










                                     RANLIB

            Library of Fortran Routines for Random Number Generation








                                     README








                            Compiled and Written by:

                                 Barry W. Brown
                                  James Lovato
                                   









                     Department of Biomathematics, Box 237
                     The University of Texas, M.D. Anderson Cancer Center
                     1515 Holcombe Boulevard
                     Houston, TX      77030


 This work was supported by grant CA-16672 from the National Cancer Institute.


                          SUMMARY OF RANLIB

The bottom level routines provide 32 virtual random number generators.
Each generator can provide 1,048,576 blocks of numbers, and each block
is of length 1,073,741,824.  Any generator can be set to the beginning
or end  of the current  block or to  its starting value.  Packaging is
provided   so  that  if  these capabilities  are not  needed, a single
generator with period 2.3 X 10^18 is seen.

Using this base, routines are provided that return:
    (1)  Beta random deviates
    (2)  Chi-square random deviates
    (3)  Exponential random deviates
    (4)  F random deviates
    (5)  Gamma random deviates
    (6)  Multivariate normal random deviates (mean and covariance
         matrix specified)
    (7)  Noncentral chi-square random deviates
    (8)  Noncentral F random deviates
    (9)  Univariate normal random deviates
    (10) Random permutations of an integer array
    (11) Real uniform random deviates between specified limits
    (12) Binomial random deviates
    (13) Poisson random deviates
    (14) Integer uniform deviates between specified limits
    (15) Seeds for the random number generator calculated from a
         character string

                             INSTALLATION

Directory src contains the Fortran  source for most of  the  routines.
Directory  linpack  contains  two  linpack  routines  needed   by  the
multivariate  generator.  If  linpack is present  on your machine, you
won't need  these routines.   The Fortran  code from these directories
should be compiled and placed in a library.   Directory  test contains
three test programs for this code.

                            DOCUMENTATION

Documentation  is  on directory doc on the  distribution.   All of the
documentation is  in the  form   of  character  (ASCII)    files.   An
explanation of the concepts involved in the base generator and details
of its implementation are contained in Basegen.doc.  A summary  of all
of the  available  routines is  contained  in ranlib.chs  (chs  is  an
abbreviation of 'cheat sheet').  The 'chs'  file  will probably be the
reference to ranlib  that is primarily used.   The  file, ranlib.fdoc,
contains all comments heading  each routine.   There is somewhat  more
information   in  'fdoc' than  'chs',  but  the additional information
consists primarily of references to the literature.




                               SOURCES

The following routines,  which  were  written by others   and  lightly
modified for consistency in packaging, are included in RANLIB.

                        Bottom Level Routines

These routines are a transliteration of the Pascal in the reference to
Fortran.

L'Ecuyer, P. and  Cote, S. "Implementing  a Random Number Package with
Splitting  Facilities."  ACM  Transactions   on Mathematical Software,
17:98-111 (1991)

                             Exponential

This code was obtained from Netlib.

Ahrens,  J.H. and  Dieter, U.   Computer Methods for Sampling From the
Exponential and Normal  Distributions.  Comm. ACM,  15,10 (Oct. 1972),
873 - 882.

                                Gamma

(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.  Adaptation of algorithm GS.

                                Normal

This code was obtained from netlib.

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.

                               Binomial

This code was kindly sent me by Dr. Kachitvichyanukul.

Kachitvichyanukul,  V. and Schmeiser, B.   W.  Binomial Random Variate
Generation.  Communications of the ACM, 31, 2 (February, 1988) 216.

                               Poisson

This code was obtained from netlib.

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




                                 Beta

This code was written by us following the recipe in the following.

R. C.  H.   Cheng Generating  Beta Variables  with  Nonintegral  Shape
Parameters. Communications of  the ACM,  21:317-322 (1978) (Algorithms
BB and BC)

                               Linpack

Routines SPOFA and SDOT are used to perform the Cholesky decomposition
of  the covariance  matrix  in  SETGMN  (used  for  the  generation of
multivariate normal deviates).

Dongarra, J.  J., Moler,   C.  B., Bunch, J.   R. and  Stewart, G.  W.
Linpack User's Guide.  SIAM Press, Philadelphia.  (1979)


                              LEGALITIES

Code that appeared  in an    ACM  publication  is subject  to    their
algorithms policy:

     Submittal of  an  algorithm    for publication  in   one of   the  ACM
     Transactions implies that unrestricted use  of the algorithm within  a
     computer is permissible.   General permission  to copy and  distribute
     the algorithm without fee is granted provided that the copies  are not
     made  or   distributed for  direct   commercial  advantage.    The ACM
     copyright notice and the title of the publication and its date appear,
     and  notice is given that copying  is by permission of the Association
     for Computing Machinery.  To copy otherwise, or to republish, requires
     a fee and/or specific permission.

     Krogh, F.  Algorithms  Policy.  ACM  Tran.   Math.  Softw.   13(1987),
     183-186.

We place the Ranlib code that we have written in the public domain.  

                                 NO WARRANTY
     
     WE PROVIDE ABSOLUTELY  NO WARRANTY  OF ANY  KIND  EITHER  EXPRESSED OR
     IMPLIED,  INCLUDING BUT   NOT LIMITED TO,  THE  IMPLIED  WARRANTIES OF
     MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.  THE ENTIRE RISK
     AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS  WITH YOU.  SHOULD
     THIS PROGRAM PROVE  DEFECTIVE, YOU ASSUME  THE COST  OF  ALL NECESSARY
     SERVICING, REPAIR OR CORRECTION.
     
     IN NO  EVENT  SHALL THE UNIVERSITY  OF TEXAS OR  ANY  OF ITS COMPONENT
     INSTITUTIONS INCLUDING M. D.   ANDERSON HOSPITAL BE LIABLE  TO YOU FOR
     DAMAGES, INCLUDING ANY  LOST PROFITS, LOST MONIES,   OR OTHER SPECIAL,
     INCIDENTAL   OR  CONSEQUENTIAL DAMAGES   ARISING   OUT  OF  THE USE OR
     INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA OR
     ITS ANALYSIS BEING  RENDERED INACCURATE OR  LOSSES SUSTAINED  BY THIRD
     PARTIES) THE PROGRAM.
     
     (Above NO WARRANTY modified from the GNU NO WARRANTY statement.)
