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Add Padua points #15

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dedbd5b
feat: add padua nodes
alexfikl Dec 20, 2020
c01cf9b
chore: update baseline
alexfikl Jul 30, 2025
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202 changes: 202 additions & 0 deletions .basedpyright/baseline.json
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Expand Up @@ -438,6 +438,192 @@
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Expand Down Expand Up @@ -3795,6 +3981,22 @@
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75 changes: 75 additions & 0 deletions examples/plot-padua-nodes.py
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@@ -0,0 +1,75 @@
from __future__ import annotations

from typing import TYPE_CHECKING

import matplotlib.pyplot as plt
import numpy as np

import modepy as mp


if TYPE_CHECKING:
from modepy.typing import ArrayF


def _first_padua_curve(n: int, t: ArrayF) -> ArrayF:
return np.vstack([-np.cos((n + 1) * t), -np.cos(n * t)])


def _second_padua_curve(n: int, t: ArrayF) -> ArrayF:
return np.vstack([-np.cos(n * t), -np.cos((n + 1) * t)])


def _third_padua_curve(n: int, t: ArrayF) -> ArrayF:
return np.vstack([np.cos((n + 1) * t), np.cos(n * t)])


def _fourth_padua_curve(n: int, t: ArrayF) -> ArrayF:
return np.vstack([np.cos(n * t), np.cos((n + 1) * t)])


def plot_padua_nodes(alpha: float, beta: float, order: int, family: str) -> None:
if family == "first":
curve_fn = _first_padua_curve
elif family == "second":
curve_fn = _second_padua_curve
elif family == "third":
curve_fn = _third_padua_curve
elif family == "fourth":
curve_fn = _fourth_padua_curve
else:
raise ValueError(f"Unknown Padua curve family: '{family}'")

t = np.linspace(0, np.pi, 512)
curve = curve_fn(order, t)
nodes = mp.padua_jacobi_nodes(alpha, beta, order, family)
assert nodes.shape[1] == ((order + 1) * (order + 2) // 2)

fig = plt.figure()
ax = fig.gca()
ax.grid()

ax.plot(curve[0], curve[1])
for i, xi in enumerate(nodes.T):
ax.plot(nodes[0], nodes[1], "ko", markersize=8)
ax.text(*xi, str(i), color="k", fontsize=24, fontweight="bold")

ax.set_xlim((-1, 1))
ax.set_ylim((-1, 1))
ax.set_aspect("equal")
fig.savefig(f"padua_nodes_order_{order:02d}_family_{family}")
plt.show()


if __name__ == "__main__":
import argparse

parser = argparse.ArgumentParser()
parser.add_argument("--order", type=int, default=5)
parser.add_argument("--family", default="first",
choices=["first", "second", "third", "fourth"])
parser.add_argument("--alpha", type=float, default=-0.5)
parser.add_argument("--beta", type=float, default=-0.5)
args = parser.parse_args()

plot_padua_nodes(args.alpha, args.beta, args.order, args.family)
4 changes: 4 additions & 0 deletions modepy/__init__.py
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Expand Up @@ -61,6 +61,8 @@
legendre_gauss_lobatto_tensor_product_nodes,
legendre_gauss_tensor_product_nodes,
node_tuples_for_space,
padua_jacobi_nodes,
padua_nodes,
random_nodes_for_shape,
tensor_product_nodes,
warp_and_blend_nodes,
Expand Down Expand Up @@ -168,6 +170,8 @@
"nodal_quadrature_test_matrix",
"node_tuples_for_space",
"orthonormal_basis_for_space",
"padua_jacobi_nodes",
"padua_nodes",
"quadrature_for_space",
"random_nodes_for_shape",
"resampling_matrix",
Expand Down
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