hilbertMapping {hilbertSimilarity}

Map High Dimensional Coordinates to Hilbert Index and back

Description

hilbertMapping will compute the Hilbert index for each row of a matrix of integer coordinates corresponding to sub-cubes in a high dimensional space.

Arguments

x

a matrix of a matrix of integer coordinates (see do.hilbert)

bits

the hilbert order, i.e. the number of cuts in each dimension

Details

Functions: TransposetoAxes AxestoTranspose Purpose: Transform in-place between Hilbert transpose and geometrical axes Example: b=5 bits for each of n=3 coordinates. 15-bit Hilbert integer = A B C D E F G H I J K L M N O is stored as its Transpose X[0] = A D G J M X[2]| X[1] = B E H K N <——-> | /X[1] X[2] = C F I L O axes |/ high low 0—— X[0] Axes are stored conventionally as b-bit integers. Author: John Skilling 20 Apr 2001 to 11 Oct 2003

The source code includes the correction suggested in the following StackOverflow discussion.

Value

a vector of hilbert index, one for each line in x

Author(s)

Marilisa Neri

Yann Abraham

John Skilling