectors
   cat("character susetting is by magnitude slower than integer subsettting\n")
   timefactor( x[ni] , x[i] , 10, 10000)
   cat("character susetting is approx as slow as matching\n")
   timefactor( x[ni] , x[match(ni,names(x))] , 10, 10)
   cat("for small fractions of n indexing is much faster\n")
   timefactor( x[ni] , x[indexMatch(ind,ni)] , 10, 100)

   # test dataframes
   cat("character susetting is by magnitude slower than integer subsettting\n")
   timefactor( d[ni,] , d[i,] , 1, 100)
   cat("obvious implementation problem (in R-2.5.1 subsetting is much slower than via matching)\n")
   timefactor( d[ni,] , d[match(ni,rownames(d)),] , 1, 1)
   cat("for small fractions of n indexing is much faster\n")
   timefactor( d[ni,] , d[indexMatch(ind,ni),] , 1, 10)


## End(Not run)

rindex documentation built on Sept. 1, 2018, 1:04 a.m.