difficult_problem.py

import numpy as np

def f_of_x(X,w):
    n,d = X.shape
    X_dot_w = np.dot(X,w)
    y = np.zeros(n)
    # the inner product goes through a sin
    # or a cos, depending on simple condition
    cos_flag = X[:,0] < 0.0
    sin_flag = ~cos_flag
    y[cos_flag] = np.cos(X_dot_w[cos_flag])
    y[sin_flag] = np.sin(X_dot_w[sin_flag])
    return y


# generate some simulated data
d = 10
n = 100000
w = np.random.rand(d)
X = np.random.randn(n,d)
y = f_of_x(X,w)