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document notation of OAs
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wkjarosz committed Dec 7, 2023
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26 changes: 23 additions & 3 deletions include/sampler/OA.h
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Expand Up @@ -17,10 +17,30 @@ enum OffsetType : unsigned
};

/**
Base class for all Orthogonal Array-based samplers.
Base class for all Orthogonal Array-based samplers.
Provides member variables and functions for strength, randomization,
sub-strata jitter, and style of substrata offsets.
Provides member variables and functions for strength, randomization, sub-strata jitter, and style of substrata
offsets.
In the literature, an orthogonal array OA(N, k, n, t) denotes a (k × N) matrix whose entries are the numbers 1...n
with the property that in any subset of t rows of the matrix, each of the n^t possible t-tuples of these numbers
appears precisely λ times.
These parameters are typically given the following names (with interpretation for Monte Carlo sampling in
parenthases):
N is the number of experimental runs (number of points),
k is the number of factors (dimensions),
n is the number of levels (number of strata per dimension),
t is the strength (number of simultaneous dimensions that are stratified), and
λ is the index (number of points per stratum).
The definition of strength leads to the parameter relation
N = λnt.
In many constructions, n is a prime or a power of a prime.
Sometimes an OA is defined transposed to the above.
*/
class OrthogonalArray : public TSamplerMinMaxDim<2, (unsigned)-1>
{
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