function VECTOR = LPTAU(I, N) % % I.M. SOBOL', V.I. TURCHANINOV, Yu.L. LEVITAN, B.V. SHUKHMAN % KELDYSH INSTITUTE OF APPLIED MATHEMATICS % RUSSIAN ACADEMY OF SCIENCES % % QUASIRANDOM SEQUENCE GENERATORS % ------------------------------- % % 28.11.1991 % % NOTE TO THE USER BY the NEA Data Bank: % This quasi random number generator has been made available to % you on condition that its identity is preserved when used % in computer programs. If its use leads to scientific publication % of results you should cite it in the references, in addition % no commercial use should be made unless agreed upon with the % main author (Prof. I.M. Sobol') % % ABSTRACT % ........ % % POINTS BELONGING TO LP-TAU SEQUENCES UNIFORMLY DISTRIBUTED IN THE % N-DIMENSIONAL UNIT CUBE ARE OFTEN USED IN NUMERICAL MATHEMATICS: % % - AS NODES FOR MULTIDIMENSIONAL INTEGRATION; % - AS SEARCHING POINTS IN GLOBAL OPTIMIZATION; % - AS TRIAL POINTS IN MULTI-CRITERIA DECISION MAKING; % - AS QUASIRANDOM POINTS FOR QUASI-MONTECARLO ALGORITHMS; % - ETC. % % THIS SUBROUTINE CONTAINS THE ALGORITHM FOR FAST GENERATION OF % LP-TAU SEQUENCES THAT ARE SUITABLE FOR MULTI-PROCESSOR COMPUTATIONS. % THE DIMENSIONS N.LE.51, THE NUMBER OF POINTS N.LT.2**30. % THE PROGRAMMING LANGUAGE IS FORTRAN-77. THIS SUBROUTINE IS AVAILABLE % ALSO IN %-LANGUAGE. % THE REPORT DESCRIBING THE ALGORITHM CONTAINS THE DESCRIPTION OF THE % ALGORITHM AND CERTAIN IMPORTANT PROPERTIES OF LP-TAU SEQUENCES AND % THEIR GENERALIZATIONS ARE DISCUSSED. % % REFERENCE: % I.M. SOBOL', V.I. TURCHANINOV, Yu.L. LEVITAN, B.V. SHUKHMAN % KELDYSH INSTITUTE OF APPLIED MATHEMATICS % RUSSIAN ACADEMY OF SCIENCES % % QUASIRANDOM SEQUENCE GENERATORS % MOSCOW 1992, IPM ZAK. NO.30 (100 COPIES) % % ------------------------------------------------------------------------ % % INPUT PARAMETERS: % % I - NUMBER OF THE POINT (I=(0,2**30-1)), % N - DIMENSION OF THE POINT (0MAXNUM) | (N>MAXDIM)), disp('LP-TAU CALL FAILED') disp(' PRESS TO EXIT LPTAU') pause return end if ((PRVNUM+1==I) & (N<=PRVDIM)), % % RECURRENT GENERATION OF THE POINT % % % SEARCH POSITION OF THE RIGHTMOST "1" % IN THE BINARY REPRESENTATION OF I % L=0; POS=0; while L