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Advanced Research Compu2ng

Before We Start •  Sign in •  If you would like to play with the examples (not required), see the SNOW Exercises sheet. – Follow the instruc2ons from – See also the Basic Linux Commands handout

Parallelizing R with the Snow Library Advanced Research Computing April 15, 2014


Outline

•  Introduc2on •  Snow Basics •  Examples •  Conclusions

Advanced Research Compu2ng 4

INTRODUCTION


R

•  Programming language and environment for sta2s2cal compu2ng

•  Free •  Intrinsic support for wide array of sta2s2cal func2onality

•  Huge number of user-‐created packages to add or improve func2onality


An Aside: Op2mizing R

•  Pre-‐allocate Variables •  Vectorize (or perhaps apply func2ons)

–  Yes: z = x * y –  No:

for (i in 1:length(x)) { z[i] = x[i] * y[i] }

•  Reference: The R Inferno hTp://www.burns-‐stat.com/documents/books/the-‐r-‐inferno/


An Aside: Op2mizing R (con2nued) •  Many R opera2ons use Basic Linear Algebra Subrou2nes (BLAS)

•  Build R with op2mized BLAS è op2mized R

0"

50"

100"

150"

200"

250"

300"

gcc" Intel"

Run$Time$(s)$

Run$Time$for$R$2.5$Benchmark$by$Build$Type$

Standard"

Op4mized"BLAS"


The Need for Parallelism


SNOW


Snow Basics

•  Simple Network of Worksta2ons (SNOW) •  For embarrassingly parallel tasks •  Master/Slave model: $ ps -u jkrometi -o cmd | grep R

R -f time_mh.r --restore –no-save

R –slave <etc>

R –slave <etc>


Snow: Start/Stop Cluster

•  Load libraries: library(snow) library(Rmpi)

•  Start a cluster with ncores cores: cl <- makeCluster(ncores, type = 'MPI')

•  Ini2alize random number generator: clusterSetupRNG(cl, type = 'RNGstream')

•  Stop the cluster (important): stopCluster(cl)


Snow: Compu2ng

•  Call same func2on across cluster (ncores 2mes): clusterCall(cl, fun, ...)

•  Parallel versions of apply: clusterApply(cl, x, fun, ...)

parApply(cl, X, MARGIN, FUN, ...) parLapply(cl, x, fun, ...)

parRapply(cl, x, fun, ...) parCapply(cl, x, fun, ...)


EXAMPLES


Monte Carlo: Calcula2ng π

•  The ra2o of the area of the unit circle to the area of the unit square is

•  So: – Randomly pick S points in the unit square – Count the number in the unit circle (C) – Then

π4

π ≈ 4CS


MC π: Code mcpi <- function(n.pts) { #generate n.pts (x,y) points in the unit square

m = matrix(runif(2*n.pts),n.pts,2)

#determine if they are in the unit circle

in.ucir = function(x) {as.integer((x[1]^2 + x[2]^2)<=1)} cir = apply(m, 1, in.ucir )

#return the proportion of points in the unit circle * 4 return (4*mean(cir))

}


MC π: Parallelize #start up and initialize the cluster cl <- makeCluster(ncores, type = 'MPI') clusterSetupRNG(cl, type = 'RNGstream') #determine if points are in the unit circle cir = parRapply(cl, m, in.ucir ) #calculate pi pi.approx = 4*mean(cir) #stop the cluster stopCluster(cl)


MC π: An Op2miza2on Example > n.pts <- 500000

> m = matrix(runif(2*n.pts),n.pts,2) > in.ucir <- function(x) { as.integer((x[1]^2 + x[2]^2) <= 1) }

> system.time( apply(m, 1, in.ucir ) )

user system elapsed

5.037 0.025 5.069

> system.time( as.integer(m[,1]^2 + m[,2]^2 <= 1) )

user system elapsed

0.02 0.00 0.02


MCMC: Metropolis-‐Has2ngs

•  Goal: Draw random samples with probability density approxima2ng given distribu2on

•  Used to model stochas2c inputs •  Do not need to know normalizing factor

– Func2ons in high dimensions


MCMC: Metropolis-‐Has2ngs •  Given a:

–  Target distribu2on –  Jumping distribu2on –  Ini2al sample

•  Choose candidate sample from jumping distribu2on centered at ini2al sample

•  Accept candidate as new sample: – Always if candidate is beTer fit (per target dist) – With probability <1 if candidate is worse fit

•  Repeat with new sample as ini2al sample


M-‐H: Code (Markov Chain Part) #function to calculate next sample theta.update <- function(theta.cur) { #candidate sample theta.can <- jump(theta.cur) #acceptance probability accept.prob <- samp(theta.can)/samp(theta.cur) #compare with sample from uniform dist (0 to 1) if (runif(1) <= accept.prob) theta.can else theta.cur }

Reference: Lam, Patrick. "MCMC Methods: Gibbs Sampling and the Metropolis-‐HasDngs Algorithm."


Metropolis-‐Has2ngs: Code #function to generate (n.sims-burnin) samples mh <- function(n.sims, start, burnin, samp, jump) { theta.cur <- start draws <- c() #call theta.update() n.sims times for (i in 1:n.sims) { draws[i] <- theta.cur <- theta.update(theta.cur) } #return the samples after the burn in return( draws[(burnin + 1):n.sims] ) }

Reference: Lam, Patrick. "MCMC Methods: Gibbs Sampling and the Metropolis-‐HasDngs Algorithm."


Metropolis-‐Has2ngs: Parallelize #start up and initialize the cluster cl <- makeCluster(ncores, type = 'MPI') clusterSetupRNG(cl, type = 'RNGstream') #samples per core core mh.n.sims.cl <- ceiling(mh.n.sims / ncores) #call mh on each core mh.draws.cl <- clusterCall(cl, mh, mh.n.sims.cl, start = 1, burnin = mh.burnin, samp = samp.fcn, jump = jump.fcn) #reduce list to 1-D mh.draws <- unlist(mh.draws.cl) #stop the cluster stopCluster(cl)


CONCLUSIONS


R on ARC’s Systems

•  R 3.0.x, 2.14.1 •  Ploeng via cairo •  Each R build comes with Rmpi and Snow

– For OpenMPI only

•  To use: module load intel <or> module load gcc module load openmpi module load R


Geeng Started on ARC’s Systems

•  Request an account (anyone with a VT PID): hTp://www.arc.vt.edu/forms/account_request.php – Can also request for external collaborators

•  Request a system unit alloca2on: hTp://www.arc.vt.edu/userinfo/alloca2ons.php –  MIC nodes are “charged” the same as normal

nodes


References

•  Snow Manual: hTp://cran.r-‐project.org/web/packages/snow/snow.pdf

•  Snow Func2ons: hTp://www.sfu.ca/~sblay/R/snow.html

•  ARC’s R page: hTp://www.arc.vt.edu/resources/sokware/r

•  Course Slides: hTp://www.arc.vt.edu/userinfo/training/2014Spring_NLI.php#parallelr


Ques2ons?

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