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

1 2 3 4 5 6 | ```
index(x, uni = NULL, batch = NULL, verbose = FALSE)
## S3 method for class 'index'
c(...)
indexAddTree(obj, batch = NULL)
indexDelTree(obj)
indexAutobatch(n, batch = 64)
``` |

`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 |

`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’ |

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` |

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 |

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.

1 2 3 4 5 6 7 | ```
.
/ \
. .
/ \ / \ 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`

.

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)

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 neededbuilding 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`

).

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?

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.

Jens Oehlschl<e4>gel

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | ```
#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)
``` |

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