Hello,
I'm trying to permute a vector of positive integers > 0 with the constraint
that each element must be <= twice the element before it (i.e. for some
vector x, x[i] <= 2*x[i-1]), assuming the "0th" element is 1. Hence the
first element of the vector must always be 1 or 2 (by assuming the "0th"
element is 1). Similarly, the 2nd must always be below/= 4, the 3rd always
below/= 6, etc.
Here's an example, suppose I have the vector x
x <- 2:6
This vector already fits the constraint, and a permutation such as
x.good <- c(2,4,6,5,3)
would also fit the constraint, but the vector
x.bad1 <- c(4,6,5,3,2)
does not work because of the 4 in the first position. The vector
x.bad2 <- c(2,6,5,3,4)
does not work because of the 6 in the second position.
Does anyone know of a pre-made function to permute a vector under such a
constrain? Or perhaps a clever way to somehow use a function (e.g. ---)
that permutes a contingency table constrained by the marginals?
If such possibilities are not out there, what about this idea:
Assume the given vector already complies with the constraint (e.g. x <-
2:6).
First "cut" the vector (like cutting a deck of cards) at some random (given
condition*) position p:
x1 <- x[1:(p-1)]
x2 <- x[p:length(x)]
x <- c(x2,x1)
* the condition is that p must be chosen such that x2[1] <= 2.
Then "shuffle" the updated vector x by swapping two of its elements, e.g.
temp.x <- x[i]
x[i] <- x[j]
x[j] <- temp.x
Here i and j must be chosen such that the resulting swap does not violate
the condition x[i] <= 2*x[i-1]. Ideally, all the possible swaps could be
represented in a matrix of 0/1 or FALSE/TRUE, such as
z <- c(2,4,6,5,3)
Z <- matrix(c( 1,0,0,0,0,
0,1,0,0,1,
0,0,1,1,1,
0,0,1,1,1,
0,1,1,1,1),5,5)
Then one would repeat these two processes many times, each time randomly
choosing to either cut or shuffle.
My issue is I don't really know how to get the matrix of allowable swaps--I
don't know how to automate distinguishing which swaps are allowable and
which aren't.
So my questions here are: most importantly does this method even seem sound
(i.e. are all possible solutions likely to have equal probability)? and
secondly, how would I find all possible swaps?
Thanks in advance for any insight.
-Andy
[[alternative HTML version deleted]]
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
