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U_fun.py
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import numpy as np
from scipy import stats
from numba import njit
rng = np.random.default_rng(66)
# Pearson correlation function
def pearson_fun(x1, x2, x3, x4, x5):
return np.abs((x1 - x2 * x3) / np.sqrt((x4 - x2 ** 2) * (x5 - x3 ** 2)))
# Pearson correlation method，X and Y are lists
def pearson_com(X, Y, N, m, p):
pearson_mid1 = np.zeros((m, p))
pearson_mid2 = np.zeros((m, p))
pearson_mid3 = np.zeros((m, p))
pearson_mid4 = np.zeros((m, p))
pearson_mid5 = np.zeros((m, p))
for i in range(m):
pearson_mid1[i, :] = np.sum( X[i] * Y[i].reshape(-1, 1), axis=0 )
pearson_mid2[i, :] = np.sum(X[i], axis=0)
pearson_mid3[i, :] = np.repeat( np.sum(Y[i]), p )
pearson_mid4[i, :] = np.sum(X[i] ** 2, axis=0)
pearson_mid5[i, :] = np.repeat( np.sum(Y[i] ** 2), p )
pearson_x1 = np.sum(pearson_mid1, axis=0) / N
pearson_x2 = np.sum(pearson_mid2, axis=0) / N
pearson_x3 = np.sum(pearson_mid3, axis=0) / N
pearson_x4 = np.sum(pearson_mid4, axis=0) / N
pearson_x5 = np.sum(pearson_mid5, axis=0) / N
pearson_value = pearson_fun(pearson_x1, pearson_x2, pearson_x3, pearson_x4, pearson_x5)
return pearson_value
# X and Y are lists
def pearson_threshold(X, Y, N, m, n, p, q_new):
X_new = [
rng.multivariate_normal(
mean=np.zeros(q_new), cov=np.eye(q_new), size=n)
for _ in range(m)
]
threshold_new = pearson_com(X_new, Y, N, m, q_new)
threshold_value = pearson_com(X, Y, N, m, p)
index = np.where(threshold_value >= np.max(threshold_new))[0]
modified_vector = np.zeros(p)
modified_vector[index] = threshold_value[index]
beta_value = modified_vector
return {'index': index, 'beta_value': beta_value}
# Kendall τ function
def Kend_fun(x1):
return np.abs(x1 - 1 / 4)
# Kendall τ method，X and Y are lists
# @njit
def kend_com(X, Y, N, m, n, p):
Kendall_x1 = np.zeros(p)
for q in range(p):
mid = np.zeros(m)
for i in range(m):
mid[i] = np.sum((X[i][:, q].reshape(-1, 1) < X[i][:, q]) * (Y[i].reshape(-1,1) < Y[i]))
Kendall_x1[q] = np.sum(mid) / (m * n * (n - 1))
Kend_value = Kend_fun(Kendall_x1)
return Kend_value
# X and Y are lists
# @njit
def Kendall_threshold(X, Y, N, m, n, p, q_new):
X_new = [
rng.multivariate_normal(
mean=np.zeros(q_new), cov=np.eye(q_new), size=n )
for _ in range(m)
]
threshold_new = kend_com(X_new, Y, N, m, n, q_new)
threshold_value = kend_com(X, Y, N, m, n, p)
index = np.where(threshold_value >= np.max(threshold_new))[0]
modified_vector = np.zeros(p)
modified_vector[index] = threshold_value[index]
beta_value = modified_vector
return {'index': index, 'beta_value': beta_value}
# SIRS correlation method，X and Y are lists
# @njit
def SIRS_com(X, Y, N, m, n, p):
SIRS_x1 = np.zeros(p)
for q in range(p):
mid = np.zeros(m)
for i in range(m):
mid1 = Y[i].reshape(-1,1) < Y[i]
mid2 = np.sum( mid1 * X[i][:, q].reshape(-1, 1), axis=0 )
mid[i] = np.sum(mid2 ** 2)
SIRS_x1[q] = np.sum(mid) / (m * n * (n - 1) * (n - 2))
return SIRS_x1
def SIRS_threshold(X, Y, N, m, n, p, q_new):
X_new = [
rng.multivariate_normal(
mean=np.zeros(q_new), cov=np.eye(q_new), size=n)
for _ in range(m)
]
X_new = [ stats.zscore(X_new[i], ddof=1) for i in range(m) ]
X = [ stats.zscore(X[i], ddof=1) for i in range(m) ]
Y = [ stats.zscore(Y[i], ddof=1) for i in range(m) ]
threshold_new = SIRS_com(X_new, Y, N, m, n, q_new)
threshold_value = SIRS_com(X, Y, N, m, n, p)
index = np.where(threshold_value >= np.max(threshold_new))[0]
modified_vector = np.zeros(p)
modified_vector[index] = threshold_value[index]
beta_value = modified_vector
return {'index': index, 'beta_value': beta_value}
# DC function
@njit
def DC_fun(x1, x2, x3, x4, x5, x6, x7, x8):
value = (x1 + x2 * x3 - 2 * x4) / np.sqrt( (x5 + x2 ** 2 - 2 * x6) * (x7 + x3 ** 2 - 2 * x8) )
return value
# DC method，X and Y are lists
# @njit
def DC_com(X, Y, N, m, n, p):
DC_x1 = np.zeros(p)
DC_x2 = np.zeros(p)
DC_x3 = np.zeros(p)
DC_x4 = np.zeros(p)
DC_x5 = np.zeros(p)
DC_x6 = np.zeros(p)
DC_x7 = np.zeros(p)
DC_x8 = np.zeros(p)
for q in range(p):
mid1 = np.zeros(m)
mid2 = np.zeros(m)
mid3 = np.zeros(m)
mid4 = np.zeros(m)
mid5 = np.zeros(m)
mid6 = np.zeros(m)
mid7 = np.zeros(m)
mid8 = np.zeros(m)
for i in range(m):
x_q = X[i][:, q]
y_i = Y[i]
mid1[i] = np.sum( np.abs(x_q.reshape(-1,1) - x_q) * np.abs( y_i.reshape(-1,1) - y_i ) )
mid2[i] = np.sum( np.abs(y_i.reshape(-1,1) - y_i) )
mid3[i] = np.sum( np.abs(x_q.reshape(-1,1) - x_q) )
mid4[i] = np.sum(
np.sum( np.abs(x_q.reshape(-1,1) - x_q), axis=0 )
* np.sum( np.abs(y_i.reshape(-1,1) - y_i), axis=0 )
)
mid5[i] = np.sum( (y_i.reshape(-1,1) - y_i)**2 )
mid6[i] = np.sum(
np.sum( np.abs(y_i.reshape(-1,1) - y_i), axis=0 )**2
)
mid7[i] = np.sum( (x_q.reshape(-1,1) - x_q)**2 )
mid8[i] = np.sum(
np.sum(np.abs(x_q.reshape(-1,1) - x_q), axis=0)**2
)
DC_x1[q] = np.sum(mid1) / (m * n * (n - 1))
DC_x2[q] = np.sum(mid2) / (m * n * (n - 1))
DC_x3[q] = np.sum(mid3) / (m * n * (n - 1))
DC_x4[q] = np.sum(mid4) / (m * n * (n - 1) * (n - 2))
DC_x5[q] = np.sum(mid5) / (m * n * (n - 1))
DC_x6[q] = np.sum(mid6) / (m * n * (n - 1) * (n - 2))
DC_x7[q] = np.sum(mid7) / (m * n * (n - 1))
DC_x8[q] = np.sum(mid8) / (m * n * (n - 1) * (n - 2))
return DC_fun(DC_x1, DC_x2, DC_x3, DC_x4, DC_x5, DC_x6, DC_x7, DC_x8)
# X and Y are lists
def DC_threshold(X, Y, N, m, n, p, q_new):
X_new = [
rng.multivariate_normal(
mean=np.zeros(q_new), cov=np.eye(q_new), size=n)
for _ in range(m)
]
threshold_new = DC_com(X_new, Y, N, m, n, q_new)
threshold_value = DC_com(X, Y, N, m, n, p)
index = np.where(threshold_value >= np.max(threshold_new))[0]
modified_vector = np.zeros(p)
modified_vector[index] = threshold_value[index]
beta_value = modified_vector
return {'index': index, 'beta_value': beta_value}