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#!/usr/bin/env python3
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 1, 1000)
# Linear function
y_linear = x
# Step function
y_step = np.piecewise(
x,
[
x < 0.125,
(x >= 0.125) & (x < 0.375),
(x >= 0.375) & (x < 0.625),
(x >= 0.625) & (x < 0.875),
x >= 0.875
],
[0.0, 1/4, 2/4, 3/4, 1.0]
)
y_step2 = np.piecewise(
x,
[
x < 0.0625,
(x >= 0.0625) & (x < 0.1875),
(x >= 0.1875) & (x < 0.3125),
(x >= 0.3125) & (x < 0.4375),
(x >= 0.4375) & (x < 0.5625),
(x >= 0.5625) & (x < 0.6875),
(x >= 0.6875) & (x < 0.8125),
(x >= 0.8125) & (x < 0.9375),
x >= 0.9375
],
[0/8, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1.0]
)
# Smooth cos²-like ramp from 0 → 1 over full domain
y_cos2 = np.sin((np.pi / 2.0) * x) ** 2
y_cos2_shift = np.sin((np.pi / 2.0) * (x+0.125)/1.25) ** 2
# Plot
plt.figure(figsize=(8, 6))
plt.plot(x, y_linear, label="y = x", linewidth=2)
plt.step(x, y_step, where="post", label="PSM subgrid of 8", linewidth=2)
plt.step(x, y_step2, where="post", label="PSM subgrid of 8", linewidth=2)
plt.plot(x, y_cos2, label=r'HLBM e_h:cell size 1:1', linewidth=2)
plt.plot(x, y_cos2_shift, label=r'HLBM e_h:cell size 1.25:1', linewidth=2)
plt.xlim(0, 1)
plt.ylim(0, 1)
plt.grid(True)
plt.legend()
plt.xlabel("x")
plt.ylabel("y")
plt.title("Linear + Step + Smooth Cos² Ramp")
plt.show()
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