functional programming - Manual pearson correlation in r -

how create function manually calculates pearson correlation in r. know there native function called cor, if want apply below equation in r each combination of columns in data frame, how it?

i wish knew how, believe requires many for-loops, nested for-loops etc make happen , not strong @ programming yet. hope attempt such newbie me can learn. thanks

example:

  set.seed(1)   df = data.frame(v1 = rnorm(10), v2=rnorm(10), v3=rnorm(10), v4=rnorm(10))    #     v1    v2    v3    v4   # v1  1.00 -0.38 -0.72 -0.24   # v2 -0.38  1.00  0.60  0.18   # v3 -0.72  0.60  1.00  0.08   # v4 -0.24  0.18  0.08  1.00 

first write helper function calculate covariance:

v <- function(x,y=x) mean(x*y) - mean(x)*mean(y) 

then use calculate correlation:

my_corr <- function(x,y) v(x,y) / sqrt(v(x) * v(y)) 

here's quick check works correctly:

> my_corr(df$v1, df$v2) [1] -0.3767034 > cor(df$v1, df$v2) [1] -0.3767034 

note calculating correlation way numerically unstable.

edit:

to apply combinations of columns, use outer :

> outer(df, df, vectorize(my_corr))                    v1    v2    v3    v4             # v1  1.00 -0.38 -0.72 -0.24             # v2 -0.38  1.00  0.60  0.18             # v3 -0.72  0.60  1.00  0.08             # v4 -0.24  0.18  0.08  1.00