R benchmarking program

[Baker D.J.]

Hi All,

I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.

Regards -- David.


# R Benchmark 2.3 (21 April 2004)
# Warning: changes are not carefully checked yet!
# version 2.3 adapted to R 1.9.0
# Many thanks to Douglas Bates (bates@...) for improvements!
# version 2.2 adapted to R 1.8.0
# version 2.1 adapted to R 1.7.0
# 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@...
# 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@...)
# Reference for Escoufier's equivalents vectors (test III.5):
# Escoufier Y., 1970. Echantillonnage dans une population de variables
# aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.

...
Error in getClass(Class, where = topenv(parent.frame())) :
  "geMatrix" is not a defined class
Calls: new -> getClass
Execution halted

______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Philippe Grosjean]

Hello,

I did this bechmark test. Perhaps is it a good oppotunity to rewrite it
and make it compatible with R 2.7.0, David?
Best,

Philippe Grosjean
..............................................<°}))><........
  ) ) ) ) )
( ( ( ( (    Prof. Philippe Grosjean
  ) ) ) ) )
( ( ( ( (    Numerical Ecology of Aquatic Systems
  ) ) ) ) )   Mons-Hainaut University, Belgium
( ( ( ( (
..............................................................

Baker D.J. wrote:

> Hi All,
>
> I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.
>
> Regards -- David.
>
>
> # R Benchmark 2.3 (21 April 2004)
> # Warning: changes are not carefully checked yet!
> # version 2.3 adapted to R 1.9.0
> # Many thanks to Douglas Bates (bates@...) for improvements!
> # version 2.2 adapted to R 1.8.0
> # version 2.1 adapted to R 1.7.0
> # 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@...
> # 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@...)
> # Reference for Escoufier's equivalents vectors (test III.5):
> # Escoufier Y., 1970. Echantillonnage dans une population de variables
> # aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
>
> ...
> Error in getClass(Class, where = topenv(parent.frame())) :
>   "geMatrix" is not a defined class
> Calls: new -> getClass
> Execution halted
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Baker D.J.]

Hi All,

I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.

Regards -- David.


# R Benchmark 2.3 (21 April 2004)
# Warning: changes are not carefully checked yet!
# version 2.3 adapted to R 1.9.0
# Many thanks to Douglas Bates (bates@...) for improvements!
# version 2.2 adapted to R 1.8.0
# version 2.1 adapted to R 1.7.0
# 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@...
# 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@...)
# Reference for Escoufier's equivalents vectors (test III.5):
# Escoufier Y., 1970. Echantillonnage dans une population de variables
# aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.

...
Error in getClass(Class, where = topenv(parent.frame())) :
  "geMatrix" is not a defined class
Calls: new -> getClass
Execution halted

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Baker D.J.]

Hello Philippe,

Thank for your reply. I agree that this is an interesting project. As I say we have just started to buy Intel quad core machines after years of offered a service on AMD machines. I recompiled R with the GoTo BLAS, and did some basic tests..things like matrix cross products, solve, svd, etc, etc. The speed up on the Intels was stunning vs our AMD machines. Previously we have always worked with R + ACML BLAS on the AMDs (perhaps we have missing out on GoTo performance).

It would be great to bring the benchmarking programme up to date, and run it. My knowledge of R is basic -- I am a Unix administrator. Would you be able to spend some time working on the program please or do you know any colleagues who would be keen to put some effort in to this?

Regards -- David.

-----Original Message-----
From: Philippe Grosjean [mailto:phgrosjean@...]
Sent: 13 May 2008 15:10
To: Baker D.J.
Cc: r-help@...
Subject: Re: [R] R benchmarking program

Hello,

I did this bechmark test. Perhaps is it a good oppotunity to rewrite it
and make it compatible with R 2.7.0, David?
Best,

Philippe Grosjean
..............................................<°}))><........
  ) ) ) ) )
( ( ( ( (    Prof. Philippe Grosjean
  ) ) ) ) )
( ( ( ( (    Numerical Ecology of Aquatic Systems
  ) ) ) ) )   Mons-Hainaut University, Belgium
( ( ( ( (
..............................................................

Baker D.J. wrote:

> Hi All,
>
> I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.
>
> Regards -- David.
>
>
> # R Benchmark 2.3 (21 April 2004)
> # Warning: changes are not carefully checked yet!
> # version 2.3 adapted to R 1.9.0
> # Many thanks to Douglas Bates (bates@...) for improvements!
> # version 2.2 adapted to R 1.8.0
> # version 2.1 adapted to R 1.7.0
> # 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@...
> # 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@...)
> # Reference for Escoufier's equivalents vectors (test III.5):
> # Escoufier Y., 1970. Echantillonnage dans une population de variables
> # aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
>
> ...
> Error in getClass(Class, where = topenv(parent.frame())) :
>   "geMatrix" is not a defined class
> Calls: new -> getClass
> Execution halted
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Prof Brian Ripley]

The best benchmark is a calculation you really want to do.  For most
people matrix algebra is an insignificant proportion of what they do in R.
A few need complex matrix arithmetic (where compilers and BLAS differ a
lot in speed).  So there is no universal benchmark.

Also, the reference BLAS supplied with R is usually more accurate than the
optimized BLAS, and many users will prefer accuracy to speed.  There are
packages that will not complete their tests with an optimized BLAS.

On Tue, 13 May 2008, Baker D.J. wrote:

> Hi All,
>
> I've just rebuild the latest R with the Goto BLAS on our new Intel quad
> core machines.

I do wonder why -- as the manual says, the easiest and most efficient way
to do this is to link the Goto BLAS to R_HOME/lib/libRblas.so (assuming
this is Linux). No rebuilding is needed.

> I did a few basic matrix calculations, and I was very
> impressed by the performance I saw. I wonder if anyone has a more
> rigorous benchmarking program for R. I downloaded a old R
> test/benchmarking program (see below), and this didn't work with the
> current R, and so I wondered if anyone could please direct me to a more
> recent program that does a good all round test of R.
>
> Regards -- David.
>
>
> # R Benchmark 2.3 (21 April 2004)
> # Warning: changes are not carefully checked yet!
> # version 2.3 adapted to R 1.9.0
> # Many thanks to Douglas Bates (bates@...) for improvements!
> # version 2.2 adapted to R 1.8.0
> # version 2.1 adapted to R 1.7.0
> # 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@...
> # 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@...)
> # Reference for Escoufier's equivalents vectors (test III.5):
> # Escoufier Y., 1970. Echantillonnage dans une population de variables
> # aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
>
> ...
> Error in getClass(Class, where = topenv(parent.frame())) :
>  "geMatrix" is not a defined class
> Calls: new -> getClass
> Execution halted
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Brian D. Ripley,                  ripley@...
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  [phone] (self)
1 South Parks Road,                     [phone] (PA)
Oxford OX1 3TG, UK                Fax:  [phone]
______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Martin Maechler]

>>>>> "PhGr" == Philippe Grosjean <phgrosjean@...>
>>>>>     on Tue, 13 May 2008 16:10:15 +0200 writes:

    PhGr> Hello,
    PhGr> I did this bechmark test. Perhaps is it a good oppotunity to rewrite it
    PhGr> and make it compatible with R 2.7.0, David?

I'll not really rewrite it (to make it "nice" in my eyes),
but I'm fixing the problems with the fact that the 'Matrix'
package you were using back then has been much changed in the
mean time.

Expect a corrected benchmark R script within a day or so.

Martin Maechler, ETH Zurich

    PhGr> Best,
    PhGr> Philippe Grosjean
    PhGr> ..............................................<°}))><........
    PhGr> ) ) ) ) )
    PhGr> ( ( ( ( (    Prof. Philippe Grosjean
    PhGr> ) ) ) ) )
    PhGr> ( ( ( ( (    Numerical Ecology of Aquatic Systems
    PhGr> ) ) ) ) )   Mons-Hainaut University, Belgium
    PhGr> ( ( ( ( (
    PhGr> ..............................................................

    PhGr> Baker D.J. wrote:
    >> Hi All,
    >>
    >> I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.
    >>
    >> Regards -- David.
    >>
    >>
    >> # R Benchmark 2.3 (21 April 2004)
    >> # Warning: changes are not carefully checked yet!
    >> # version 2.3 adapted to R 1.9.0
    >> # Many thanks to Douglas Bates (bates@...) for improvements!
    >> # version 2.2 adapted to R 1.8.0
    >> # version 2.1 adapted to R 1.7.0
    >> # 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@...
    >> # 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@...)
    >> # Reference for Escoufier's equivalents vectors (test III.5):
    >> # Escoufier Y., 1970. Echantillonnage dans une population de variables
    >> # aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
    >>
    >> ...
    >> Error in getClass(Class, where = topenv(parent.frame())) :
    >> "geMatrix" is not a defined class
    >> Calls: new -> getClass
    >> Execution halted

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Philippe Grosjean]

Martin Maechler wrote:

>>>>>> "PhGr" == Philippe Grosjean <phgrosjean@...>
>>>>>>     on Tue, 13 May 2008 16:10:15 +0200 writes:
>
>     PhGr> Hello,
>     PhGr> I did this bechmark test. Perhaps is it a good oppotunity to rewrite it
>     PhGr> and make it compatible with R 2.7.0, David?
>
> I'll not really rewrite it (to make it "nice" in my eyes),
> but I'm fixing the problems with the fact that the 'Matrix'
> package you were using back then has been much changed in the
> mean time.
>
> Expect a corrected benchmark R script within a day or so.

Thank you, Martin.

> Martin Maechler, ETH Zurich
>
>     PhGr> Best,
>     PhGr> Philippe Grosjean
>     PhGr> ..............................................<°}))><........
>     PhGr> ) ) ) ) )
>     PhGr> ( ( ( ( (    Prof. Philippe Grosjean
>     PhGr> ) ) ) ) )
>     PhGr> ( ( ( ( (    Numerical Ecology of Aquatic Systems
>     PhGr> ) ) ) ) )   Mons-Hainaut University, Belgium
>     PhGr> ( ( ( ( (
>     PhGr> ..............................................................
>
>     PhGr> Baker D.J. wrote:
>     >> Hi All,
>     >>
>     >> I've just rebuild the latest R with the Goto BLAS on our new Intel quad core machines. I did a few basic matrix calculations, and I was very impressed by the performance I saw. I wonder if anyone has a more rigorous benchmarking program for R. I downloaded a old R test/benchmarking program (see below), and this didn't work with the current R, and so I wondered if anyone could please direct me to a more recent program that does a good all round test of R.
>     >>
>     >> Regards -- David.
>     >>
>     >>
>     >> # R Benchmark 2.3 (21 April 2004)
>     >> # Warning: changes are not carefully checked yet!
>     >> # version 2.3 adapted to R 1.9.0
>     >> # Many thanks to Douglas Bates (bates@...) for improvements!
>     >> # version 2.2 adapted to R 1.8.0
>     >> # version 2.1 adapted to R 1.7.0
>     >> # 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@...
>     >> # 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@...)
>     >> # Reference for Escoufier's equivalents vectors (test III.5):
>     >> # Escoufier Y., 1970. Echantillonnage dans une population de variables
>     >> # aleatoires réles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47.
>     >>
>     >> ...
>     >> Error in getClass(Class, where = topenv(parent.frame())) :
>     >> "geMatrix" is not a defined class
>     >> Calls: new -> getClass
>     >> Execution halted
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Martin Maechler]

>>>>> "MM" == Martin Maechler <maechler@...>
>>>>>     on Wed, 14 May 2008 12:05:00 +0200 writes:

>>>>> "PhGr" == Philippe Grosjean <phgrosjean@...>
>>>>>     on Tue, 13 May 2008 16:10:15 +0200 writes:

    PhGr> Hello,
    PhGr> I did this bechmark test. Perhaps is it a good oppotunity to rewrite it
    PhGr> and make it compatible with R 2.7.0, David?

    MM> I'll not really rewrite it (to make it "nice" in my eyes),
    MM> but I'm fixing the problems with the fact that the 'Matrix'
    MM> package you were using back then has been much changed in the
    MM> mean time.

    MM> Expect a corrected benchmark R script within a day or so.

Here, it is {attachament in 'text/plain' which is allowed for R-help}

Note that I *do* agree with Prof. Brian Ripley about the
usefulness of benchmarks.

Martin Maechler, ETH Zurich


#### R Benchmark 2.4 (May 2008)
benchVersion <- structure(2.4,
                          date = as.Date("2008-05-14"))
#### adapted to run in R 2.7.0 with Matrix 0.999735-9, Martin Maechler ETH Zurich
##
#### R Benchmark 2.3 (21 April 2004)
#### Warning: changes are not carefully checked yet!
#### version 2.3 adapted to R 1.9.0
#### Many thanks to Douglas Bates (bates@...) for improvements!
#### version 2.2 adapted to R 1.8.0
#### version 2.1 adapted to R 1.7.0
#### 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@...
#### 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@...)
#### 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.

#### source("<this file>") to start the test
#### ---------------------
#### TODO: Rewrite all this to work nicely with 'R CMD BATCH'

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)
maybeFlush <- function()
    if(R.Version()$os %in% c("Win32", "mingw32")) flush.console()

MatrixRnorm <- function(n, m=n) Matrix(Rnorm(n * m), nrow = n, ncol = m)

cat("\n\n   R Benchmark", benchVersion,
      "\n   ===============\n",
    "\nNumber of times each test is run__________________________: ", runs,
    "\n\n")


cat("   I. Matrix calculation\n")
cat("   ---------------------\n")
maybeFlush()

## (1)
cumulate <- 0; a <- 0; b <- 0
for (i in 1:runs) {
  timing <- system.time({
    a <- 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("Creation, transp., deformation of a 1500x1500 matrix (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (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("800x800 normal distributed random matrix ^1000______ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (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("Sorting of 2,000,000 random values__________________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (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("700x700 cross-product matrix (b = a' * a)___________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (5)
cumulate <- 0; c <- 0; qra <-0
for (i in 1:runs) {
  a <- MatrixRnorm(600)
  b <- as.double(1:600)
  timing <- system.time({
    c <- solve(crossprod(a), crossprod(a,b))
  })[3]
  cumulate <- cumulate + timing

  ## This is the old method
  ##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("Linear regression over a 600x600 matrix (c = a \\ b') (sec): ", timing, "\n")
remove("a", "b", "c", "qra")
maybeFlush()

times[ , 1] <- sort(times[ , 1])
cat("                      --------------------------------------------\n")
cat("                 Trimmed geom. mean (2 extremes eliminated): ",
    exp(mean(log(times[2:4, 1]))), "\n\n")

cat("   II. Matrix functions\n")
cat("   --------------------\n")
maybeFlush()


## (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("FFT over 800,000 random values______________________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (2) a) traditional matrix
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- array(Rnorm(320*320), dim = c(320, 320))
  timing <- system.time({
  b <- eigen(a, symmetric=FALSE, only.values=TRUE)$Value
  ## Rem: on my machine, it is faster than:
  ## b <- La.eigen(a, symmetric=F, only.values=T, method="dsyevr")$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("Eigenvalues of a 320x320 random matrix______________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()
##
## (2) b) "Matrix"
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- MatrixRnorm(320)
  timing <- system.time({
      b <- eigen(a, symmetric=FALSE, only.values=TRUE)$Value
  })[3]
  cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[2, 2] <- timing
cat("Eigenvalues of a 320x320 random Matrix______________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()


## (3) a) traditional matrix
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- Rnorm(650*650); dim(a) <- c(650, 650)
  timing <- system.time({
    ##b <- determinant(a, logarithm=F)
    ## Rem: the following is slower on my computer!
    ## b <- det.default(a)
    b <- determinant(a)
  })[3]
  cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[3, 2] <- timing
cat("Determinant of a 650x650 random matrix______________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()
##
## (3)  b) --- using "Matrix"
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- MatrixRnorm(650)
  timing <- system.time({
      b <- determinant(a)
  })[3]
  cumulate <- cumulate + timing
}
timing <- cumulate/runs
times[3, 2] <- timing
cat("Determinant of a 650x650 random Matrix______________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()


## (4)
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- crossprod(MatrixRnorm(900))
  ##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("Cholesky decomposition of a 900x900 matrix__________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (5)
cumulate <- 0; b <- 0
for (i in 1:runs) {
  a <- MatrixRnorm(400)
  ##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("Inverse of a 400x400 random matrix__________________ (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

times[ , 2] <- sort(times[ , 2])
cat("                      --------------------------------------------\n")
cat("                Trimmed geom. mean (2 extremes eliminated): ",
    exp(mean(log(times[2:4, 2]))), "\n\n")

cat("   III. Programmation\n")
cat("   ------------------\n")
maybeFlush()


## (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("750,000 Fibonacci numbers calculation (vector calc)_ (sec): ", timing, "\n")
remove("a", "b", "phi")
maybeFlush()

## (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("Creation of a 2250x2250 Hilbert matrix (matrix calc) (sec): ", timing, "\n")
remove("a", "b")
maybeFlush()

## (3)
cumulate <- 0; c <- 0
gcd2 <- function(x, y) {
    if (sum(y > 1e-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("Grand common divisors of 70,000 pairs (recursion)___ (sec): ", timing, "\n")
remove("a", "b", "c", "gcd2")
maybeFlush()

## (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("Creation of a 220x220 Toeplitz matrix (loops)_______ (sec): ", timing, "\n")
remove("b", "j", "k")
maybeFlush()

## (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("Escoufier's method on a 37x37 matrix (mixed)________ (sec): ", timing, "\n")
remove("x", "p", "vt", "vr", "vrt", "rvt", "RV", "j", "k",
       "x2", "R", "Rxx", "Ryy", "Rxy", "Ryx", "Rvmax", "Trace")
maybeFlush()


times[ , 3] <- sort(times[ , 3])
cat("                      --------------------------------------------\n")
cat("                Trimmed geom. mean (2 extremes eliminated): ",
    exp(mean(log(times[2:4, 3]))), "\n\n\n")

cat("Total time for all 15 tests_________________________ (sec): ", sum(times),"\n")
cat("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")

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