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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*); float genbet(float aa,float bb) /* ********************************************************************** 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) ********************************************************************** */ { #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; 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 } 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; 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; } 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; 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; } 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