running_sum {fromo}

Compute sums or means over a sliding window.

Description

Compute the mean or sum over an infinite or finite sliding window, returning a vector the same size as the input.

Usage

running_sum(v, window = NULL, wts = NULL, na_rm = FALSE,
  restart_period = 10000L, check_wts = FALSE)

running_mean(v, window = NULL, wts = NULL, na_rm = FALSE, min_df = 0L,
  restart_period = 10000L, check_wts = FALSE)

Arguments

v

a vector.

window

the window size. if given as finite integer or double, passed through. If NULL, NA_integer_, NA_real_ or Inf are given, equivalent to an infinite window size. If negative, an error will be thrown.

wts

an optional vector of weights. Weights are ‘replication’ weights, meaning a value of 2 is shorthand for having two observations with the corresponding v value. If NULL, corresponds to equal unit weights, the default. Note that weights are typically only meaningfully defined up to a multiplicative constant, meaning the units of weights are immaterial, with the exception that methods which check for minimum df will, in the weighted case, check against the sum of weights. For this reason, weights less than 1 could cause NA to be returned unexpectedly due to the minimum condition. When weights are NA, the same rules for checking v are applied. That is, the observation will not contribute to the moment if the weight is NA when na_rm is true. When there is no checking, an NA value will cause the output to be NA.

na_rm

whether to remove NA, false by default.

restart_period

the recompute period. because subtraction of elements can cause loss of precision, the computation of moments is restarted periodically based on this parameter. Larger values mean fewer restarts and faster, though potentially less accurate results. Unlike in the computation of even order moments, loss of precision is unlikely to be disastrous, so the default value is rather large.

check_wts

a boolean for whether the code shall check for negative weights, and throw an error when they are found. Default false for speed.

min_df

the minimum df to return a value, otherwise NaN is returned, only for the means computation. This can be used to prevent moments from being computed on too few observations. Defaults to zero, meaning no restriction.

Details

Computes the mean or sum of the elements, using a Kahan's Compensated Summation Algorithm, a numerically robust one-pass method.

Given the length n vector x, we output matrix M where M_{i,1} is the sum or mean of x_{i-window+1},x_{i-window+2},...,x_{i}. Barring NA or NaN, this is over a window of size window. During the 'burn-in' phase, we take fewer elements. If fewer than min_df for running_mean, returns NA.

Value

A vector the same size as the input.

Note

The moment computations provided by fromo are numerically robust, but will often not provide the same results as the 'standard' implementations, due to differences in roundoff. We make every attempt to balance speed and robustness. User assumes all risk from using the fromo package.

Author(s)

Steven E. Pav [e-mail]

References

Terriberry, T. "Computing Higher-Order Moments Online." http://people.xiph.org/~tterribe/notes/homs.html

J. Bennett, et. al., "Numerically Stable, Single-Pass, Parallel Statistics Algorithms," Proceedings of IEEE International Conference on Cluster Computing, 2009. https://www.semanticscholar.org/paper/Numerically-stable-single-pass-parallel-statistics-Bennett-Grout/a83ed72a5ba86622d5eb6395299b46d51c901265

Cook, J. D. "Accurately computing running variance." http://www.johndcook.com/standard_deviation.html

Cook, J. D. "Comparing three methods of computing standard deviation." http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation

Kahan, W. "Further remarks on reducing truncation errors," Communications of the ACM, 8 (1), 1965. https://doi.org/10.1145/363707.363723

Wikipedia contributors "Kahan summation algorithm," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Kahan_summation_algorithm&oldid=777164752 (accessed May 31, 2017).

Examples

x <- rnorm(1e5)
xs <- running_sum(x,10)
xm <- running_mean(x,100)