# [Rcpp-devel] Best way to compute M'M if M is triangular using RcppArmadillo

Dirk Eddelbuettel edd at debian.org
Wed Apr 17 15:16:57 CEST 2013

```On 17 April 2013 at 14:24, F.Tusell wrote:
| Not a question strictly about Rcpp but hope this is a right
|
| I am trying to find out what is the fastest possible way to compute
| M'M for M upper triangular. I have coded,
|
| // [[Rcpp::export]]
| SEXP Prod1(SEXP M_) {
|   const mat M = as<mat>(M_) ;
|   mat prodM = M ;
|   prodM = trans(M) * M  ;
|   return(wrap(prodM)) ;
| }
|
| // [[Rcpp::export]]
| SEXP Prod2(SEXP M_) {
|   const mat M = as<mat>(M_) ;
|   mat prodM = M ;
|   prodM = trimatu(M).t() * trimatu(M)  ;
|   return(wrap(prodM)) ;
| }
|
|
| // [[Rcpp::export]]
| SEXP Prod3(SEXP M_) {
|   mat M = as<mat>(M_) ;
|   int d = M.n_rows ;
|   mat prodM = M ;
|   double * vM = M.memptr() ;
|   double * vprodM = prodM.memptr() ;
|   const double one = 1 ;
|   const double zero = 0 ;
|   F77_CALL(dsyrk)("L","T",&d,&d,&one,vM,&d,&zero,vprodM,&d)  ;
|   return(wrap(prodM)) ;
| }
|
| and then tested with:
|
| require(microbenchmark)
| sourceCpp("prods.cpp")
| d <- 50
| a <- chol(crossprod(matrix(rnorm(d*d),d,d)))
|
| m <- microbenchmark(
|        r1 <- Prod1(a),
|        r2 <- Prod2(a),
|        r3 <- Prod3(a),
|        times=100
| 	       )
|
| This is what I get:
|
| > m
| Unit: microseconds
|            expr     min       lq   median       uq      max neval
|  r1 <- Prod1(a) 138.749 144.2260 148.4815 159.0830 2456.146   100
|  r2 <- Prod2(a) 296.193 320.0275 329.4770 342.4185 2763.041   100
|  r3 <- Prod3(a) 132.150 138.2590 140.9270 152.3675  218.719   100
|
| Prod3 using BLAS dsyrk is about as fast as Prod1, using Armadillo.
| I expected that telling Armadillo that M is upper triangular would
| make for a fastest product, and the contrary seems true; Prod2 takes
| about twice as much time as Prod1 and Prod3.
|
| Is there a faster way?

Now, d=50 is not big so your (relative) savings will be rather small.  Plus,
the way you instantiate the Arma object DOES create extra copies on the arma
object instantiation [ see discussion this list just last week ] as well as
on exit -- which may dominate the timing. Try d=100, 200, ... 500 for
comparison.

Lastly, you could write prod3 without going to arma.

Dirk

--
Dirk Eddelbuettel | edd at debian.org | http://dirk.eddelbuettel.com
```