# Ranges-class

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##### Ranges objects

The Ranges virtual class is a general container for storing a set of integer ranges.

Keywords
classes, methods
##### Details

A Ranges object is a vector-like object where each element describes a "range of integer values".

A "range of integer values" is a finite set of consecutive integer values. Each range can be fully described with exactly 2 integer values which can be arbitrarily picked up among the 3 following values: its "start" i.e. its smallest (or first, or leftmost) value; its "end" i.e. its greatest (or last, or rightmost) value; and its "width" i.e. the number of integer values in the range. For example the set of integer values that are greater than or equal to -20 and less than or equal to 400 is the range that starts at -20 and has a width of 421. In other words, a range is a closed, one-dimensional interval with integer end points and on the domain of integers.

The starting point (or "start") of a range can be any integer (see start below) but its "width" must be a non-negative integer (see width below). The ending point (or "end") of a range is equal to its "start" plus its "width" minus one (see end below). An "empty" range is a range that contains no value i.e. a range that has a null width. Depending on the context, it can be interpreted either as just the empty set of integers or, more precisely, as the position between its "end" and its "start" (note that for an empty range, the "end" equals the "start" minus one).

The length of a Ranges object is the number of ranges in it, not the number of integer values in its ranges.

A Ranges object is considered empty iff all its ranges are empty.

Ranges objects have a vector-like semantic i.e. they only support single subscript subsetting (unlike, for example, standard R data frames which can be subsetted by row and by column).

The Ranges class itself is a virtual class. The following classes derive directly from the Ranges class: IRanges and IntervalTree.

##### Methods

In the code snippets below, x, y and object are Ranges objects. Not all the functions described below will necessarily work with all kinds of Ranges objects but they should work at least for IRanges objects. Note that many more operations on Ranges objects are described in other man pages of the IRanges package. See for example the man page for intra range transformations (e.g. shift(), see ?intra-range-methods), or the man page for inter range transformations (e.g. reduce(), see ?inter-range-methods), or the man page for findOverlaps methods (see ?findOverlaps-methods), or the man page for RangesList objects where the split method for Ranges objects is documented.

length(x): The number of ranges in x.
start(x): The start values of the ranges. This is an integer vector of the same length as x.
width(x): The number of integer values in each range. This is a vector of non-negative integers of the same length as x.
end(x): start(x) + width(x) - 1L
mid(x): returns the midpoint of the range, start(x) + floor((width(x) - 1)/2).
names(x): NULL or a character vector of the same length as x.
update(object, ...): Convenience method for combining multiple modifications of object in one single call. For example object <- update(object, start=start(object)-2L, end=end(object)+2L) is equivalent to start(object) <- start(object)-2L; end(object) <- end(object)+2L.
tile(x, n, width, ...): Splits each range in x into subranges as specified by n (number of ranges) or width. Only one of n or width can be specified. The return value is a IRangesList the same length as x. Ranges with a width less than the width argument are returned unchanged.
isEmpty(x): Return a logical value indicating whether x is empty or not.
as.matrix(x, ...): Convert x into a 2-column integer matrix containing start(x) and width(x). Extra arguments (...) are ignored.
as.data.frame(x, row.names=NULL, optional=FALSE, ...): Convert x into a standard R data frame object. row.names must be NULL or a character vector giving the row names for the data frame, and optional and any additional argument (...) is ignored. See ?as.data.frame for more information about these arguments.
as.integer(x): Convert x into an integer vector, by converting each range into the integer sequence formed by from:to and concatenating them together.
unlist(x, recursive = TRUE, use.names = TRUE): Similar to as.integer(x) except can add names to elements.
x[[i]]: Return integer vector start(x[i]):end(x[i]) denoted by i. Subscript i can be a single integer or a character string.
x[i]: Return a new Ranges object (of the same type as x) made of the selected ranges. i can be a numeric vector, a logical vector, NULL or missing. If x is a NormalIRanges object and i a positive numeric subscript (i.e. a numeric vector of positive values), then i must be strictly increasing.
rep(x, times, length.out, each): Repeats the values in x through one of the following conventions:
times
Vector giving the number of times to repeat each element if of length length(x), or to repeat the Ranges elements if of length 1.
length.out
Non-negative integer. The desired length of the output vector.
each
Non-negative integer. Each element of x is repeated each times.
c(x, ...): Combine x and the Ranges objects in ... together. Any object in ... must belong to the same class as x, or to one of its subclasses, or must be NULL. The result is an object of the same class as x. NOTE: Only works for IRanges (and derived) objects for now.
x * y: The arithmetic operation x * y is for centered zooming. It symmetrically scales the width of x by 1/y, where y is a numeric vector that is recycled as necessary. For example, x * 2 results in ranges with half their previous width but with approximately the same midpoint. The ranges have been “zoomed in”. If y is negative, it is equivalent to x * (1/abs(y)). Thus, x * -2 would double the widths in x. In other words, x has been “zoomed out”.
x + y: Expands the ranges in x on either side by the corresponding value in the numeric vector y.
show(x): By default the show method displays 5 head and 5 tail lines. The number of lines can be altered by setting the global options showHeadLines and showTailLines. If the object length is less than the sum of the options, the full object is displayed. These options affect GRanges, GAlignments, Ranges and XString objects.

##### Normality

A Ranges object x is implicitly representing an arbitrary finite set of integers (that are not necessarily consecutive). This set is the set obtained by taking the union of all the values in all the ranges in x. This representation is clearly not unique: many different Ranges objects can be used to represent the same set of integers. However one and only one of them is guaranteed to be "normal". By definition a Ranges object is said to be "normal" when its ranges are: (a) not empty (i.e. they have a non-null width); (b) not overlapping; (c) ordered from left to right; (d) not even adjacent (i.e. there must be a non empty gap between 2 consecutive ranges). Here is a simple algorithm to determine whether x is "normal": (1) if length(x) == 0, then x is normal; (2) if length(x) == 1, then x is normal iff width(x) >= 1; (3) if length(x) >= 2, then x is normal iff:

start(x)[i] <= end(x)[i]="" <="" start(x)[i+1]="">
for every 1 <= i < length(x). The obvious advantage of using a "normal" Ranges object to represent
a given finite set of integers is that it is the smallest in terms of
number of ranges and therefore in terms of storage space.
Also the fact that we impose its ranges to be ordered from left to
right makes it unique for this representation. A special container (NormalIRanges) is provided for holding
a "normal" IRanges object: a NormalIRanges object is
just an IRanges object that is guaranteed to be "normal". Here are some methods related to the notion of "normal" Ranges:
isNormal(x): Return TRUE or FALSE indicating whether x is "normal" or not.
whichFirstNotNormal(x): Return NA if x is normal, or the smallest valid indice i in x for which x[1:i] is not "normal".

##### Disjoint ranges

A Ranges object x is considered to be "disjoint" if its ranges are disjoint (i.e. non-overlapping). The isDisjoint function is provided for testing whether a Ranges object is "disjoint" or not:

isDisjoint(x): Return TRUE or FALSE indicating whether x is "disjoint" or not. isDisjoint handles empty ranges (a.k.a. zero-width ranges) as follow: single empty range A is considered to overlap with single range B iff it's contained in B without being on the edge of B (in which case it would be ambiguous whether A is contained in or adjacent to B). In other words, single empty range A is considered to overlap with single range B iff
start(B) < start(A) and end(A) < end(B)
Because A is an empty range it verifies end(A) = start(A) - 1 so the above is equivalent to:
start(B) < start(A) <= end(b)<="" pre="">
and also equivalent to:

start(B) <= end(a)="" <="" end(b)<="" pre="">
Finally, it is also equivalent to:

compare(A, B) == 2
See ?Ranges-comparison for the meaning of the codes returned by the compare function.
Note that a "normal" Ranges object is always "disjoint" but the opposite is not true.

##### Aliases
• class:Ranges
• Ranges-class
• Ranges
• length,Ranges-method
• elementLengths,Ranges-method
• width
• start,Ranges-method
• width,Ranges-method
• end,Ranges-method
• mid
• mid,Ranges-method
• start<-
• width<-
• end<-
• as.matrix,Ranges-method
• as.data.frame.Ranges
• as.data.frame,Ranges-method
• as.integer,Ranges-method
• unlist,Ranges-method
• show,Ranges-method
• showAsCell,Ranges-method
• isEmpty,Ranges-method
• isNormal
• isNormal,Ranges-method
• whichFirstNotNormal
• whichFirstNotNormal,Ranges-method
• isDisjoint
• isDisjoint,Ranges-method
• update,Ranges-method
• tile
• tile,Ranges-method
##### Examples
## ---------------------------------------------------------------------
## Basic manipulation
## ---------------------------------------------------------------------
x <- IRanges(start=c(2:-1, 13:15), width=c(0:3, 2:0))
x
length(x)
start(x)
width(x)
end(x)
isEmpty(x)
as.matrix(x)
as.data.frame(x)

## Subsetting:
x[4:2]                  # 3 ranges
x[-1]                   # 6 ranges
x[FALSE]                # 0 range
x0 <- x[width(x) == 0]  # 2 ranges
isEmpty(x0)

## Use the replacement methods to resize the ranges:
width(x) <- width(x) * 2 + 1
x
end(x) <- start(x)            # equivalent to width(x) <- 0
x
width(x) <- c(2, 0, 4)
x
start(x)[3] <- end(x)[3] - 2  # resize the 3rd range
x

## Name the elements:
names(x)
names(x) <- c("range1", "range2")
x
x[is.na(names(x))]  # 5 ranges
x[!is.na(names(x))]  # 2 ranges

ir <- IRanges(c(1,5), c(3,10))
ir*1 # no change
ir*c(1,2) # zoom second range by 2X
ir*-2 # zoom out 2X

## ---------------------------------------------------------------------
## isDisjoint()
## ---------------------------------------------------------------------

## On a Ranges object:
isDisjoint(IRanges(c(2,5,1), c(3,7,3)))  # FALSE
isDisjoint(IRanges(c(2,9,5), c(3,9,6)))  # TRUE
isDisjoint(IRanges(1, 5))  # TRUE

## Handling of empty ranges:
x <- IRanges(c(11, 16, 11, -2, 11), c(15, 29, 10, 10, 10))
stopifnot(isDisjoint(x))

## Sliding an empty range along a non-empty range:
sapply(11:17,
function(i) compare(IRanges(i, width=0), IRanges(12, 15)))

sapply(11:17,
function(i) isDisjoint(c(IRanges(i, width=0), IRanges(12, 15))))
Documentation reproduced from package IRanges, version 2.0.1, License: Artistic-2.0

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