from sklearn import linear_model
import numpy as np

gamma = 0.5

clf = linear_model.Lasso(alpha=gamma, fit_intercept=False)
x = np.array([[1,3,4,2],[2,2,1,3],[2,1,33,1],[3,1,2,2]], dtype=float).T
y = np.array([[5,7,6,8]], dtype=float).T

clf.fit(x, y)
print(clf.coef_)
m = x.shape[0]
n = x.shape[1]
result = clf.coef_

fitError = np.square(np.linalg.norm(np.dot(x,result)-y,2))/(2.0*m) + gamma * np.linalg.norm(result, 1)
print "Fit error:", fitError

[ 0.90047945  1.95962233  0.01235545  0.        ]
Fit error: 4.30144267082

from cvxpy import *
import numpy as np
from sklearn import linear_model

gamma = 0.5

x = np.array([[1,3,4,2],[2,2,1,3],[2,1,33,1],[3,1,2,2]], dtype=float).T
y = np.array([[5,7,6,8]], dtype=float).T
m = x.shape[0]
n = x.shape[1]

# http://scikit-learn.org/stable/modules/linear_model.html#lasso
w = Variable(n)
cost = sum_squares(x*w - y)/(2.0*m) + gamma * norm(w, 1)
prob = Problem(Minimize(cost), [])
prob.solve()
print "status:", prob.status
print "optimal value (P*): ", prob.value
print "optimal point (w*) transpose: ", w.value.T

result = w.value
fitError = np.linalg.norm(np.dot(x,result)-y)**2/(2.0*m) + gamma * np.linalg.norm(result, 1)

print "Fit error %g:" % (fitError)

status: optimal
optimal value (P*):  1.46804740158
optimal point (w*) transpose:  [[  8.98760414e-01   1.96090538e+00   1.25244441e-02   3.69147798e-10]]
Fit error 1.46805: