From: Douglas Bates <bates_at_stat.wisc.edu>

Date: Tue, 19 Jul 2011 10:00:47 -0500

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Received on Tue 19 Jul 2011 - 15:02:58 GMT

Date: Tue, 19 Jul 2011 10:00:47 -0500

On Thu, Jul 14, 2011 at 10:21 AM, Alireza Mahani
<alireza.s.mahani_at_gmail.com> wrote:

> (I am using a LINUX machine)

*>
**> Jeff,
**>
**> In creating reproducible results, I 'partially' answered my question. I have
**> attached two scripts, 'mvMultiply.r' and 'mvMultiply.cc'. Please copy both
**> files into your chosen directory, then run 'Rscript mvMultiply.r' in that
**> directory while changing the two boolean parameters 'INCLUDE_DATAPREP' and
**> 'ROWMAJOR' to all four permutations. (The variable 'diffVec' is there to
**> verify that the two methods produce the same output vector.)
**>
**> Below are the results that I get, along with discussion (tR and tCall are in
**> sec):
**>
**> INCLUDE_DATAPREP,ROWMAJOR,tR,tCall
**> F,F,13.536,13.875
**> F,T,13.824,14.299
**> T,F,13.688,18.167
**> T,T,13.982,30.730
**>
**> Interpretation: The execution time for the .Call line is nearly identical to
**> the call to R operator '%*%'. Two data preparation lines for the .Call
**> method create the overhead:
**>
**> A <- t(A) (~12sec, or 12usec per call)
**> dim(A) <- dim(A)[1] * dim(A)[2] (~4sec, or 4usec per call)
**>
**> While the first line can be avoided by providing options in c++ function (as
**> is done in the BLAS API), I wonder if the second line can be avoided, aside
**> from the obvious option of rewriting the R scripts to use vectors instead of
**> matrices. But this defies one of the primary advantages of using R, which is
**> succinct, high-level coding. In particular, if one has several matrices as
**> input into a .Call function, then the overhead from matrix-to-vector
**> transformations can add up. To summarize, my questions are:
**>
**> 1- Do the above results seem reasonable to you? Is there a similar penalty
**> in R's '%*%' operator for transforming matrices to vectors before calling
**> BLAS functions?
**> 2- Are there techniques for reducing the above overhead for developers
**> looking to augment their R code with compiled code?
**>
**> Regards,
**> Alireza
**>
**> ---------------------------------------
**> # mvMultiply.r
**> # comparing performance of matrix multiplication in R (using '%*%' operator)
**> vs. calling compiled code (using .Call function)
**> # y [m x 1] = A [m x n] %*% x [n x 1]
**>
**> rm(list = ls())
**> system("R CMD SHLIB mvMultiply.cc")
**> dyn.load("mvMultiply.so")
**>
**> INCLUDE_DATAPREP <- F
**> ROWMAJOR <- F #indicates whether the c++ function treats A in a row-major or
**> column-major fashion
**>
**> m <- 100
**> n <- 10
**> N <- 1000000
**>
**> diffVec <- array(0, dim = N)
**> tR <- 0.0
**> tCall <- 0.0
**> for (i in 1:N) {
**>
**> A <- runif(m*n); dim(A) <- c(m,n)
**> x <- runif(n)
**>
**> t1 <- proc.time()[3]
**> y1 <- A %*% x
**> tR <- tR + proc.time()[3] - t1
**>
**> if (INCLUDE_DATAPREP) {
**> t1 <- proc.time()[3]
**> }
**> if (ROWMAJOR) { #since R will convert matrix to vector in a column-major
**> fashion, if the c++ function expects a row-major format, we need to
**> transpose A before converting it to a vector
**> A <- t(A)
**> }
**> dim(A) <- dim(A)[1] * dim(A)[2]
**> if (!INCLUDE_DATAPREP) {
**> t1 <- proc.time()[3]
**> }
**> y2 <- .Call("matvecMultiply", as.double(A), as.double(x),
**> as.logical(c(ROWMAJOR)))
**> tCall <- tCall + proc.time()[3] - t1
**>
**> diffVec[i] <- max(abs(y2 - y1))
**> }
**> cat("Data prep time for '.Call' included: ", INCLUDE_DATAPREP, "\n")
**> cat("C++ function expects row-major matrix: ", ROWMAJOR, "\n")
**> cat("Time - Using '%*%' operator in R: ", tR, "sec\n")
**> cat("Time - Using '.Call' function: ", tCall, "sec\n")
**> cat("Maximum difference between methods: ", max(diffVec), "\n")
**>
**> dyn.unload("mvMultiply.so")
**> ---------------------------------------
**> # mvMultiply.cc
**> #include <Rinternals.h>
**> #include <R.h>
**>
**> extern "C" {
**>
**> SEXP matvecMultiply(SEXP A, SEXP x, SEXP rowmajor) {
**> double *rA = REAL(A), *rx = REAL(x), *ry;
**> int *rrm = LOGICAL(rowmajor);
**> int n = length(x);
**> int m = length(A) / n;
**> SEXP y;
**> PROTECT(y = allocVector(REALSXP, m));
**> ry = REAL(y);
**> for (int i = 0; i < m; i++) {
**> ry[i] = 0.0;
**> for (int j = 0; j < n; j++) {
**> if (rrm[0] == 1) {
**> ry[i] += rA[i * n + j] * rx[j];
**> } else {
**> ry[i] += rA[j * m + i] * rx[j];
**> }
**> }
**> }
**> UNPROTECT(1);
**> return(y);
**> }
**>
**> }
**>
*

I realize that you are just beginning to use the .C and .Call interfaces and your example is therefore a simple one. However, if you plan to continue with such development it is worthwhile learning of some of the tools available. I think one of the most important is the "inline" package that can take a C or C++ code segment as a text string and go through all the steps of creating and loading a .Call'able compiled function.

Second, if you are going to use C++ (the code you show could be C code as it doesn't use any C++ extensions) then you should look at the Rcpp package written by Dirk Eddelbuettel and Romain Francois which allows for comparatively painless interfacing of R objects and C++ objects. The Rcpp-devel list, which I have copied on this reply, is for questions related to that system. The inline package allows for various "plugin" constructions to wrap your code in the appropriate headers and point the compiler to the locations of header files and libraries. There are two extensions to Rcpp for numerical linear algebra in C++, RcppArmadillo and RcppEigen. I show the use of RcppEigen here.

Third there are several packages in R that do the busy work of benchmarking expressions and neatly formulating the results. I use the rbenchmark package.

Putting all these together yields the enclosed script and results.

In Eigen, a MatrixXd object is the equivalent of R's numeric matrix (similarly MatrixXi for integer and MatrixXcd for complex) and a VectorXd object is the equivalent of a numeric vector. A "mapped" matrix or vector is one that uses the storage allocated by R, thereby avoiding a copy operation (similar to your accessing elements of the arrays through the pointer returned by REAL()). To adhere to R's functional programming semantics it is a good idea to declare such objects as const. The 'as' and 'wrap' functions are provided by Rcpp with extensions in RcppEigen to the Eigen classes in the development version. In the released versions of Rcpp and RcppEigen we use intermediate Rcpp objects. These functions have the advantage of checking the types of R objects being passed. The Eigen code for matrix multiplication will check the consistency of dimensions in the operation.

Given the size of the matrix you are working with it is not surprising that interpretation overhead and checking will be a large part of the elapsed time, hence the relative differences between different methods of doing the numerical calculation will be small. The operation of multiplying a 100 x 10 matrix by a 10-vector involves "only" 1000 floating point operations. Furthermore, each element of the matrix is used only once so sophisticated methods of manipulating cache contents won't buy you much. These benchmark results are from a system that uses Atlas BLAS (basic linear algebra subroutines); other systems will provide different results. Interestingly, I found on some systems using R's BLAS, which are not accelerated, the R code is closer in speed to the code using Eigen. An example is given in the second version of the output.

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