[Rcpp-devel] How to increase the coding efficiency

I tried out that if the dim of the matrix less than or equal to 4, inv()
and solve() have the same speed.


Best wishes!

Honglang Wang

Office C402 Wells Hall
Department of Statistics and Probability
Michigan State University
1579 I Spartan Village, East Lansing, MI 48823
wangho16 at msu.edu



On Mon, Dec 10, 2012 at 8:05 AM, c s <conradsand.arma at gmail.com> wrote:

Hi Honglang,

I recommend looking into using the solve() function in Armadillo, instead
of inv(). Using solve() will be considerably faster.

More details here:
http://arma.sourceforge.net/docs.html#solve



On Thursday, December 6, 2012, Honglang Wang <wanghonglang2008 at gmail.com>
wrote:

The following is a full example although I don't know whether it's

minimal or not:

library(Rcpp)
library(RcppArmadillo)
sourceCpp("betahat_mod.cpp")

#The following is data generation.
  n=200
  m=20
  p=2
  t=runif(m*n,min=0, max=1)
  X1=rnorm(m*n,0,1)
  X1=as.matrix(1+2*exp(t)+X1)
  X2=rnorm(m*n,0,1)
  X2=as.matrix(3-4*t^2+X2)
  X=cbind(X1,X2)
  beta1=0.5*sin(t)
  beta2=beta1
  rho=0.2
  sig2=1

eps=unlist(lapply(1:n,function(x){as.matrix(arima.sim(list(ar=rho),m,sd=sqrt(sig2*(1-rho^2))))}))

  y=as.matrix(X1*beta1+X2*beta2+eps)

#A simple kernel function.
ker=function(x,h)
  {
    ans=x
    lo=(abs(x)<h)
    ans[lo]=(3/4)*(1-(x[lo]/h)^2)/h
    ans[!lo]=0
    return(ans)
  }


h=0.3

#assess the time for evaluating bethat of 100 t's:
system.time((betahatt=t(apply(as.matrix(t[1:100]),1,function(x)

betahat(ker,x,X,y,t,h,m)$betahat))))

And the .cpp file is the following:

// [[Rcpp::depends(RcppArmadillo)]]

#include <RcppArmadillo.h>

using namespace Rcpp;

// [[Rcpp::export]]
List betahat(Function ker, double t0, NumericMatrix Xr, NumericMatrix

yr, NumericVector tr, double h, int m) {

  int n = Xr.nrow(), p = Xr.ncol();
  arma::mat X(Xr.begin(), n, p, false);
  arma::mat y(yr.begin(), n, 1, false);
  arma::colvec t(tr.begin(), tr.size(), false);
  arma::mat T = X;
  T.each_col() %= (t-t0)/h;
  arma::mat D = arma::join_rows(X,T);
  arma::vec kk =as<arma::vec>(ker(tr-t0,h));
  arma::mat W = (arma::diagmat(kk))/m;
  arma::mat Inv = arma::trans(D)*W*D;
  arma::vec betahat = arma::inv(Inv)*arma::trans(D)*W*y;
  arma::colvec betahat0(betahat.begin(),betahat.size()/2,false);
  return List::create(Named("betahat") = betahat0);
}

Best wishes!

Honglang Wang

Office C402 Wells Hall
Department of Statistics and Probability
Michigan State University
1579 I Spartan Village, East Lansing, MI 48823
wangho16 at msu.edu


On Wed, Dec 5, 2012 at 4:07 AM, Christian Gunning <xian at unm.edu> wrote:

Can you post a minimal full example?
-Christian

On Tue, Dec 4, 2012 at 8:39 PM, Honglang Wang
<wanghonglang2008 at gmail.com> wrote:

Yes, the main issue for my coding is the allocation of memory.  And

I have

fixed one of the biggest memory allocation issue: 4000 by 4000

diagonal

matrix. And since I am not familiar with Rcpp and RcppArmadillo, I

have no

idea how to reuse the memory. I hope I can have some materials to

learn

this. Thanks.

What exactly do these timings show?  A single call you your

function?

How many calls?

Here I called my function for 100 times.

Building on Romain's point: -- a portion of your function's runtime

is

in memory allocation
(and you have a lot of allocations here).
If you're calling your function thousands or millions of times, then
it might pay to closely
examine your memory allocation strategies and figure out what's
temporary, for example.
It looks like you're already using  copy_aux_mem = false in a number
of places, but you're
allocating a lot of objects -- of approx what size?

For example, wouldn't this work just as well with one less

allocation?

arma::vec kk = t;
arma::uvec q1 = arma::find(arma::abs(tp)<h);
kk.elem(q1) = ((1-arma::pow(tp.elem(q1)/h,2))/h)*0.75;
// done with q1.  let's reuse it.
q1 = arma::find(arma::abs(tp)>=h);
// was q2
kk.elem(q1).zeros();

You could potentially allocate memory for temporary working space in
R, grab it with copy_aux_mem = false, write your temp results there,
and reuse these objects in subsequent function calls.  It doesn't

make

sense to go to this trouble, though, if your core algorithm consumes
the bulk of runtime.

Have you looked on the armadillo notes r.e. inv?  Matrix inversion

has

O(>n^2).  You may be aided by pencil-and-paper math here.
http://arma.sourceforge.net/docs.html#inv

Here my matrix for inverse is only 4 by 4, so I think it's ok.

best,
Christian

Dear All,
I have tried out the first example by using RcppArmadillo, but I

am not

sure whether the code is efficient or not. And I did the

comparison of

the
computation time.

1) R code using for loop in R: 87.22s
2) R code using apply: 77.86s
3) RcppArmadillo by using for loop in C++: 53.102s
4) RcppArmadillo together with apply in R: 47.310s

It is kind of not so big increase. I am wondering whether I used

an

inefficient way for the C++ coding:

--
A man, a plan, a cat, a ham, a yak, a yam, a hat, a canal ? Panama!

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A man, a plan, a cat, a ham, a yak, a yam, a hat, a canal ? Panama!