Low Discrepancy Sequences

Issue 1136: Provide Matousek scrambling for Sobol sequence

Reported by Michael Baudin, Mar 30, 2013

Provide Matousek scrambling for Sobol sequence

http://www.mathworks.fr/fr/help/stats/qrandset.scramble.html

Matousek, J. "On the L2-Discrepancy for Anchored Boxes." 
Journal of Complexity. Vol. 14, No. 4, 1998, pp. 527–556.

http://people.sc.fsu.edu/~hcc8471/ssobol.pdf

Comment 1 by Michael Baudin, Apr 5, 2013

The scrambling used in Matlab ("A random linear scramble 
combined with a random digital shift") must be the "Random 
linear digit-scrambling" described in Matousek (1998). 

Let 

x=(0. a1 a2 ...)_b

be the b-ary decomposition of x in base b, possibly prime. 

sigma_j(a)=h_j*a+d_j (mod b)

where h_j in {1,2,...,b-1} and g_j in {0,1,...,b-1}.

"If the hj's and gj's are chosen uniformly and independently at 
random, we speak of a random linear digit-scrambling."

Comment 3 by Michael Baudin, Apr 6, 2013

Contact Dirk Nuyens and clarify the licence:

http://people.cs.kuleuven.be/~dirk.nuyens/#AboutMe

Comment 4 by Michael Baudin, Apr 6, 2013

Scrambled C and F versions.

Comment 5 by Michael Baudin, Apr 6, 2013

C:\Users\Gros\Documents\SciForge\TMP>f2c ssobol.f
'f2c' n'est pas reconnu en tant que commande interne
ou externe, un programme exécutable ou un fichier de commandes.

C:\Users\Gros\Documents\SciForge\TMP>f2c.exe ssobol.f
ssobol.f:
   bdsobl:
   BLOCK DATA bdsobl:
   inssobl:
Error processing common blocks before line 127 of ssobol.f: 
Declaration error for recipd: common alignment
Warning on line 324 of ssobol.f: local variable digit never used
Warning on line 324 of ssobol.f: local variable output never used
   genscrml:
Warning on line 342 of ssobol.f: incompatible lengths for common 
block sobol
   genscrmu:
Warning on line 383 of ssobol.f: incompatible lengths for common 
block sobol
Warning on line 398 of ssobol.f: local variable l never used
Warning on line 398 of ssobol.f: local variable p never used
Warning on line 398 of ssobol.f: local variable ll never used
   uni:
   gossobl:
Error processing common blocks before line 468 of ssobol.f: 
Declaration error for recipd: common alignment
   exor:
   MAIN genssob:
Warning on line 585 of ssobol.f: local variable ei never used

Comment 6 by Michael Baudin, Apr 21, 2013

The ssobol sequence provides Owen, Faure-Tezuka and 
Owen-Faure-Tezuka scramblings, but not Matousek's scrambling.

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