deletions | additions       diff --git a/C++ Functions.tex b/C++ Functions.tex  index 287d58e..2b55984 100644  --- a/C++ Functions.tex  +++ b/C++ Functions.tex 
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\section{Implementing the Objective and Gradient in C++}  The package supports the implementation of the objective and gradient functions in C++, which may yield significant speed improvements over the respective R implementations. The optimization routine's API accepts both R function objects and external pointers to compiled C++ functions. To perform optimization on the Rosenbrock function, we begin by defining the C++ implementations of the objective and of the gradient as character strings: strings, using the RCPP library:  \begin{lstlisting}  objective.include <- 'Rcpp::NumericVector rosenbrock(SEXP xs) {  
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out[1] = g2;  return(out);  }'  \end{lstlisting}  Then we assign two character strings with the bodies of two functions to generate external pointers to the objective and the gradient:  \begin{lstlisting}  objective.body <- '  typedef Rcpp::NumericVector (*funcPtr)(SEXP);  return(XPtr(new funcPtr(&rosenbrock)));  '  gradient.body <- '  typedef Rcpp::NumericVector (*funcPtr)(SEXP);  return(XPtr(new funcPtr(&rosengrad)));  '  \end{lstlisting}  Finally, we compile this ensemble using the inline package:  \begin{lstlisting}  objective <- cxxfunction(signature(), body=objective.body,   inc=objective.include, plugin="Rcpp")  gradient <- cxxfunction(signature(), body=gradient.body,   inc=gradient.include, plugin="Rcpp")  \end{lstlisting}  The external pointers to the objective and the gradient generated by the two pointer-assigners can then be supplied to the lbfgs routine:  \begin{lstlisting}  out.CPP <- lbfgs(objective(), gradient(), c(-1.2,1), invisible=1)  \end{lstlisting}  We define the same functions in R for comparison purposes:  \begin{lstlisting}  objective.R <- function(x) {   100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2  }  gradient.R <- function(x) {  c(-400 * x[1] * (x[2] - x[1]^2) - 2 * (1 - x[1]),  200 * (x[2] - x[1]^2))  }  \end{lstlisting}  A quick microbenchmark comparison performed on OS X, Version 10.9.3, with a 2.9 GHx Intel Core i7 processor and 8 GB 1600 MHz DDR3 memory, reveals significant speed improvements:  \begin{lstlisting}  microbenchmark(out.CPP <- lbfgs(objective(), gradient(), c(-1.2,1), invisible=1),  out.R <- lbfgs(objective.R, gradient.R, c(-1.2,1), invisible=1))  \end{lstlisting}  The results are the following:  \begin{lstlisting}  Unit: microseconds  expr min lq  out.CPP <- lbfgs(objective(), gradient(), c(-1.2, 1), invisible = 1) 79.159 83.3620  out.R <- lbfgs(objective.R, gradient.R, c(-1.2, 1), invisible = 1) 275.400 285.6185    median uq max neval  88.1875 93.8975 189.992 100  303.1600 316.7580 1393.450 100  \end{lstlisting}