def transform_vector(v, components):
return [dot(v, w) for w in components]
def project(v, w):
"""return the projection of v onto w"""
coefficient = dot(v, w)
return scalar_multiply(coefficient, w)
def directional_variance_i(x_i, w):
"""the variance of the row x_i in the direction w"""
return dot(x_i, direction(w)) ** 2
def directional_variance_gradient_i(x_i, w):
"""the contribution of row x_i to the gradient of
the direction-w variance"""
projection_length = dot(x_i, direction(w))
return [2 * projection_length * x_ij for x_ij in x_i]
def covariance(x, y):
n = len(x)
return vo.dot(de_mean(x), de_mean(y)) / (n - 1)