from __future__ import division
import numpy as np
import cvxpy as cp
import matplotlib.pyplot as plt

np.random.seed(1)
n = 20
m = 1000
TEST = m
DENSITY = 0.2
beta_true = np.random.randn(n, 1)
idxs = np.random.choice(range(n), int((1-DENSITY)*n), replace=False)
for idx in idxs:
    beta_true[idx] = 0
offset = 0
sigma = 45
X = np.random.normal(0, 5, size=(m, n))
Y = np.sign(X.dot(beta_true) +
            offset +
            np.random.normal(0, sigma, size=(m, 1)))
X_test = np.random.normal(0, 5, size=(TEST, n))
Y_test = np.sign(X_test.dot(beta_true) +
                 offset +
                 np.random.normal(0, sigma, size=(TEST, 1)))