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DOUBLE PRECISION FUNCTION genbet(aa,bb)
C**********************************************************************
C
C DOUBLE PRECISION FUNCTION GENBET( A, B )
C GeNerate BETa random deviate
C
C
C Function
C
C
C Returns a single random deviate from the beta distribution with
C parameters A and B. The density of the beta is
C x^(a-1) * (1-x)^(b-1) / B(a,b) for 0 < x < 1
C
C
C Arguments
C
C
C A --> First parameter of the beta distribution
C DOUBLE PRECISION A
C JJV (A > 1.0E-37)
C
C B --> Second parameter of the beta distribution
C DOUBLE PRECISION B
C JJV (B > 1.0E-37)
C
C
C Method
C
C
C R. C. H. Cheng
C Generating Beta Variates with Nonintegral Shape Parameters
C Communications of the ACM, 21:317-322 (1978)
C (Algorithms BB and BC)
C
C**********************************************************************
C .. Parameters ..
C Close to the largest number that can be exponentiated
DOUBLE PRECISION expmax
C JJV changed this - 89 was too high, and LOG(1.0E38) = 87.49823
PARAMETER (expmax=87.49823)
C Close to the largest representable single precision number
DOUBLE PRECISION infnty
PARAMETER (infnty=1.0E38)
C JJV added the parameter minlog
C Close to the smallest number of which a LOG can be taken.
DOUBLE PRECISION minlog
PARAMETER (minlog=1.0E-37)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION aa,bb
C ..
C .. Local Scalars ..
DOUBLE PRECISION a,alpha,b,beta,delta,gamma,k1,k2,olda,oldb,r,s,t,
+ u1,u2,v,w,y,z
LOGICAL qsame
C ..
C .. External Functions ..
DOUBLE PRECISION ranf
EXTERNAL ranf
C ..
C .. Intrinsic Functions ..
INTRINSIC exp,log,max,min,sqrt
C ..
C .. Save statement ..
C JJV added a,b
SAVE olda,oldb,alpha,beta,gamma,k1,k2,a,b
C ..
C .. Data statements ..
C JJV changed these to ridiculous values
DATA olda,oldb/-1.0E37,-1.0E37/
C ..
C .. Executable Statements ..
qsame = (olda.EQ.aa) .AND. (oldb.EQ.bb)
IF (qsame) GO TO 20
C JJV added small minimum for small log problem in calc of W
C in Rand.c
10 olda = aa
oldb = bb
20 IF (.NOT. (min(aa,bb).GT.1.0)) GO TO 100
C Alborithm BB
C
C Initialize
C
IF (qsame) GO TO 30
a = min(aa,bb)
b = max(aa,bb)
alpha = a + b
beta = sqrt((alpha-2.0)/ (2.0*a*b-alpha))
gamma = a + 1.0/beta
30 CONTINUE
40 u1 = ranf()
C
C Step 1
C
u2 = ranf()
v = beta*log(u1/ (1.0-u1))
C JJV altered this
IF (v.GT.expmax) GO TO 55
C JJV added checker to see if a*exp(v) will overflow
C JJV 50 _was_ w = a*exp(v); also note here a > 1.0
50 w = exp(v)
IF (w.GT.infnty/a) GO TO 55
w = a*w
GO TO 60
55 w = infnty
60 z = u1**2*u2
r = gamma*v - 1.3862944
s = a + r - w
C
C Step 2
C
IF ((s+2.609438).GE. (5.0*z)) GO TO 70
C
C Step 3
C
t = log(z)
IF (s.GT.t) GO TO 70
C
C Step 4
C
C JJV added checker to see if log(alpha/(b+w)) will
C JJV overflow. If so, we count the log as -INF, and
C JJV consequently evaluate conditional as true, i.e.
C JJV the algorithm rejects the trial and starts over
C JJV May not need this here since ALPHA > 2.0
IF (alpha/(b+w).LT.minlog) GO TO 40
IF ((r+alpha*log(alpha/ (b+w))).LT.t) GO TO 40
C
C Step 5
C
70 IF (.NOT. (aa.EQ.a)) GO TO 80
genbet = w/ (b+w)
GO TO 90
80 genbet = b/ (b+w)
90 GO TO 230
C Algorithm BC
C
C Initialize
C
100 IF (qsame) GO TO 110
a = max(aa,bb)
b = min(aa,bb)
alpha = a + b
beta = 1.0/b
delta = 1.0 + a - b
k1 = delta* (0.0138889+0.0416667*b)/ (a*beta-0.777778)
k2 = 0.25 + (0.5+0.25/delta)*b
110 CONTINUE
120 u1 = ranf()
C
C Step 1
C
u2 = ranf()
IF (u1.GE.0.5) GO TO 130
C
C Step 2
C
y = u1*u2
z = u1*y
IF ((0.25*u2+z-y).GE.k1) GO TO 120
GO TO 170
C
C Step 3
C
130 z = u1**2*u2
IF (.NOT. (z.LE.0.25)) GO TO 160
v = beta*log(u1/ (1.0-u1))
C JJV instead of checking v > expmax at top, I will check
C JJV if a < 1, then check the appropriate values
IF (a.GT.1.0) GO TO 135
C JJV A < 1 so it can help out if EXP(V) would overflow
IF (v.GT.expmax) GO TO 132
w = a*exp(v)
GO TO 200
132 w = v + log(a)
IF (w.GT.expmax) GO TO 140
w = exp(w)
GO TO 200
C JJV in this case A > 1
135 IF (v.GT.expmax) GO TO 140
w = exp(v)
IF (w.GT.infnty/a) GO TO 140
w = a*w
GO TO 200
140 w = infnty
GO TO 200
160 IF (z.GE.k2) GO TO 120
C
C Step 4
C
C
C Step 5
C
170 v = beta*log(u1/ (1.0-u1))
C JJV same kind of checking as above
IF (a.GT.1.0) GO TO 175
C JJV A < 1 so it can help out if EXP(V) would overflow
IF (v.GT.expmax) GO TO 172
w = a*exp(v)
GO TO 190
172 w = v + log(a)
IF (w.GT.expmax) GO TO 180
w = exp(w)
GO TO 190
C JJV in this case A > 1
175 IF (v.GT.expmax) GO TO 180
w = exp(v)
IF (w.GT.infnty/a) GO TO 180
w = a*w
GO TO 190
180 w = infnty
C JJV here we also check to see if log overlows; if so, we treat it
C JJV as -INF, which means condition is true, i.e. restart
190 IF (alpha/(b+w).LT.minlog) GO TO 120
IF ((alpha* (log(alpha/ (b+w))+v)-1.3862944).LT.log(z)) GO TO 120
C
C Step 6
C
200 IF (.NOT. (a.EQ.aa)) GO TO 210
genbet = w/ (b+w)
GO TO 220
210 genbet = b/ (b+w)
220 CONTINUE
230 RETURN
END
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