"""
For comparison with sklearn.linear_model.LogisticRegression

Computes a regularzation path with both packages.  The coefficient values in
    either path are related by a "constant" in the sense that for any fixed
    value of the constraint C and log likelihood, there exists an l1
    regularization constant alpha such that the optimal solutions should be
    the same.  Note that alpha(C) is a nonlinear function in general.  Here we
    find alpha(C) by finding a reparameterization of the statsmodels path that
    makes the paths match up.  An equation is available, but to use it I would
    need to hack the sklearn code to extract the gradient of the log
    likelihood.


The results "prove" that the regularization paths are the same.  Note that
    finding the reparameterization is non-trivial since the coefficient paths
    are NOT monotonic.  As a result, the paths do not match up perfectly.
"""
from statsmodels.compat.python import lrange

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model

import statsmodels.api as sm

## Decide which dataset to use
# Use either spector or anes96
use_spector = False

#### Load data
## The Spector and Mazzeo (1980) data from statsmodels
if use_spector:
    spector_data = sm.datasets.spector.load()
    X = spector_data.exog
    Y = spector_data.endog
else:
    raise Exception(
        "The anes96 dataset is now loaded in as a short version that cannot "\
        "be used here")
    anes96_data = sm.datasets.anes96.load_pandas()
    Y = anes96_data.exog.vote

#### Fit and plot results
N = 200  # number of points to solve at
K = X.shape[1]

## statsmodels
logit_mod = sm.Logit(Y, X)
sm_coeff = np.zeros((N, K))  # Holds the coefficients
if use_spector:
    alphas = 1 / np.logspace(-1, 2, N)  # for spector_data
else:
    alphas = 1 / np.logspace(-3, 2, N)  # for anes96_data
for n, alpha in enumerate(alphas):
    logit_res = logit_mod.fit_regularized(
            method='l1', alpha=alpha, disp=False, trim_mode='off')
    sm_coeff[n,:] = logit_res.params
## Sklearn
sk_coeff = np.zeros((N, K))
if use_spector:
    Cs = np.logspace(-0.45, 2, N)
else:
    Cs = np.logspace(-2.6, 0, N)
for n, C in enumerate(Cs):
    clf = linear_model.LogisticRegression(
            C=C, penalty='l1', fit_intercept=False)
    clf.fit(X, Y)
    sk_coeff[n, :] = clf.coef_

## Get the reparametrization of sm_coeff that makes the paths equal
# Do this by finding one single re-parameterization of the second coefficient
# that makes the path for the second coefficient (almost) identical.  This
# same parameterization will work for the other two coefficients since the
# the regularization coefficients (in sk and sm) are related by a constant.
#
# special_X is chosen since this coefficient becomes non-zero before the
# other two...and is relatively monotonic...with both datasets.
sk_special_X = np.fabs(sk_coeff[:,2])
sm_special_X = np.fabs(sm_coeff[:,2])
s = np.zeros(N)
# Note that sk_special_X will not always be perfectly sorted...
s = np.searchsorted(sk_special_X, sm_special_X)

## Plot
plt.figure(2)
plt.clf()
plt.grid()
plt.xlabel('Index in sklearn simulation')
plt.ylabel('Coefficient value')
plt.title('Regularization Paths')
colors = ['b', 'r', 'k', 'g', 'm', 'c', 'y']
for coeff, name in [(sm_coeff, 'sm'), (sk_coeff, 'sk')]:
    if name == 'sk':
        ltype = 'x'  # linetype
        t = lrange(N)  # The 'time' parameter
    else:
        ltype = 'o'
        t = s
    for i in range(K):
        plt.plot(t, coeff[:,i], ltype+colors[i], label=name+'-X'+str(i))
plt.legend(loc='best')
plt.show()
