/* another library of funtions to support the rand number generator
Copyright (C) 1992-2000 Michigan State University
The CAPA system is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The CAPA system 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the CAPA system; see the file COPYING. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
As a special exception, you have permission to link this program
with the TtH/TtM library and distribute executables, as long as you
follow the requirements of the GNU GPL in regard to all of the
software in the executable aside from TtH/TtM.
*/
#include "ranlib.h"
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define min(a,b) ((a) <= (b) ? (a) : (b))
#define max(a,b) ((a) >= (b) ? (a) : (b))
/*
**********************************************************************
float genbet(float aa,float bb)
GeNerate BETa random deviate
Function
Returns a single random deviate from the beta distribution with
parameters A and B. The density of the beta is
x^(a-1) * (1-x)^(b-1) / B(a,b) for 0 < x < 1
Arguments
aa --> First parameter of the beta distribution
bb --> Second parameter of the beta distribution
Method
R. C. H. Cheng
Generating Beta Variatew with Nonintegral Shape Parameters
Communications of the ACM, 21:317-322 (1978)
(Algorithms BB and BC)
**********************************************************************
*/
float genbet(float aa,float bb)
{
#define expmax 89.0
#define infnty 1.0E38
static float olda = -1.0;
static float oldb = -1.0;
static float genbet,a,alpha,b,beta,delta,gamma,k1,k2,r,s,t,u1,u2,v,w,y,z;
static long qsame;
qsame = olda == aa && oldb == bb;
if(qsame) goto S20;
if(!(aa <= 0.0 || bb <= 0.0)) goto S10;
puts(" AA or BB <= 0 in GENBET - Abort!");
printf(" AA: %16.6E BB %16.6E\n",aa,bb);
exit(1);
S10:
olda = aa;
oldb = bb;
S20:
if(!(min(aa,bb) > 1.0)) goto S100;
/*
Algorithm BB
Initialize
*/
if(qsame) goto S30;
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;
S30:
S40:
u1 = ranf();
/*
Step 1
*/
u2 = ranf();
v = beta*log(u1/(1.0-u1));
if(!(v > expmax)) goto S50;
w = infnty;
goto S60;
S50:
w = a*exp(v);
S60:
z = pow(u1,2.0)*u2;
r = gamma*v-1.3862944;
s = a+r-w;
/*
Step 2
*/
if(s+2.609438 >= 5.0*z) goto S70;
/*
Step 3
*/
t = log(z);
if(s > t) goto S70;
/*
Step 4
*/
if(r+alpha*log(alpha/(b+w)) < t) goto S40;
S70:
/*
Step 5
*/
if(!(aa == a)) goto S80;
genbet = w/(b+w);
goto S90;
S80:
genbet = b/(b+w);
S90:
goto S230;
S100:
/*
Algorithm BC
Initialize
*/
if(qsame) goto S110;
a = max(aa,bb);
b = min(aa,bb);
alpha = a+b;
beta = 1.0/b;
delta = 1.0+a-b;
k1 = delta*(1.38889E-2+4.16667E-2*b)/(a*beta-0.777778);
k2 = 0.25+(0.5+0.25/delta)*b;
S110:
S120:
u1 = ranf();
/*
Step 1
*/
u2 = ranf();
if(u1 >= 0.5) goto S130;
/*
Step 2
*/
y = u1*u2;
z = u1*y;
if(0.25*u2+z-y >= k1) goto S120;
goto S170;
S130:
/*
Step 3
*/
z = pow(u1,2.0)*u2;
if(!(z <= 0.25)) goto S160;
v = beta*log(u1/(1.0-u1));
if(!(v > expmax)) goto S140;
w = infnty;
goto S150;
S140:
w = a*exp(v);
S150:
goto S200;
S160:
if(z >= k2) goto S120;
S170:
/*
Step 4
Step 5
*/
v = beta*log(u1/(1.0-u1));
if(!(v > expmax)) goto S180;
w = infnty;
goto S190;
S180:
w = a*exp(v);
S190:
if(alpha*(log(alpha/(b+w))+v)-1.3862944 < log(z)) goto S120;
S200:
/*
Step 6
*/
if(!(a == aa)) goto S210;
genbet = w/(b+w);
goto S220;
S210:
genbet = b/(b+w);
S230:
S220:
return genbet;
#undef expmax
#undef infnty
}
float genchi(float df)
/*
**********************************************************************
float genchi(float df)
Generate random value of CHIsquare variable
Function
Generates random deviate from the distribution of a chisquare
with DF degrees of freedom random variable.
Arguments
df --> Degrees of freedom of the chisquare
(Must be positive)
Method
Uses relation between chisquare and gamma.
**********************************************************************
*/
{
static float genchi;
if(!(df <= 0.0)) goto S10;
puts("DF <= 0 in GENCHI - ABORT");
printf("Value of DF: %16.6E\n",df);
exit(1);
S10:
genchi = 2.0*gengam(1.0,df/2.0);
return genchi;
}
float genexp(float av)
/*
**********************************************************************
float genexp(float av)
GENerate EXPonential random deviate
Function
Generates a single random deviate from an exponential
distribution with mean AV.
Arguments
av --> The mean of the exponential distribution from which
a random deviate is to be generated.
Method
Renames SEXPO from TOMS as slightly modified by BWB to use RANF
instead of SUNIF.
For details see:
Ahrens, J.H. and Dieter, U.
Computer Methods for Sampling From the
Exponential and Normal Distributions.
Comm. ACM, 15,10 (Oct. 1972), 873 - 882.
**********************************************************************
*/
{
static float genexp;
genexp = sexpo()*av;
return genexp;
}
float genf(float dfn,float dfd)
/*
**********************************************************************
float genf(float dfn,float dfd)
GENerate random deviate from the F distribution
Function
Generates a random deviate from the F (variance ratio)
distribution with DFN degrees of freedom in the numerator
and DFD degrees of freedom in the denominator.
Arguments
dfn --> Numerator degrees of freedom
(Must be positive)
dfd --> Denominator degrees of freedom
(Must be positive)
Method
Directly generates ratio of chisquare variates
**********************************************************************
*/
{
static float genf,xden,xnum;
if(!(dfn <= 0.0 || dfd <= 0.0)) goto S10;
puts("Degrees of freedom nonpositive in GENF - abort!");
printf("DFN value: %16.6EDFD value: %16.6E\n",dfn,dfd);
exit(1);
S10:
xnum = genchi(dfn)/dfn;
/*
GENF = ( GENCHI( DFN ) / DFN ) / ( GENCHI( DFD ) / DFD )
*/
xden = genchi(dfd)/dfd;
if(!(xden <= 9.999999999998E-39*xnum)) goto S20;
puts(" GENF - generated numbers would cause overflow");
printf(" Numerator %16.6E Denominator %16.6E\n",xnum,xden);
puts(" GENF returning 1.0E38");
genf = 1.0E38;
goto S30;
S20:
genf = xnum/xden;
S30:
return genf;
}
float gengam(float a,float r)
/*
**********************************************************************
float gengam(float a,float r)
GENerates random deviates from GAMma distribution
Function
Generates random deviates from the gamma distribution whose
density is
(A**R)/Gamma(R) * X**(R-1) * Exp(-A*X)
Arguments
a --> Location parameter of Gamma distribution
r --> Shape parameter of Gamma distribution
Method
Renames SGAMMA from TOMS as slightly modified by BWB to use RANF
instead of SUNIF.
For details see:
(Case R >= 1.0)
Ahrens, J.H. and Dieter, U.
Generating Gamma Variates by a
Modified Rejection Technique.
Comm. ACM, 25,1 (Jan. 1982), 47 - 54.
Algorithm GD
(Case 0.0 <= R <= 1.0)
Ahrens, J.H. and Dieter, U.
Computer Methods for Sampling from Gamma,
Beta, Poisson and Binomial Distributions.
Computing, 12 (1974), 223-246/
Adapted algorithm GS.
**********************************************************************
*/
{
static float gengam;
gengam = sgamma(r);
gengam /= a;
return gengam;
}
void genmn(float *parm,float *x,float *work)
/*
**********************************************************************
void genmn(float *parm,float *x,float *work)
GENerate Multivariate Normal random deviate
Arguments
parm --> Parameters needed to generate multivariate normal
deviates (MEANV and Cholesky decomposition of
COVM). Set by a previous call to SETGMN.
1 : 1 - size of deviate, P
2 : P + 1 - mean vector
P+2 : P*(P+3)/2 + 1 - upper half of cholesky
decomposition of cov matrix
x <-- Vector deviate generated.
work <--> Scratch array
Method
1) Generate P independent standard normal deviates - Ei ~ N(0,1)
2) Using Cholesky decomposition find A s.t. trans(A)*A = COVM
3) trans(A)E + MEANV ~ N(MEANV,COVM)
**********************************************************************
*/
{
static long i,icount,j,p,D1,D2,D3,D4;
static float ae;
p = (long) (*parm);
/*
Generate P independent normal deviates - WORK ~ N(0,1)
*/
for(i=1; i<=p; i++) *(work+i-1) = snorm();
for(i=1,D3=1,D4=(p-i+D3)/D3; D4>0; D4--,i+=D3) {
/*
PARM (P+2 : P*(P+3)/2 + 1) contains A, the Cholesky
decomposition of the desired covariance matrix.
trans(A)(1,1) = PARM(P+2)
trans(A)(2,1) = PARM(P+3)
trans(A)(2,2) = PARM(P+2+P)
trans(A)(3,1) = PARM(P+4)
trans(A)(3,2) = PARM(P+3+P)
trans(A)(3,3) = PARM(P+2-1+2P) ...
trans(A)*WORK + MEANV ~ N(MEANV,COVM)
*/
icount = 0;
ae = 0.0;
for(j=1,D1=1,D2=(i-j+D1)/D1; D2>0; D2--,j+=D1) {
icount += (j-1);
ae += (*(parm+i+(j-1)*p-icount+p)**(work+j-1));
}
*(x+i-1) = ae+*(parm+i);
}
}
float gennch(float df,float xnonc)
/*
**********************************************************************
float gennch(float df,float xnonc)
Generate random value of Noncentral CHIsquare variable
Function
Generates random deviate from the distribution of a noncentral
chisquare with DF degrees of freedom and noncentrality parameter
xnonc.
Arguments
df --> Degrees of freedom of the chisquare
(Must be > 1.0)
xnonc --> Noncentrality parameter of the chisquare
(Must be >= 0.0)
Method
Uses fact that noncentral chisquare is the sum of a chisquare
deviate with DF-1 degrees of freedom plus the square of a normal
deviate with mean XNONC and standard deviation 1.
**********************************************************************
*/
{
static float gennch;
if(!(df <= 1.0 || xnonc < 0.0)) goto S10;
puts("DF <= 1 or XNONC < 0 in GENNCH - ABORT");
printf("Value of DF: %16.6E Value of XNONC%16.6E\n",df,xnonc);
exit(1);
S10:
gennch = genchi(df-1.0)+pow(gennor(sqrt(xnonc),1.0),2.0);
return gennch;
}
float gennf(float dfn,float dfd,float xnonc)
/*
**********************************************************************
float gennf(float dfn,float dfd,float xnonc)
GENerate random deviate from the Noncentral F distribution
Function
Generates a random deviate from the noncentral F (variance ratio)
distribution with DFN degrees of freedom in the numerator, and DFD
degrees of freedom in the denominator, and noncentrality parameter
XNONC.
Arguments
dfn --> Numerator degrees of freedom
(Must be >= 1.0)
dfd --> Denominator degrees of freedom
(Must be positive)
xnonc --> Noncentrality parameter
(Must be nonnegative)
Method
Directly generates ratio of noncentral numerator chisquare variate
to central denominator chisquare variate.
**********************************************************************
*/
{
static float gennf,xden,xnum;
static long qcond;
qcond = dfn <= 1.0 || dfd <= 0.0 || xnonc < 0.0;
if(!qcond) goto S10;
puts("In GENNF - Either (1) Numerator DF <= 1.0 or");
puts("(2) Denominator DF < 0.0 or ");
puts("(3) Noncentrality parameter < 0.0");
printf("DFN value: %16.6EDFD value: %16.6EXNONC value: \n%16.6E\n",dfn,dfd,
xnonc);
exit(1);
S10:
xnum = gennch(dfn,xnonc)/dfn;
/*
GENNF = ( GENNCH( DFN, XNONC ) / DFN ) / ( GENCHI( DFD ) / DFD )
*/
xden = genchi(dfd)/dfd;
if(!(xden <= 9.999999999998E-39*xnum)) goto S20;
puts(" GENNF - generated numbers would cause overflow");
printf(" Numerator %16.6E Denominator %16.6E\n",xnum,xden);
puts(" GENNF returning 1.0E38");
gennf = 1.0E38;
goto S30;
S20:
gennf = xnum/xden;
S30:
return gennf;
}
float gennor(float av,float sd)
/*
**********************************************************************
float gennor(float av,float sd)
GENerate random deviate from a NORmal distribution
Function
Generates a single random deviate from a normal distribution
with mean, AV, and standard deviation, SD.
Arguments
av --> Mean of the normal distribution.
sd --> Standard deviation of the normal distribution.
Method
Renames SNORM from TOMS as slightly modified by BWB to use RANF
instead of SUNIF.
For details see:
Ahrens, J.H. and Dieter, U.
Extensions of Forsythe's Method for Random
Sampling from the Normal Distribution.
Math. Comput., 27,124 (Oct. 1973), 927 - 937.
**********************************************************************
*/
{
float gennor;
float tmp_f;
tmp_f = snorm();
gennor = sd*tmp_f+av;
return (gennor);
}
float capa_gennor(double *num_d, float av,float sd)
/*
**********************************************************************
float gennor(float av,float sd)
GENerate random deviate from a NORmal distribution
Function
Generates a single random deviate from a normal distribution
with mean, AV, and standard deviation, SD.
Arguments
av --> Mean of the normal distribution.
sd --> Standard deviation of the normal distribution.
Method
Renames SNORM from TOMS as slightly modified by BWB to use RANF
instead of SUNIF.
For details see:
Ahrens, J.H. and Dieter, U.
Extensions of Forsythe's Method for Random
Sampling from the Normal Distribution.
Math. Comput., 27,124 (Oct. 1973), 927 - 937.
**********************************************************************
*/
{
float gen_num;
float tmp_f;
tmp_f = snorm();
gen_num = sd*tmp_f+av;
/* printf("SNORM()=%f,GENNOR()=%f,%f*%f+%f\n",tmp_f,gen_num,sd,tmp_f,av); */
*num_d = (double)gen_num;
gen_num = (float)37.358341;
return (gen_num);
}
void genprm(long *iarray,int larray)
/*
**********************************************************************
void genprm(long *iarray,int larray)
GENerate random PeRMutation of iarray
Arguments
iarray <--> On output IARRAY is a random permutation of its
value on input
larray <--> Length of IARRAY
**********************************************************************
*/
{
static long i,itmp,iwhich,D1,D2;
for(i=1,D1=1,D2=(larray-i+D1)/D1; D2>0; D2--,i+=D1) {
iwhich = ignuin(i,larray);
itmp = *(iarray+iwhich-1);
*(iarray+iwhich-1) = *(iarray+i-1);
*(iarray+i-1) = itmp;
}
}
float genunf(float low,float high)
/*
**********************************************************************
float genunf(float low,float high)
GeNerate Uniform Real between LOW and HIGH
Function
Generates a real uniformly distributed between LOW and HIGH.
Arguments
low --> Low bound (exclusive) on real value to be generated
high --> High bound (exclusive) on real value to be generated
**********************************************************************
*/
{
static float genunf;
if(!(low > high)) goto S10;
printf("LOW > HIGH in GENUNF: LOW %16.6E HIGH: %16.6E\n",low,high);
puts("Abort");
exit(1);
S10:
genunf = low+(high-low)*ranf();
return genunf;
}
void gscgn(long getset,long *g)
/*
**********************************************************************
void gscgn(long getset,long *g)
Get/Set GeNerator
Gets or returns in G the number of the current generator
Arguments
getset --> 0 Get
1 Set
g <-- Number of the current random number generator (1..32)
**********************************************************************
*/
{
#define numg 32L
static long curntg = 1;
if(getset == 0) *g = curntg;
else {
if(*g < 0 || *g > numg) {
puts(" Generator number out of range in GSCGN");
exit(0);
}
curntg = *g;
}
#undef numg
}
void gsrgs(long getset,long *qvalue)
/*
**********************************************************************
void gsrgs(long getset,long *qvalue)
Get/Set Random Generators Set
Gets or sets whether random generators set (initialized).
Initially (data statement) state is not set
If getset is 1 state is set to qvalue
If getset is 0 state returned in qvalue
**********************************************************************
*/
{
static long qinit = 0;
if(getset == 0) *qvalue = qinit;
else qinit = *qvalue;
}
void gssst(long getset,long *qset)
/*
**********************************************************************
void gssst(long getset,long *qset)
Get or Set whether Seed is Set
Initialize to Seed not Set
If getset is 1 sets state to Seed Set
If getset is 0 returns T in qset if Seed Set
Else returns F in qset
**********************************************************************
*/
{
static long qstate = 0;
if(getset != 0) qstate = 1;
else *qset = qstate;
}
long ignbin(long n,float pp)
/*
**********************************************************************
long ignbin(long n,float pp)
GENerate BINomial random deviate
Function
Generates a single random deviate from a binomial
distribution whose number of trials is N and whose
probability of an event in each trial is P.
Arguments
n --> The number of trials in the binomial distribution
from which a random deviate is to be generated.
p --> The probability of an event in each trial of the
binomial distribution from which a random deviate
is to be generated.
ignbin <-- A random deviate yielding the number of events
from N independent trials, each of which has
a probability of event P.
Method
This is algorithm BTPE from:
Kachitvichyanukul, V. and Schmeiser, B. W.
Binomial Random Variate Generation.
Communications of the ACM, 31, 2
(February, 1988) 216.
**********************************************************************
SUBROUTINE BTPEC(N,PP,ISEED,JX)
BINOMIAL RANDOM VARIATE GENERATOR
MEAN .LT. 30 -- INVERSE CDF
MEAN .GE. 30 -- ALGORITHM BTPE: ACCEPTANCE-REJECTION VIA
FOUR REGION COMPOSITION. THE FOUR REGIONS ARE A TRIANGLE
(SYMMETRIC IN THE CENTER), A PAIR OF PARALLELOGRAMS (ABOVE
THE TRIANGLE), AND EXPONENTIAL LEFT AND RIGHT TAILS.
BTPE REFERS TO BINOMIAL-TRIANGLE-PARALLELOGRAM-EXPONENTIAL.
BTPEC REFERS TO BTPE AND "COMBINED." THUS BTPE IS THE
RESEARCH AND BTPEC IS THE IMPLEMENTATION OF A COMPLETE
USABLE ALGORITHM.
REFERENCE: VORATAS KACHITVICHYANUKUL AND BRUCE SCHMEISER,
"BINOMIAL RANDOM VARIATE GENERATION,"
COMMUNICATIONS OF THE ACM, FORTHCOMING
WRITTEN: SEPTEMBER 1980.
LAST REVISED: MAY 1985, JULY 1987
REQUIRED SUBPROGRAM: RAND() -- A UNIFORM (0,1) RANDOM NUMBER
GENERATOR
ARGUMENTS
N : NUMBER OF BERNOULLI TRIALS (INPUT)
PP : PROBABILITY OF SUCCESS IN EACH TRIAL (INPUT)
ISEED: RANDOM NUMBER SEED (INPUT AND OUTPUT)
JX: RANDOMLY GENERATED OBSERVATION (OUTPUT)
VARIABLES
PSAVE: VALUE OF PP FROM THE LAST CALL TO BTPEC
NSAVE: VALUE OF N FROM THE LAST CALL TO BTPEC
XNP: VALUE OF THE MEAN FROM THE LAST CALL TO BTPEC
P: PROBABILITY USED IN THE GENERATION PHASE OF BTPEC
FFM: TEMPORARY VARIABLE EQUAL TO XNP + P
M: INTEGER VALUE OF THE CURRENT MODE
FM: FLOATING POINT VALUE OF THE CURRENT MODE
XNPQ: TEMPORARY VARIABLE USED IN SETUP AND SQUEEZING STEPS
P1: AREA OF THE TRIANGLE
C: HEIGHT OF THE PARALLELOGRAMS
XM: CENTER OF THE TRIANGLE
XL: LEFT END OF THE TRIANGLE
XR: RIGHT END OF THE TRIANGLE
AL: TEMPORARY VARIABLE
XLL: RATE FOR THE LEFT EXPONENTIAL TAIL
XLR: RATE FOR THE RIGHT EXPONENTIAL TAIL
P2: AREA OF THE PARALLELOGRAMS
P3: AREA OF THE LEFT EXPONENTIAL TAIL
P4: AREA OF THE RIGHT EXPONENTIAL TAIL
U: A U(0,P4) RANDOM VARIATE USED FIRST TO SELECT ONE OF THE
FOUR REGIONS AND THEN CONDITIONALLY TO GENERATE A VALUE
FROM THE REGION
V: A U(0,1) RANDOM NUMBER USED TO GENERATE THE RANDOM VALUE
(REGION 1) OR TRANSFORMED INTO THE VARIATE TO ACCEPT OR
REJECT THE CANDIDATE VALUE
IX: INTEGER CANDIDATE VALUE
X: PRELIMINARY CONTINUOUS CANDIDATE VALUE IN REGION 2 LOGIC
AND A FLOATING POINT IX IN THE ACCEPT/REJECT LOGIC
K: ABSOLUTE VALUE OF (IX-M)
F: THE HEIGHT OF THE SCALED DENSITY FUNCTION USED IN THE
ACCEPT/REJECT DECISION WHEN BOTH M AND IX ARE SMALL
ALSO USED IN THE INVERSE TRANSFORMATION
R: THE RATIO P/Q
G: CONSTANT USED IN CALCULATION OF PROBABILITY
MP: MODE PLUS ONE, THE LOWER INDEX FOR EXPLICIT CALCULATION
OF F WHEN IX IS GREATER THAN M
IX1: CANDIDATE VALUE PLUS ONE, THE LOWER INDEX FOR EXPLICIT
CALCULATION OF F WHEN IX IS LESS THAN M
I: INDEX FOR EXPLICIT CALCULATION OF F FOR BTPE
AMAXP: MAXIMUM ERROR OF THE LOGARITHM OF NORMAL BOUND
YNORM: LOGARITHM OF NORMAL BOUND
ALV: NATURAL LOGARITHM OF THE ACCEPT/REJECT VARIATE V
X1,F1,Z,W,Z2,X2,F2, AND W2 ARE TEMPORARY VARIABLES TO BE
USED IN THE FINAL ACCEPT/REJECT TEST
QN: PROBABILITY OF NO SUCCESS IN N TRIALS
REMARK
IX AND JX COULD LOGICALLY BE THE SAME VARIABLE, WHICH WOULD
SAVE A MEMORY POSITION AND A LINE OF CODE. HOWEVER, SOME
COMPILERS (E.G.,CDC MNF) OPTIMIZE BETTER WHEN THE ARGUMENTS
ARE NOT INVOLVED.
ISEED NEEDS TO BE DOUBLE PRECISION IF THE IMSL ROUTINE
GGUBFS IS USED TO GENERATE UNIFORM RANDOM NUMBER, OTHERWISE
TYPE OF ISEED SHOULD BE DICTATED BY THE UNIFORM GENERATOR
**********************************************************************
*****DETERMINE APPROPRIATE ALGORITHM AND WHETHER SETUP IS NECESSARY
*/
{
static float psave = -1.0;
static long nsave = -1;
static long ignbin,i,ix,ix1,k,m,mp,T1;
static float al,alv,amaxp,c,f,f1,f2,ffm,fm,g,p,p1,p2,p3,p4,q,qn,r,u,v,w,w2,x,x1,
x2,xl,xll,xlr,xm,xnp,xnpq,xr,ynorm,z,z2;
if(pp != psave) goto S10;
if(n != nsave) goto S20;
if(xnp < 30.0) goto S150;
goto S30;
S10:
/*
*****SETUP, PERFORM ONLY WHEN PARAMETERS CHANGE
*/
psave = pp;
p = min(psave,1.0-psave);
q = 1.0-p;
S20:
xnp = n*p;
nsave = n;
if(xnp < 30.0) goto S140;
ffm = xnp+p;
m = ffm;
fm = m;
xnpq = xnp*q;
p1 = (long) (2.195*sqrt(xnpq)-4.6*q)+0.5;
xm = fm+0.5;
xl = xm-p1;
xr = xm+p1;
c = 0.134+20.5/(15.3+fm);
al = (ffm-xl)/(ffm-xl*p);
xll = al*(1.0+0.5*al);
al = (xr-ffm)/(xr*q);
xlr = al*(1.0+0.5*al);
p2 = p1*(1.0+c+c);
p3 = p2+c/xll;
p4 = p3+c/xlr;
S30:
/*
*****GENERATE VARIATE
*/
u = ranf()*p4;
v = ranf();
/*
TRIANGULAR REGION
*/
if(u > p1) goto S40;
ix = xm-p1*v+u;
goto S170;
S40:
/*
PARALLELOGRAM REGION
*/
if(u > p2) goto S50;
x = xl+(u-p1)/c;
v = v*c+1.0-abs(xm-x)/p1;
if(v > 1.0 || v <= 0.0) goto S30;
ix = x;
goto S70;
S50:
/*
LEFT TAIL
*/
if(u > p3) goto S60;
ix = xl+log(v)/xll;
if(ix < 0) goto S30;
v *= ((u-p2)*xll);
goto S70;
S60:
/*
RIGHT TAIL
*/
ix = xr-log(v)/xlr;
if(ix > n) goto S30;
v *= ((u-p3)*xlr);
S70:
/*
*****DETERMINE APPROPRIATE WAY TO PERFORM ACCEPT/REJECT TEST
*/
k = abs(ix-m);
if(k > 20 && k < xnpq/2-1) goto S130;
/*
EXPLICIT EVALUATION
*/
f = 1.0;
r = p/q;
g = (n+1)*r;
T1 = m-ix;
if(T1 < 0) goto S80;
else if(T1 == 0) goto S120;
else goto S100;
S80:
mp = m+1;
for(i=mp; i<=ix; i++) f *= (g/i-r);
goto S120;
S100:
ix1 = ix+1;
for(i=ix1; i<=m; i++) f /= (g/i-r);
S120:
if(v <= f) goto S170;
goto S30;
S130:
/*
SQUEEZING USING UPPER AND LOWER BOUNDS ON ALOG(F(X))
*/
amaxp = k/xnpq*((k*(k/3.0+0.625)+0.1666666666666)/xnpq+0.5);
ynorm = -(k*k/(2.0*xnpq));
alv = log(v);
if(alv < ynorm-amaxp) goto S170;
if(alv > ynorm+amaxp) goto S30;
/*
STIRLING'S FORMULA TO MACHINE ACCURACY FOR
THE FINAL ACCEPTANCE/REJECTION TEST
*/
x1 = ix+1.0;
f1 = fm+1.0;
z = n+1.0-fm;
w = n-ix+1.0;
z2 = z*z;
x2 = x1*x1;
f2 = f1*f1;
w2 = w*w;
if(alv <= xm*log(f1/x1)+(n-m+0.5)*log(z/w)+(ix-m)*log(w*p/(x1*q))+(13860.0-
(462.0-(132.0-(99.0-140.0/f2)/f2)/f2)/f2)/f1/166320.0+(13860.0-(462.0-
(132.0-(99.0-140.0/z2)/z2)/z2)/z2)/z/166320.0+(13860.0-(462.0-(132.0-
(99.0-140.0/x2)/x2)/x2)/x2)/x1/166320.0+(13860.0-(462.0-(132.0-(99.0
-140.0/w2)/w2)/w2)/w2)/w/166320.0) goto S170;
goto S30;
S140:
/*
INVERSE CDF LOGIC FOR MEAN LESS THAN 30
*/
qn = pow(q,(double)n);
r = p/q;
g = r*(n+1);
S150:
ix = 0;
f = qn;
u = ranf();
S160:
if(u < f) goto S170;
if(ix > 110) goto S150;
u -= f;
ix += 1;
f *= (g/ix-r);
goto S160;
S170:
if(psave > 0.5) ix = n-ix;
ignbin = ix;
return ignbin;
}
long ignpoi(float mu)
/*
**********************************************************************
long ignpoi(float mu)
GENerate POIsson random deviate
Function
Generates a single random deviate from a Poisson
distribution with mean AV.
Arguments
av --> The mean of the Poisson distribution from which
a random deviate is to be generated.
genexp <-- The random deviate.
Method
Renames KPOIS from TOMS as slightly modified by BWB to use RANF
instead of SUNIF.
For details see:
Ahrens, J.H. and Dieter, U.
Computer Generation of Poisson Deviates
From Modified Normal Distributions.
ACM Trans. Math. Software, 8, 2
(June 1982),163-179
**********************************************************************
**********************************************************************
P O I S S O N DISTRIBUTION
**********************************************************************
**********************************************************************
FOR DETAILS SEE:
AHRENS, J.H. AND DIETER, U.
COMPUTER GENERATION OF POISSON DEVIATES
FROM MODIFIED NORMAL DISTRIBUTIONS.
ACM TRANS. MATH. SOFTWARE, 8,2 (JUNE 1982), 163 - 179.
(SLIGHTLY MODIFIED VERSION OF THE PROGRAM IN THE ABOVE ARTICLE)
**********************************************************************
INTEGER FUNCTION IGNPOI(IR,MU)
INPUT: IR=CURRENT STATE OF BASIC RANDOM NUMBER GENERATOR
MU=MEAN MU OF THE POISSON DISTRIBUTION
OUTPUT: IGNPOI=SAMPLE FROM THE POISSON-(MU)-DISTRIBUTION
MUPREV=PREVIOUS MU, MUOLD=MU AT LAST EXECUTION OF STEP P OR B.
TABLES: COEFFICIENTS A0-A7 FOR STEP F. FACTORIALS FACT
COEFFICIENTS A(K) - FOR PX = FK*V*V*SUM(A(K)*V**K)-DEL
SEPARATION OF CASES A AND B
*/
{
extern float fsign( float num, float sign );
static float a0 = -0.5;
static float a1 = 0.3333333;
static float a2 = -0.2500068;
static float a3 = 0.2000118;
static float a4 = -0.1661269;
static float a5 = 0.1421878;
static float a6 = -0.1384794;
static float a7 = 0.125006;
static float muold = 0.0;
static float muprev = 0.0;
static float fact[10] = {
1.0,1.0,2.0,6.0,24.0,120.0,720.0,5040.0,40320.0,362880.0
};
static long ignpoi,j,k,kflag,l,m;
static float b1,b2,c,c0,c1,c2,c3,d,del,difmuk,e,fk,fx,fy,g,omega,p,p0,px,py,q,s,
t,u,v,x,xx,pp[35];
if(mu == muprev) goto S10;
if(mu < 10.0) goto S120;
/*
C A S E A. (RECALCULATION OF S,D,L IF MU HAS CHANGED)
*/
muprev = mu;
s = sqrt(mu);
d = 6.0*mu*mu;
/*
THE POISSON PROBABILITIES PK EXCEED THE DISCRETE NORMAL
PROBABILITIES FK WHENEVER K >= M(MU). L=IFIX(MU-1.1484)
IS AN UPPER BOUND TO M(MU) FOR ALL MU >= 10 .
*/
l = (long) (mu-1.1484);
S10:
/*
STEP N. NORMAL SAMPLE - SNORM(IR) FOR STANDARD NORMAL DEVIATE
*/
g = mu+s*snorm();
if(g < 0.0) goto S20;
ignpoi = (long) (g);
/*
STEP I. IMMEDIATE ACCEPTANCE IF IGNPOI IS LARGE ENOUGH
*/
if(ignpoi >= l) return ignpoi;
/*
STEP S. SQUEEZE ACCEPTANCE - SUNIF(IR) FOR (0,1)-SAMPLE U
*/
fk = (float)ignpoi;
difmuk = mu-fk;
u = ranf();
if(d*u >= difmuk*difmuk*difmuk) return ignpoi;
S20:
/*
STEP P. PREPARATIONS FOR STEPS Q AND H.
(RECALCULATIONS OF PARAMETERS IF NECESSARY)
.3989423=(2*PI)**(-.5) .416667E-1=1./24. .1428571=1./7.
THE QUANTITIES B1, B2, C3, C2, C1, C0 ARE FOR THE HERMITE
APPROXIMATIONS TO THE DISCRETE NORMAL PROBABILITIES FK.
C=.1069/MU GUARANTEES MAJORIZATION BY THE 'HAT'-FUNCTION.
*/
if(mu == muold) goto S30;
muold = mu;
omega = 0.3989423/s;
b1 = 4.166667E-2/mu;
b2 = 0.3*b1*b1;
c3 = 0.1428571*b1*b2;
c2 = b2-15.0*c3;
c1 = b1-6.0*b2+45.0*c3;
c0 = 1.0-b1+3.0*b2-15.0*c3;
c = 0.1069/mu;
S30:
if(g < 0.0) goto S50;
/*
'SUBROUTINE' F IS CALLED (KFLAG=0 FOR CORRECT RETURN)
*/
kflag = 0;
goto S70;
S40:
/*
STEP Q. QUOTIENT ACCEPTANCE (RARE CASE)
*/
if(fy-u*fy <= py*exp(px-fx)) return ignpoi;
S50:
/*
STEP E. EXPONENTIAL SAMPLE - SEXPO(IR) FOR STANDARD EXPONENTIAL
DEVIATE E AND SAMPLE T FROM THE LAPLACE 'HAT'
(IF T <= -.6744 THEN PK < FK FOR ALL MU >= 10.)
*/
e = sexpo();
u = ranf();
u += (u-1.0);
t = 1.8+fsign(e,u);
if(t <= -0.6744) goto S50;
ignpoi = (long) (mu+s*t);
fk = (float)ignpoi;
difmuk = mu-fk;
/*
'SUBROUTINE' F IS CALLED (KFLAG=1 FOR CORRECT RETURN)
*/
kflag = 1;
goto S70;
S60:
/*
STEP H. HAT ACCEPTANCE (E IS REPEATED ON REJECTION)
*/
if(c*fabs(u) > py*exp(px+e)-fy*exp(fx+e)) goto S50;
return ignpoi;
S70:
/*
STEP F. 'SUBROUTINE' F. CALCULATION OF PX,PY,FX,FY.
CASE IGNPOI .LT. 10 USES FACTORIALS FROM TABLE FACT
*/
if(ignpoi >= 10) goto S80;
px = -mu;
py = pow(mu,(double)ignpoi)/ *(fact+ignpoi);
goto S110;
S80:
/*
CASE IGNPOI .GE. 10 USES POLYNOMIAL APPROXIMATION
A0-A7 FOR ACCURACY WHEN ADVISABLE
.8333333E-1=1./12. .3989423=(2*PI)**(-.5)
*/
del = 8.333333E-2/fk;
del -= (4.8*del*del*del);
v = difmuk/fk;
if(fabs(v) <= 0.25) goto S90;
px = fk*log(1.0+v)-difmuk-del;
goto S100;
S90:
px = fk*v*v*(((((((a7*v+a6)*v+a5)*v+a4)*v+a3)*v+a2)*v+a1)*v+a0)-del;
S100:
py = 0.3989423/sqrt(fk);
S110:
x = (0.5-difmuk)/s;
xx = x*x;
fx = -0.5*xx;
fy = omega*(((c3*xx+c2)*xx+c1)*xx+c0);
if(kflag <= 0) goto S40;
goto S60;
S120:
/*
C A S E B. (START NEW TABLE AND CALCULATE P0 IF NECESSARY)
*/
muprev = 0.0;
if(mu == muold) goto S130;
muold = mu;
m = max(1L,(long) (mu));
l = 0;
p = exp(-mu);
q = p0 = p;
S130:
/*
STEP U. UNIFORM SAMPLE FOR INVERSION METHOD
*/
u = ranf();
ignpoi = 0;
if(u <= p0) return ignpoi;
/*
STEP T. TABLE COMPARISON UNTIL THE END PP(L) OF THE
PP-TABLE OF CUMULATIVE POISSON PROBABILITIES
(0.458=PP(9) FOR MU=10)
*/
if(l == 0) goto S150;
j = 1;
if(u > 0.458) j = min(l,m);
for(k=j; k<=l; k++) {
if(u <= *(pp+k-1)) goto S180;
}
if(l == 35) goto S130;
S150:
/*
STEP C. CREATION OF NEW POISSON PROBABILITIES P
AND THEIR CUMULATIVES Q=PP(K)
*/
l += 1;
for(k=l; k<=35; k++) {
p = p*mu/(float)k;
q += p;
*(pp+k-1) = q;
if(u <= q) goto S170;
}
l = 35;
goto S130;
S170:
l = k;
S180:
ignpoi = k;
return ignpoi;
}
long ignuin(long low,long high)
/*
**********************************************************************
long ignuin(long low,long high)
GeNerate Uniform INteger
Function
Generates an integer uniformly distributed between LOW and HIGH.
Arguments
low --> Low bound (inclusive) on integer value to be generated
high --> High bound (inclusive) on integer value to be generated
Note
If (HIGH-LOW) > 2,147,483,561 prints error message on * unit and
stops the program.
**********************************************************************
IGNLGI generates integers between 1 and 2147483562
MAXNUM is 1 less than maximum generable value
*/
{
#define maxnum 2147483561L
static long ignuin,ign,maxnow,range,ranp1;
if(!(low > high)) goto S10;
puts(" low > high in ignuin - ABORT");
exit(1);
S10:
range = high-low;
if(!(range > maxnum)) goto S20;
puts(" high - low too large in ignuin - ABORT");
exit(1);
S20:
if(!(low == high)) goto S30;
ignuin = low;
return ignuin;
S30:
/*
Number to be generated should be in range 0..RANGE
Set MAXNOW so that the number of integers in 0..MAXNOW is an
integral multiple of the number in 0..RANGE
*/
ranp1 = range+1;
maxnow = maxnum/ranp1*ranp1;
S40:
ign = ignlgi()-1;
if(!(ign <= maxnow)) goto S50;
ignuin = low+ign%ranp1;
return ignuin;
S50:
goto S40;
#undef maxnum
#undef err1
#undef err2
}
long lennob( char *str )
/*
Returns the length of str ignoring trailing blanks but not
other white space.
*/
{
long i, i_nb;
for (i=0, i_nb= -1L; *(str+i); i++)
if ( *(str+i) != ' ' ) i_nb = i;
return (i_nb+1);
}
long mltmod(long a,long s,long m)
/*
**********************************************************************
long mltmod(long a,long s,long m)
Returns (A*S) MOD M
This is a transcription from Pascal to Fortran of routine
MULtMod_Decompos from the paper
L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package
with Splitting Facilities." ACM Transactions on Mathematical
Software, 17:98-111 (1991)
Arguments
a, s, m -->
**********************************************************************
*/
{
#define h 32768L
static long mltmod,a0,a1,k,p,q,qh,rh;
/*
H = 2**((b-2)/2) where b = 32 because we are using a 32 bit
machine. On a different machine recompute H
*/
if(!(a <= 0 || a >= m || s <= 0 || s >= m)) goto S10;
puts(" a, m, s out of order in mltmod - ABORT!");
printf(" a = %12ld s = %12ld m = %12ld\n",a,s,m);
puts(" mltmod requires: 0 < a < m; 0 < s < m");
exit(1);
S10:
if(!(a < h)) goto S20;
a0 = a;
p = 0;
goto S120;
S20:
a1 = a/h;
a0 = a-h*a1;
qh = m/h;
rh = m-h*qh;
if(!(a1 >= h)) goto S50;
a1 -= h;
k = s/qh;
p = h*(s-k*qh)-k*rh;
S30:
if(!(p < 0)) goto S40;
p += m;
goto S30;
S40:
goto S60;
S50:
p = 0;
S60:
/*
P = (A2*S*H)MOD M
*/
if(!(a1 != 0)) goto S90;
q = m/a1;
k = s/q;
p -= (k*(m-a1*q));
if(p > 0) p -= m;
p += (a1*(s-k*q));
S70:
if(!(p < 0)) goto S80;
p += m;
goto S70;
S90:
S80:
k = p/qh;
/*
P = ((A2*H + A1)*S)MOD M
*/
p = h*(p-k*qh)-k*rh;
S100:
if(!(p < 0)) goto S110;
p += m;
goto S100;
S120:
S110:
if(!(a0 != 0)) goto S150;
/*
P = ((A2*H + A1)*H*S)MOD M
*/
q = m/a0;
k = s/q;
p -= (k*(m-a0*q));
if(p > 0) p -= m;
p += (a0*(s-k*q));
S130:
if(!(p < 0)) goto S140;
p += m;
goto S130;
S150:
S140:
mltmod = p;
return mltmod;
#undef h
}
void phrtsd(char* phrase,long *seed1,long *seed2)
/*
**********************************************************************
void phrtsd(char* phrase,long *seed1,long *seed2)
PHRase To SeeDs
Function
Uses a phrase (character string) to generate two seeds for the RGN
random number generator.
Arguments
phrase --> Phrase to be used for random number generation
seed1 <-- First seed for generator
seed2 <-- Second seed for generator
Note
Trailing blanks are eliminated before the seeds are generated.
Generated seed values will fall in the range 1..2^30
(1..1,073,741,824)
**********************************************************************
*/
{
static char table[] =
"abcdefghijklmnopqrstuvwxyz\
ABCDEFGHIJKLMNOPQRSTUVWXYZ\
0123456789\
!@#$%^&*()_+[];:'\\\"<>?,./";
long ix;
static long twop30 = 1073741824L;
static long shift[5] = {
1L,64L,4096L,262144L,16777216L
};
static long i,ichr,j,lphr,values[5];
extern long lennob(char *str);
*seed1 = 1234567890L;
*seed2 = 123456789L;
lphr = lennob(phrase);
if(lphr < 1) return;
for(i=0; i<=(lphr-1); i++) {
for (ix=0; table[ix]; ix++) if (*(phrase+i) == table[ix]) break;
if (!table[ix]) ix = 0;
ichr = ix % 64;
if(ichr == 0) ichr = 63;
for(j=1; j<=5; j++) {
*(values+j-1) = ichr-j;
if(*(values+j-1) < 1) *(values+j-1) += 63;
}
for(j=1; j<=5; j++) {
*seed1 = ( *seed1+*(shift+j-1)**(values+j-1) ) % twop30;
*seed2 = ( *seed2+*(shift+j-1)**(values+6-j-1) ) % twop30;
}
}
#undef twop30
}
float ranf(void)
/*
**********************************************************************
float ranf(void)
RANDom number generator as a Function
Returns a random floating point number from a uniform distribution
over 0 - 1 (endpoints of this interval are not returned) using the
current generator
This is a transcription from Pascal to Fortran of routine
Uniform_01 from the paper
L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package
with Splitting Facilities." ACM Transactions on Mathematical
Software, 17:98-111 (1991)
**********************************************************************
*/
{
static float ranf;
long tmp_l;
double tmp_d;
/*
4.656613057E-10 is 1/M1 M1 is set in a data statement in IGNLGI
and is currently 2147483563. If M1 changes, change this also.
*/
tmp_l = ignlgi();
tmp_d = (double)tmp_l * (double)4.656613057E-10;
ranf = (float)tmp_d;
/* printf("RANF()=%f\n",ranf); */
return ranf;
}
float capa_ranf(void)
/*
**********************************************************************
float ranf(void)
RANDom number generator as a Function
Returns a random floating point number from a uniform distribution
over 0 - 1 (endpoints of this interval are not returned) using the
current generator
This is a transcription from Pascal to Fortran of routine
Uniform_01 from the paper
L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package
with Splitting Facilities." ACM Transactions on Mathematical
Software, 17:98-111 (1991)
**********************************************************************
*/
{
float ran_f;
long my_ran;
double my_doub;
/*
4.656613057E-10 is 1/M1 M1 is set in a data statement in IGNLGI
and is currently 2147483563. If M1 changes, change this also.
*/
my_ran = ignlgi();
/* printf("MY_ignlgi=%ld -- first time\n",my_ran); */
/* ran_f = my_ran * 4.656613057E-10; */
my_doub = (double)my_ran * (double)4.656613057E-10;
printf("MY_ranf in double=%.15g -- first time\n",my_doub);
ran_f = (float)my_doub;
return (ran_f);
}
void setgmn(float *meanv,float *covm,long p,float *parm)
/*
**********************************************************************
void setgmn(float *meanv,float *covm,long p,float *parm)
SET Generate Multivariate Normal random deviate
Function
Places P, MEANV, and the Cholesky factoriztion of COVM
in GENMN.
Arguments
meanv --> Mean vector of multivariate normal distribution.
covm <--> (Input) Covariance matrix of the multivariate
normal distribution
(Output) Destroyed on output
p --> Dimension of the normal, or length of MEANV.
parm <-- Array of parameters needed to generate multivariate norma
deviates (P, MEANV and Cholesky decomposition of
COVM).
1 : 1 - P
2 : P + 1 - MEANV
P+2 : P*(P+3)/2 + 1 - Cholesky decomposition of COVM
Needed dimension is (p*(p+3)/2 + 1)
**********************************************************************
*/
{
extern void spofa(float *a,long lda,long n,long *info);
static long T1;
static long i,icount,info,j,D2,D3,D4,D5;
T1 = p*(p+3)/2+1;
/*
TEST THE INPUT
*/
if(!(p <= 0)) goto S10;
puts("P nonpositive in SETGMN");
printf("Value of P: %12ld\n",p);
exit(1);
S10:
*parm = p;
/*
PUT P AND MEANV INTO PARM
*/
for(i=2,D2=1,D3=(p+1-i+D2)/D2; D3>0; D3--,i+=D2) *(parm+i-1) = *(meanv+i-2);
/*
Cholesky decomposition to find A s.t. trans(A)*(A) = COVM
*/
spofa(covm,p,p,&info);
if(!(info != 0)) goto S30;
puts(" COVM not positive definite in SETGMN");
exit(1);
S30:
icount = p+1;
/*
PUT UPPER HALF OF A, WHICH IS NOW THE CHOLESKY FACTOR, INTO PARM
COVM(1,1) = PARM(P+2)
COVM(1,2) = PARM(P+3)
:
COVM(1,P) = PARM(2P+1)
COVM(2,2) = PARM(2P+2) ...
*/
for(i=1,D4=1,D5=(p-i+D4)/D4; D5>0; D5--,i+=D4) {
for(j=i-1; j<p; j++) {
icount += 1;
*(parm+icount-1) = *(covm+i-1+j*p);
}
}
}
float sexpo(void)
/*
**********************************************************************
(STANDARD-) E X P O N E N T I A L DISTRIBUTION
**********************************************************************
**********************************************************************
FOR DETAILS SEE:
AHRENS, J.H. AND DIETER, U.
COMPUTER METHODS FOR SAMPLING FROM THE
EXPONENTIAL AND NORMAL DISTRIBUTIONS.
COMM. ACM, 15,10 (OCT. 1972), 873 - 882.
ALL STATEMENT NUMBERS CORRESPOND TO THE STEPS OF ALGORITHM
'SA' IN THE ABOVE PAPER (SLIGHTLY MODIFIED IMPLEMENTATION)
Modified by Barry W. Brown, Feb 3, 1988 to use RANF instead of
SUNIF. The argument IR thus goes away.
**********************************************************************
Q(N) = SUM(ALOG(2.0)**K/K!) K=1,..,N , THE HIGHEST N
(HERE 8) IS DETERMINED BY Q(N)=1.0 WITHIN STANDARD PRECISION
*/
{
static float q[8] = {
0.6931472,0.9333737,0.9888778,0.9984959,0.9998293,0.9999833,0.9999986,1.0
};
static long i;
static float sexpo,a,u,ustar,umin;
static float *q1 = q;
a = 0.0;
u = ranf();
goto S30;
S20:
a += *q1;
S30:
u += u;
if(u <= 1.0) goto S20;
u -= 1.0;
if(u > *q1) goto S60;
sexpo = a+u;
return sexpo;
S60:
i = 1;
ustar = ranf();
umin = ustar;
S70:
ustar = ranf();
if(ustar < umin) umin = ustar;
i += 1;
if(u > *(q+i-1)) goto S70;
sexpo = a+umin**q1;
return sexpo;
}
float sgamma(float a)
/*
**********************************************************************
(STANDARD-) G A M M A DISTRIBUTION
**********************************************************************
**********************************************************************
PARAMETER A >= 1.0 !
**********************************************************************
FOR DETAILS SEE:
AHRENS, J.H. AND DIETER, U.
GENERATING GAMMA VARIATES BY A
MODIFIED REJECTION TECHNIQUE.
COMM. ACM, 25,1 (JAN. 1982), 47 - 54.
STEP NUMBERS CORRESPOND TO ALGORITHM 'GD' IN THE ABOVE PAPER
(STRAIGHTFORWARD IMPLEMENTATION)
Modified by Barry W. Brown, Feb 3, 1988 to use RANF instead of
SUNIF. The argument IR thus goes away.
**********************************************************************
PARAMETER 0.0 < A < 1.0 !
**********************************************************************
FOR DETAILS SEE:
AHRENS, J.H. AND DIETER, U.
COMPUTER METHODS FOR SAMPLING FROM GAMMA,
BETA, POISSON AND BINOMIAL DISTRIBUTIONS.
COMPUTING, 12 (1974), 223 - 246.
(ADAPTED IMPLEMENTATION OF ALGORITHM 'GS' IN THE ABOVE PAPER)
**********************************************************************
INPUT: A =PARAMETER (MEAN) OF THE STANDARD GAMMA DISTRIBUTION
OUTPUT: SGAMMA = SAMPLE FROM THE GAMMA-(A)-DISTRIBUTION
COEFFICIENTS Q(K) - FOR Q0 = SUM(Q(K)*A**(-K))
COEFFICIENTS A(K) - FOR Q = Q0+(T*T/2)*SUM(A(K)*V**K)
COEFFICIENTS E(K) - FOR EXP(Q)-1 = SUM(E(K)*Q**K)
PREVIOUS A PRE-SET TO ZERO - AA IS A', AAA IS A"
SQRT32 IS THE SQUAREROOT OF 32 = 5.656854249492380
*/
{
extern float fsign( float num, float sign );
static float q1 = 4.166669E-2;
static float q2 = 2.083148E-2;
static float q3 = 8.01191E-3;
static float q4 = 1.44121E-3;
static float q5 = -7.388E-5;
static float q6 = 2.4511E-4;
static float q7 = 2.424E-4;
static float a1 = 0.3333333;
static float a2 = -0.250003;
static float a3 = 0.2000062;
static float a4 = -0.1662921;
static float a5 = 0.1423657;
static float a6 = -0.1367177;
static float a7 = 0.1233795;
static float e1 = 1.0;
static float e2 = 0.4999897;
static float e3 = 0.166829;
static float e4 = 4.07753E-2;
static float e5 = 1.0293E-2;
static float aa = 0.0;
static float aaa = 0.0;
static float sqrt32 = 5.656854;
static float sgamma,s2,s,d,t,x,u,r,q0,b,si,c,v,q,e,w,p;
if(a == aa) goto S10;
if(a < 1.0) goto S120;
/*
STEP 1: RECALCULATIONS OF S2,S,D IF A HAS CHANGED
*/
aa = a;
s2 = a-0.5;
s = sqrt(s2);
d = sqrt32-12.0*s;
S10:
/*
STEP 2: T=STANDARD NORMAL DEVIATE,
X=(S,1/2)-NORMAL DEVIATE.
IMMEDIATE ACCEPTANCE (I)
*/
t = snorm();
x = s+0.5*t;
sgamma = x*x;
if(t >= 0.0) return sgamma;
/*
STEP 3: U= 0,1 -UNIFORM SAMPLE. SQUEEZE ACCEPTANCE (S)
*/
u = ranf();
if(d*u <= t*t*t) return sgamma;
/*
STEP 4: RECALCULATIONS OF Q0,B,SI,C IF NECESSARY
*/
if(a == aaa) goto S40;
aaa = a;
r = 1.0/ a;
q0 = ((((((q7*r+q6)*r+q5)*r+q4)*r+q3)*r+q2)*r+q1)*r;
/*
APPROXIMATION DEPENDING ON SIZE OF PARAMETER A
THE CONSTANTS IN THE EXPRESSIONS FOR B, SI AND
C WERE ESTABLISHED BY NUMERICAL EXPERIMENTS
*/
if(a <= 3.686) goto S30;
if(a <= 13.022) goto S20;
/*
CASE 3: A .GT. 13.022
*/
b = 1.77;
si = 0.75;
c = 0.1515/s;
goto S40;
S20:
/*
CASE 2: 3.686 .LT. A .LE. 13.022
*/
b = 1.654+7.6E-3*s2;
si = 1.68/s+0.275;
c = 6.2E-2/s+2.4E-2;
goto S40;
S30:
/*
CASE 1: A .LE. 3.686
*/
b = 0.463+s-0.178*s2;
si = 1.235;
c = 0.195/s-7.9E-2+1.6E-2*s;
S40:
/*
STEP 5: NO QUOTIENT TEST IF X NOT POSITIVE
*/
if(x <= 0.0) goto S70;
/*
STEP 6: CALCULATION OF V AND QUOTIENT Q
*/
v = t/(s+s);
if(fabs(v) <= 0.25) goto S50;
q = q0-s*t+0.25*t*t+(s2+s2)*log(1.0+v);
goto S60;
S50:
q = q0+0.5*t*t*((((((a7*v+a6)*v+a5)*v+a4)*v+a3)*v+a2)*v+a1)*v;
S60:
/*
STEP 7: QUOTIENT ACCEPTANCE (Q)
*/
if(log(1.0-u) <= q) return sgamma;
S70:
/*
STEP 8: E=STANDARD EXPONENTIAL DEVIATE
U= 0,1 -UNIFORM DEVIATE
T=(B,SI)-DOUBLE EXPONENTIAL (LAPLACE) SAMPLE
*/
e = sexpo();
u = ranf();
u += (u-1.0);
t = b+fsign(si*e,u);
/*
STEP 9: REJECTION IF T .LT. TAU(1) = -.71874483771719
*/
if(t < -0.7187449) goto S70;
/*
STEP 10: CALCULATION OF V AND QUOTIENT Q
*/
v = t/(s+s);
if(fabs(v) <= 0.25) goto S80;
q = q0-s*t+0.25*t*t+(s2+s2)*log(1.0+v);
goto S90;
S80:
q = q0+0.5*t*t*((((((a7*v+a6)*v+a5)*v+a4)*v+a3)*v+a2)*v+a1)*v;
S90:
/*
STEP 11: HAT ACCEPTANCE (H) (IF Q NOT POSITIVE GO TO STEP 8)
*/
if(q <= 0.0) goto S70;
if(q <= 0.5) goto S100;
w = exp(q)-1.0;
goto S110;
S100:
w = ((((e5*q+e4)*q+e3)*q+e2)*q+e1)*q;
S110:
/*
IF T IS REJECTED, SAMPLE AGAIN AT STEP 8
*/
if(c*fabs(u) > w*exp(e-0.5*t*t)) goto S70;
x = s+0.5*t;
sgamma = x*x;
return sgamma;
S120:
/*
ALTERNATE METHOD FOR PARAMETERS A BELOW 1 (.3678794=EXP(-1.))
*/
aa = 0.0;
b = 1.0+0.3678794*a;
S130:
p = b*ranf();
if(p >= 1.0) goto S140;
sgamma = exp(log(p)/ a);
if(sexpo() < sgamma) goto S130;
return sgamma;
S140:
sgamma = -log((b-p)/ a);
if(sexpo() < (1.0-a)*log(sgamma)) goto S130;
return sgamma;
}
float snorm(void)
/*
**********************************************************************
(STANDARD-) N O R M A L DISTRIBUTION
**********************************************************************
**********************************************************************
FOR DETAILS SEE:
AHRENS, J.H. AND DIETER, U.
EXTENSIONS OF FORSYTHE'S METHOD FOR RANDOM
SAMPLING FROM THE NORMAL DISTRIBUTION.
MATH. COMPUT., 27,124 (OCT. 1973), 927 - 937.
ALL STATEMENT NUMBERS CORRESPOND TO THE STEPS OF ALGORITHM 'FL'
(M=5) IN THE ABOVE PAPER (SLIGHTLY MODIFIED IMPLEMENTATION)
Modified by Barry W. Brown, Feb 3, 1988 to use RANF instead of
SUNIF. The argument IR thus goes away.
**********************************************************************
THE DEFINITIONS OF THE CONSTANTS A(K), D(K), T(K) AND
H(K) ARE ACCORDING TO THE ABOVEMENTIONED ARTICLE
*/
{
static float 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 float 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 float 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 float 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 float snorm,u,s,ustar,aa,w,y,tt;
u = ranf();
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-(float)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 = ranf();
w = u*(*(a+i)-aa);
tt = (0.5*w+aa)*w;
goto S80;
S70:
tt = u;
ustar = ranf();
S80:
if(ustar > tt) goto S50;
u = ranf();
if(ustar >= u) goto S70;
ustar = ranf();
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 = ranf();
if(ustar > tt) goto S50;
u = ranf();
if(ustar >= u) goto S150;
u = ranf();
goto S140;
}
float fsign( float num, float sign )
/* Transfers sign of argument sign to argument num */
{
if ( ( sign>0.0f && num<0.0f ) || ( sign<0.0f && num>0.0f ) )
return -num;
else return num;
}
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