very fast OLS regression?

check the following options:

ols1 <- function (y, x) {
     coef(lm(y ~ x - 1))
}

ols2 <- function (y, x) {
     xy <- t(x)%*%y
     xxi <- solve(t(x)%*%x)
     b <- as.vector(xxi%*%xy)
     b
}

ols3 <- function (y, x) {
     XtX <- crossprod(x)
     Xty <- crossprod(x, y)
     solve(XtX, Xty)
}

ols4 <- function (y, x) {
     lm.fit(x, y)$coefficients
}

# check timings
MC <- 500
N <- 10000

set.seed(0)
x <- matrix(rnorm(N*MC), N, MC)
y <- matrix(rnorm(N*MC), N, MC)

invisible({gc(); gc(); gc()})
system.time(for (mc in 1:MC) ols1(y[, mc], x[, mc]))

invisible({gc(); gc(); gc()})
system.time(for (mc in 1:MC) ols2(y[, mc], x[, mc]))

invisible({gc(); gc(); gc()})
system.time(for (mc in 1:MC) ols3(y[, mc], x[, mc]))

invisible({gc(); gc(); gc()})
system.time(for (mc in 1:MC) ols4(y[, mc], x[, mc, drop = FALSE]))

Hi Dimitris and Ivo

I think this is not a fair comparison, look this

x[8,100]<-NA

system.time(for (mc in 1:MC) ols1(y[, mc], x[, mc]))
   user  system elapsed 
  8.765   0.000   8.762 
 

 system.time(for (mc in 1:MC) ols2(y[, mc], x[, mc]))
Error in solve.default(t(x) %*% x) : 
  system is computationally singular: reciprocal condition number = 0
Timing stopped at: 0 0 0.002 
 

 system.time(for (mc in 1:MC) ols3(y[, mc], x[, mc]))
Error in solve.default(XtX, Xty) : 
  system is computationally singular: reciprocal condition number = 0
Timing stopped at: 0 0 0.001 
 

 system.time(for (mc in 1:MC) ols4(y[, mc], x[, mc, drop = FALSE]))
Error in lm.fit(x, y) : NA/NaN/Inf in foreign function call (arg 1)
Timing stopped at: 0 0 0.001 

So routines ols2, ols3 and ols4 only functional in fully matrix if have
one NA this functions don't run.

Bernardo Rangel Tura, M.D,MPH,Ph.D
National Institute of Cardiology
Brazil