resampling to avoid limit - nchoosek

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I am investigating the combination of vehicles and houses.
My equation for this is:
i=nchoosek(1:numel(VID1),size(Hcombos,2));
Where VID1 is a cell containing all the possible combinations of vechicles for one house and size(Hcombos2,2) is the number of households.
My problem is that I have 429 vehicles and 36 households. I need to limit the number of combinations I generate: when I combine 429 vehicles with 36 houses, I should get out 1000 (arbitrary) of those combinations. .
  1 Comment
Adam Danz
Adam Danz on 14 Apr 2021
Sounds like you need to use randperm.
To choose 1000 unique random samples from values 1:429,
randperm(429, 1000)

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Accepted Answer

Steven Lord
Steven Lord on 14 Apr 2021
Assuming VID1 has 429 elements and Hcombos has 36 rows, that means you're trying to generate one of this many combinations:
N = nchoosek(429, 36)
Warning: Result may not be exact. Coefficient is greater than 9.007199e+15 and is only accurate to 15 digits
N = 3.4817e+52
If you were planning to operate on each combination in turn, how fast can you perform those operations? Let's assume you could process a million combinations a second. How long would it take?
years(seconds(N/1e6))
ans = 1.1033e+39
To think about that period of time you need to look at the timeline of the far future.
Let's talk about the bigger picture for a second. What exactly do these combinations represent? Do you just want a logical matrix of size [numel(VID1),size(Hcombos,2)] with restrictions on how many true values can be in each row and/or each column, to map households and vehicles? Do you want random permutation matrices?
  2 Comments
Steven Lord
Steven Lord on 15 Apr 2021
Okay, so what you're looking for is a matrix of size [numberOfHouses numberOfVehicles] where each row has exactly one value equal to 1 and the rest are 0 and where each column has either no value equal to 1 or exactly one value equal to 1?
If you want the transpose of that matrix instead with the limitations on rows and columns swapped accordingly that's fine, I mainly just want to make sure I understand the problem.

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