Chebyshev - rebuilt with polysynth

%matplotlib inline
import warnings; warnings.filterwarnings("ignore")
import numpy as np
import matplotlib.pyplot as plt
import polysynth as ps

Basis

Chebyshev 1st & 2nd kind from the library; weighted variants via ps.Weighted.

cheb_t_w = ps.Weighted(ps.ChebyshevT(), lambda x: 1 / np.sqrt(1 - x**2) ** 0.5, "chebyshev_1st_weighted")
cheb_u_w = ps.Weighted(ps.ChebyshevU(), lambda x: np.sqrt(1 - x**2) ** 0.5, "chebyshev_2nd_weighted")

Visualization

1-D basis functions.

ps.plot_1d([ps.ChebyshevT(), ps.ChebyshevU(), cheb_t_w, cheb_u_w], n_max=8);

Masks Visualization

Random-coefficient fields (normalized to [0, 1]); each binary panel thresholds the same field at 0.5.

ps.plot_field_grid(ps.ChebyshevT(), 6, seed=0);

ps.plot_field_grid(ps.ChebyshevT(), 6, seed=0, binary=True);

ps.plot_field_grid(ps.ChebyshevT(), 8, seed=1);

ps.plot_field_grid(ps.ChebyshevT(), 8, seed=1, binary=True);

ps.plot_field_grid(ps.ChebyshevT(), 12, seed=2);

ps.plot_field_grid(ps.ChebyshevT(), 12, seed=2, binary=True);

ps.plot_field_grid(ps.ChebyshevU(), 6, seed=3);

ps.plot_field_grid(ps.ChebyshevU(), 6, seed=3, binary=True);

ps.plot_field_grid(cheb_u_w, 6, seed=4);

ps.plot_field_grid(cheb_u_w, 6, seed=4, binary=True);