[Rd] efficiency of sample() with prob.
Prof Brian Ripley
ripley at stats.ox.ac.uk
Fri Jun 24 08:10:46 CEST 2005
`Research' involves looking at all the competitor methods, devising a
near-optimal strategy and selecting amongst methods according to that
strategy. It is not a quick fix we are looking for but something that
will be good for the long term.
On Thu, 23 Jun 2005, Bo Peng wrote:
>> We suggest that you take up your own suggestion, research this area and
>> offer the R project the results of your research for consideration as your
>> contribution.
>
> I implemented Walker's alias method and re-compiled R. Here is what
> I did:
>
> 1. replace function ProcSampleReplace in R-2.1.0/src/main/random.c
> with the following one
>
> static void ProbSampleReplace(int n, double *p, int *perm, int nans, int *ans)
> {
> /* allocate memory for a, p and HL */
> double * q = Calloc(n, double);
> int * a = Calloc(n, int);
> int * HL = Calloc(n, int);
> int * H = HL;
> int * L = HL+n-1;
> int i, j, k;
> double rU; /* U[0,1)*n */
>
> /* set up alias table */
> /* initialize q with n*p0,...n*p_n-1 */
> for(i=0; i<n; ++i)
> q[i] = p[i]*n;
>
> /* initialize a with indices */
> for(i=0; i<n; ++i)
> a[i] = i;
>
> /* set up H and L */
> for(i=0; i<n; ++i) {
> if( q[i] >= 1.)
> *H++ = i;
> else
> *L-- = i;
> }
>
> while( H != HL && L != HL+n-1) {
> j = *(L+1);
> k = *(H-1);
> a[j] = k;
> q[k] += q[j] - 1;
> L++; /* remove j from L */
> if( q[k] < 1. ) {
> *L-- = k; /* add k to L */
> --H; /* remove k */
> }
> }
>
> /* generate sample */
> for (i = 0; i < nans; ++i) {
> rU = unif_rand() * n;
>
> k = (int)(rU);
> rU -= k; /* rU becomes rU-[rU] */
>
> if( rU < q[k] )
> ans[i] = k+1;
> else
> ans[i] = a[k]+1;
> }
> Free(HL);
> Free(a);
> Free(q);
> }
>
> 2. make and make install
>
> 3. test the new sample function by code like
>
>> b=sample(seq(1,100), prob=seq(1,100), replace=TRUE, size=1000000)
>> table(b)/1000000*sum(seq(1,100))
>
> 4. run the following code in current R 2.1.0 and updated R.
>
> for(prob in seq(1,4)){
> for(sample in seq(1,4)){
> x = seq(1:(10^prob)) # short to long x
> p = abs(rnorm(length(x))) # prob vector
> times = 10^(6-prob) # run shorter cases more times
> Rprof(paste("sample_", prob, "_", sample, ".prof", sep=''))
> for(t in seq(1,times)){
> sample(x, prob=p, size=10^sample, replace=TRUE )
> }
> Rprof(NULL)
> }
> }
>
> Basically, I tried to test the performance of sample(replace=TRUE, prob=..)
> with different length of x and size.
>
> 5. process the profiles and here is the result.
> p: length of prob and x
> size: size of sample
> cell: execution time of old/updated sample()
>
> size\p 10 10^2 10^3 10^4
> 10 2.4/1.6 0.32/0.22 0.20/0.08 0.24/0.06
> 10^2 3.1/2.6 0.48/0.28 0.28/0.06 0.30/0.06
> 10^3 11.8/11.1 1.84/1.14 0.94/0.18 0.96/0.08
> 10^4 96.8/96.6 15.34/9.68 7.54/1.06 7.48/0.16
> run: 10000 1000 100 10 times
>
> We can see that the alias method is quicker than the linear search
> method in all cases. The performance difference is greatest (>50 times)
> when the original algorithm need to search in a long prob vector.
>
> I have not thoroughly tested the new function. I will do so if you
> (the developers) think that this has the potential to be incorporated
> into R.
>
> Thanks.
>
> Bo Peng
> Department of Statistics
> Rice University
>
>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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