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Lab5.py
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Lab5.py
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import scipy.stats as st
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse
sizes = [20, 60, 100]
ro = [0, 0.5, 0.9]
def E(z):
return np.mean(z)
def E_2(z):
return np.mean(np.power(z, 2))
def D(z):
return np.var(z)
def quadr(x, y):
medx = np.median(x)
medy = np.median(y)
sum_e = 0
for i in range(0, len(x)):
sum_e = sum_e + np.sign(x[i] - medx) * np.sign(y[i] - medy)
return sum_e / len(x)
def pearsonr(x, y):
return st.pearsonr(x, y)[0]
def spearmanr(x, y):
return st.spearmanr(x, y)[0]
cor_coef = {
'pearson': pearsonr,
'spearman': spearmanr,
'quadr': quadr
}
def normal_dist(ro_e, N):
x_mean = 0
y_mean = 0
std_x = 1
std_y = 1
cov = [[std_x**2, std_x*std_y*ro_e], [std_x*std_y*ro_e, std_y**2]]
return st.multivariate_normal.rvs(mean=[x_mean, y_mean], cov=cov, size=N)
def mix_norm_dist(N):
x_mean1 = 0
y_mean1 = 0
std_x1 = 1
std_y1 = 1
x_mean2 = 0
y_mean2 = 0
std_x2 = 10
std_y2 = 10
ro1 = 0.9
ro2 = -0.9
cov1 = [[std_x1**2, std_x1*std_y1*ro1], [std_x1*std_y1*ro1, std_y1**2]]
cov2 = [[std_x2**2, std_x2*std_y2*ro2], [std_x2*std_y2*ro2, std_y2**2]]
return 0.9 * st.multivariate_normal.rvs(mean=[x_mean1, y_mean1], cov=cov1, size=N) + 0.1 * st.multivariate_normal.rvs(mean=[x_mean2, y_mean2], cov=cov2, size=N)
def eigsorted(cov):
vals, vecs = np.linalg.eigh(cov)
order = vals.argsort()[::-1]
return vals[order], vecs[:, order]
file = open('out.txt', 'w')
for size in sizes:
for coef in cor_coef.keys():
file.write(coef + str(size) + '------------\n')
for r in ro:
vares = [normal_dist(r, size) for i in range(0, 1000)]
vars_x = [[r[0] for r in var] for var in vares]
vars_y = [[r[1] for r in var] for var in vares]
cor_arr = [cor_coef[coef](vars_x[i], vars_y[i]) for i in range(0, len(vars_x))]
file.write(str(r) + ': E=' + str(E(cor_arr)) + ' E_2=' + str(E_2(cor_arr)) + ' D=' + str(D(cor_arr)) + '\n')
vares = [mix_norm_dist(size) for i in range(0, 1000)]
vars_x = [[r[0] for r in var] for var in vares]
vars_y = [[r[1] for r in var] for var in vares]
cor_arr = [cor_coef[coef](vars_x[i], vars_y[i]) for i in range(0, len(vars_x))]
file.write('for mixin: E=' + str(E(cor_arr)) + ' E_2=' + str(E_2(cor_arr)) + ' D=' + str(D(cor_arr)) + '\n')
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14, 12))
ax = axes.flatten()
for i in range(0, 4):
if i != 3:
points = normal_dist(ro[i], size)
ax[i].set_title('n = ' + str(size) + ', r=' + str(ro[i]))
else:
points = mix_norm_dist(size)
ax[i].set_title('n = ' + str(size) + ', mix')
nstd = 2
r_x = [point[0] for point in points]
r_y = [point[1] for point in points]
ax[i].plot(r_x, r_y, 'bo', ms=4)
cov = np.cov(r_x, r_y)
vals, vecs = eigsorted(cov)
theta = np.degrees(np.arctan2(*vecs[:, 0][::-1]))
w, h = 2 * nstd * np.sqrt(vals)
ell = Ellipse(xy=(np.mean(r_x), np.mean(r_y)),
width=w, height=h,
angle=theta, color='black')
ell.set_facecolor('none')
ax[i].add_artist(ell)
plt.tight_layout()
fig.savefig('ellipse n=' + str(size))