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object HilbertIndex

The following code is based on this paper: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=bfd6d94c98627756989b0147a68b7ab1f881a0d6 with optimizations around matrix manipulation taken from this one: https://pdfs.semanticscholar.org/4043/1c5c43a2121e1bc071fc035e90b8f4bb7164.pdf

At a high level you construct a GeneratorTable with the getStateGenerator method. That represents the information necessary to construct a state list for a given number of dimension, N. Once you have the generator table for your dimension you can construct a state list. You can then turn those state lists into compact state lists that store all the information in one large array of longs.

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  11. def getStateGenerator(n: Int): GeneratorTable

    Construct the generator table for a space of dimension n.

    Construct the generator table for a space of dimension n. This table consists of 2n rows, each row containing Y, X1, and TY. Y The index in the array representing the table. (0 to (2n - 1)) X1 A coordinate representing points on the curve expressed as an n-point. These are arranged such that if two rows differ by 1 in Y then the binary representation of their X1 values differ by exactly one bit. These are the "Gray-codes" of their Y value. TY A transformation matrix that transforms X2(1) to the X1 value where Y is zero and transforms X2(2) to the X1 value where Y is (2^n - 1)

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