PLALGO

(Software written in 1980 and updated in 1985. Not supported.
Reasonable in-line comments, and very limited documentation*
available. See the users' manual, scanned into the two files
Usersmanual1.pdf and Usersmanual2.pdf.)

     The files in this directory contain the program PLALGO for
solving zero-finding problems, using a piecewise-linear
homotopy method.

    The program is in the files mpsa.for, endcyc.for,
endcyc2.for, basis.for, linalg.for, and subdiv.for.
mpsa.for contains the main program and subroutines
plalgo, setup, and accel. Comments in the main program
and in plalgo and setup describe the input required;
see also the sample .dat files included.

    Only one of endcyc.for and endcyc2.for should be used.
Endcyc is used for standard zero-finding problems, while
endcyc2 is appropriate when the point-to-set mapping
has special structure (it's the convex union of smooth
functions), as described in section 12 of the documentation.

     Also included are three subroutines FNEVAL: s1020.for,
for the example of section 10 of the documentation
with dimension 20, post2.for, for the post office problem, 
and econ.for for economic equilibrium problems. Econ 
includes its own version of subroutine endcyc, so this 
should be omitted.

     The program is written in "vanilla" fortran, and few
changes should be necessary for any compiler. The code has
been verified to conform to PFORT, a portable subset of
American National Standard Fortran, with the exception of
the following features. The main program has open statements
which may be unnecessary or undesirable in your environment.
It also has character variables, which should be changed to
integer for FORTRAN 66 compilers; character variables are also
used in subroutine PRTPCE in subdiv.for. In addition, the
intrinsic function DBLE is used instead of DFLOAT to convert
integer variables to double precision, in subroutines PLALGO
and ACCEL in mpsa.for, in subroutines FSTBAS, NEWBAS, and
MINRAT in basis.for, in subroutines NEWPCE and LSTPCE in
subdiv.for and in subroutine ECON in econ.for.

     There are also data files: s1020.dat for s1020, post1.dat
for post2, and e3.dat, ep19.dat and ep29.dat for econ.

     Good luck and happy computing!

     For more information, contact me at the address below.

  -- M.J. Todd

  School of Operations Research                   (607)255-9135
  Rhodes Hall
  Cornell University
  Ithaca, NY 14853-3801

  FAX: (607)255-9129          e-mail: mjt7@cornell.edu
                                      miketodd@orie.cornell.edu
  URL:    http://www.people.orie.cornell.edu/~miketodd/todd.html

* The documentation cited is the following technical report:
``PLALGO:  A FORTRAN implementation of a
piecewise-linear homotopy algorithm for solving
systems of nonlinear equations,'' Technical
Report No. 452, School of Operations Research and
Industrial Engineering, Cornell University
(April 1980, revised Nov. 1981 and July 1985).

Very  limited quantities are available, and there is no
electronic version. There is a rather poor-quality scanned
version, in this directory as Usersmanual1.pdf and
Usersmanual2.pdf. If you wish to experiment with the
software, I hope you will be able to use the examples
provided and the comments in the programs. If you are
planning more extensive testing and you need more details,
please contact me by e-mail at the address above.