cmn(), cvari() and ccorr() compute the
mean, the sample variance and the Pearson correlation in compiled code.
They are thin R wrappers over the kernels in the package's C/C++ core,
the same ones that other packages call through
LinkingTo: rmoriebricklayer, so an R result and a compiled
result agree exactly. Use them where you want those shared kernels; for
everyday work mean(), var() and cor() give the same
numbers.
Details
With \(n\) values,
$$\bar x = \frac{1}{n}\sum_i x_i, \qquad
s^2 = \frac{1}{n - 1}\sum_i (x_i - \bar x)^2, \qquad
r = \frac{\sum_i (x_i - \bar x)(y_i - \bar y)}
{\sqrt{\sum_i (x_i - \bar x)^2 \sum_i (y_i - \bar y)^2}}.$$
The variance uses the \(n - 1\) (sample) denominator, as
var does. The mean is accumulated so that a sum of
finite values that would overflow a double (for example two values of
1e308) still gives the finite mean.
There is no na.rm: any NA or NaN gives NA or
NaN; remove missing values first, for example with
na.omit. Edge cases return NaN rather than an
error: an empty vector for the mean, fewer than two values for the
variance, and a constant vector for the correlation.
Errors: input that is a character vector, factor, list or data frame
(logical input is accepted and read as 0/1); x and y of
different lengths in ccorr().
Examples
## cmn(): sample mean (NA/NaN propagate; no na.rm)
cmn(1:10) # 5.5
#> [1] 5.5
cmn(c(1, 2, NA)) # NA -- call stats::na.omit() first if needed
#> [1] NA
cmn(stats::na.omit(c(1, 2, NA)))
#> [1] 1.5
cmn(c(1e308, 1e308)) # no overflow
#> [1] 1e+308
## cvari(): n-1 (sample) variance, matching stats::var()
cvari(c(2, 4, 4, 4, 5, 5, 7, 9))
#> [1] 4.571429
all.equal(cvari(1:10), stats::var(1:10)) # agrees with base R
#> [1] TRUE
## ccorr(): Pearson correlation of two equal-length vectors
ccorr(1:10, (1:10)^2) # strong positive, near 0.97
#> [1] 0.9745586
ccorr(1:10, 10:1) # perfect negative: -1
#> [1] -1
## refusals
try(cmn(c("1", "2"))) # character input is not coerced
#> Error : cmn: `x` must be numeric, got character
try(ccorr(1:3, 1:4)) # lengths differ
#> Error : ccorr: `x` and `y` must have the same length