Rank Distance Correlation (RDC)

import math

from pyxla import rdc
from pyxla.util import load_data
from pyxla.sampling import HilbertCurveSampler

sphere_sample = {
    "name": "Sphere",
    "X": HilbertCurveSampler(sample_size=100, dim=1, l_bound=-5, u_bound=5, seed=42),
    "F": lambda x: x**2,
    "V": [lambda x: x**2 - 2, lambda x: 8 * math.sin(20 * x)]
}

load_data(sphere_sample)

WARNING:root:The Hilbert curve with dimension 1 is just a number line. You are sampling around points on a number line.

rdc(sphere_sample)

WARNING:root:No D file is present, thus, computing the D file... Computing an entire D file can be time consuming. Instead, you can call the function with the keyword argument `compute_D_file` set to `False` to speed up computation, as only the required distances will be calculated.
INFO:root:D file has been loaded to the current sample and is saved to ./Sphere_D.csv

({'rdc_f0': np.float64(0.9994749459239282),
  'rdc_v0': np.float64(0.9995663926684593),
  'rdc_v1': np.float64(0.9077450192462247),
  'rdc_paretoV': np.float64(0.9563581206360782),
  'rdc_Deb': np.float64(0.9378577857785776),
  'rdc_paretoFV': np.float64(0.9993788346108831)},
 <Figure size 3000x500 with 6 Axes>)