2D smoothing with Polyfit2DModel

Polyfit2DModel extends local polynomial regression to two-dimensional inputs. Bandwidths for each dimension are selected independently (or forced identical with same_bandwidth_for_2dim=True).

Basic usage

import numpy as np
from pflm.smooth import Polyfit2DModel, KernelType

rng = np.random.default_rng(0)
x1 = np.linspace(-1, 1, 40)
x2 = np.linspace(-1, 1, 40)
X1, X2 = np.meshgrid(x1, x2, indexing="ij")
Z = np.sin(np.pi * X1) * np.cos(np.pi * X2) + 0.1 * rng.standard_normal(X1.shape)

X = np.column_stack([X1.ravel(), X2.ravel()])
y = Z.ravel()

model = Polyfit2DModel(
    kernel_type=KernelType.GAUSSIAN,
    degree=1,
    interp_kind="linear",
)
model.fit(X, y, bandwidth_selection_method="gcv", num_points_reg_grid=80)
print("Bandwidths:", model.bandwidth1_, model.bandwidth2_)

# Predict on a finer grid
X1q = np.linspace(-1, 1, 100)
X2q = np.linspace(-1, 1, 100)
Zq = model.predict(X1q, X2q)
print("Output shape:", Zq.shape)

Shared bandwidth across dimensions

When you expect similar smoothness along both axes, force the solver to pick a single bandwidth.

model_shared = Polyfit2DModel(kernel_type=KernelType.GAUSSIAN, degree=1)
model_shared.fit(
    X, y,
    bandwidth_selection_method="gcv",
    same_bandwidth_for_2dim=True,
    num_points_reg_grid=80,
)
print("Shared bandwidth:", model_shared.bandwidth1_, "==", model_shared.bandwidth2_)

Fixed bandwidths

model_fixed = Polyfit2DModel(kernel_type=KernelType.EPANECHNIKOV, degree=1)
model_fixed.fit(X, y, bandwidth1=0.2, bandwidth2=0.3, num_points_reg_grid=80)
print("Fixed bw:", model_fixed.bandwidth1_, model_fixed.bandwidth2_)