How to divide each value of matrix by square root of sums of Respective columns of that matrix?

Question

How I can obtained by dividing each original value by the square root of the sum of squared original values for that column in the original matrix.

data(longley)
X <- as.matrix(longley[,-7])

X/sqrt(colSums(X^2))

Getting wrong results.

Answer 1

Try this:

t(t(X)/sqrt(colSums(X^2)))

Benchmarks:

library(microbenchmark)
microbenchmark(t(t(X)/sqrt(colSums(X^2))),
               apply(X, 2 , function(x) x/sqrt(sum(x^2))))
# Unit: microseconds
#                                      expr     min       lq   median       uq     max neval
# t(t(X)/sqrt(colSums(X^2)))                 28.783  33.1305  34.9455  40.5640  68.147   100
# apply(X, 2, function(x) x/sqrt(sum(x^2))) 100.307 105.1940 106.9975 108.1075 193.015   100