This is the home page for Gosset. It contains sections called

• OVERVIEW OF GOSSET


• GETTING THE FILES


• INSTALLATION


• UPDATES AND BUG FIXES


• APPLICATIONS


• FOR FURTHER INFORMATION

Last modified August 12, 2017

This replaces the "README" file that was included with older releases of Gosset.

• Variables may be discrete or continuous (or both). Discrete variables may be numeric or symbolic (or both). Continuous variables may range over a cube or a ball (or both).
• The variables may be required to satisfy linear equalities or inequalities.
• The model to be fitted may be any low degree polynomial (e.g. a quadratic). Much more general models can also be used - see Section 3.12 of the manual.
• The number of observations is specified by the user.
• The design may be required to include a specified set of points. (so a sequence of designs can be found, each of which is optimal given that the earlier measurements have been made).
• The region where the model is to be fitted need not be the same as the region where measurements are to be made (so the designs can be used for extrapolation).
• The following types of designs can be requested: I-, A-, D- or E-optimal, the same but with protection against loss of one trial, or packings (if no model is available).
• Blocked designs and designs with correlated errors can also be obtained.
• The algorithm is powerful enough to routinely minimize functions of 1000 variables (e.g. can find optimal or nearly optimal designs for a quadratic model involving 12 variables).
• An extensive library of precomputed optimal designs is included for linear and quadratic designs in the cube, ball and simplex, involving up to 14 variables.
• The user does not have to specify starting points for the search. The user also has control over how much effort is expended by the algorithm, and can if desired monitor the progress of the search.
• Applications so far include VLSI production, conductivity of diamond films, growth of protein crystals, flow through a catalytic converter, laser welding, etc.

Gosset is described in more detail in the following documents.

• R. H. Hardin and N. J. A. Sloane, "Gosset: A General-Purpose Program for Constructing Experimental Designs (Second Edition)" [postscript file], 2003. (Also included with the source files.)
  [When viewing this postscript file with ghostview, set the "PageSize" option, the 6th button at the top, to "Letter" rather than "Automatic" or "BBox"]
• R. H. Hardin and N. J. A. Sloane, "A New Approach to the Construction of Optimal Designs", J. Statistical Planning and Inference, vol. 37, 1993, pp. 339-369 [Abstract, postscript or pdf].

• R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (I) The Sphere" (Abstract, pdf, ps).
• R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (II) The Cube" (Abstract, pdf, ps).

We are doing this since - as of August 12 2017 - we have decided to put Gosset in the public domain. You are also welcome to set up mirror sites to distribute Gosset.

Comments: We are a bit surprised that Gosset still works, because it depends on the format of the linux/unix ps (process status) command, which fortunately hasn't changed. Maybe somebody will now organize the code into modern modules and create a makefile, which would be a plus to its survival.

Of course, "anything free comes with no guarantee".

If you publish anything that makes use of a design that was partly obtained using Gosset, please cite Gosset, just as you would acknowledge a design that a colleague constructed for you. The citation could read something like this:

R. H. Hardin and N. J. A. Sloane, Gosset: A general-purpose program for designing experiments, (Gosset was developed at AT&T during 1991-2003 by R. H. Hardin and N. J. A. Sloane)

Getting the files:

You need to download two files:

System administrators please note: if you are installing gosset for multiple users, the instructions are slightly different - see below.

INSTALLING A PRIVATE COPY OF GOSSET

1. First choose a base directory for gosset.
   Subdirectories will be created off this for work on individual problems.
2. Place the files index.html (this file) and codemart.cpio in the base directory.
3. Change directory to the base directory.
   To print the manual, which is about 130 pages long, type

   $ lp manual.ps

   (possibly replacing "lp" by your local printer command, e.g. "lpr").
   (If you view this postscript file with ghostview, set the "PageSize" option, the 6th button at the top, to "Letter" rather than "Automatic" or "BBox")

4. Extract everything in codemart.cpio :
   $ cpio -icu < codemart.cpio

   (some users have found that it is necessary to use

   $ cpio -iu < codemart.cpio instead)

   and compile several files:

   $ cc -w M*.c -o gosset -lm
   $ rm */vtrace */vvv */moments */interp

   (The latter command is needed only if you already had a copy of gosset. It removes some out-of-date files.)

   The archive file codelib.a does not need to be touched.

5. To find a design, start by entering gosset :

   $ gosset

   The program responds by asking you to name a working subdirectory:

   please type 'cd something' to name a local directory for your work

   At this point you will probably enter the specifications for a new design - see Sects. 2, 3, .... of the manual.

INSTALLING GOSSET FOR MULTIPLE USERS

1. First choose a directory for the gosset source files, say /u/g/sources.
2. Place index.html and codemart.cpio in /u/g/sources
3. Change directory to /u/g/sources.
   To print the manual, which is about 130 pages long, type

   $ lp manual.ps

   (possibly replacing "lp" by your local printer command, e.g. "lpr").
   (If you view this postscript file with ghostview, set the "PageSize" option, the 6th button at the top, to "Letter" rather than "Automatic" or "BBox")

4. Extract everything in codemart.cpio :

   $ cpio -icu < codemart.cpio

   (some users have found that it is necessary to use

   $ cpio -iu < codemart.cpio instead)

   and compile several files:

   $ cc -DGOSSETSRC=\"/u/g/sources\" -DCODELIB=\"/u/g/sources\" M*.c -o gosset -lm

   which will create a version of gosset that expects the source files to be in /u/g/sources. The escapes are necessary on the quotes, because they are part of the definition.

5. The executable file gosset can be moved anywhere, say into /usr/local/bin , and can be executed from anywhere.
6. Be warned, however - working directories will be created by gosset wherever the user is, instead of from a single base directory. So the user must exercise some discipline when invoking gosset, to avoid chaos in the directory structure.

7. If gosset was already installed on your system, users should execute

   $ rm vtrace vvv moments interp

   in each working subdirectory, to remove out-of-date files.

8. The archive file codelib.a does not need to be touched.
9. When someone wants to find a design, they change to a base directory (typically $HOME/gosset), from which working subdirectories will be created, and enter gosset:

   $ gosset

   The program responds by asking them to name a working subdirectory:

   please type 'cd something' to name a local directory for your work

   At this point they will probably enter the specifications for a new design - see Sects. 2, 3, .... of the manual.

• The current version (May 07 2003) incorporates several changes to fix error messages produced by different C compilers.
• As C compilers have evolved they have become more picky.
  Running Gosset often produces harmless but irritating warning messages from the C compiler.
  To avoid this, we recommend that you compile the source files with cc -w (as shown above)
  and that you run Gosset with the command:
  gosset 'cflags -w'

  If you forget, and just run "gosset", start by typing

  cflags -w

  and we also usually type

  compiler=gcc
  prompt %
  

• Bill Kappele (Bill(AT)mathoptions.com) has written a graphical interface that creates an input file for Gosset. It can be run in Windows or Unix/Linux. A Tcl/Tk interpreter is required. It can be found on his website

There have been three kinds of applications:

Applications to industrial problems

• J. Hagen, M. Heinen and W. Salber: DOE in der Optimierung von Ottomotoren mit vollvariabler Ventilsteuerung; paper for the conference "Design of Experiments in der Motorenentwicklung", Haus der Technik, Dec. 2001.
• Charles W. Carter has used Gosset successfully in designing several experiments.
• Optimization of Resist Formulation and Processing with Disulfone Photo Acid Generators Using Design of Experiments, O. Nalamasu, A. Freeny, E. Reichmanis, N.J.A. Sloane and L. F. Thompson, AT&T Bell Labs Memorandum, 1993.

Applications to theoretical understanding of optimal designs

• R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (I) The Sphere" (Abstract, pdf, ps).
• R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (II) The Cube" (Abstract, pdf, ps).
• Several other papers are in preparation.

Applications to mathematical problems

• Packing Lines, Planes, etc.: Packings in Grassmannian Space [Abstract, postscript, pdf], J. H. Conway, R. H. Hardin and N. J. A. Sloane, Experimental Math., 5 (1996), pp. 139-159.
• Codes (Spherical) and Designs (Experimental) [pdf of body of paper, pdf of references], by R. H. Hardin and N. J. A. Sloane, in Different Aspects of Coding Theory, ed. A. R. Calderbank, AMS Series Proceedings Symposia Applied Math., Vol. 50, 1995, pp. 179-206.
• McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions [Abstract, postscript, pdf] [note: Fig. 1a and Fig. 1b are in separate files] R. H. Hardin and N. J. A. Sloane, Discrete and Computational Geometry, 15 (1996), pp. 429-441.
• Minimal-Energy Clusters of Hard Spheres [Abstract, postscript, pdf] [note: Fig. 11 , Fig. 12 and "photos" of the putatively optimal clusters of 4 to 10 and 13 to 20 spheres are in separate files], by N. J. A. Sloane, R. H. Hardin, T. S. Duff and J. H. Conway, Discrete Computational Geom., 14 (1995), pp. 237-259.
• Expressing (a^2 + b^2 + c^2 + d^2 )^2 as a Sum of 23 Sixth Powers [Abstract, postscript, pdf], R. H. Hardin and N. J. A. Sloane, Journal of Combinatorial Theory, Series A, 68 (1994), pp. 481-485. Also DIMACS Technical Report 93-54, August 1993.
• New Spherical 4-Designs [ Abstract, postscript, pdf], R. H. Hardin and N. J. A. Sloane, Discrete Mathematics, 106/107 (1992), pp. 255-264 (Topics in Discrete Mathematics, vol. 7, "A Collection of Contributions in Honour of Jack Van Lint", ed. P. J. Cameron and H. C. A. van Tilborg, North-Holland, 1992).
• Spherical Designs in Four Dimensions (Extended Abstract) [Abstract, pdf, ps], N. J. A. Sloane, R. H. Hardin and P. Cara, Proceedings Information Theory Workshop (Paris, April 2003), 2003.

N. J. A. Sloane
11 South Adelaide Ave
Highland Park, NJ 08904 USA
Email address: njasloane@gmail.com