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figures_neoclassical_growth_concave_convex.py
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figures_neoclassical_growth_concave_convex.py
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import jax.numpy as jnp
import matplotlib.pyplot as plt
import numpy as np
import os
from neoclassical_growth_concave_convex_matern import (
neoclassical_growth_concave_convex_matern,
)
from mpl_toolkits.axes_grid1.inset_locator import (
zoomed_inset_axes,
mark_inset,
inset_axes,
)
fontsize = 14
ticksize = 14
figsize = (15, 5)
params = {
"font.family": "serif",
"figure.figsize": figsize,
"figure.dpi": 80,
"figure.edgecolor": "k",
"figure.constrained_layout.use": True, # Adjust layout to prevent overlap
"font.size": fontsize,
"axes.labelsize": fontsize,
"axes.titlesize": fontsize,
"xtick.labelsize": ticksize,
"ytick.labelsize": ticksize,
}
plt.rcParams.update(params)
## Plots for concave-convex production function
sol_1 = neoclassical_growth_concave_convex_matern(k_0=0.5, train_points=20)
sol_2 = neoclassical_growth_concave_convex_matern(k_0=1.0, train_points=20)
sol_3 = neoclassical_growth_concave_convex_matern(k_0=3.0, train_points=20)
sol_4 = neoclassical_growth_concave_convex_matern(k_0=4.0, train_points=20)
output_path = "figures/neoclassical_growth_model_concave_convex.pdf"
plt.figure(figsize=(15, 5))
k_hat_1 = sol_1["k_test"]
k_hat_2 = sol_2["k_test"]
k_hat_3 = sol_3["k_test"]
k_hat_4 = sol_4["k_test"]
c_hat_1 = sol_1["c_test"]
c_hat_2 = sol_2["c_test"]
c_hat_3 = sol_3["c_test"]
c_hat_4 = sol_4["c_test"]
T = sol_1["t_train"].max()
t = sol_1["t_test"]
ax_capital = plt.subplot(1, 2, 1)
plt.plot(t, k_hat_1, color="b", label=r"$\hat{x}(t): x_0 = 0.5$")
plt.plot(t, k_hat_2, color="gray", label=r"$\hat{x}(t): x_0 = 1$")
plt.plot(t, k_hat_3, color="r", label=r"$\hat{x}(t): x_0 = 3$")
plt.plot(t, k_hat_4, color="c", label=r"$\hat{x}(t): x_0 = 4$")
# plt.axhline(y=sol_1["k_ss_low"], linestyle="-.", color="k", label=r"$x_1^*$: Steady-State")
# plt.axhline(y=sol_1["k_ss_high"], linestyle="dashed", color="k", label=r"$x_2^*$: Steady-State")
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Capital: $x(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
ax_consumption = plt.subplot(1, 2, 2)
plt.plot(t, c_hat_1, color="b", label=r"$\hat{y}(t): x_0 = 0.5$")
plt.plot(t, c_hat_2, color="gray", label=r"$\hat{y}(t): x_0 = 1$")
plt.plot(t, c_hat_3, color="r", label=r"$\hat{y}(t): x_0 = 3$")
plt.plot(t, c_hat_4, color="c", label=r"$\hat{y}(t): x_0 = 4$")
# plt.axhline(y=sol_1["c_ss_low"], linestyle="-.", color="k", label=r"$y_1^*$: Steady-State")
# plt.axhline(y=sol_1["c_ss_high"], linestyle="dashed", color="k", label=r"$y_2^*$: Steady-State")
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Consumption: $y(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
plt.savefig(output_path, format="pdf")
sols = [
neoclassical_growth_concave_convex_matern(k_0=k_0, train_points=20)
for k_0 in np.linspace(0.5, 4.0, 70)
]
output_path = "figures/neoclassical_growth_model_concave_convex_threshold.pdf"
plt.figure(figsize=(15, 5))
T = sols[0]["t_train"].max()
t = sols[0]["t_test"]
ax_capital = plt.subplot(1, 2, 1)
for sol in sols:
plt.plot(t, sol["k_test"], color="gray")
# plt.axhline(
# y=sols[0]["k_ss_low"], linestyle="-.", color="k", label=r"$k_1^*$: Steady-State"
# )
# plt.axhline(
# y=sols[0]["k_ss_high"],
# linestyle="dashed",
# color="k",
# label=r"$k_2^*$: Steady-State",
# )
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Capital: $x(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
ax_consumption = plt.subplot(1, 2, 2)
for sol in sols:
plt.plot(t, sol["c_test"], color="b")
# plt.axhline(
# y=sols[0]["c_ss_low"], linestyle="-.", color="k", label=r"$c_1^*$: Steady-State"
# )
# plt.axhline(
# y=sols[0]["c_ss_high"],
# linestyle="dashed",
# color="k",
# label=r"$c_2^*$: Steady-State",
# )
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Consumption: $y(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
plt.savefig(output_path, format="pdf")