# R Benchmark 2 (8 March 2003)
# version 2, scaled to get 1 +/- 0.1 sec with R 1.6.2
# using the standard ATLAS library (Rblas.dll)
# on a Pentium IV 1.6 Ghz with 1 Gb Ram on Win XP pro
# revised and optimized for R v. 1.5.x, 8 June 2002
# Requires additionnal libraries: Matrix, SuppDists
# Author : Philippe Grosjean
# eMail : phgrosjean@sciviews.org
# Web : http://www.sciviews.org
# License: GPL 2 or above at your convenience (see: http://www.gnu.org)
#
# Several tests are adapted from the Splus Benchmark Test V. 2
# by Stephan Steinhaus (stst@informatik.uni-frankfurt.de) #
# Reference for Escoufier's equivalents vectors (test III.5):
# Escoufier Y., 1970. Echantillonnage dans une population de variables
# aleatoires réelles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
#
# type source("c:/
/R2.R") to start the test
runs <- 3 # Number of times the tests are executed
times <- rep(0, 15); dim(times) <- c(5,3)
require(Matrix) # Optimized matrix operations
require(SuppDists) # Optimized random number generators
Runif <- rMWC1019 # The fast uniform number generator
# If you don't have SuppDists, you can use: Runif <- runif
a <- rMWC1019(10, new.start=TRUE, seed=492166) # Init. the generator
Rnorm <- rziggurat # The fast normal number generator
# If you don't have SuppDists, you can use: Rnorm <- rnorm
b <- rziggurat(10, new.start=TRUE) # Init. the generator
remove("a", "b")
options(object.size=100000000)
cat("\n\n R Benchmark 2\n")
cat(" =============\n")
cat(c("Number of times each test is run__________________________: ", runs))
cat("\n\n")
cat(" I. Matrix calculation\n")
cat(" ---------------------\n")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (1)
cumulate <- 0; a <- 0; b <- 0
for (i in 1:runs) {
timing <- system.time({
a <- abs(matrix(Rnorm(1500*1500)/10, ncol=1500, nrow=1500));
b <- t(a);
dim(b) <- c(750, 3000);
a <- t(b)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[1, 1] <- timing
cat(c("Creation, transp., deformation of a 1500x1500 matrix (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (2)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- abs(matrix(Rnorm(800*800)/2, ncol=800, nrow=800));
timing <- system.time({
b <- a^1000
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[2, 1] <- timing
cat(c("800x800 normal distributed random matrix ^1000______ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (3)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(2000000)
timing <- system.time({
b <- sort(a, method="quick") # Sort is modified in v. 1.5.x
# And there is now a quick method that better competes with other packages!!!
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[3, 1] <- timing
cat(c("Sorting of 2,000,000 random values__________________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (4)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(700*700); dim(a) <- c(700, 700)
timing <- system.time({
b <- crossprod(a) # equivalent to: b <- t(a) %*% a
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[4, 1] <- timing
cat(c("700x700 cross-product matrix (b = a' * a)___________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (5)
cumulate <- 0; c <- 0; qra <-0
for (i in 1:runs) {
a <- Rnorm(600*600); dim(a) <- c(600,600)
b <- 1:600
timing <- system.time({
qra <- qr(a, tol = 1e-7);
c <- qr.coef(qra, b)
#Rem: a little faster than c <- lsfit(a, b, inter=F)$coefficients
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[5, 1] <- timing
cat(c("Linear regression over a 600x600 matrix (c = a \\ b') (sec): ", timing, "\n"))
remove("a", "b", "c", "qra")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
times[ , 1] <- sort(times[ , 1])
cat(" --------------------------------------------\n")
cat(c(" Trimmed geom. mean (2 extremes eliminated): ", exp(mean(log(times[2:4, 1]))), "\n\n"))
cat(" II. Matrix functions\n")
cat(" --------------------\n")
if (R.Version()$os == "Win32") flush.console()
# (1)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(800000)
timing <- system.time({
b <- fft(a)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[1, 2] <- timing
cat(c("FFT over 800,000 random values______________________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (2)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(320*320); dim(a) <- c(320, 320)
# Only needed if using eigen.Matrix(): Matrix.class(a)
timing <- system.time({
b <- eigen.default(a, symmetric=F, only.values=T)$Value
# Rem: on my machine, it is faster than:
# b <- La.eigen(a, symmetric=F, only.values=T, method="dsyevr")$Value
# b <- La.eigen(a, symmetric=F, only.values=T, method="dsyev")$Value
# b <- eigen.Matrix(a, vectors = F)$Value
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[2, 2] <- timing
cat(c("Eigenvalues of a 320x320 random matrix______________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (3)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(650*650); dim(a) <- c(650, 650)
Matrix.class(a)
timing <- system.time({
b <- det.Matrix(a, logarithm=F)
# Rem: the following is slower on my computer!
# b <- det.default(a)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[3, 2] <- timing
cat(c("Determinant of a 650x650 random matrix______________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (4)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(900*900); dim(a) <- c(900, 900)
a <- crossprod(a, a)
timing <- system.time({
b <- chol(a)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[4, 2] <- timing
cat(c("Cholesky decomposition of a 900x900 matrix__________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (5)
cumulate <- 0; b <- 0
for (i in 1:runs) {
a <- Rnorm(400*400); dim(a) <- c(400, 400)
timing <- system.time({
# b <- qr.solve(a)
# Rem: a little faster than
b <- solve(a)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[5, 2] <- timing
cat(c("Inverse of a 400x400 random matrix__________________ (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
times[ , 2] <- sort(times[ , 2])
cat(" --------------------------------------------\n")
cat(c(" Trimmed geom. mean (2 extremes eliminated): ", exp(mean(log(times[2:4, 2]))), "\n\n"))
cat(" III. Programmation\n")
cat(" ------------------\n")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (1)
cumulate <- 0; a <- 0; b <- 0; phi <- 1.6180339887498949
for (i in 1:runs) {
a <- floor(Runif(750000)*1000)
timing <- system.time({
b <- (phi^a - (-phi)^(-a))/sqrt(5)
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[1, 3] <- timing
cat(c("750,000 Fibonacci numbers calculation (vector calc)_ (sec): ", timing, "\n"))
remove("a", "b", "phi")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (2)
cumulate <- 0; a <- 2250; b <- 0
for (i in 1:runs) {
timing <- system.time({
b <- rep(1:a, a); dim(b) <- c(a, a);
b <- 1 / (t(b) + 0:(a-1))
# Rem: this is twice as fast as the following code proposed by R programmers
# a <- 1:a; b <- 1 / outer(a - 1, a, "+")
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[2, 3] <- timing
cat(c("Creation of a 2250x2250 Hilbert matrix (matrix calc) (sec): ", timing, "\n"))
remove("a", "b")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (3)
cumulate <- 0; c <- 0
gcd2 <- function(x, y) {if (sum(y > 1.0E-4) == 0) x else {y[y == 0] <- x[y == 0]; Recall(y, x %% y)}}
for (i in 1:runs) {
a <- ceiling(Runif(70000)*1000)
b <- ceiling(Runif(70000)*1000)
timing <- system.time({
c <- gcd2(a, b) # gcd2 is a recursive function
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[3, 3] <- timing
cat(c("Grand common divisors of 70,000 pairs (recursion)___ (sec): ", timing, "\n"))
remove("a", "b", "c", "gcd2")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (4)
cumulate <- 0; b <- 0
for (i in 1:runs) {
b <- rep(0, 220*220); dim(b) <- c(220, 220)
timing <- system.time({
# Rem: there are faster ways to do this
# but here we want to time loops (220*220 'for' loops)!
for (j in 1:220) {
for (k in 1:220) {
b[k,j] <- abs(j - k) + 1
}
}
})[3]
cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[4, 3] <- timing
cat(c("Creation of a 220x220 Toeplitz matrix (loops)_______ (sec): ", timing, "\n"))
remove("b", "j", "k")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
# (5)
cumulate <- 0; p <- 0; vt <- 0; vr <- 0; vrt <- 0; rvt <- 0; RV <- 0; j <- 0; k <- 0;
x2 <- 0; R <- 0; Rxx <- 0; Ryy <- 0; Rxy <- 0; Ryx <- 0; Rvmax <- 0
# Calculate the trace of a matrix (sum of its diagonal elements)
Trace <- function(y) {sum(c(y)[1 + 0:(min(dim(y)) - 1) * (dim(y)[1] + 1)], na.rm=FALSE)}
for (i in 1:runs) {
x <- abs(Rnorm(37*37)); dim(x) <- c(37, 37)
timing <- system.time({
# Calculation of Escoufier's equivalent vectors
p <- ncol(x)
vt <- 1:p # Variables to test
vr <- NULL # Result: ordered variables
RV <- 1:p # Result: correlations
vrt <- NULL
for (j in 1:p) { # loop on the variable number
Rvmax <- 0
for (k in 1:(p-j+1)) { # loop on the variables
x2 <- cbind(x, x[,vr], x[,vt[k]])
R <- cor(x2) # Correlations table
Ryy <- R[1:p, 1:p]
Rxx <- R[(p+1):(p+j), (p+1):(p+j)]
Rxy <- R[(p+1):(p+j), 1:p]
Ryx <- t(Rxy)
rvt <- Trace(Ryx %*% Rxy) / sqrt(Trace(Ryy %*% Ryy) * Trace(Rxx %*% Rxx)) # RV calculation
if (rvt > Rvmax) {
Rvmax <- rvt # test of RV
vrt <- vt[k] # temporary held variable
}
}
vr[j] <- vrt # Result: variable
RV[j] <- Rvmax # Result: correlation
vt <- vt[vt!=vr[j]] # reidentify variables to test
}
})[3]
cumulate <- cumulate + timing
}
times[5, 3] <- timing
cat(c("Escoufier's method on a 37x37 matrix (mixed)________ (sec): ", timing, "\n"))
remove("x", "p", "vt", "vr", "vrt", "rvt", "RV", "j", "k")
remove("x2", "R", "Rxx", "Ryy", "Rxy", "Ryx", "Rvmax", "Trace")
if (R.Version()$os == "Win32" || R.Version()$os == "mingw32") flush.console()
times[ , 3] <- sort(times[ , 3])
cat(" --------------------------------------------\n")
cat(c(" Trimmed geom. mean (2 extremes eliminated): ", exp(mean(log(times[2:4, 3]))), "\n\n\n"))
cat(c("Total time for all 15 tests_________________________ (sec): ", sum(times), "\n"))
cat(c("Overall mean (sum of I, II and III trimmed means/3)_ (sec): ", exp(mean(log(times[2:4, ]))), "\n"))
remove("cumulate", "timing", "times", "runs", "i")
cat(" --- End of test ---\n\n")