sum.exact, cumsum.exact & runsum.exact {caTools} | R Documentation |
Functions for performing basic sum operations without round-off errors
sum.exact(..., na.rm = FALSE) cumsum.exact(x) runsum.exact(x,k)
x |
numeric vector |
... |
numeric vector(s), numbers or other objects to be summed |
na.rm |
logical. Should missing values be removed? |
k |
width of moving window; must be an odd integer between one and n |
All three functions use full precision summation using multiple doubles for intermediate values. The sum of numbers x & y is a=x+y with error term b=error(a+b). That way a+b is equal exactly x+y, so sum of 2 numbers is stored as 2 or fewer values, which when added would under-flow. By extension sum of n numbers is calculated with intermediate results stored as array of numbers that can not be added without introducing an error. Only final result is converted to a single number
Function sum.exact
returns single number. Function cumsum.exact
returns vector of the same length as x
. Function runsum.exact
returns vector of length length(x)-k
and attribute "count" containing
number of finite (as in is.finite
) elements in each window.
Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com based on code by Vadim Ogranovich, which is based on algorithms described in references, pointed out by Gabor Grothendieck.
Round-off error correction is based on: Shewchuk, Jonathan, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps and its implementation found at: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090
McCullough, D.B., (1998) Assessing the Reliability of Statistical Software, Part I, The American Statistician, Vol. 52 No 4, http://www.amstat.org/publications/tas/mccull-1.pdf
McCullough, D.B., (1999) Assessing the Reliability of Statistical Software, Part II, The American Statistician, Vol. 53 No 2 http://www.amstat.org/publications/tas/mccull.pdf
NIST Statistical Reference Datasets (StRD) website http://www.nist.gov/itl/div898/strd
sum
is faster but not error-save version of
sum.exact
cumsum
is equivalent to cumsum.exact
runmean(x,k,endrule="trim")
is similar to
runsum.exact
.
x = c(1, 1e20, 1e40, -1e40, -1e20, -1) a = sum(x); print(a) b = sum.exact(x); print(b) stopifnot(b==0) a = cumsum(x); print(a) b = cumsum.exact(x); print(b) stopifnot(b[6]==0)