EMPR vs HDMR on a 2D Tensor

Run EMPR and HDMR on the same 2D tensor, compare the reconstructions, and visualize the remaining approximation errors.

Input shape: (32, 32)
EMPR mean absolute error: 4.1843427594362437e-19
HDMR mean absolute error: 2.879912020664621e-20
Mean absolute difference between reconstructions: 4.0657581468206416e-19

import matplotlib.pyplot as plt
import numpy as np

from hdmrlib import EMPR, HDMR


x = np.linspace(0.0, 1.0, 32)
y = np.linspace(0.0, 1.0, 32)

X = (
    0.5
    + np.sin(np.pi * x)[:, None]
    + 0.8 * np.cos(np.pi * y)[None, :]
    + 0.5 * np.outer(x, y)
    + 0.3 * np.exp(-40.0 * ((x[:, None] - 0.7) ** 2 + (y[None, :] - 0.3) ** 2))
)

empr = EMPR(X, order=2)
X_empr = np.asarray(empr.reconstruct(), dtype=np.float64)

hdmr = HDMR(X, order=2)
X_hdmr = np.asarray(hdmr.reconstruct(), dtype=np.float64)

empr_abs_err = np.abs(X - X_empr)
hdmr_abs_err = np.abs(X - X_hdmr)
recon_diff = np.abs(X_empr - X_hdmr)

print("Input shape:", X.shape)
print("EMPR mean absolute error:", float(np.mean(empr_abs_err)))
print("HDMR mean absolute error:", float(np.mean(hdmr_abs_err)))
print("Mean absolute difference between reconstructions:", float(np.mean(recon_diff)))

vmin = min(X.min(), X_empr.min(), X_hdmr.min())
vmax = max(X.max(), X_empr.max(), X_hdmr.max())

err_vmax = max(empr_abs_err.max(), hdmr_abs_err.max(), recon_diff.max())

fig = plt.figure(figsize=(12, 7), constrained_layout=True)
gs = fig.add_gridspec(2, 4, width_ratios=[1, 1, 1, 0.05])

ax00 = fig.add_subplot(gs[0, 0])
ax01 = fig.add_subplot(gs[0, 1])
ax02 = fig.add_subplot(gs[0, 2])
cax0 = fig.add_subplot(gs[0, 3])

ax10 = fig.add_subplot(gs[1, 0])
ax11 = fig.add_subplot(gs[1, 1])
ax12 = fig.add_subplot(gs[1, 2])
cax1 = fig.add_subplot(gs[1, 3])

im0 = ax00.imshow(X, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
ax00.set_title("Original tensor")

ax01.imshow(X_empr, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
ax01.set_title("EMPR reconstruction")

ax02.imshow(X_hdmr, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
ax02.set_title("HDMR reconstruction")

fig.colorbar(im0, cax=cax0)

im1 = ax10.imshow(empr_abs_err, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
ax10.set_title("EMPR absolute error")

ax11.imshow(hdmr_abs_err, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
ax11.set_title("HDMR absolute error")

ax12.imshow(recon_diff, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
ax12.set_title("Absolute difference")

fig.colorbar(im1, cax=cax1)

plt.show()