ORIGIN 'betaenv'; BODY 'private/randombody'; (* * COPYRIGHT * Copyright (C) Mjolner Informatics, 1995-96 * All rights reserved. *) --- lib: attributes --- initgn: external (* * INIT-ialize current G-e-N-erator * Reinitializes the state of the current generator * * Arguments * isdtyp -> The state to which the generator is to be set * isdtyp = -1 => sets the seeds to their initial value * isdtyp = 0 => sets the seeds to the first value of the * current block * isdtyp = 1 => sets the seeds to the first value of the * next block * * Method * This is a transcription from Pascal to Fortran of routine * Init_Generator 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) *) (# isdtyp: @integer enter (isdtyp) #); gscgn: external (* * 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) *) (# getset, g: @integer enter (getset, g) #); setsd: external (* * SET S-ee-D of current generator * Resets the initial seed of the current generator to ISEED1 * and ISEED2. The seeds of the other generators remain * unchanged. * Arguments * iseed1 -> First integer seed * iseed2 -> Second integer seed * Method * This is a transcription from Pascal to Fortran of routine * Set_Seed 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) *) (# iseed1, iseed2: @integer enter (iseed1, iseed2) #); getsd: external (* * GET SeeD * Returns the value of two integer seeds of the current * generator * Arguments * iseed1 <- First integer seed of generator G * iseed2 <- Second integer seed of generator G * Method * This is a transcription from Pascal to Fortran of routine * Get_State 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) *) (# iseed1, iseed2: @integer enter (iseed1, iseed2) #); setall: external (* * SET ALL random number generators * Sets the initial seed of generator 1 to ISEED1 and * ISEED2. The initial seeds of the other generators are set * accordingly, and all generators states are set to these seeds. * * Arguments * iseed1 -> First of two integer seeds * iseed2 -> Second of two integer seeds * * Method * This is a transcription from Pascal to Fortran of routine * Set_Initial_Seed 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) *) (# iseed1, iseed2: @integer enter (iseed1, iseed2) #); setant: external (* * SET ANTithetic Sets whether the current generator produces * antithetic values. If X is the value normally returned from * a uniform [0,1] random number generator then 1 - X is the * antithetic value. If X is the value normally returned from a * uniform [0,N] random number generator then N - 1 - X is the * antithetic value. All generators are initialized to NOT * generate antithetic values. * Arguments * qvalue -> nonzero if generator G is to generating antithetic * values, otherwise zero * Method * This is a transcription from Pascal to Fortran of routine * Set_Antithetic 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) *) (# qvalue: @integer enter qvalue #); advnst: external (* * ADV-a-N-ce ST-ate * Advances the state of the current generator by 2^K values * and resets the initial seed to that value. * Arguments * k -> The generator is advanced by2^K values * Method: routine Advance_State 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) *) (# k: @integer enter k #); (*=================================================================*) (*===== Integer random number generators ==========================*) (*=================================================================*) ignlgi: external (* * Integer GeNerate LarGe Integer * Returns a random integer following a uniform distribution * over (1, 2147483562) using the current generator. * * Method * This is a transcription from Pascal to Fortran of routine * Random 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) *) (# random: @integer exit random #); ignuin: external (* * GeNerate Uniform INteger * 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. *) (# low, high: @integer; random: @integer enter (low, high) exit random #); ignbin: external (* * Integer GeNerate BINomial random deviate * 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. *) (# n: @integer; p: @real; random: @integer enter (n, p) exit random #); ignnbn: external (* * Integer GeNerate Negative BiNomial random deviate * 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. *) (# n: @integer; p: @real; random: @integer enter (n, p) exit random #); ignpoi: external (* * GENerate POIsson random deviate * Generates a single random deviate from a Poisson * distribution with mean AV. * * Arguments * mu --> The mean of the Poisson distribution from which a * random deviate is to be generated. * * 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 *) (# mu: @real; random: @integer enter mu exit random #); (*=================================================================*) (*===== Real random number generators =============================*) (*=================================================================*) ranf: external (* * RANnom 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 * * Method * 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) *) (# random: @real exit random #); genunf: external (* * GENerate UNiForm real * 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 *) (# low, high: @real; random: @real enter (low, high) exit random #); genbet: external (* * GeNerate BETa random deviate * 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 * * Method: described in R. C. H. Cheng Generating Beta Variatew with * Nonintegral Shape Parameters Communications of the ACM, * 21:317-322 (1978) (Algorithms BB and BC) *) (# aa, bb: @real; random: @real enter (aa,bb) exit random #); genchi: external (* * GENerate random value of CHIsquare variable * 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. *) (# df: @real; random: @real enter df exit random #); genexp: external (* * GENerate EXPonential random deviate * 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. *) (# av: @real; random: @real enter av exit random #); genf: external (* * GENerate random deviate from the F distribution * 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 *) (# dfn, dfd: @real; random: @real enter (dfn, dfd) exit random #); gengam: external (* GENerates random deviates from GAMma distribution * 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. *) (# a, r: @real; random: @real enter (a, r) exit random #); gennch: external (* GENerate random value of Noncentral CHisquare variable * 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. *) (# df, xnonc: @real; random: @real enter (df, xnonc) exit random #); gennf: external (* GENerate random deviate from the Noncentral F distribution * 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. *) (# dfn, dfd, xnonc: @real; random: @real enter (dfn, dfd, xnonc) exit random #); gennor: external (* * GENerate random deviate from a NORmal distribution * 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. *) (# av, sd: @real; random: @real enter (av, sd) exit random #); sexpo: external (* * Standard EXPonential distribution * * Method * 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 *) (# random: @real exit random #); sgamma: external (* * Standard GAMMA distribution * * 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) * * Arguments * A ---> Parameter (mean) of the standard GAMMA distribution * Method * CASE 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. * CASE 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) *) (# a: @real; random: @real enter a exit random #); snorm: external (* * Standard NORmal distribution * * Method * 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. *) (# random: @real exit random #)
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