| /* |
| * R : A Computer Language for Statistical Data Analysis |
| * Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka |
| * Copyright (C) 2000--2016 The R Core Team |
| * Copyright (C) 2001--2016 The R Foundation |
| * |
| * 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, a copy is available at |
| * https://www.R-project.org/Licenses/ |
| */ |
| |
| /* Reference: |
| * R. C. H. Cheng (1978). |
| * Generating beta variates with nonintegral shape parameters. |
| * Communications of the ACM 21, 317-322. |
| * (Algorithms BB and BC) |
| */ |
| |
| #include "nmath.h" |
| |
| #define expmax (DBL_MAX_EXP * M_LN2)/* = log(DBL_MAX) */ |
| |
| double rbeta(double aa, double bb) |
| { |
| if (ISNAN(aa) || ISNAN(bb) || aa < 0. || bb < 0.) |
| ML_ERR_return_NAN; |
| if (!R_FINITE(aa) && !R_FINITE(bb)) // a = b = Inf : all mass at 1/2 |
| return 0.5; |
| if (aa == 0. && bb == 0.) // point mass 1/2 at each of {0,1} : |
| return (unif_rand() < 0.5) ? 0. : 1.; |
| // now, at least one of a, b is finite and positive |
| if (!R_FINITE(aa) || bb == 0.) |
| return 1.0; |
| if (!R_FINITE(bb) || aa == 0.) |
| return 0.0; |
| |
| double a, b, alpha; |
| double r, s, t, u1, u2, v, w, y, z; |
| int qsame; |
| /* FIXME: Keep Globals (properly) for threading */ |
| /* Uses these GLOBALS to save time when many rv's are generated : */ |
| static double beta, gamma, delta, k1, k2; |
| static double olda = -1.0; |
| static double oldb = -1.0; |
| |
| /* Test if we need new "initializing" */ |
| qsame = (olda == aa) && (oldb == bb); |
| if (!qsame) { olda = aa; oldb = bb; } |
| |
| a = fmin2(aa, bb); |
| b = fmax2(aa, bb); /* a <= b */ |
| alpha = a + b; |
| |
| #define v_w_from__u1_bet(AA) \ |
| v = beta * log(u1 / (1.0 - u1)); \ |
| if (v <= expmax) { \ |
| w = AA * exp(v); \ |
| if(!R_FINITE(w)) w = DBL_MAX; \ |
| } else \ |
| w = DBL_MAX |
| |
| |
| if (a <= 1.0) { /* --- Algorithm BC --- */ |
| |
| /* changed notation, now also a <= b (was reversed) */ |
| |
| if (!qsame) { /* initialize */ |
| beta = 1.0 / a; |
| delta = 1.0 + b - a; |
| k1 = delta * (0.0138889 + 0.0416667 * a) / (b * beta - 0.777778); |
| k2 = 0.25 + (0.5 + 0.25 / delta) * a; |
| } |
| /* FIXME: "do { } while()", but not trivially because of "continue"s:*/ |
| for(;;) { |
| u1 = unif_rand(); |
| u2 = unif_rand(); |
| if (u1 < 0.5) { |
| y = u1 * u2; |
| z = u1 * y; |
| if (0.25 * u2 + z - y >= k1) |
| continue; |
| } else { |
| z = u1 * u1 * u2; |
| if (z <= 0.25) { |
| v_w_from__u1_bet(b); |
| break; |
| } |
| if (z >= k2) |
| continue; |
| } |
| |
| v_w_from__u1_bet(b); |
| |
| if (alpha * (log(alpha / (a + w)) + v) - 1.3862944 >= log(z)) |
| break; |
| } |
| return (aa == a) ? a / (a + w) : w / (a + w); |
| |
| } |
| else { /* Algorithm BB */ |
| |
| if (!qsame) { /* initialize */ |
| beta = sqrt((alpha - 2.0) / (2.0 * a * b - alpha)); |
| gamma = a + 1.0 / beta; |
| } |
| do { |
| u1 = unif_rand(); |
| u2 = unif_rand(); |
| |
| v_w_from__u1_bet(a); |
| |
| z = u1 * u1 * u2; |
| r = gamma * v - 1.3862944; |
| s = a + r - w; |
| if (s + 2.609438 >= 5.0 * z) |
| break; |
| t = log(z); |
| if (s > t) |
| break; |
| } |
| while (r + alpha * log(alpha / (b + w)) < t); |
| |
| return (aa != a) ? b / (b + w) : w / (b + w); |
| } |
| } |