ranlib.c

一个很好用的常用数学分布实现代码集合

    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;
}
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.
**********************************************************************
*/
{
static float 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;
    }
}
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;
    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,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 ignnbn(long n,float p)
/*
**********************************************************************
 
     long ignnbn(long n,float 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 float 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 = (float)n;
    a = p/(1.0F-p);
    y = gengam(a,r);
/*
     Generate a random Poisson(y) variable
*/
    ignnbn = ignpoi(y);
    return ignnbn;
}
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