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PolarQuant polar-transformation quantization

Source: R/polqnt_native.R
morie_polqnt.Rd

Recursively replaces coordinate pairs by (radius, angle), quantizes only the angles on uniform grids and keeps the final radius exactly (Han et al. 2025, Definition 1). Level-1 angles span \([0, 2\pi)\) and are given bits_first bits; deeper levels span \([0, \pi/2]\) and get bits_rest.

Usage

morie_polqnt(x, bits_first = 4L, bits_rest = 2L, quantize = TRUE)

Arguments

x

Vector whose length is a power of two, at least 2.

bits_first

Bits per level-1 angle.

bits_rest

Bits per deeper angle.

quantize

TRUE (default) quantizes the angles; FALSE reconstructs from the exact angles, which isolates the transformation from the quantization and must be lossless. Both routes are available.

Value

A list with reconstruction, estimate, radius, codes, mse, relative_l2, bits_per_coord, n, method.

References

Han, I., Kacham, P., Karbasi, A., Mirrokni, V. and Zandieh, A. (2025). PolarQuant. arXiv:2502.02617.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_polqnt(V)
#> $reconstruction
#> [1] 2.449244 3.665552 3.665552 5.485886 3.665552 5.485886 5.485886 8.210209
#> 
#> $estimate
#> [1] 2.449244 3.665552 3.665552 5.485886 3.665552 5.485886 5.485886 8.210209
#> 
#> $radius
#> [1] 14.28286
#> 
#> $codes
#> [1] 2 2 2 2 2 2 2
#> 
#> $mse
#> [1] 1.488373
#> 
#> $relative_l2
#> [1] 0.2415938
#> 
#> $bits_per_coord
#> [1] 2.75
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "PolarQuant polar-transformation quantization"
#>