from matplotlib import gridspec
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm


linspace_size = 5000
linspace_left = -4
linspace_right = 4
x = np.linspace(linspace_left, linspace_right, linspace_size)
pdf = norm.pdf(x, 0)
pdf_cond = norm.pdf(x, 0) * 2
pdf_cond[x <= 0] = 0
cdf = np.cumsum(pdf) / (linspace_size / (linspace_right - linspace_left))
cdf_cond = np.cumsum(pdf_cond) / (linspace_size / (linspace_right - linspace_left))

fig = plt.figure()
gs = gridspec.GridSpec(2, 1)
ax0 = plt.subplot(gs[0])
plt.plot([], [], ' ', label="$X \sim \mathcal{N}(0, 1)$", color="black")
plt.plot(x, pdf, label="$f_X$")
plt.plot(x, pdf_cond, label="$f_{X|\{X>0\}}$")
plt.legend(prop={"size": 14})
plt.tick_params(
    axis='x', 
    which='both',
    bottom=False,      
    top=False,         
    labelbottom=False)

ax1 = plt.subplot(gs[1], sharex = ax0)
plt.plot(x, cdf, label="$F_X$")
plt.plot(x, cdf_cond, label="$F_{X|\{X>0\}}$")
plt.legend(prop={"size": 14})
plt.subplots_adjust(hspace=.05)

plt.savefig('plots/conditional_norm.svg')