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ranlibComplete.c
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ranlibComplete.c
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#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))
void ftnstop(char*);
double genbet(double aa,double bb)
/*
**********************************************************************
double genbet(double aa,double 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)
**********************************************************************
*/
{
#define expmax 89.0
#define infnty 1.0E38
static double olda = -1.0;
static double oldb = -1.0;
static double 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;
fputs(" AA or BB <= 0 in GENBET - Abort!",stderr);
fprintf(stderr," 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;
/*
Alborithm 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
}
double genchi(double df)
/*
**********************************************************************
double genchi(double 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 double genchi;
if(!(df <= 0.0)) goto S10;
fputs("DF <= 0 in GENCHI - ABORT",stderr);
fprintf(stderr,"Value of DF: %16.6E\n",df);
exit(1);
S10:
genchi = 2.0*gengam(1.0,df/2.0);
return genchi;
}
double genexp(double av)
/*
**********************************************************************
double genexp(double 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 double genexp;
genexp = sexpo()*av;
return genexp;
}
double genf(double dfn,double dfd)
/*
**********************************************************************
double genf(double dfn,double 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 double genf,xden,xnum;
if(!(dfn <= 0.0 || dfd <= 0.0)) goto S10;
fputs("Degrees of freedom nonpositive in GENF - abort!",stderr);
fprintf(stderr,"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;
fputs(" GENF - generated numbers would cause overflow",stderr);
fprintf(stderr," Numerator %16.6E Denominator %16.6E\n",xnum,xden);
fputs(" GENF returning 1.0E38",stderr);
genf = 1.0E38;
goto S30;
S20:
genf = xnum/xden;
S30:
return genf;
}
double gengam(double a,double r)
/*
**********************************************************************
double gengam(double a,double 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 double gengam;
gengam = sgamma(r);
gengam /= a;
return gengam;
}
void genmn(double *parm,double *x,double *work)
/*
**********************************************************************
void genmn(double *parm,double *x,double *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 double 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);
}
}
void genmul(long n,double *p,long ncat,long *ix)
/*
**********************************************************************
void genmul(int n,double *p,int ncat,int *ix)
GENerate an observation from the MULtinomial distribution
Arguments
N --> Number of events that will be classified into one of
the categories 1..NCAT
P --> Vector of probabilities. P(i) is the probability that
an event will be classified into category i. Thus, P(i)
must be [0,1]. Only the first NCAT-1 P(i) must be defined
since P(NCAT) is 1.0 minus the sum of the first
NCAT-1 P(i).
NCAT --> Number of categories. Length of P and IX.
IX <-- Observation from multinomial distribution. All IX(i)
will be nonnegative and their sum will be N.
Method
Algorithm from page 559 of
Devroye, Luc
Non-Uniform Random Variate Generation. Springer-Verlag,
New York, 1986.
**********************************************************************
*/
{
static double prob,ptot,sum;
static long i,icat,ntot;
if(n < 0) ftnstop("N < 0 in GENMUL");
if(ncat <= 1) ftnstop("NCAT <= 1 in GENMUL");
ptot = 0.0F;
for(i=0; i<ncat-1; i++) {
if(*(p+i) < 0.0F) ftnstop("Some P(i) < 0 in GENMUL");
if(*(p+i) > 1.0F) ftnstop("Some P(i) > 1 in GENMUL");
ptot += *(p+i);
}
if(ptot > 0.99999F) ftnstop("Sum of P(i) > 1 in GENMUL");
/*
Initialize variables
*/
ntot = n;
sum = 1.0F;
for(i=0; i<ncat; i++) ix[i] = 0;
/*
Generate the observation
*/
for(icat=0; icat<ncat-1; icat++) {
prob = *(p+icat)/sum;
*(ix+icat) = ignbin(ntot,prob);
ntot -= *(ix+icat);
if(ntot <= 0) return;
sum -= *(p+icat);
}
*(ix+ncat-1) = ntot;
/*
Finished
*/
return;
}
double gennch(double df,double xnonc)
/*
**********************************************************************
double gennch(double df,double 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 double gennch;
if(!(df <= 1.0 || xnonc < 0.0)) goto S10;
fputs("DF <= 1 or XNONC < 0 in GENNCH - ABORT",stderr);
fprintf(stderr,"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;
}
double gennf(double dfn,double dfd,double xnonc)
/*
**********************************************************************
double gennf(double dfn,double dfd,double 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 double gennf,xden,xnum;
static long qcond;
qcond = dfn <= 1.0 || dfd <= 0.0 || xnonc < 0.0;
if(!qcond) goto S10;
fputs("In GENNF - Either (1) Numerator DF <= 1.0 or",stderr);
fputs("(2) Denominator DF < 0.0 or ",stderr);
fputs("(3) Noncentrality parameter < 0.0",stderr);
fprintf(stderr,
"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;
fputs(" GENNF - generated numbers would cause overflow",stderr);
fprintf(stderr," Numerator %16.6E Denominator %16.6E\n",xnum,xden);
fputs(" GENNF returning 1.0E38",stderr);
gennf = 1.0E38;
goto S30;
S20:
gennf = xnum/xden;
S30:
return gennf;
}
double gennor(double av,double sd)
/*
**********************************************************************
double gennor(double av,double 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.
**********************************************************************
*/
{
static double gennor;
gennor = sd*snorm()+av;
return gennor;
}
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;
}
}
double genunf(double low,double high)
/*
**********************************************************************
double genunf(double low,double 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 double genunf;
if(!(low > high)) goto S10;
fprintf(stderr,"LOW > HIGH in GENUNF: LOW %16.6E HIGH: %16.6E\n",low,high);
fputs("Abort",stderr);
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) {
fputs(" Generator number out of range in GSCGN",stderr);
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,double pp)
/*
**********************************************************************
long ignbin(long n,double 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: DOUBLEING 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 DOUBLEING 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 double psave = -1.0;
static long nsave = -1;
static long ignbin,i,ix,ix1,k,m,mp,T1;
static double 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 ignnbn(long n,double p)
/*
**********************************************************************
long ignnbn(long n,double p)
GENerate Negative BiNomial random deviate
Function
Generates a single random deviate from a negative binomial
distribution.
Arguments
N --> The number of trials in the negative binomial distribution
from which a random deviate is to be generated.
P --> The probability of an event.
Method
Algorithm from page 480 of
Devroye, Luc
Non-Uniform Random Variate Generation. Springer-Verlag,
New York, 1986.
**********************************************************************
*/
{
static long ignnbn;
static double y,a,r;
/*
..
.. Executable Statements ..
*/
/*
Check Arguments
*/
if(n < 0) ftnstop("N < 0 in IGNNBN");
if(p <= 0.0F) ftnstop("P <= 0 in IGNNBN");
if(p >= 1.0F) ftnstop("P >= 1 in IGNNBN");
/*
Generate Y, a random gamma (n,(1-p)/p) variable
*/
r = (double)n;
a = p/(1.0F-p);
y = gengam(a,r);
/*
Generate a random Poisson(y) variable
*/
ignnbn = ignpoi(y);
return ignnbn;
}
long ignpoi(double mu)
/*
**********************************************************************
long ignpoi(double 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 double fsign( double num, double sign );
static double a0 = -0.5;
static double a1 = 0.3333333;
static double a2 = -0.2500068;
static double a3 = 0.2000118;
static double a4 = -0.1661269;
static double a5 = 0.1421878;
static double a6 = -0.1384794;
static double a7 = 0.125006;
static double muold = 0.0;
static double muprev = 0.0;
static double 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 double 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];