Function Space Examples

This example demonstrates how to create and visualize different function spaces.

import numpy as np
from fdg import BasisSpecs, FunctionSpace
from matplotlib import pyplot as plt

2D Function Space Example

This example creates a 2D function space using Bernstein basis functions of degrees 2 and 3, then plots the basis functions over a grid.

x, y = np.meshgrid(np.linspace(-1, 1, 51), np.linspace(-1, 1, 51))


space_2d = FunctionSpace(
    BasisSpecs("bernstein", 2),
    BasisSpecs("bernstein", 3),
)
bv = space_2d.evaluate(x, y)
assert np.allclose((np.sum(bv, axis=(-2, -1))), 1.0)  # Should be all ones

orders = space_2d.orders
fig_2d, axes_2d = plt.subplots(orders[0] + 1, orders[1] + 1, figsize=(12, 6))

for i in range(orders[0] + 1):
    for j in range(orders[1] + 1):
        ax = axes_2d[i, j]
        c = ax.contourf(x, y, bv[:, :, i, j], levels=11, cmap="viridis", vmin=0, vmax=1)
        fig_2d.colorbar(c, ax=ax)
        ax.set_title(f"2D Basis Function {i}, {j}")

fig_2d.tight_layout()
plt.show()