// Octave modules for the Mersenne Twister (MT199337) Random Number Generator // // Wrapper code around the implemtation by Shawn Cokus of the Mersenne // Twister RNG by Makoto Matsumoto and Takuji Nishimura. See // http://www.math.keio.ac.jp/~matumoto/emt.html // for more on the algorithm. // // This file provides three Octave functions: // randmt for Uniform random number // randmtn for Normal random number // randmtseed to set the seed of the RNG // // Copyright (C) 1998, 1999 Dirk Eddelbuettel // // This program is free software; you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation; either version 2 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program; if not, write to the Free Software // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. // // \$Id\$ #include "config.h" #include "oct-obj.h" #include "oct-map.h" #include "defun-dld.h" #include typedef unsigned long uint32; extern "C" { // include as C void seedMT(uint32 seed); inline uint32 randomMT(void); } inline double randomMTunit(void) { // multiply by 1/0xFFFFFFFF) // code taken from mt199379-1.c return (double)randomMT() * 2.328306437080794e-10; } DEFUN_DLD (randmt, args, nargout, "Usage: U = randmt( n [, k])\n\n\ Generates uniform random numbers using the Mersenne Twister algorithm by\n\ Makoto Matsumoto and Takuji Nishimura, using the even faster implementation\n\ by Shawn Cokus.\n\ See http://www.math.keio.ac.jp/~matumoto/emt.html for more on the algorithm.\n\n\ randmt(n, k) returns n*k matrix with uncorrelated U(0, 1) deviates\n\ randmt(n) returns n*n matrix with uncorrelated U(0, 1) deviates\n") { octave_value_list retval; // list of return values int nargs = args.length (); // number of arguments supplied if (nargs<1 || nargs>2) { // if not enough arguments, show message usage("Try 'help randmt' for info"); return retval; // and return empty } long n,k; n = long(args(0).double_value()); if (nargs == 2) k = long(args(1).double_value()); else k = n; Matrix X(n, k); for (long i=0; i on 1 Aug 1999 to use randomMTunit() instead of RANF ********************************************************************** THE DEFINITIONS OF THE CONSTANTS A(K), D(K), T(K) AND H(K) ARE ACCORDING TO THE ABOVEMENTIONED ARTICLE */ { static double a[32] = { 0.0,3.917609E-2,7.841241E-2,0.11777,0.1573107,0.1970991,0.2372021,0.2776904, 0.3186394,0.36013,0.4022501,0.4450965,0.4887764,0.5334097,0.5791322, 0.626099,0.6744898,0.7245144,0.7764218,0.8305109,0.8871466,0.9467818, 1.00999,1.077516,1.150349,1.229859,1.318011,1.417797,1.534121,1.67594, 1.862732,2.153875 }; static double d[31] = { 0.0,0.0,0.0,0.0,0.0,0.2636843,0.2425085,0.2255674,0.2116342,0.1999243, 0.1899108,0.1812252,0.1736014,0.1668419,0.1607967,0.1553497,0.1504094, 0.1459026,0.14177,0.1379632,0.1344418,0.1311722,0.128126,0.1252791, 0.1226109,0.1201036,0.1177417,0.1155119,0.1134023,0.1114027,0.1095039 }; static double t[31] = { 7.673828E-4,2.30687E-3,3.860618E-3,5.438454E-3,7.0507E-3,8.708396E-3, 1.042357E-2,1.220953E-2,1.408125E-2,1.605579E-2,1.81529E-2,2.039573E-2, 2.281177E-2,2.543407E-2,2.830296E-2,3.146822E-2,3.499233E-2,3.895483E-2, 4.345878E-2,4.864035E-2,5.468334E-2,6.184222E-2,7.047983E-2,8.113195E-2, 9.462444E-2,0.1123001,0.136498,0.1716886,0.2276241,0.330498,0.5847031 }; static double h[31] = { 3.920617E-2,3.932705E-2,3.951E-2,3.975703E-2,4.007093E-2,4.045533E-2, 4.091481E-2,4.145507E-2,4.208311E-2,4.280748E-2,4.363863E-2,4.458932E-2, 4.567523E-2,4.691571E-2,4.833487E-2,4.996298E-2,5.183859E-2,5.401138E-2, 5.654656E-2,5.95313E-2,6.308489E-2,6.737503E-2,7.264544E-2,7.926471E-2, 8.781922E-2,9.930398E-2,0.11556,0.1404344,0.1836142,0.2790016,0.7010474 }; static long i; static double snorm,u,s,ustar,aa,w,y,tt; u = randomMTunit(); s = 0.0; if(u > 0.5) s = 1.0; u += (u-s); u = 32.0*u; i = (long) (u); if(i == 32) i = 31; if(i == 0) goto S100; /* START CENTER */ ustar = u-(double)i; aa = *(a+i-1); S40: if(ustar <= *(t+i-1)) goto S60; w = (ustar-*(t+i-1))**(h+i-1); S50: /* EXIT (BOTH CASES) */ y = aa+w; snorm = y; if(s == 1.0) snorm = -y; return snorm; S60: /* CENTER CONTINUED */ u = randomMTunit(); w = u*(*(a+i)-aa); tt = (0.5*w+aa)*w; goto S80; S70: tt = u; ustar = randomMTunit(); S80: if(ustar > tt) goto S50; u = randomMTunit(); if(ustar >= u) goto S70; ustar = randomMTunit(); goto S40; S100: /* START TAIL */ i = 6; aa = *(a+31); goto S120; S110: aa += *(d+i-1); i += 1; S120: u += u; if(u < 1.0) goto S110; u -= 1.0; S140: w = u**(d+i-1); tt = (0.5*w+aa)*w; goto S160; S150: tt = u; S160: ustar = randomMTunit(); if(ustar > tt) goto S50; u = randomMTunit(); if(ustar >= u) goto S150; u = randomMTunit(); goto S140; } DEFUN_DLD (randmtn, args, nargout, "Usage: N = randmtn( n [, k])\n\n\ Generates standard-normal random numbers using the Mersenne Twister algorithm by\n\ Makoto Matsumoto and Takuji Nishimura, using the even faster implementation\n\ by Shawn Cokus. Uses Ahrens and Dieter (1973) to transform from U to N(0,1).\n\ See http://www.math.keio.ac.jp/~matumoto/emt.html for more on the algorithm.\n\n\ randmtn(n, k) returns n*k matrix with uncorrelated N(0, 1) deviates\n\ randmtn(n) returns n*n matrix with uncorrelated N(0, 1) deviates\n") { octave_value_list retval; // list of return values int nargs = args.length (); // number of arguments supplied if (nargs<1 || nargs>2) { // if not enough arguments, show message usage("Try 'help randmtn' for info"); return retval; // and return empty } long n,k; n = long(args(0).double_value()); if (nargs == 2) k = long(args(1).double_value()); else k = n; Matrix X(n, k); for (long i=0; i