import numpy as np

import sys

eps = sys.float_info.epsilon

def to_zero_mean(x):

return x - np.expand_dims(np.mean(x, axis=1), axis=1)

def cci_pca(x, dim_out):

assert x.shape[0] >= dim_out, "The dimension of input should be no less than the dimension of output!"

num_sample = x.shape[1]

x_mean = 0

base_vector = np.zeros((x.shape[0], dim_out))

for t in range(num_sample):

x_mean = t * x_mean / (t + 1) + x[:, t] / (t + 1)

x_iter = x[:, t] - x_mean

for i in range(min(t + 1, dim_out)):

if i == t and t == 0:

base_vector[:, i] = x[:, i]

elif i == t:

base_vector[:, i] = x_iter

else:

base_vector[:, i] = \

t * base_vector[:, i] / (t + 1) + ((np.expand_dims(x_iter, axis=1)

@ np.expand_dims(x_iter, axis=0))

@ np.expand_dims(base_vector[:, i] / (np.linalg.norm

(base_vector[:, i]) + eps),

axis=1))[:, 0] / (t + 1)

base_norm = base_vector[:, i] / (np.linalg.norm(base_vector[:, i]) + eps)

x_iter = x_iter - np.dot(x_iter, base_norm) * base_norm

for i in range(dim_out):

base_vector[:, i] = base_vector[:, i] / (np.linalg.norm(base_vector[:, i]) + eps)

return base_vector.T @ x, base_vector