Algorithm - 2023.2 English

Vitis Libraries

Release Date
2023.2 English

Low-Discrepancy (LD) Sequence is an indicator for how evenly a random sequence is distributed in sample space. The definition of discrepancy,

\[D_{N}(P) = \underset{B \in J} {sup} \lvert \frac {A(B)}{N} - \lambda _{s}(B) \rvert\]

A digital radical inverse

\[\Phi _{b,C}(i) = (b^{-1} \cdots b^{-M}) \begin{bmatrix} C( a_{0}(i) \cdots a_{M-1}(i))^{T} \end{bmatrix}\]

where \(i =\sum_{l=0}^{M-1} a_{l}(i)b^{l}\), \(b\) is a non-negative integer. For each dimension of sobol sequence, it is comprised by a \(b=2\) radical inversion, which have a individual matrix C inside.