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一个很好用的常用数学分布实现代码集合

                                    RANLIB.C

               Library of C 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.




                       THANKS TO OUR SUPPORTERS

This work  was supported  in part by  grant CA-16672 from the National
Cancer Institute.  We are grateful  to Larry and  Pat McNeil of Corpus
Cristi for their generous support.  Some equipment used in this effort
was provided by IBM as part of a cooperative study agreement; we thank
them.

                          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) Negative Binomial random deviates
    (14) Multinomial random deviates
    (15) Poisson random deviates
    (16) Integer uniform deviates between specified limits
    (17) Seeds for the random number generator calculated from a
         character string




                 COMMENTS ON THE C VERSION OF RANLIB

The C version was  obtained by converting the original  Fortran RANLIB
to C using PROMULA.FORTRAN  and performing  some hand  crafting of the
result.  Information on PROMULA.FORTRAN can be obtained from

                   PROMULA Development Corporation
                    3620 N. High Street, Suite 301
                         Columbus, Ohio 43214
                            [phone]

RANLIB.C  was tested  using the xlc  compiler under AIX  3.1 on an IBM
RS/6000.  The code  was  also examined  with lint  on the same system.
The RANLIB test  programs were also  successfully run using   the  gcc
compiler (see below) on a Solbourne.

RANLIB.C can be  obtained from  statlib.  Send mail  whose message  is
'send ranlib.c.shar from general' to [e-mail].

RANLIB.C can also be obtained by anonymous ftp  to odin.mda.uth.tmc.edu
(129.106.3.17) where is is available as
                        /pub/unix/ranlib.c.tar.Z

For  obvious   reasons, the   original   RANLIB  (in    Fortran)   has
been renamed to
                        /pub/unix/ranlib.f.tar.Z
on the same machine.






                                 CAVEAT

RANLIB.C is written in ANSI C and makes  heavy use  of prototypes.  It
will not compile under old style (KR) C compilers (such as the default
Sun cc compiler). The decision to  distribute in  ANSI C was mine; the
version of Promula that was used --  2.0 --  writes old style headers.
Converting RANLIB to  old style C  is not a  totally trivial task; the
type of many arguments to functions will have to be changed from float
to double.  Also note that all ints have been changed  to longs.  This
is a result of my being a Fortraner,  a  novice at C, and knowing that
the underlying generators require at least a 32 bit integer.

I don't  recommend conversion to an  obsolete C dialect.  Instead, get
the  Free  Software Foundation's  excellent  ANSI C compiler,  gcc. It
compiles KR C as well as  ANSI C. A  version of gcc that  runs on many
varieties of Unix is available by anonymous ftp as
                        /pub/gnu/gcc-1.40.tar.Z
at prep.ai.mit.edu  (18.71.0.38).   A Vax version  is also  present on
/pub/gnu.  The compilers  are also available  on tape.  Write the Free
Software Foundation at:

                    Free Software Foundation, Inc.
                       675 Massachusetts Avenue
                         Cambridge, MA  02139
                        Phone: [phone]

A MSDOS port of gcc, performed by DJ Delorie is also available by ftp.

File location:

    host:      grape.ecs.clarkson.edu
    login:     ftp
    password:  send your e-mail address
    directory: ~ftp/pub/msdos/djgcc

File in .ZIP format - djgpp.zip - one 2.2M file, contains everything.





                             INSTALLATION

Directory src contains the  C source for most   of the routines.   The
files  com.c   and  ranlib.c  constitute  RANLIB.  The file   ranlib.h
contains prototypes for  the RANLIB  routines that should be used (and
not  for  a few internal  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.
The file ranlib.h in directory test is a copy of that in src.



                            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.)






                         WHAT'S NEW IN VERSION 1.1?

  
Random number generation  for  the Negative Binomial  and  Multinomial
distributions has been included.

Two errors in the code  which generates random  numbers from the Gamma
distribution were fixed.