def cmidcutd(x, y, z, slice_num=20):
#under condition z
x_vec = np.transpose(np.array([x]))
y_vec = np.transpose(np.array([slice(y, slice_num)]))
z_vec = np.transpose(np.array([z]))
return ee.cmidd(x_vec, y_vec, z_vec)
def casual_entropy(i, j, K, data):
x = data[i]
y = data[j]
if len(K) == 0:
return casual_entropy_empty(i, j, K, data)
#slice_num = int(np.power(len(x),1.0/2)/2)
slice_num = int(np.power(len(x), 0.4) / 2)
if x.dtype == 'float64':
x = slice(x, slice_num)
x_vec = np.array([[s] for s in x])
else:
x_vec = np.array([[s] for s in x])
if y.dtype == "float64":
y = slice(y, slice_num)
y_vec = np.array([[s] for s in y])
else:
y_vec = np.array([[s] for s in y])
print("index j " + j + "is discrete")
z_all = []
for k in K:
z = data[k]
if z.dtype == "float64":
z = slice(z, slice_num)
z_vec = np.array([[s] for s in z])
else:
z_vec = np.array([[s] for s in z])
z_all.append(z_vec)
z_combine = np.c_[tuple(z_all)]
#x_clone = np.copy(x_vec)
y_clone = np.copy(y_vec)
ns = 200
ci = 0.95
outputs = []
#outputs2 = []
for i in range(ns):
np.random.shuffle(y_clone)
outputs.append(ee.cmidd(x_vec, y_clone, z_combine, base=2))
# outputs2.append(ee.midd(x_clone,y_vec,base=2))
outputs.sort()
# outputs2.sort()
v = ee.cmidd(x_vec, y_vec, z_combine, base=2)
ave = np.mean(outputs)
ci0 = outputs[int((1. - ci) / 2 * ns)]
ci1 = outputs[int((1. + ci) / 2 * ns)]
if v > ci1:
if_large_zero = True
else:
if_large_zero = False
n = 200
useful_result = if_large_zero * v
std_modified = np.sqrt((n - 1) / n) * np.std(outputs)
# multi = abs(v-ave)/np.std(outputs)
multi = 0
#(statistic, pvalue) = stats.ttest_ind_from_stats(mean1=ave, std1=std_modified, nobs1=200, mean2=v, std2=0, nobs2=2,equal_val=False)
# res = stats.ttest_1samp(np.array(outputs),[ave,0])
statistic = 1
print("index " + j + " function: casual_entropy, the length of data",
len(x), "the slice number is", slice_num, "useful value is ",
useful_result, "multi sigma is ", multi)
# print("statistic, pvalue",statistic,pvalue)
return useful_result, v, ave, (
ci0, ci1), if_large_zero, abs(statistic) * if_large_zero
def cmi(self, X, Y, Z):
np.random.seed(0)
return ee.cmidd(X.copy(order='C'),
Y.copy(order='C'),
z=Z.copy(order='C'))
err.append((tempmean - tempent[samplo], tempent[samphi] - tempmean))
print('samples used', Ntry)
print('estimated MI', ent)
print('95% conf int.\n', err)
# DISCRETE ESTIMATORS
print("\n\nTest of the discrete entropy estimators\n")
print("For z = y xor x, w/x, y uniform random binary, we should get H(x)=H(y)=H(z) = 1, H(x:y) etc = 0, H(x:y|z) = 1")
x = [0, 0, 0, 0, 1, 1, 1, 1]
y = [0, 1, 0, 1, 0, 1, 0, 1]
z = [0, 1, 0, 1, 1, 0, 1, 0]
print("H(x), H(y), H(z)", ee.entropyd(x), ee.entropyd(y), ee.entropyd(z))
print("H(x:y), etc", ee.midd(x, y), ee.midd(z, y), ee.midd(x, z))
print("H(x:y|z), etc", ee.cmidd(x, y, z), ee.cmidd(z, y, x), ee.cmidd(x, z, y))
# KL Div estimator
print("\n\nKl divergence estimator (not symmetric, not required to have same num samples in each sample set")
print("should be 0 for same distribution")
sample1 = [[2 * random.random()] for i in range(200)]
sample2 = [[2 * random.random()] for i in range(300)]
print('result:', ee.kldiv(sample1, sample2))
print("should be infinite for totally disjoint distributions (but this estimator has an upper bound like log(dist) between disjoint prob. masses)")
sample2 = [[3 + 2 * random.random()] for i in range(300)]
print('result:', ee.kldiv(sample1, sample2))
def test_discrete(size=1000, y_func=lambda x: x**2):
print("\nTest discrete.")
print('samples used', Ntry)
print('estimated MI', ent)
print('95% conf int.\n', err)
# DISCRETE ESTIMATORS
print("\n\nTest of the discrete entropy estimators\n")
print(
"For z = y xor x, w/x, y uniform random binary, we should get H(x)=H(y)=H(z) = 1, H(x:y) etc = 0, H(x:y|z) = 1"
)
x = [0, 0, 0, 0, 1, 1, 1, 1]
y = [0, 1, 0, 1, 0, 1, 0, 1]
z = [0, 1, 0, 1, 1, 0, 1, 0]
print("H(x), H(y), H(z)", ee.entropyd(x), ee.entropyd(y), ee.entropyd(z))
print("H(x:y), etc", ee.midd(x, y), ee.midd(z, y), ee.midd(x, z))
print("H(x:y|z), etc", ee.cmidd(x, y, z), ee.cmidd(z, y, x), ee.cmidd(x, z, y))
# KL Div estimator
print(
"\n\nKl divergence estimator (not symmetric, not required to have same num samples in each sample set"
)
print("should be 0 for same distribution")
sample1 = [[2 * random.random()] for i in range(200)]
sample2 = [[2 * random.random()] for i in range(300)]
print('result:', ee.kldiv(sample1, sample2))
print(
"should be infinite for totally disjoint distributions (but this estimator has an upper bound like log(dist) between disjoint prob. masses)"
)
sample2 = [[3 + 2 * random.random()] for i in range(300)]
print('result:', ee.kldiv(sample1, sample2))
def first_plot():
el = EdgeList()
file_name = './BA_network_all.xlsx'
el.load_records(file_name)
#el.smooth_and_normalize_records(sl_normalize_indices=['degree'],smooth_length=100)
degree, if_rand = merge(el.records["degree"], el.records_random["degree"])
distances, if_rand = merge(el.records["distance"],
el.records_random["distance"])
print(if_rand.dtype == 'int64')
print(degree.dtype == 'float64')
#print(len(distances),len(if_rand),len(degree))
step_num = len(if_rand)
step_size = step_num // 10
edge_nums = np.arange(step_size, len(if_rand), step_size)
ent1 = []
ent2 = []
ent3 = []
ent4 = []
ent5 = []
ent6 = []
ent0 = []
ent7 = []
ents = {}
for i in edge_nums:
if_rand_cut = if_rand[i - step_size:i]
degree_cut = degree[i - step_size:i]
distances_cut = distances[i - step_size:i]
#print(len(if_rand_cut),len(degree_cut))
k = int(np.sqrt(len(degree_cut)))
slice_num = 20
slice_num = int(np.power(len(degree_cut), 1.0 / 3))
# print("length of datas, number of spaces",len(degree_cut),slice_num)
#print(k)
ent1.append(ep.midcut(if_rand_cut, degree_cut, slice_num=slice_num))
ent2.append(ep.midc(if_rand_cut, degree_cut, k=20))
# ent0.append(ep.cmidcutd(if_rand_cut, degree_cut,distances_cut))
k = 20
a, b = ep.cmiddc(if_rand_cut, distances_cut, degree_cut, k=k)
ent6.append(a)
ent7.append(b)
ent3.append(ep.cmiddcut(if_rand_cut, distances_cut, degree_cut))
if_rand_cut_copy = if_rand_cut.copy()
random.shuffle(if_rand_cut_copy)
ent4.append(ep.cmiddcut(if_rand_cut_copy, distances_cut, degree_cut))
random.shuffle(distances_cut)
ent5.append(ep.cmiddcut(if_rand_cut, distances_cut, degree_cut))
#ent5.append(ep.cmidcutd(if_rand_cut,degree_cut,distances_cut))
#print(a.all(),b.all(),c.all())
#ent5.append(ep.cmicut(if_rand_cut, degree_cut,distances_cut))
#ent6.append(ep.cmi(if_rand_cut, degree_cut,distances_cut))
print('len')
print(len(ent6))
print(len(ent0))
# print(ent6)
# x_vec = np.array([[s] for s in if_rand ])
# y_vec = np.array([[s] for s in degree ])
# print("midc",ee.midc(x_vec,y_vec,base=2,k=20))
# print("midc",ep.midc(if_rand,degree,k=40,base=2))
# print(ee.shuffle_test(ee.midc,x_vec,y_vec,base=2,k=10))
# print(ep.midc(if_rand,degree,k=20,base=2))
slice_num = int(np.power(len(degree), 1.0 / 2))
print(ep.midd(if_rand, distances))
x_vec = np.transpose(np.array([if_rand]))
y_vec = np.transpose(np.array([distances]))
z_vec = np.transpose(np.array([ep.slice(degree, slice_num)]))
print(ee.shuffle_test(ee.midd, x_vec, y_vec, base=2))
print(ee.shuffle_test(ee.midd, x_vec, z_vec, base=2))
print(ee.cmidd(x_vec, z_vec, y_vec, base=2))
# print(ee.shuffle_test(ee.cmidd,x_vec,y_vec,z_vec,base=2))
# plt.plot(ent0,label = r'0')
# plt.plot(ent6,label = r"6")
plt.plot(ent7, label=r"7")
plt.plot(ent1, 'vb-', label=r'1')
plt.plot(ent2, 'or--', label=r'2')
plt.plot(ent3, label=r'3')
plt.plot(ent4, label=r'4')
plt.plot(ent5, label=r'5')
# plt.plot(edge_nums, ent5, 'b',label='5')
# plt.plot(edge_nums, ent6, 'b--',label='6')
plt.legend()
plt.show()