how to produce every permutation of positioning 20 values of -1 in a 1-by-41 vector of ones?

Question

I have written different code to produce different permutations of ones and minus ones. they work for matrixes with small dimensions:

for example:

S=[-1          


        

Answer 1

I'm not an expert in Matlab so I can't speak for all of the resources available, however, I know that your task is feasible on a standard laptop without any fancy high performance services such as https://aws.amazon.com/hpc/.

I have authored a package in R called RcppAlgos that is capable of completing this task comfortably in a few hours. Here is the code:

options(scipen = 999)
library(parallel)
library(RcppAlgos)

## WARNING Don't run this unless you have a few hours on your hand

## break up into even intervals of one million
firstPart <- mclapply(seq(1, 269128000000, 10^6), function(x) {
    temp <- permuteGeneral(c(1L,-1L), freqs = c(21,20), lower = x, upper = x + 999999)
    ## your analysis here
    x
}, mc.cores = 8)

## get the last few results and complete analysis
lastPart <- permuteGeneral(c(1L, -1L), freqs = c(21, 20), 
                           lower = 269128000000, upper = 269128937220)
## analysis for last part goes here

And to give you a demonstration of the efficiency of this setup, we will demonstrate how fast the first one billion results are completed.

system.time(mclapply(seq(1, 10^9, 10^6), function(x) {
    temp <- permuteGeneral(c(1L, -1L), freqs = c(21, 20), lower = x, upper = x + 999999)
    ## your analysis here
    x
}, mc.cores = 8))

   user  system elapsed 
121.158  64.057  27.182

Under 30 seconds for 1000000000 results!!!!!!!

So, this will not take over 3000 days as @CrisLuengo calculated but rather a conservative estimate of 30 seconds per billion gives :

(269128937220 / 1000000000 / 60) * 30 ~= 134.5645 minutes

I should also note that with the setup above you are only using 1251.2 Mb at a time, so your memory will not explode.

testSize <- object.size(permuteGeneral(c(1L,-1L), freqs = c(21,20), upper = 1e6))
print(testSize, units = "Mb")
156.4 Mb ## per core

All results were obtained on a MacBook Pro 2.8GHz quad core (with 4 virtual cores.. 8 total).

Edit:

As @CrisLuengo points out, the above only measures generating that many permutations and does not factor in the time taken for analysis of each computation. After some more clarification and a new question, we have that answer now... about 2.5 days!!!