coverage-methods {IRanges} | R Documentation

## Coverage of a set of ranges

### Description

For each position in the space underlying a set of ranges, counts the number of ranges that cover it.

### Usage

    coverage(x, shift=0L, width=NULL, weight=1L, ...)

    ## S4 method for signature 'IntegerRanges'
    coverage(x, shift=0L, width=NULL, weight=1L,
                method=c("auto", "sort", "hash", "naive"))

    ## S4 method for signature 'IntegerRangesList'
    coverage(x, shift=0L, width=NULL, weight=1L,
                method=c("auto", "sort", "hash", "naive"))

### Arguments

`x` | A IntegerRanges, Views, or IntegerRangesList object. See `?`coverage-methods`` in the GenomicRanges package for `coverage` methods for other objects.
`shift, weight` | `shift` specifies how much each range in `x` should be shifted before the coverage is computed. A positive shift value will shift the corresponding range in `x` to the right, and a negative value to the left. NAs are not allowed. `weight` assigns a weight to each range in `x`. If `x` is an IntegerRanges or Views object: each of these arguments must be an integer or numeric vector parallel to `x` (will get recycled if necessary). Alternatively, each of these arguments can also be specified as a single string naming a metadata column in `x` (i.e. a column in `mcols(x)`) to be used as the `shift` (or `weight`) vector. Note that when `x` is an IPos object, each of these arguments can only be a single number. If `x` is an IntegerRangesList object: each of these arguments must be a numeric vector or list-like object of the same length as `x` (will get recycled if necessary). If it's a numeric vector, it's first turned into a list with `as.list`. After recycling, each list element `shift[[i]]` (or `weight[[i]]`) must be an integer or numeric vector parallel to `x[[i]]` (will get recycled if necessary). If `weight` is an integer vector or list-like object of integer vectors, the coverage vector(s) will be returned as integer-Rle object(s). If it's a numeric vector or list-like object of numeric vectors, the coverage vector(s) will be returned as numeric-Rle object(s).
`width` | Specifies the length of the returned coverage vector(s). If `x` is an IntegerRanges object: `width` must be `NULL` (the default), an NA, or a single non-negative integer. After being shifted, the ranges in `x` are always clipped on the left to keep only their positive portion i.e. their intersection with the [1, +inf) interval. If `width` is a single non-negative integer, then they're also clipped on the right to keep only their intersection with the [1, width] interval. In that case `coverage` returns a vector of length `width`. Otherwise, it returns a vector that extends to the last position in the underlying space covered by the shifted ranges. If `x` is a Views object: Same as for a IntegerRanges object, except that, if `width` is `NULL` then it's treated as if it was `length(subject(x))`. If `x` is a IntegerRangesList object: `width` must be `NULL` or an integer vector parallel to `x` (i.e. with one element per list element in `x`). If not `NULL`, the vector must contain NAs or non-negative integers and it will get recycled to the length of `x` if necessary. If `NULL`, it is replaced with `NA` and recycled to the length of `x`. Finally `width[i]` is used to compute the coverage vector for `x[[i]]` and is therefore treated like explained above (when `x` is a IntegerRanges object).
`method` | If `method` is set to `"sort"`, then `x` is sorted previous to the calculation of the coverage. If `method` is set to `"hash"` or `"naive"`, then `x` is hashed directly to a vector of length `width` without previous sorting. The `"hash"` method is faster than the `"sort"` method when `x` is large (i.e. contains a lot of ranges). When `x` is small and `width` is big (e.g. `x` represents a small set of reads aligned to a big chromosome), then `method="sort"` is faster and uses less memory than `method="hash"`. The `"naive"` method is a slower version of the `"hash"` method that has the advantage of avoiding floating point artefacts in the no-coverage regions of the numeric-Rle object returned by `coverage()` when the weights are supplied as a numeric vector of type `double`. See "FLOATING POINT ARITHMETIC CAN BRING A SURPRISE" section in the Examples below for more information. Using `method="auto"` selects between the `"sort"` and `"hash"` methods, picking the one that is predicted to be faster based on `length(x)` and `width`.
`...` | Further arguments to be passed to or from other methods.

### Value

If `x` is a IntegerRanges or Views object: An integer- or numeric-Rle object depending on whether `weight` is an integer or numeric vector.

If `x` is a IntegerRangesList object: An RleList object with one coverage vector per list element in `x`, and with `x` names propagated to it. The i-th coverage vector can be either an integer- or numeric-Rle object, depending on the type of `weight[[i]]` (after `weight` has gone thru `as.list` and recycling, like described previously).

### Author(s)

H. Pagès and P. Aboyoun

### See Also

- coverage-methods in the GenomicRanges package for more `coverage` methods.

- The `slice` function for slicing the Rle or RleList object returned by `coverage`.

- IntegerRanges, IPos, IntegerRangesList, Rle, and RleList objects.

### Examples

    ## ---------------------------------------------------------------------
    ## A. COVERAGE OF AN IRanges OBJECT
    ## ---------------------------------------------------------------------
    x <- IRanges(start=c(-2L, 6L, 9L, -4L, 1L, 0L, -6L, 10L),
                 width=c( 5L, 0L, 6L,  1L, 4L, 3L,  2L,  3L))
    coverage(x)
    coverage(x, shift=7)
    coverage(x, shift=7, width=27)
    coverage(x, shift=c(-4, 2))  # 'shift' gets recycled
    coverage(x, shift=c(-4, 2), width=12)
    coverage(x, shift=-max(end(x)))

    coverage(restrict(x, 1, 10))
    coverage(reduce(x), shift=7)
    coverage(gaps(shift(x, 7), start=1, end=27))

    ## With weights:
    coverage(x, weight=as.integer(10^(0:7)))  # integer-Rle
    coverage(x, weight=c(2.8, -10))  # numeric-Rle, 'shift' gets recycled

    ## ---------------------------------------------------------------------
    ## B. FLOATING POINT ARITHMETIC CAN BRING A SURPRISE
    ## ---------------------------------------------------------------------
    ## Please be aware that rounding errors in floating point arithmetic can
    ## lead to some surprising results when computing a weighted coverage:
    y <- IRanges(c(4, 10), c(18, 15))
    w1 <- 0.958
    w2 <- 1e4
    cvg <- coverage(y, width=100, weight=c(w1, w2))
    cvg  # non-zero coverage at positions 19 to 100!

    ## This is an artefact of floating point arithmetic and the algorithm
    ## used to compute the weighted coverage. It can be observed with basic
    ## floating point arithmetic:
    w1 + w2 - w2 - w1  # very small non-zero value!

    ## Note that this only happens with the "sort" and "hash" methods but
    ## not with the "naive" method:
    coverage(y, width=100, weight=c(w1, w2), method="sort")
    coverage(y, width=100, weight=c(w1, w2), method="hash")
    coverage(y, width=100, weight=c(w1, w2), method="naive")

    ## These very small non-zero coverage values in the no-coverage regions
    ## of the numeric-Rle object returned by coverage() are not always
    ## present. But when they are, they can cause problems downstream or
    ## in unit tests. For example downstream code that relies on things
    ## like 'cvg != 0' to find regions with coverage won't work properly.
    ## This can be mitigated either by selecting the "naive" method (be aware
    ## that this can slow down things significantly) or by "cleaning" 'cvg'
    ## first e.g. with something like 'cvg <- round(cvg, digits)' where
    ## 'digits' is a carefully chosen number of digits:
    cvg <- round(cvg, digits=3)

    ## Note that this rounding will also have the interesting side effect of
    ## reducing the memory footprint of the Rle object in general (because
    ## some runs might get merged into a single run as a consequence of the
    ## rounding).

    ## ---------------------------------------------------------------------
    ## C. COVERAGE OF AN IPos OBJECT
    ## ---------------------------------------------------------------------
    pos_runs <- IRanges(c(1, 5, 9), c(10, 8, 15))
    ipos <- IPos(pos_runs)
    coverage(ipos)

    ## ---------------------------------------------------------------------
    ## D. COVERAGE OF AN IRangesList OBJECT
    ## ---------------------------------------------------------------------
    x <- IRangesList(A=IRanges(3*(4:-1), width=1:3), B=IRanges(2:10, width=5))
    cvg <- coverage(x)
    cvg

    stopifnot(identical(cvg[[1]], coverage(x[[1]])))
    stopifnot(identical(cvg[[2]], coverage(x[[2]])))

    coverage(x, width=c(50, 9))
    coverage(x, width=c(NA, 9))
    coverage(x, width=9)  # 'width' gets recycled

    ## Each list element in 'shift' and 'weight' gets recycled to the length
    ## of the corresponding element in 'x'.
    weight <- list(as.integer(10^(0:5)), -0.77)
    cvg2 <- coverage(x, weight=weight)
    cvg2  # 1st coverage vector is an integer-Rle, 2nd is a numeric-Rle

    identical(mapply(coverage, x=x, weight=weight), as.list(cvg2))

    ## ---------------------------------------------------------------------
    ## E. SOME MATHEMATICAL PROPERTIES OF THE coverage() FUNCTION
    ## ---------------------------------------------------------------------

    ## PROPERTY 1: The coverage vector is not affected by reordering the
    ## input ranges:
    set.seed(24)
    x <- IRanges(sample(1000, 40, replace=TRUE), width=17:10)
    cvg0 <- coverage(x)
    stopifnot(identical(coverage(sample(x)), cvg0))

    ## Of course, if the ranges are shifted and/or assigned weights, then
    ## this doesn't hold anymore, unless the 'shift' and/or 'weight'
    ## arguments are reordered accordingly.

    ## PROPERTY 2: The coverage of the concatenation of 2 IntegerRanges
    ## objects 'x' and 'y' is the sum of the 2 individual coverage vectors:
    y <- IRanges(sample(-20:280, 36, replace=TRUE), width=28)
    stopifnot(identical(coverage(c(x, y), width=100),
                        coverage(x, width=100) + coverage(y, width=100)))

    ## Note that, because adding 2 vectors in R recycles the shortest to
    ## the length of the longest, the following is generally FALSE:
    identical(coverage(c(x, y)), coverage(x) + coverage(y))  # FALSE

    ## It would only be TRUE if the 2 coverage vectors that we add had the
    ## same length, which would only happen by chance. By using the same
    ## 'width' value when we computed the 2 coverages previously, we made
    ## sure they had the same length.

    ## Because of properties 1 & 2, we have:
    x1 <- x[c(TRUE, FALSE)]  # pick up 1st, 3rd, 5th, etc... ranges
    x2 <- x[c(FALSE, TRUE)]  # pick up 2nd, 4th, 6th, etc... ranges
    cvg1 <- coverage(x1, width=100)
    cvg2 <- coverage(x2, width=100)
    stopifnot(identical(coverage(x, width=100), cvg1 + cvg2))

    ## PROPERTY 3: Multiplying the weights by a scalar has the effect of
    ## multiplying the coverage vector by the same scalar:
    weight <- runif(40)
    cvg3 <- coverage(x, weight=weight)
    stopifnot(all.equal(coverage(x, weight=-2.68 * weight), -2.68 * cvg3))

    ## Because of properties 1 & 2 & 3, we have:
    stopifnot(identical(coverage(x, width=100, weight=c(5L, -11L)),
                        5L * cvg1 - 11L * cvg2))

    ## PROPERTY 4: Using the sum of 2 weight vectors produces the same
    ## result as using the 2 weight vectors separately and summing the
    ## 2 results:
    weight2 <- 10 * runif(40) + 3.7
    stopifnot(all.equal(coverage(x, weight=weight + weight2),
                        cvg3 + coverage(x, weight=weight2)))

    ## PROPERTY 5: Repeating any input range N number of times is
    ## equivalent to multiplying its assigned weight by N:
    times <- sample(0:10L, length(x), replace=TRUE)
    stopifnot(all.equal(coverage(rep(x, times), weight=rep(weight, times)),
                        coverage(x, weight=weight * times)))

    ## In particular, if 'weight' is not supplied:
    stopifnot(identical(coverage(rep(x, times)), coverage(x, weight=times)))

    ## PROPERTY 6: If none of the input range actually gets clipped during
    ## the "shift and clip" process, then:
    ##
    ##     sum(cvg) = sum(width(x) * weight)
    ##
    stopifnot(sum(cvg3) == sum(width(x) * weight))

    ## In particular, if 'weight' is not supplied:
    stopifnot(sum(cvg0) == sum(width(x)))

    ## Note that this property is sometimes used in the context of a
    ## ChIP-Seq analysis to estimate "the number of reads in a peak", that
    ## is, the number of short reads that belong to a peak in the coverage
    ## vector computed from the genomic locations (a.k.a. genomic ranges)
    ## of the aligned reads. Because of property 6, the number of reads in
    ## a peak is approximately the area under the peak divided by the short
    ## read length.

    ## PROPERTY 7: If 'weight' is not supplied, then disjoining or reducing
    ## the ranges before calling coverage() has the effect of "shaving" the
    ## coverage vector at elevation 1:
    table(cvg0)
    shaved_cvg0 <- cvg0
    runValue(shaved_cvg0) <- pmin(runValue(cvg0), 1L)
    table(shaved_cvg0)

    stopifnot(identical(coverage(disjoin(x)), shaved_cvg0))
    stopifnot(identical(coverage(reduce(x)), shaved_cvg0))

    ## ---------------------------------------------------------------------
    ## F. SOME SANITY CHECKS
    ## ---------------------------------------------------------------------
    dummy_coverage <- function(x, shift=0L, width=NULL)
    {
        y <- IRanges:::unlist_as_integer(shift(x, shift))
        if (is.null(width))
            width <- max(c(0L, y))
        Rle(tabulate(y,  nbins=width))
    }

    check_real_vs_dummy <- function(x, shift=0L, width=NULL)
    {
        res1 <- coverage(x, shift=shift, width=width)
        res2 <- dummy_coverage(x, shift=shift, width=width)
        stopifnot(identical(res1, res2))
    }
    check_real_vs_dummy(x)
    check_real_vs_dummy(x, shift=7)
    check_real_vs_dummy(x, shift=7, width=27)
    check_real_vs_dummy(x, shift=c(-4, 2))
    check_real_vs_dummy(x, shift=c(-4, 2), width=12)
    check_real_vs_dummy(x, shift=-max(end(x)))

    ## With a set of distinct single positions:
    x3 <- IRanges(sample(50000, 20000), width=1)
    stopifnot(identical(sort(start(x3)), which(coverage(x3) != 0L)))

[Package IRanges version 2.24.1 Index]