Name

lowdisc_next — Returns the next term of the sequence

Calling Sequence

   [this,next] = lowdisc_next ( this )
   [this,next] = lowdisc_next ( this , imax )
   
   

Parameters

this:

the current object

imax:

the number of terms to retrieve (default = 1)

next :

a matrix of size imax x s, the next vector in the sequence. The experiment #i is stored at next(i,:) for 1<=i<=imax. The component #j of experiment #i is stored in next(i,j) with 1<=j<=dimension.

Description

The current object is updated after the call to next : both this and next are mandatory output arguments. This function is sensitive to the "-leap" option.

Because of the limitation of floating point integers, the lowdisc_next function is able to generate at most 2^52 = 4 503 599 627 370 496 experiments. Fast sequences are based on the intermediate storage of the iteration index on a 32 bits C int. This implies that these sequences are able to generate at most 2^32-1 = 4 294 967 295 experiments.

The number of simulations might be computed so that it improves the discrepancy of the sequence. This is especially true for the Sobol, Faure and Niederreiter sequences. This can lead to some trouble for non-experts. For that purpose, we designed the following functions.

  • lowdisc_haltonsuggest : provides settings for the Halton sequence,
  • lowdisc_fauresuggest : provides settings for the Faure sequence,
  • lowdisc_sobolsuggest : provides settings for the Sobol sequence,
  • lowdisc_niedersuggest : provides settings for the Niederreiter sequence.

Examples

lds = lowdisc_new("halton");
lds = lowdisc_startup (lds);
// Term #1
[lds,computed] = lowdisc_next (lds);
disp(computed)
// Term #2
[lds,computed] = lowdisc_next (lds);
disp(computed)
// Term #3, etc...
[lds,computed] = lowdisc_next (lds);
disp(computed)
lds
lds = lowdisc_destroy(lds);

// See the imax parameter in action
lds = lowdisc_new("halton");
lds = lowdisc_startup (lds);
// Term #1 to 100
[lds,computed] = lowdisc_next (lds,100);
// Term #101 to 201
[lds,computed] = lowdisc_next (lds,100);
lds
lds = lowdisc_destroy(lds);

// See the -leap option in action
lds = lowdisc_new("halton");
lds = lowdisc_configure(lds,"-leap",10);
lds = lowdisc_startup (lds);
// Term #1
[lds,computed] = lowdisc_next (lds);
// Term #11
[lds,computed] = lowdisc_next (lds);
// Term #21
[lds,computed] = lowdisc_next (lds);
lds
lds = lowdisc_destroy(lds);

// See the -skip option in action.
lds = lowdisc_new("fauref");
lds = lowdisc_configure(lds,"-dimension",4);
// Skip qs^4 - 1 terms, as in TOMS implementation
qs = lowdisc_get ( lds , "-faurefprime" );
lds = lowdisc_configure(lds,"-skip", qs^4 - 2);
lds
lds = lowdisc_startup (lds);
[lds,computed]=lowdisc_next(lds);
// Terms #1 to #100
[lds,computed]=lowdisc_next(lds,100);
for i = 1:100
mprintf ("%8d %14.6f %14.6f %14.6f %14.6f\n", i , computed(i,1) , computed(i,2) , computed(i,3) , computed(i,4) )
end
lds = lowdisc_destroy(lds);

   

Authors

Michael Baudin - 2008-2009 - INRIA
Michael Baudin - 2010 - DIGITEO