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aliases2(basis [,effect:vec] [,length:j]), REAL matrix basis of alias
  generators, REAL vector vec of 0's and 1's, positive integer j

Keywords: aliasing, design, factorial
aliases2(basis) finds all aliases of I in a 2^(k-p) fractional factorial
and returns a CHARACTER vector of these aliases as its value.  k must be
no larger than 25, and factors are labeled A, B, C, ..., H, J, ... Z
(skipping I).

The p x k matrix basis contains the generators for the aliasing, one row
for each generator and one column for each factor in the design.  The
elements in basis are 0, -1, or 1.  A nonzero entry indicates that a
factor is present in the generator for that row. The sign of a generator
is the product of the signs of the nonzero elements of the generator.
For example, 1 0 1 0 0 -1 means -ACF is a generator (alias of I).

If basis is a (column) vector, it is changed to a row vector (1 by k
matrix) before proceding.

aliases2(basis,effect:vec) returns the aliases of vec, a vector of k 0s
and 1s that specifies an effect.

aliases2(basis [,effect:vec],length:j) does the same but returns only
aliases of length j.

 Cmd> print(format:"2.0f",b) # Matrix b is 2x5, so 2^(5-2) design
 (1,1)  1  1  1  0  0       [ABC is a generator]
 (2,1)  0  0  1  1 -1       [-CDE is a generator]

 Cmd> aliases2(b)   # aliases of I
 (1) "I"
 (2) "ABC"
 (3) "-CDE"
 (4) "-ABDE"

 Cmd> aliases2(b,length:3)  # length 3 aliases of I
 (1) "I"
 (2) "ABC"
 (3) "-CDE"

 Cmd> aliases2(b,effect:vector(1,1,0,0,0)) # aliases of AB
 (1) "AB"
 (2) "C"
 (3) "-ABCDE"
 (4) "-DE"

See also aliases3(), confound2(), choosedef2() and choosegen2().

Gary Oehlert 2003-01-15