resampling to avoid limit - nchoosek

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. .

[Adam Danz]

Sounds like you need to use randperm.

To choose 1000 unique random samples from values 1:429,

randperm(429, 1000)

Answer 1

[Steven Lord]

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?

[Joel Schelander]

I have 36 houses and 429 electric vehicles. So what the combinations do is:

What happens to the total power demand of house 1, 2 and 3 if they each have a vehicle?

nchoosek(429,3).

And study from 1 House to 36 Houses combined.

nchoosek(429,1)..nchoosek(429,2)... and so on.

Random permutation matrices is more what im looking for yes.

[Steven Lord]

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.