滚动平均值随大型数据集的窗口大小而变化 [英] Rolling mean with changing window size on a large dataset

问题描述

我想计算向量上的滚动平均值，由此窗口随向量中的每个条目而增长.基本上，我希望所有元素的均值一直到第 i 个， i + 1 -个， i + 2 -个等等.

I want to compute the rolling mean over a vector whereby the window grows with each entry in the vector. Basically, I want to have the mean of all elements up to the i-th, i+1-th, i+2-th, and so forth.

为了更加清楚，我将提供一个示例和一个解决方案，该示例和解决方案适用于较小的数据集，但无法很好地扩展:

To make it more clear, I'll provide an example and a solution which works for smaller datasets but does not scale up well:

library(zoo)

# data:
x <- 1:100

# solution:
rolling_average <- rollapply(x, seq_along(x), mean, align = "right")

# result:
rolling_average
# [1]  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0  7.5  8.0  8.5  9.0  9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5
# [27] 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5
# [53] 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5
# [79] 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5

将这种方法用于具有500000个条目的向量，将在几秒钟内填满我的内存，并使我的PC无法使用.另外，我尝试使用 RcppRoll 中的 roll_mean ，但由于 RcppRoll :: roll_mean 仅接受，因此无法提出解决方案整数作为窗口长度.

Using this approach for a vector with 500000 entries fills up my memory within seconds and renders my PC unusable. Alternatively, I've tried using roll_mean from RcppRoll, but wasn't able to come up with a solution because RcppRoll::roll_mean only accepts integers as window lengths.

那么，大规模解决此问题的最佳方法是什么?任何帮助，我们将不胜感激.

So, what is the best approach to solve this problem on a large scale? Any help is greatly appreciated.

推荐答案

我们可以做到

cumsum(x) / seq_along(x)
#  [1]  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0  7.5  8.0  8.5  9.0  9.5 10.0 10.5
# [21] 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5
# [41] 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5
# [61] 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5
# [81] 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5

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