Contents

choosegen2()

Usage:

choosegen2(k,p, all:T [,res:r]), positive integers k, p, r.
choosegen2(k,p, tries:m [,res:r]), positive integers k, p, m, and r.

Keywords: aliasing, design, factorial

choosegen2(k,p,all:T) , where k, p and r are positive integers, searches
all potential sets of generators for a 2^(k-p) fractional factorial
design.  It returns information on a generator with maximum resolution.

choosegen2(k,p, tries:m), where m > 0 is an integer, does the same,
except it searches only m randomly selected sets of generators.

choosegen2(k,p,all:T,res:r) and choosegen2(k,p,tries:m,res:r), where r
is a positive integer, do the same, except they stop the search at the
first design of resolution r.  If none is found, they return information
on a set having the highest resolution found.

The value returned is
  structure(resolution:bestres,generators:bestgen,aberration:aber,\
      basis:genmat)

Integer bestres > 0 is the best resolution found.

bestgen is a CHARACTER vector of length p with the names such as "ABDF"
of the defining contrasts in the set chosen.

aber is a vector of k integers >= 0 with ab[i] containing the number
of contrast with i letters that are confounded with "I".

genmat is a p by k matrix with entries 0 and 1, one row for each element
of bestgen.  genmat[i,j] is 1 if and only if factor j is bestgen[i].
For example, if bestgen[i] is "ABDF", genmat[i,] is vector(1,1,0,1,0,1
[,...])'.  genmat can be used as an argument to aliases2() to determine
all the aliases of any contrast.

Examples:
  Cmd> choosegen2(5,2,all:T)  # find best resolution
  component: resolution
  (1)           3
  component: generators
  (1) "ABCD"
  (2) "BCE"
  component: aberration
  (1)           0           0           2           1           0
  component: basis
  (1,1)           1           1           1           1           0
  (2,1)           0           1           1           0           1

  Cmd> choosegen2(5,2,all:T,res:4)  # try to find 4 (we won't)
  component: resolution
  (1)           3
  component: generators
  (1) "ABCD"
  (2) "BCE"
  component: aberration
  (1)           0           0           2           1           0
  component: basis
  (1,1)           1           1           1           1           0
  (2,1)           0           1           1           0           1

  Cmd> # look for 2^(9-4) resol. 4, just make 1000 tries, since\
       there are lots of combinations to explore

  Cmd> choosegen2(9,4,tries:1000,res:4)# look for 2^(9-4) resol. 4
  component: resolution
  (1)           4
  component: generators
  (1) "CDEF"
  (2) "BDEG"
  (3) "ABCEH"
  (4) "BCDJ"
  component: aberration
  (1)           0           0           0           7           7
  (6)           0           0           0           1
  component: basis
  (1,1)           0           0           1           1           1
  (1,6)           1           0           0           0
  (2,1)           0           1           0           1           1
  (2,6)           0           1           0           0
  (3,1)           1           1           1           0           1
  (3,6)           0           0           1           0
  (4,1)           0           1           1           1           0
  (4,6)           0           0           0           1

See also aliases2(), choosedef2(), confound2().