# Transforming a Matrix in Parallel using RcppParallel

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The RcppParallel package includes
high level functions for doing parallel programming with Rcpp. For example,
the `parallelFor`

function can be used to convert the work of a standard
serial “for” loop into a parallel one. This article describes using
RcppParallel to transform an R matrix in parallel.

### Serial Version

First a serial version of the matrix transformation. We take the square root
of each item of a matrix and return a new matrix with the tranformed values.
We do this by using `std::transform`

to call the `sqrt`

function on each
element of the matrix:

#include <Rcpp.h> using namespace Rcpp; #include <cmath> #include <algorithm> // [[Rcpp::export]] NumericMatrix matrixSqrt(NumericMatrix orig) { // allocate the matrix we will return NumericMatrix mat(orig.nrow(), orig.ncol()); // transform it std::transform(orig.begin(), orig.end(), mat.begin(), ::sqrt); // return the new matrix return mat; }

### Parallel Version

Now we’ll adapt our code to run in parallel using the `parallelFor`

function.
RcppParallel takes care of dividing up work between threads, our job is to
implement a “Worker” function object that is called by the RcppParallel
scheduler.

The `SquareRoot`

function object below includes pointers to the input matrix
as well as the output matrix. Within it’s `operator()`

method it performs a
`std::transform`

with the `sqrt`

function on the array elements specified by
the `begin`

and `end`

arguments:

// [[Rcpp::depends(RcppParallel)]] #include <RcppParallel.h> using namespace RcppParallel; struct SquareRoot : public Worker { // source matrix const RMatrix<double> input; // destination matrix RMatrix<double> output; // initialize with source and destination SquareRoot(const NumericMatrix input, NumericMatrix output) : input(input), output(output) {} // take the square root of the range of elements requested void operator()(std::size_t begin, std::size_t end) { std::transform(input.begin() + begin, input.begin() + end, output.begin() + begin, ::sqrt); } };

Note that `SquareRoot`

derives from `RcppParallel::Worker`

. This is required
for function objects passed to `parallelFor`

.

Note also that we use the `RMatrix<double>`

type for accessing the matrix.
This is because this code will execute on a background thread where it’s not
safe to call R or Rcpp APIs. The `RMatrix`

class is included in the
RcppParallel package and provides a lightweight, thread-safe wrapper around R
matrixes.

Here’s the parallel version of our matrix transformation function that makes
uses of the `SquareRoot`

function object. The main difference is that rather
than calling `std::transform`

directly, the `parallelFor`

function is called
with the range to operate on (in this case based on the length of the input
matrix) and an instance of `SquareRoot`

:

// [[Rcpp::export]] NumericMatrix parallelMatrixSqrt(NumericMatrix x) { // allocate the output matrix NumericMatrix output(x.nrow(), x.ncol()); // SquareRoot functor (pass input and output matrixes) SquareRoot squareRoot(x, output); // call parallelFor to do the work parallelFor(0, x.length(), squareRoot); // return the output matrix return output; }

### Benchmarks

A comparison of the performance of the two functions shows the parallel version performing about 2.5 times as fast on a machine with 4 cores:

# allocate a matrix m <- matrix(as.numeric(c(1:1000000)), nrow = 1000, ncol = 1000) # ensure that serial and parallel versions give the same result stopifnot(identical(matrixSqrt(m), parallelMatrixSqrt(m))) # compare performance of serial and parallel library(rbenchmark) res <- benchmark(matrixSqrt(m), parallelMatrixSqrt(m), order="relative") res[,1:4] test replications elapsed relative 2 parallelMatrixSqrt(m) 100 0.294 1.000 1 matrixSqrt(m) 100 0.755 2.568

Note that performance gains will typically be 30-50% less on Windows systems as a result of less sophisticated thread scheduling (RcppParallel does not currently use TBB on Windows whereas it does on the Mac and Linux).

You can learn more about using RcppParallel at https://github.com/RcppCore/RcppParallel.

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