"""
==============================
Lasso on dense and sparse data
==============================

We show that glm.Lasso and glm.sparse.Lasso
provide the same results and that in the case of
sparse data glm.sparse.Lasso improves the speed.

"""

from time import time
import numpy as np
from scipy import sparse
from scipy import linalg

from scikits.learn.glm.sparse import Lasso as SparseLasso
from scikits.learn.glm import Lasso as DenseLasso


###############################################################################
# The two Lasso implementations on Dense data
print "--- Dense matrices"

n_samples, n_features = 200, 10000
np.random.seed(0)
y = np.random.randn(n_samples)
X = np.random.randn(n_samples, n_features)

alpha = 1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False)

t0 = time()
sparse_lasso.fit(X, y, maxit=1000)
print "Sparse Lasso done in %fs" % (time() - t0)

t0 = time()
dense_lasso.fit(X, y, maxit=1000)
print "Dense Lasso done in %fs" % (time() - t0)

print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_
                                                        - dense_lasso.coef_)

###############################################################################
# The two Lasso implementations on Sparse data
print "--- Sparse matrices"

Xs = X.copy()
Xs[Xs < 2.5] = 0.0
Xs = sparse.coo_matrix(Xs)
Xs = Xs.tocsc()

print "Matrix density : %s %%" % (Xs.nnz / float(X.size) * 100)

alpha = 0.1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False)

t0 = time()
sparse_lasso.fit(Xs, y, maxit=1000)
print "Sparse Lasso done in %fs" % (time() - t0)

t0 = time()
dense_lasso.fit(Xs.todense(), y, maxit=1000)
print "Dense Lasso done in %fs" % (time() - t0)

print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_
                                                        - dense_lasso.coef_)