my first attempt of using rcpp and rcpparmadilloandy.leung/files/seminars-talks/2012/03/... · my...

Outline Motivation How to use it? Main Rcpp classes Extending to RcppArmadillo

My first attempt of using Rcpp andRcppArmadillo

Andy Leung

University of British Columbia

March 22, 2012

Andy Leung University of British Columbia

My first attempt of using Rcpp and RcppArmadillo


Outline

1. Motivation

2. How to use it?I Where can I get it?I How to compile it?

3. Main Rcpp classesI List of classesI Coversion between R and C++I Some syntatic sugarI Small examples

4. Extending to RcppArmadilloI List of classesI Member functions and variablesI Examples




Outline

1. Motivation

2. How to use it?I Where can I get it?I How do I compile it?






Motivation

PROS CONS

I SPEED!!

I SPEED!!

I and SPEED!!

I “Steep” learning curve

I Bugs bite

I Less readable code




Speed Example: Mahalanobis distance

Example: Compute mahalanobis distance (xi − µ)TΣ−1(xi − µ) forobservations xi , i = 1, ..., n given µ and Σ

Let’s skip all the syntax etc. but focus on speed result. We’ll comeback to this example.

## Using R

mahalanobis_R <- function(X, Mu, Sigma){

md <- rep(NA, nrow(X) )

for(i in 1:nrow(X) )

md[i] <- mahalanobis(X[i,], center=Mu, cov=Sigma)

return(md)

}




Speed Example: Mahalanobis distance

## Using RcppArmadillo

code <- ’arma::mat x = Rcpp::as<arma::mat>(X);

arma::mat mu = Rcpp::as<arma::mat>(Mu);

arma::mat sigma = Rcpp::as<arma::mat>(Sigma);

int n = x.n_rows;

arma::vec md(n);

for (int i=0; i<n; i++){

arma::mat x_i = x.row(i) - mu;

arma::mat Y = arma::solve( sigma, arma::trans(x_i) );

md(i) = arma::as_scalar(x_i * Y);

}

return wrap(md);’

mahalanobis_RcppArma <- cxxfunction( signature(X="numeric",

Mu="numeric", Sigma="numeric"), code, plugin="RcppArmadillo")




Speed Example: Mahalanobis distance (n=1000, p=4)

> ## Some speed test results

> benchmark(

+ mahalanobis_R(X, c(Mu), Sigma),

+ mahalanobis_RcppArma(X, Mu, Sigma),

+ columns=c("test", "replications","elapsed", "relative"),

+ replications=100,

+ order="relative")

test replications elapsed relative

2 mahalanobis_RcppArma(X, Mu, Sigma) 100 0.14 1.0000

1 mahalanobis_R(X, c(Mu), Sigma) 100 27.63 197.3571

Approximately 200 times faster!!




Outline

1. Motivation







How to use it?

I Available as an R package on CRANhttp://cran.r-project.org/web/packages/Rcpp/index.html

http://cran.r-project.org/web/packages/RcppArmadillo/index.html

I Depends on R version (≥ 2.12.0 for Rcpp v0.9.10 and ≥2.14.0 for RcppArmadillo v0.2.35)

I Compiling using R CMD SHLIB and inline



http://cran.r-project.org/web/packages/Rcpp/index.html

http://cran.r-project.org/web/packages/RcppArmadillo/index.html


How to compile it?

Compiling using R CMD SHLIB is not that trivial...For instance,

RCPP_CXXFLAGS=‘Rscript -e ’Rcpp:::CxxFlags()’‘

RCPP_LIBS=‘Rscript -e ’Rcpp:::LdFlags()’‘

export PKG_CPPFLAGS="-I ~/R/x86_64-unknown-linux-gnu-library/2.10/RcppArmadillo/include/ ${RCPP_CXXFLAGS}"

export PKG_LIBS="-larmadillo -llapack ${RCPP_LIBS}"

R CMD SHLIB file.cpp




How to compile it?

Compiling using inline is a lot easier! As all the linking andloading will be taken care of by the R function cxxfunction(...):

code <- ’NumericVector xx(x);

NumericVector yy(x);

int nn = as<int>(n);

for(int i=0; i<nn; i++) xx=xx*yy;

return wrap(xx);’

fun <- cxxfunction(signature(x="numeric", n="integer"),

body=code, plugin="Rcpp")

No more libraries path specifying and shared library loading!




Outline

1. Motivation







Main Rcpp classes

Main Rcpp Classes R typeof

I IntegerVector / Matrix

I NumericVector / Matrix

I LogicalVector / Matrix

I CharacterVector / Matrix

I List

I DataFrame

I Environment

I Function

I ...

I integer

I numeric

I logical

I character

I list

I list?

I environment

I function

I ...




Example 1: Fibonacci sequence

R, C++ conversion: as / wrap

code <- ’int nn = as<int>(n);

NumericVector xx(nn);

for(int i=0; i<nn; i++){

if(i == 0) { xx[i] = 0; }

else if(i == 1){ xx[i] = 1; }

else { xx[i] = xx[i-1] + xx[i-2]; }

}

return wrap(xx);’

fun <- cxxfunction(signature(n="integer"),


fun(20)

[1] 0 1 1 2 3 5 8 13 21 34 55 89

[13] 144 233 377




Example 2: Matrix multiplication (element-wise)

In R is simple...

matrix(1:9, 3,3)*matrix(1:9, 3,3)

[,1] [,2] [,3]

[1,] 1 16 49

[2,] 4 25 64

[3,] 9 36 81

In Rcpp...

code <- ’

NumericMatrix X = as<NumericMatrix>(mX);

return wrap(X*X);

’

fun <- cxxfunction(signature(mX="numeric"),


fun( matrix(1:9, 3,3) )

[1] 1 4 9 16 25 36 49 64 81

## Return a vector?




Example 2 (contd): Matrix multiplication (element-wise)

This way we can obtain the same matrix as in R, but not thattrivial...

## This template class is an example pulled out

## from Rcpp-FAQ.pdf from CRAN

inc <- ’template <typename T>

class square:

public std::unary_function<T,T> {

public:

T operator()( T t) const { return t*t ;}

}; ’

code <- ’NumericMatrix X = as<NumericMatrix>(mX);

std::transform( X.begin(), X.end(), X.begin(), square<double>());

return wrap(X); ’


body=code, include=inc, plugin="Rcpp")

fun( matrix(1:9, 3,3) )




Example 3: Matrix determinant and inversion

Access R functions from C++...code <- ’RNGScope scope; // properly deal with RNG settings

NumericMatrix xx(5, 5); // create 5 by 5 matrix

for(int i; i < 5; i++)

xx(i, _) = rnorm(5, 0, 1); // feature of Rcpp sugar

// Compute determinant

Environment base("package:base");

Function det = base["det"];

double dt = as<double>( det( wrap(xx) ) );

// Matrix inversion

Function solve = base["solve"];

NumericMatrix xxinv = as<NumericMatrix>( solve( wrap(xx) ) );

return List::create(Named("xx")=xx, Named("dt")=dt,

Named("xxinv")=xxinv); // Export a list

’Andy Leung University of British Columbia



Example 3 (contd): Matrix determinant and inversion

Just to show we indeed export a list...

fun <- cxxfunction(body=code, plugin="Rcpp")

(res <- fun())

$xx

[,1] [,2] [,3] [,4] [,5]

[1,] 0.85519655 -0.3439182 0.3155362 -0.897272594 -1.5510895

[2,] 0.06791312 0.8708584 1.1557379 -0.679489824 0.8083568

...

$dt

[1] -7.656185

$xxinv

[,1] [,2] [,3] [,4] [,5]

[1,] -0.01776536 0.58595182 -0.79460866 -0.2917635 -0.5765320

[2,] 0.39741299 -0.08875792 0.16766251 0.5927874 -0.1591927

...




More about Rcpp syntactic sugar

Reference:Dirk Eddelbuettel and Romain Francois. Rcpp syntactic sugar,2012. URL http://cran.r-project.org/web/packages/Rcpp/

vignettes/Rcpp-sugar.pdf. R package version 0.9.10.

Romain Francois and Dirk Eddelbuettel. Rcpp Quick ReferenceGuide, 2011. URL http://cran.r-project.org/web/

packages/Rcpp/vignettes/Rcpp-quickref.pdf. R packageversion 0.9.8.



http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-sugar.pdf

http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-sugar.pdf

http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-quickref.pdf

http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-quickref.pdf


Outline

1. Motivation







Extending to RcppArmadilloBack to Example 2: Matrix multiplication (element-wise)

In RcppArmadillo...

code <- ’arma::mat X = as<arma::mat>(mX);

return wrap( X%X );’


body=code, plugin="RcppArmadillo")

fun( matrix(1:9, 3,3) )

[,1] [,2] [,3]

[1,] 1 16 49

[2,] 4 25 64

[3,] 9 36 81




Main Armadillo classes

Matrices:

I mat (double), umat (unsigned integer), imat (signed integer),fmat (float)

Vectors:

I vec, uvec, ivec, fvec

Cubes:

I cube, ucube, icube, fcube

Main member functions and variables

I .n rows (mat), .n cols (mat), .n elem (vec, mat, cube),.n slice (cube), element access/initialization via ()

For more please refer tohttp://arma.sourceforge.net/docs.html



http://arma.sourceforge.net/docs.html


Back to our earlier Example: Mahalanobis distance

code <- ’arma::mat x = Rcpp::as<arma::mat>(X);

arma::mat mu = Rcpp::as<arma::mat>(Mu);

arma::mat sigma = Rcpp::as<arma::mat>(Sigma);

int n = x.n_rows;

arma::vec partial(n);

for (int i=0; i<n; i++){

arma::mat x_i = x.row(i) - mu;

arma::mat Y = arma::solve( sigma, arma::trans(x_i) );

partial(i) = arma::as_scalar(x_i * Y);

}

return wrap(partial);’

mahalanobis_RcppArma <- cxxfunction( signature(X="numeric",

Mu="numeric", Sigma="numeric"), code, plugin="RcppArmadillo")




More Example: Partial Mahalanobis distance

Compute partial mahalanobis distance

(x(ui )i − µ(ui ))T (Σ(ui ))−1(x

(ui )i − µ(ui )) for observations

xi , i = 1, ..., n given µ and Σ where ui denotes the available entriesof observation xi .




More Example (contd): Partial Mahalanobis distance

Let’s start with code in R...

partial_R <- function(x, Sigma){

n <- nrow(x)

p <- ncol(x)

md <- rep(0, n)

for(i in 1:n){

y <- x[i,]

u <- !is.na(y)

y.obs <- y[u]

Sigma.obs <- Sigma[u,u]

md[i] <- y.obs %*% solve(Sigma.obs) %*% y.obs

}

return(md)

}





Now using RcppArmadillo...

code <- ’try{

using namespace Rcpp;

using namespace arma;

mat x_mu_diff = as<mat>(X_mu_diff);

umat x_nonmiss = as<umat>(X_nonmiss);

mat sigma = as<mat>(Sigma);

int n = x_mu_diff.n_rows;

int p = x_mu_diff.n_cols;

vec partialVec(n);

uvec pp = sum(x_nonmiss, 1);





for(int i = 0; i < n; i++){

mat sigma_nonmiss( pp(i), pp(i) );

mat xi(1, pp(i) );

if( pp(i) < p ){

int mm = 0;

for(int j=0; j<p; j++){

int nn=mm;

if(x_nonmiss(i,j) == 1){

for(int k=j; k<p; k++){

if( x_nonmiss(i,k) == 1 ){

sigma_nonmiss(mm, nn) = sigma(j,k);

sigma_nonmiss(nn, mm) = sigma(k,j);

nn++;

}

}

xi(0,mm) = x_mu_diff(i, j);

mm++;

}

}

} else{

sigma_nonmiss = sigma;

xi = x_mu_diff.row(i);

}

mat Y = solve( sigma_nonmiss, xi.t());

partialVec(i) = as_scalar(xi * Y);

}

return wrap(partialVec);

} catch( std::exception& __ex__ ){

forward_exception_to_r( __ex__ );

} catch(...){

::Rf_error( "c++ exception " "(unknown reason)" );

}

’





else{

sigma_nonmiss = sigma;

xi = x_mu_diff.row(i);

}

mat Y = solve( sigma_nonmiss, xi.t());

partialVec(i) = as_scalar(xi * Y);

}

return wrap(partialVec);

} catch( std::exception& __ex__ ){

forward_exception_to_r( __ex__ );

} catch(...){

::Rf_error( "c++ exception " "(unknown reason)" );

}

’

partial_Rcpp <- cxxfunction(signature(X_mu_diff="numeric",

X_nonmiss="integer", Sigma="numeric"), code, plugin="RcppArmadillo")

(I admit this code is indeed too long in a presentation like this...)





Again, let’s look at the speed of the two code...Create a multivariately normal distributed (mean 0 and cov. Σ)data set with n = 1000, p = 3 and 10% missingnessp <- 3; n <- 1000; mis <- 0.1

A <- matrix(rnorm(p*p), p, p)

x <- x.na <- matrix(rnorm(n*p), n, p) %*% A

x.nonmiss <- matrix(1, n, p)

for(i in 1:round((n*mis))) {

nn <- sample(1:n, 1)

pp <- sample(1:p, 1)

x.nonmiss[nn, pp] <- 0

x.na[nn, pp] <- NA

}

pp <- apply(x.nonmiss, 1, sum)

x <- x[which(pp != 0),]

x.na <- x.na[which(pp != 0),]

x.nonmiss <- x.nonmiss[which(pp != 0),]

sigma <- cov(x)





Speed results:stopifnot( round(partial_R(x.na, sigma), 7) ==

round(partial_Rcpp(x, x.nonmiss, sigma), 7) )

## n = 1000, p = 3, 10% missingness

benchmark( partial_R(x.na, sigma),

partial_Rcpp(x, x.nonmiss, sigma),

columns=c("test", "replications","elapsed", "relative"),

replications=100, order="relative")


2 partial_Rcpp(x, x.nonmiss, sigma) 100 0.06 1.0000

1 partial_R(x.na, sigma) 100 17.47 291.1667





Speed results if we increase our dimension:## n = 1000, p = 10, 10% missingness




## n = 1000, p = 25, 10% missingness




## n = 1000, p = 50, 10% missingness




Question: why the contrast is decreasing?




Last Speed Example: Matrix multiplication

Best answer so far: [on white board]code <- ’

arma::mat x = Rcpp::as<arma::mat>(X);

int n = as<int>(N);

for (int i=0; i<n; i++)

arma::mat y = x*x;

return R_NilValue;

’

fun_Rcpp <- cxxfunction(signature(X="numeric", N="integer"),

body=code, plugin="RcppArmadillo")

fun_R <- function(x, n) for(i in 1:n) y <- x %*% x return(NULL)

## Simple setup

n <- 1000

p <- 5

x <- matrix(rnorm(p^2), p,p)




Last Speed Example: Matrix multiplication

Speed results if we increase our dimension:##n = 1000, p = 3

test replications user.self elapsed relative

1 fun_Rcpp(x, n) 100 0.02 0.02 1.0

2 fun_R(x, n) 100 0.17 0.17 8.5

##n = 1000, p = 10


1 fun_Rcpp(x, n) 100 0.28 0.28 1.000000

2 fun_R(x, n) 100 0.52 0.51 1.821429

##n = 1000, p = 50


1 fun_Rcpp(x, n) 100 23.26 24.10 1.000000

2 fun_R(x, n) 100 28.47 34.26 1.421577





More examples:May try slides from Rcpp workshop / master class held by DirkEddelbuettel and Romain Francois





Thank you! Any questions?



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