# expand-methods: Expand or contract intervals In intervals: Tools for Working with Points and Intervals

## Description

It is often useful to shrink or grow each interval in a set of intervals: to smooth over small, uninteresting gaps, or to address possible imprecision resulting from floating point arithmetic. The `expand` and `contract` methods implement this, using either absolute or relative difference.

## Usage

 ```1 2 3 4 5``` ```## S4 method for signature 'Intervals_virtual' expand(x, delta = 0, type = c("absolute", "relative")) ## S4 method for signature 'Intervals_virtual' contract(x, delta = 0, type = c("absolute", "relative")) ```

## Arguments

 `x` An `"Intervals"` or `"Intervals_full"` object. `delta` A non-negative adjustement value. A vector is permitted, and its entries will be recycled if necessary. `type` Should adjustment be based on relative or absolute difference. When `type == "relative"` intervals are expanded/contracted to include/exclude points for which a relative difference with respect to the nominal value is less than or equal to `delta`. (See the note below.) When `type == "absolute"`, absolute rather than relative difference is used, i.e., all intervals are expanded or contracted by the same amount.

## Value

A single object of appropriate class, with endpoint positions adjusted as requested. Expansion returns an object with the same dimension as `x`; contraction may lead to the elimination of now-empty rows.

## Note

Here, the relative difference between x and y is |x - y|/max(|x|, |y|).

## Examples

 ``` 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``` ```# Using adjustment to remove small gaps x <- Intervals( c(1,10,100,8,50,200), type = "Z" ) close_intervals( contract( reduce( expand(x, 1) ), 1 ) ) # Finding points for which, as a result of possible floating point # error, intersection may be ambiguous. Whether y1 intersects y2[2,] # depends on precision. delta <- .Machine\$double.eps^0.5 y1 <- Intervals( c( .5, 1 - delta / 2 ) ) y2 <- Intervals( c( .25, 1, .75, 2 ) ) # Nominal interval_intersection( y1, y2 ) # Inner limit inner <- interval_intersection( contract( y1, delta, "relative" ), contract( y2, delta, "relative" ) ) # Outer limit outer <- interval_intersection( expand( y1, delta, "relative" ), expand( y2, delta, "relative" ) ) # The ambiguous set, corresponding to points which may or may not be in # the intersection -- depending on numerical values for endpoints # which are, with respect to relative difference, indistinguishable from # the nominal values. interval_difference( outer, inner ) ```

intervals documentation built on May 30, 2017, 1:31 a.m.