Fast Robust Moments – Pick Three!
Fast, numerically robust, higher order moments in R, computed via Rcpp, mostly as an exercise to learn Rcpp. Supports computation on vectors and matrices, and Monoidal append (and unappend) of moments. Computations are via the Welford-Terriberry algorithm, as described by Bennett et al.
– Steven E. Pav, shabbychef@gmail.com
This package can be installed from CRAN, via drat, or from github:
# via CRAN:
install.packages("fromo")
# via drat:
if (require(drat)) {
drat:::add("shabbychef")
install.packages("fromo")
}
# get snapshot from github (may be buggy)
if (require(devtools)) {
install_github("shabbychef/fromo")
}Currently the package functionality can be divided into the following: * Functions which reduce a vector to an array of moments. * Functions which take a vector to a matrix of the running moments. * Functions which transform a vector to some normalized form, like a centered, rescaled, z-scored sample, or a summarized form, like the running Sharpe or t-stat. * Functions for computing the covariance of a vector robustly. * Object representations of moments with join and unjoin methods.
A function which computes, say, the kurtosis, typically also computes the mean and standard deviation, and has performed enough computation to easily return the skew. However, the default functions in R for higher order moments discard these lower order moments. So, for example, if you wish to compute Merten’s form for the standard error of the Sharpe ratio, you have to call separate functions to compute the kurtosis, skew, standard deviation, and mean.
The summary functions in fromo return all the
moments up to some order, namely the functions sd3,
skew4, and kurt5. The latter of these,
kurt5 returns an array of length 5 containing the
excess kurtosis, the skewness, the standard deviation, the
mean, and the observation count. (The number in the function name
denotes the length of the output.) Along the same lines, there are
summarizing functions that compute centered moments, standardized
moments, and ‘raw’ cumulants:
cent_moments: return a k+1-vector of the
kth centered moment, the k-1th, all the way
down to the 2nd (the variance), then the mean and the
observation count.std_moments: return a k+1-vector of the
kth standardized moment, the k-1th, all the
way down to the 3rd, then the standard deviation, the mean, and
the observation count.cent_cumulants: computes the centered cumulants (yes,
this is redundant, but they are not standardized). return a
k+1-vector of the kth raw cumulant, the
k-1th, all the way down to the second, then the mean, and
the observation count.std_cumulants: computes the standardized (and, of
course, centered) cumulants. return a k+1-vector of the
kth standardized cumulant, all the way down to the third,
then the variance, the mean, and the observation count.library(fromo)
set.seed(12345)
x <- rnorm(1000, mean = 10, sd = 2)
show(cent_moments(x, max_order = 4, na_rm = TRUE))## [1] 47.276 -0.047 3.986 10.092 1000.000show(std_moments(x, max_order = 4, na_rm = TRUE))## [1] 3.0e+00 -5.9e-03 2.0e+00 1.0e+01 1.0e+03show(cent_cumulants(x, max_order = 4, na_rm = TRUE))## [1] -0.388 -0.047 3.986 10.092 1000.000show(std_cumulants(x, max_order = 4, na_rm = TRUE))## [1] -2.4e-02 -5.9e-03 4.0e+00 1.0e+01 1.0e+03In theory these operations should be just as fast as the default functions, but faster than calling multiple default functions. Here is a speed comparison of the basic moment computations:
library(fromo)
library(moments)
library(microbenchmark)
set.seed(1234)
x <- rnorm(1000)
dumbk <- function(x) {
c(kurtosis(x) - 3, skewness(x), sd(x), mean(x),
length(x))
}
microbenchmark(kurt5(x), skew4(x), sd3(x), dumbk(x),
dumbk(x), kurtosis(x), skewness(x), sd(x), mean(x))## Unit: microseconds
## expr min lq mean median uq max neval cld
## kurt5(x) 138.1 140.5 152.3 142.8 151 326 100 a
## skew4(x) 76.6 79.0 374.5 80.2 83 29119 100 a
## sd3(x) 9.6 10.6 14.0 11.5 12 161 100 a
## dumbk(x) 192.8 207.9 272.6 216.4 229 9540 200 a
## kurtosis(x) 85.7 90.6 99.5 93.2 102 217 100 a
## skewness(x) 85.8 90.8 96.2 92.5 95 172 100 a
## sd(x) 15.4 17.8 21.6 18.9 20 72 100 a
## mean(x) 3.9 4.5 5.4 4.7 5 19 100 ax <- rnorm(1e+07, mean = 1e+12)
microbenchmark(kurt5(x), skew4(x), sd3(x), dumbk(x),
kurtosis(x), skewness(x), sd(x), mean(x), times = 10L)## Unit: milliseconds
## expr min lq mean median uq max neval cld
## kurt5(x) 1470 1481 1515 1501 1534 1593 10 c
## skew4(x) 808 813 869 834 870 1069 10 b
## sd3(x) 75 75 78 76 81 87 10 a
## dumbk(x) 1830 1852 1924 1873 1918 2328 10 d
## kurtosis(x) 906 909 947 917 945 1138 10 b
## skewness(x) 864 872 938 912 954 1184 10 b
## sd(x) 52 52 54 52 54 64 10 a
## mean(x) 19 19 20 20 20 21 10 aMany of the methods now support the computation of weighted moments. There are a few options around weights: whether to check them for negative values, whether to normalize them to unit mean.
library(fromo)
library(moments)
library(microbenchmark)
set.seed(987)
x <- rnorm(1000)
w <- runif(length(x))
# no weights:
show(cent_moments(x, max_order = 4, na_rm = TRUE))## [1] 2.9e+00 1.2e-02 1.0e+00 1.0e-02 1.0e+03# with weights:
show(cent_moments(x, max_order = 4, wts = w, na_rm = TRUE))## [1] 3.1e+00 4.1e-02 1.0e+00 1.3e-02 1.0e+03# if you turn off weight normalization, the last
# element is sum(wts):
show(cent_moments(x, max_order = 4, wts = w, na_rm = TRUE,
normalize_wts = FALSE))## [1] 3.072 0.041 1.001 0.013 493.941# let's compare for speed!
x <- rnorm(1e+07)
w <- runif(length(x))
slow_sd <- function(x, w) {
n0 <- length(x)
mu <- weighted.mean(x, w = w)
sg <- sqrt(sum(w * (x - mu)^2)/(n0 - 1))
c(sg, mu, n0)
}
microbenchmark(sd3(x, wts = w), slow_sd(x, w))## Unit: milliseconds
## expr min lq mean median uq max neval cld
## sd3(x, wts = w) 104 107 111 110 115 139 100 a
## slow_sd(x, w) 261 278 310 297 318 483 100 bThe as.centsums object performs the summary
(centralized) moment computation, and stores the centralized sums. There
is a print method that shows raw, centralized, and standardized moments
of the ingested data. This object supports concatenation and
unconcatenation. These should satisfy ‘monoidal homomorphism’, meaning
that concatenation and taking moments commute with each other. So if you
have two vectors, x1 and x2, the following
should be equal: c(as.centsums(x1,4),as.centsums(x2,4)) and
as.centsums(c(x1,x2),4). Moreover, the following should
also be equal:
as.centsums(c(x1,x2),4) %-% as.centsums(x2,4)) and
as.centsums(x1,4). This is a small step of the way towards
fast machine learning methods (along the lines of Mike Izbicki’s Hlearn library).
Some demo code:
set.seed(12345)
x1 <- runif(100)
x2 <- rnorm(100, mean = 1)
max_ord <- 6L
obj1 <- as.centsums(x1, max_ord)
# display:
show(obj1)## class: centsums
## raw moments: 100 0.0051 0.09 -0.00092 0.014 -0.00043 0.0027
## central moments: 0 0.09 -0.0023 0.014 -0.00079 0.0027
## std moments: 0 1 -0.086 1.8 -0.33 3.8# join them together
obj1 <- as.centsums(x1, max_ord)
obj2 <- as.centsums(x2, max_ord)
obj3 <- as.centsums(c(x1, x2), max_ord)
alt3 <- c(obj1, obj2)
# it commutes!
stopifnot(max(abs(sums(obj3) - sums(alt3))) < 1e-07)
# unjoin them, with this one weird operator:
alt2 <- obj3 %-% obj1
alt1 <- obj3 %-% obj2
stopifnot(max(abs(sums(obj2) - sums(alt2))) < 1e-07)
stopifnot(max(abs(sums(obj1) - sums(alt1))) < 1e-07)We also have ‘raw’ join and unjoin methods, not nicely wrapped:
set.seed(123)
x1 <- rnorm(1000, mean = 1)
x2 <- rnorm(1000, mean = 1)
max_ord <- 6L
rs1 <- cent_sums(x1, max_ord)
rs2 <- cent_sums(x2, max_ord)
rs3 <- cent_sums(c(x1, x2), max_ord)
rs3alt <- join_cent_sums(rs1, rs2)
stopifnot(max(abs(rs3 - rs3alt)) < 1e-07)
rs1alt <- unjoin_cent_sums(rs3, rs2)
rs2alt <- unjoin_cent_sums(rs3, rs1)
stopifnot(max(abs(rs1 - rs1alt)) < 1e-07)
stopifnot(max(abs(rs2 - rs2alt)) < 1e-07)There is also code for computing co-sums and co-moments, though as of this writing only up to order 2. Some demo code for the monoidal stuff here:
set.seed(54321)
x1 <- matrix(rnorm(100 * 4), ncol = 4)
x2 <- matrix(rnorm(100 * 4), ncol = 4)
max_ord <- 2L
obj1 <- as.centcosums(x1, max_ord, na.omit = TRUE)
# display:
show(obj1)## An object of class "centcosums"
## Slot "cosums":
## [,1] [,2] [,3] [,4] [,5]
## [1,] 100.0000 -0.093 0.045 -0.0046 0.046
## [2,] -0.0934 111.012 4.941 -16.4822 6.660
## [3,] 0.0450 4.941 71.230 0.8505 5.501
## [4,] -0.0046 -16.482 0.850 117.3456 13.738
## [5,] 0.0463 6.660 5.501 13.7379 100.781
##
## Slot "order":
## [1] 2# join them together
obj1 <- as.centcosums(x1, max_ord)
obj2 <- as.centcosums(x2, max_ord)
obj3 <- as.centcosums(rbind(x1, x2), max_ord)
alt3 <- c(obj1, obj2)
# it commutes!
stopifnot(max(abs(cosums(obj3) - cosums(alt3))) < 1e-07)
# unjoin them, with this one weird operator:
alt2 <- obj3 %-% obj1
alt1 <- obj3 %-% obj2
stopifnot(max(abs(cosums(obj2) - cosums(alt2))) < 1e-07)
stopifnot(max(abs(cosums(obj1) - cosums(alt1))) < 1e-07)Since an online algorithm is used, we can compute cumulative running moments. Moreover, we can remove observations, and thus compute moments over a fixed length lookback window. The code checks for negative even moments caused by roundoff, and restarts the computation to correct; periodic recomputation can be forced by an input parameter.
A demonstration:
library(fromo)
library(moments)
library(microbenchmark)
set.seed(1234)
x <- rnorm(20)
k5 <- running_kurt5(x, window = 10L)
colnames(k5) <- c("excess_kurtosis", "skew", "stdev",
"mean", "nobs")
k5## excess_kurtosis skew stdev mean nobs
## [1,] NaN NaN NaN -1.207 1
## [2,] NaN NaN 1.05 -0.465 2
## [3,] NaN -0.34 1.16 0.052 3
## [4,] -1.520 -0.13 1.53 -0.548 4
## [5,] -1.254 -0.50 1.39 -0.352 5
## [6,] -0.860 -0.79 1.30 -0.209 6
## [7,] -0.714 -0.70 1.19 -0.261 7
## [8,] -0.525 -0.64 1.11 -0.297 8
## [9,] -0.331 -0.58 1.04 -0.327 9
## [10,] -0.331 -0.42 1.00 -0.383 10
## [11,] 0.262 -0.65 0.95 -0.310 10
## [12,] 0.017 -0.30 0.95 -0.438 10
## [13,] 0.699 -0.61 0.79 -0.624 10
## [14,] -0.939 0.69 0.53 -0.383 10
## [15,] -0.296 0.99 0.64 -0.330 10
## [16,] 1.078 1.33 0.57 -0.391 10
## [17,] 1.069 1.32 0.57 -0.385 10
## [18,] 0.868 1.29 0.60 -0.421 10
## [19,] 0.799 1.31 0.61 -0.449 10
## [20,] 1.193 1.50 1.07 -0.118 10# trust but verify
alt5 <- sapply(seq_along(x), function(iii) {
rowi <- max(1, iii - 10 + 1)
kurtosis(x[rowi:iii]) - 3
}, simplify = TRUE)
cbind(alt5, k5[, 1])## alt5
## [1,] NaN NaN
## [2,] -2.000 NaN
## [3,] -1.500 NaN
## [4,] -1.520 -1.520
## [5,] -1.254 -1.254
## [6,] -0.860 -0.860
## [7,] -0.714 -0.714
## [8,] -0.525 -0.525
## [9,] -0.331 -0.331
## [10,] -0.331 -0.331
## [11,] 0.262 0.262
## [12,] 0.017 0.017
## [13,] 0.699 0.699
## [14,] -0.939 -0.939
## [15,] -0.296 -0.296
## [16,] 1.078 1.078
## [17,] 1.069 1.069
## [18,] 0.868 0.868
## [19,] 0.799 0.799
## [20,] 1.193 1.193If you like rolling computations, do also check out the following packages (I believe they are all on CRAN):
Of these three, it seems that RollingWindow implements
the optimal algorithm of reusing computations, while the other two
packages gain efficiency from parallelization and implementation in
C++.
Through template magic, the same code was modified to perform running centering, scaling, z-scoring and so on:
library(fromo)
library(moments)
library(microbenchmark)
set.seed(1234)
x <- rnorm(20)
xz <- running_zscored(x, window = 10L)
# trust but verify
altz <- sapply(seq_along(x), function(iii) {
rowi <- max(1, iii - 10 + 1)
(x[iii] - mean(x[rowi:iii]))/sd(x[rowi:iii])
}, simplify = TRUE)
cbind(xz, altz)## altz
## [1,] NaN NA
## [2,] 0.71 0.71
## [3,] 0.89 0.89
## [4,] -1.18 -1.18
## [5,] 0.56 0.56
## [6,] 0.55 0.55
## [7,] -0.26 -0.26
## [8,] -0.23 -0.23
## [9,] -0.23 -0.23
## [10,] -0.51 -0.51
## [11,] -0.17 -0.17
## [12,] -0.59 -0.59
## [13,] -0.19 -0.19
## [14,] 0.84 0.84
## [15,] 2.02 2.02
## [16,] 0.49 0.49
## [17,] -0.22 -0.22
## [18,] -0.82 -0.82
## [19,] -0.64 -0.64
## [20,] 2.37 2.37A list of the available running functions:
running_centered : from the current value, subtract the
mean over the trailing window.running_scaled: divide the current value by the
standard deviation over the trailing window.running_zscored: from the current value, subtract the
mean then divide by the standard deviation over the trailing
window.running_sharpe: divide the mean by the standard
deviation over the trailing window. There is a boolean flag to also
compute and return the Mertens’ form of the standard error of the Sharpe
ratio over the trailing window in the second column.running_tstat: compute the t-stat over the trailing
window.running_cumulants: computes cumulants over the trailing
window.running_apx_quantiles: computes approximate quantiles
over the trailing window based on the cumulants and the Cornish-Fisher
approximation.running_apx_median: uses
running_apx_quantiles to give the approximate median over
the trailing window.The functions running_centered,
running_scaled and running_zscored take an
optional lookahead parameter that allows you to peek ahead
(or behind if negative) to the computed moments for comparing against
the current value. These are not supported for
running_sharpe or running_tstat because they
do not have an idea of the ‘current value’.
Here is an example of using the lookahead to z-score some data, compared to a purely time-safe lookback. Around a timestamp of 1000, you can see the difference in outcomes from the two methods:
set.seed(1235)
z <- rnorm(1500, mean = 0, sd = 0.09)
x <- exp(cumsum(z)) - 1
xz_look <- running_zscored(x, window = 301, lookahead = 150)
xz_safe <- running_zscored(x, window = 301, lookahead = 0)
df <- data.frame(timestamp = seq_along(x), raw = x,
lookahead = xz_look, lookback = xz_safe)
library(tidyr)
gdf <- gather(df, key = "smoothing", value = "x", -timestamp)
library(ggplot2)
ph <- ggplot(gdf, aes(x = timestamp, y = x, group = smoothing,
colour = smoothing)) + geom_line()
print(ph)
The standard running moments computations listed above work on a running window of a fixed number of observations. However, sometimes one needs to compute running moments over a different kind of window. The most common form of this is over time-based windows. For example, the following computations:
These are now supported in fromo via the
t_running class of functions, which are like the
running functions, but accept also the ‘times’ at which the
input are marked, and optionally also the times at which one will ‘look
back’ to perform the computations. The times can be computed implicitly
as the cumulative sum of given (non-negative) time deltas.
Here is an example of computing the volatility of daily ‘returns’ of the Fama French Market factor, based on a one year window, computed at month ends:
# devtools::install_github('shabbychef/aqfb_data')
library(aqfb.data)
library(fromo)
# daily 'returns' of Fama French 4 factors
data(dff4)
# compute month end dates:
library(lubridate)
mo_ends <- unique(lubridate::ceiling_date(index(dff4),
"month") %m-% days(1))
res <- t_running_sd3(dff4$Mkt, time = index(dff4),
window = 365.25, min_df = 180, lb_time = mo_ends)
df <- cbind(data.frame(mo_ends), data.frame(res))
colnames(df) <- c("date", "sd", "mean", "num_days")
knitr::kable(tail(df), row.names = FALSE)| date | sd | mean | num_days |
|---|---|---|---|
| 2018-07-31 | 0.79 | 0.07 | 253 |
| 2018-08-31 | 0.78 | 0.08 | 253 |
| 2018-09-30 | 0.79 | 0.07 | 251 |
| 2018-10-31 | 0.89 | 0.03 | 253 |
| 2018-11-30 | 0.95 | 0.03 | 253 |
| 2018-12-31 | 1.09 | -0.01 | 251 |
And the plot of the time series:
library(ggplot2)
library(scales)
ph <- df %>% ggplot(aes(date, 0.01 * sd)) + geom_line() +
geom_point(alpha = 0.1) + scale_y_continuous(labels = scales::percent) +
labs(x = "lookback date", y = "standard deviation of percent returns",
title = "rolling 1 year volatility of daily Mkt factor returns, computed monthly")
print(ph)
We make every attempt to balance numerical robustness, computational efficiency and memory usage. As a bit of strawman-bashing, here we microbenchmark the running Z-score computation against the naive algorithm:
library(fromo)
library(moments)
library(microbenchmark)
set.seed(4422)
x <- rnorm(10000)
dumb_zscore <- function(x, window) {
altz <- sapply(seq_along(x), function(iii) {
rowi <- max(1, iii - window + 1)
xrang <- x[rowi:iii]
(x[iii] - mean(xrang))/sd(xrang)
}, simplify = TRUE)
}
val1 <- running_zscored(x, 250)
val2 <- dumb_zscore(x, 250)
stopifnot(max(abs(val1 - val2), na.rm = TRUE) <= 1e-14)
microbenchmark(running_zscored(x, 250), dumb_zscore(x,
250))## Unit: microseconds
## expr min lq mean median uq max neval cld
## running_zscored(x, 250) 340 359 397 387 415 576 100 a
## dumb_zscore(x, 250) 233681 256483 276580 267985 277785 398526 100 bMore seriously, here we compare the running_sd3
function, which computes the standard deviation, mean and number of
elements with the roll_sd and roll_mean
functions from the roll package.
# dare I?
library(fromo)
library(microbenchmark)
library(roll)
set.seed(4422)
x <- rnorm(1e+05)
xm <- matrix(x)
v1 <- running_sd3(xm, 250)
rsd <- roll::roll_sd(xm, 250)
rmu <- roll::roll_mean(xm, 250)
# compute error on the 1000th row:
stopifnot(max(abs(v1[1000, ] - c(rsd[1000], rmu[1000],
250))) < 1e-14)
# now timings:
microbenchmark(running_sd3(xm, 250), roll::roll_mean(xm,
250), roll::roll_sd(xm, 250))## Unit: milliseconds
## expr min lq mean median uq max neval cld
## running_sd3(xm, 250) 3.3 3.5 3.9 3.7 4 5.8 100 a
## roll::roll_mean(xm, 250) 13.0 13.1 14.0 13.4 14 24.2 100 b
## roll::roll_sd(xm, 250) 34.8 35.2 37.2 36.1 38 50.0 100 cOK, that’s not a fair comparison: roll_mean is optimized
to work columwise on a matrix. Let’s unbash this strawman. I create a
function using fromo::running_sd3 to compute a running mean
or running standard deviation columnwise on a matrix, then compare
that to roll_mean and roll_sd:
library(fromo)
library(microbenchmark)
library(roll)
set.seed(4422)
xm <- matrix(rnorm(4e+05), ncol = 100)
fromo_sd <- function(x, wins) {
apply(x, 2, function(xc) {
running_sd3(xc, wins)[, 1]
})
}
fromo_mu <- function(x, wins) {
apply(x, 2, function(xc) {
running_sd3(xc, wins)[, 2]
})
}
wins <- 1000
v1 <- fromo_sd(xm, wins)
rsd <- roll::roll_sd(xm, wins, min_obs = 3)
v2 <- fromo_mu(xm, wins)
rmu <- roll::roll_mean(xm, wins)
# compute error on the 2000th row:
stopifnot(max(abs(v1[2000, ] - rsd[2000, ])) < 1e-14)
stopifnot(max(abs(v2[2000, ] - rmu[2000, ])) < 1e-14)
# now timings: note fromo_mu and fromo_sd do
# exactly the same work, so only time one of them
microbenchmark(fromo_sd(xm, wins), roll::roll_mean(xm,
wins), roll::roll_sd(xm, wins), times = 50L)## Unit: milliseconds
## expr min lq mean median uq max neval cld
## fromo_sd(xm, wins) 35.0 36.6 45.7 37.3 38.3 134 50 b
## roll::roll_mean(xm, wins) 1.3 1.4 5.0 2.1 2.4 58 50 a
## roll::roll_sd(xm, wins) 3.7 3.7 5.4 4.4 4.9 56 50 aI suspect, however, that roll_mean is literally
recomputing moments over the entire window for every cell of the output,
instead of reusing computations, which fromo mostly
does:
library(roll)
library(microbenchmark)
set.seed(91823)
xm <- matrix(rnorm(2e+05), ncol = 10)
fromo_mu <- function(x, wins, ...) {
apply(x, 2, function(xc) {
running_sd3(xc, wins, ...)[, 2]
})
}
microbenchmark(roll::roll_mean(xm, 10, min_obs = 3),
roll::roll_mean(xm, 100, min_obs = 3), roll::roll_mean(xm,
1000, min_obs = 3), roll::roll_mean(xm, 10000,
min_obs = 3), fromo_mu(xm, 10, min_df = 3),
fromo_mu(xm, 100, min_df = 3), fromo_mu(xm, 1000,
min_df = 3), fromo_mu(xm, 10000, min_df = 3),
times = 100L)## Unit: milliseconds
## expr min lq mean median uq max neval cld
## roll::roll_mean(xm, 10, min_obs = 3) 1.5 1.7 1.9 1.8 1.9 3.4 100 a
## roll::roll_mean(xm, 100, min_obs = 3) 10.5 10.8 11.4 11.1 11.8 15.7 100 a
## roll::roll_mean(xm, 1000, min_obs = 3) 95.9 99.4 105.6 102.2 107.4 166.9 100 d
## roll::roll_mean(xm, 10000, min_obs = 3) 738.0 770.1 803.5 781.6 803.1 1086.6 100 e
## fromo_mu(xm, 10, min_df = 3) 6.2 6.8 7.6 7.3 8.4 12.5 100 a
## fromo_mu(xm, 100, min_df = 3) 7.7 8.1 10.0 8.6 9.8 94.7 100 a
## fromo_mu(xm, 1000, min_df = 3) 20.3 21.6 23.2 22.6 23.9 34.5 100 b
## fromo_mu(xm, 10000, min_df = 3) 81.7 84.5 90.3 87.6 94.3 130.6 100 cThe runtime for operations from roll grow with the
window size. The equivalent operations from fromo also
consume more time for longer windows. In theory they would be invariant
with respect to window size, but I coded them to ‘restart’ the
computation periodically for improved accuracy. The user has control
over how often this happens, in order to balance speed and accuracy.
Here I set that parameter very large to show that runtimes need not grow
with window size:
library(fromo)
library(microbenchmark)
set.seed(91823)
xm <- matrix(rnorm(2e+05), ncol = 10)
fromo_mu <- function(x, wins, ...) {
apply(x, 2, function(xc) {
running_sd3(xc, wins, ...)[, 2]
})
}
rp <- 1L + nrow(xm)
microbenchmark(fromo_mu(xm, 10, min_df = 3, restart_period = rp),
fromo_mu(xm, 100, min_df = 3, restart_period = rp),
fromo_mu(xm, 1000, min_df = 3, restart_period = rp),
fromo_mu(xm, 10000, min_df = 3, restart_period = rp),
times = 100L)## Unit: milliseconds
## expr min lq mean median uq max neval cld
## fromo_mu(xm, 10, min_df = 3, restart_period = rp) 6.1 6.6 7.3 6.9 7.9 10 100 a
## fromo_mu(xm, 100, min_df = 3, restart_period = rp) 6.3 6.8 7.4 7.1 7.8 11 100 a
## fromo_mu(xm, 1000, min_df = 3, restart_period = rp) 6.1 6.7 7.4 7.1 7.8 12 100 a
## fromo_mu(xm, 10000, min_df = 3, restart_period = rp) 6.3 6.8 7.5 7.1 8.2 13 100 aHere are some more benchmarks, also against the
rollingWindow package, for running sums:
library(microbenchmark)
library(fromo)
library(RollingWindow)
library(roll)
set.seed(12345)
x <- rnorm(10000)
xm <- matrix(x)
wins <- 1000
# run fun on each wins sized window...
silly_fun <- function(x, wins, fun, ...) {
xout <- rep(NA, length(x))
for (iii in seq_along(x)) {
xout[iii] <- fun(x[max(1, iii - wins + 1):iii],
...)
}
xout
}
vals <- list(running_sum(x, wins, na_rm = FALSE), RollingWindow::RollingSum(x,
wins, na_method = "ignore"), roll::roll_sum(xm,
wins), silly_fun(x, wins, sum, na.rm = FALSE))
# check all equal?
stopifnot(max(unlist(lapply(vals[2:length(vals)], function(av) {
err <- vals[[1]] - av
max(abs(err[wins:length(err)]), na.rm = TRUE)
}))) < 1e-12)
# benchmark it
microbenchmark(running_sum(x, wins, na_rm = FALSE),
RollingWindow::RollingSum(x, wins), running_sum(x,
wins, na_rm = TRUE), RollingWindow::RollingSum(x,
wins, na_method = "ignore"), roll::roll_sum(xm,
wins))## Unit: microseconds
## expr min lq mean median uq max neval cld
## running_sum(x, wins, na_rm = FALSE) 70 73 89 79 105 197 100 a
## RollingWindow::RollingSum(x, wins) 108 116 146 129 165 329 100 b
## running_sum(x, wins, na_rm = TRUE) 101 105 138 109 133 1918 100 ab
## RollingWindow::RollingSum(x, wins, na_method = "ignore") 353 369 415 403 434 697 100 c
## roll::roll_sum(xm, wins) 4153 4205 4309 4236 4338 5570 100 dAnd running means:
library(microbenchmark)
library(fromo)
library(RollingWindow)
library(roll)
set.seed(12345)
x <- rnorm(10000)
xm <- matrix(x)
wins <- 1000
vals <- list(running_mean(x, wins, na_rm = FALSE),
RollingWindow::RollingMean(x, wins, na_method = "ignore"),
roll::roll_mean(xm, wins), silly_fun(x, wins, mean,
na.rm = FALSE))
# check all equal?
stopifnot(max(unlist(lapply(vals[2:length(vals)], function(av) {
err <- vals[[1]] - av
max(abs(err[wins:length(err)]), na.rm = TRUE)
}))) < 1e-12)
# benchmark it:
microbenchmark(running_mean(x, wins, na_rm = FALSE,
restart_period = 1e+05), RollingWindow::RollingMean(x,
wins), running_mean(x, wins, na_rm = TRUE, restart_period = 1e+05),
RollingWindow::RollingMean(x, wins, na_method = "ignore"),
roll::roll_mean(xm, wins))## Unit: microseconds
## expr min lq mean median uq max neval cld
## running_mean(x, wins, na_rm = FALSE, restart_period = 1e+05) 71 78 101 96 115 225 100 a
## RollingWindow::RollingMean(x, wins) 133 167 230 218 268 466 100 b
## running_mean(x, wins, na_rm = TRUE, restart_period = 1e+05) 102 111 165 137 164 2271 100 ab
## RollingWindow::RollingMean(x, wins, na_method = "ignore") 376 451 570 534 669 1170 100 c
## roll::roll_mean(xm, wins) 5014 5260 5667 5530 5952 7535 100 d