import warnings
from nose.tools import assert_equal

import numpy as np
from scipy import linalg

from sklearn.utils.testing import assert_array_almost_equal
from sklearn.utils.testing import assert_true
from sklearn.utils.testing import assert_less
from sklearn.utils.testing import assert_greater
from sklearn.utils.testing import assert_raises

from sklearn import linear_model, datasets

diabetes = datasets.load_diabetes()
X, y = diabetes.data, diabetes.target

# TODO: use another dataset that has multiple drops


def test_simple():
    """
    Principle of Lars is to keep covariances tied and decreasing
    """

    # also test verbose output
    from cStringIO import StringIO
    import sys
    old_stdout = sys.stdout
    sys.stdout = StringIO()

    alphas_, active, coef_path_ = linear_model.lars_path(
        diabetes.data, diabetes.target, method="lar", verbose=10)

    sys.stdout = old_stdout

    for (i, coef_) in enumerate(coef_path_.T):
        res = y - np.dot(X, coef_)
        cov = np.dot(X.T, res)
        C = np.max(abs(cov))
        eps = 1e-3
        ocur = len(cov[C - eps < abs(cov)])
        if i < X.shape[1]:
            assert_true(ocur == i + 1)
        else:
            # no more than max_pred variables can go into the active set
            assert_true(ocur == X.shape[1])


def test_simple_precomputed():
    """
    The same, with precomputed Gram matrix
    """

    G = np.dot(diabetes.data.T, diabetes.data)
    alphas_, active, coef_path_ = linear_model.lars_path(
        diabetes.data, diabetes.target, Gram=G, method="lar")

    for i, coef_ in enumerate(coef_path_.T):
        res = y - np.dot(X, coef_)
        cov = np.dot(X.T, res)
        C = np.max(abs(cov))
        eps = 1e-3
        ocur = len(cov[C - eps < abs(cov)])
        if i < X.shape[1]:
            assert_true(ocur == i + 1)
        else:
            # no more than max_pred variables can go into the active set
            assert_true(ocur == X.shape[1])


def test_all_precomputed():
    """
    Test that lars_path with precomputed Gram and Xy gives the right answer
    """
    X, y = diabetes.data, diabetes.target
    G = np.dot(X.T, X)
    Xy = np.dot(X.T, y)
    for method in 'lar', 'lasso':
        output = linear_model.lars_path(X, y, method=method)
        output_pre = linear_model.lars_path(X, y, Gram=G, Xy=Xy, method=method)
        for expected, got in zip(output, output_pre):
            assert_array_almost_equal(expected, got)


def test_lars_lstsq():
    """
    Test that Lars gives least square solution at the end
    of the path
    """
    X1 = 3 * diabetes.data  # use un-normalized dataset
    clf = linear_model.LassoLars(alpha=0.)
    clf.fit(X1, y)
    coef_lstsq = np.linalg.lstsq(X1, y)[0]
    assert_array_almost_equal(clf.coef_, coef_lstsq)


def test_lasso_gives_lstsq_solution():
    """
    Test that Lars Lasso gives least square solution at the end
    of the path
    """
    alphas_, active, coef_path_ = linear_model.lars_path(X, y, method="lasso")
    coef_lstsq = np.linalg.lstsq(X, y)[0]
    assert_array_almost_equal(coef_lstsq, coef_path_[:, -1])


def test_collinearity():
    """Check that lars_path is robust to collinearity in input"""
    X = np.array([[3., 3., 1.],
                  [2., 2., 0.],
                  [1., 1., 0]])
    y = np.array([1., 0., 0])

    _, _, coef_path_ = linear_model.lars_path(X, y, alpha_min=0.01)
    assert_true(not np.isnan(coef_path_).any())
    residual = np.dot(X, coef_path_[:, -1]) - y
    assert_less((residual ** 2).sum(), 1.)  # just make sure it's bounded

    n_samples = 10
    X = np.random.rand(n_samples, 5)
    y = np.zeros(n_samples)
    _, _, coef_path_ = linear_model.lars_path(X, y, Gram='auto', copy_X=False,
                                              copy_Gram=False, alpha_min=0.,
                                              method='lasso', verbose=0,
                                              max_iter=500)
    assert_array_almost_equal(coef_path_, np.zeros_like(coef_path_))


def test_no_path():
    """
    Test that the ``return_path=False`` option returns the correct output
    """

    alphas_, active_, coef_path_ = linear_model.lars_path(
        diabetes.data, diabetes.target, method="lar")
    alpha_, active, coef = linear_model.lars_path(
        diabetes.data, diabetes.target, method="lar", return_path=False)

    assert_array_almost_equal(coef, coef_path_[:, -1])
    assert_true(alpha_ == alphas_[-1])


def test_no_path_precomputed():
    """
    Test that the ``return_path=False`` option with Gram remains correct
    """

    G = np.dot(diabetes.data.T, diabetes.data)

    alphas_, active_, coef_path_ = linear_model.lars_path(
        diabetes.data, diabetes.target, method="lar", Gram=G)
    alpha_, active, coef = linear_model.lars_path(
        diabetes.data, diabetes.target, method="lar", Gram=G,
        return_path=False)

    assert_array_almost_equal(coef, coef_path_[:, -1])
    assert_true(alpha_ == alphas_[-1])


def test_no_path_all_precomputed():
    """
    Test that the ``return_path=False`` option with Gram and Xy remains correct
    """
    X, y = 3 * diabetes.data, diabetes.target
    G = np.dot(X.T, X)
    Xy = np.dot(X.T, y)

    alphas_, active_, coef_path_ = linear_model.lars_path(
        X, y, method="lasso", Gram=G, Xy=Xy, alpha_min=0.9)
    print "---"
    alpha_, active, coef = linear_model.lars_path(
        X, y, method="lasso", Gram=G, Xy=Xy, alpha_min=0.9, return_path=False)

    assert_array_almost_equal(coef, coef_path_[:, -1])
    assert_true(alpha_ == alphas_[-1])


def test_singular_matrix():
    # Test when input is a singular matrix
    # In this test the "drop for good strategy" of lars_path is necessary
    # to give a good answer
    X1 = np.array([[1, 1.], [1., 1.]])
    y1 = np.array([1, 1])
    with warnings.catch_warnings(record=True) as warning_list:
        warnings.simplefilter("always", UserWarning)
        alphas, active, coef_path = linear_model.lars_path(X1, y1)
    assert_true(len(warning_list) > 0)
    assert_true('Dropping a regressor' in warning_list[0].message.args[0])

    assert_array_almost_equal(coef_path.T, [[0, 0], [1, 0]])


def test_rank_deficient_design():
    # consistency test that checks that LARS Lasso is handling rank
    # deficient input data (with n_features < rank) in the same way
    # as coordinate descent Lasso
    y = [5, 0, 5]
    for X in ([[5,   0],
               [0,   5],
               [10, 10]],

              [[10,     10,  0],
               [1e-32,   0,  0],
               [0,       0,  1]],
              ):
        # To be able to use the coefs to compute the objective function,
        # we need to turn off normalization
        lars = linear_model.LassoLars(.1, normalize=False)
        coef_lars_ = lars.fit(X, y).coef_
        obj_lars = (1. / (2. * 3.)
                    * linalg.norm(y - np.dot(X, coef_lars_)) ** 2
                    + .1 * linalg.norm(coef_lars_, 1))
        coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
        coef_cd_ = coord_descent.fit(X, y).coef_
        obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
                  + .1 * linalg.norm(coef_cd_, 1))
        assert_array_almost_equal(obj_lars, obj_cd)


def test_lasso_lars_vs_lasso_cd(verbose=False):
    """
    Test that LassoLars and Lasso using coordinate descent give the
    same results
    """
    X = 3 * diabetes.data

    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = np.linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)

    # similar test, with the classifiers
    for alpha in np.linspace(1e-2, 1 - 1e-2):
        clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
        clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
                                  normalize=False).fit(X, y)
        err = np.linalg.norm(clf1.coef_ - clf2.coef_)
        assert_less(err, 1e-3)

    # same test, with normalized data
    X = diabetes.data
    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
                                  tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = np.linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)


def test_lasso_lars_vs_lasso_cd_early_stopping(verbose=False):
    """
    Test that LassoLars and Lasso using coordinate descent give the
    same results when early stopping is used.
    (test : before, in the middle, and in the last part of the path)
    """
    alphas_min = [10, 0.9, 1e-4]
    for alphas_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=0.9)
        lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = np.linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01)

    alphas_min = [10, 0.9, 1e-4]
    # same test, with normalization
    for alphas_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=0.9)
        lasso_cd = linear_model.Lasso(fit_intercept=True, normalize=True,
                                      tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = np.linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01)


def test_lasso_lars_path_length():
    # Test that the path length of the LassoLars is right
    lasso = linear_model.LassoLars()
    lasso.fit(X, y)
    lasso2 = linear_model.LassoLars(alpha=lasso.alphas_[2])
    lasso2.fit(X, y)
    np.testing.assert_array_equal(lasso.alphas_[:3], lasso2.alphas_)
    # Also check that the sequence of alphas is always decreasing
    assert_true(np.all(np.diff(lasso.alphas_) < 0))


def test_lasso_lars_vs_lasso_cd_ill_conditioned():
    # Test lasso lars on a very ill-conditioned design, and check that
    # it does not blow up, and stays somewhat close to a solution given
    # by the coordinate descent solver
    rng = np.random.RandomState(42)

    # Generate data
    n, m = 80, 100
    k = 5
    X = rng.randn(n, m)
    w = np.zeros((m, 1))
    i = np.arange(0, m)
    rng.shuffle(i)
    supp = i[:k]
    w[supp] = np.sign(rng.randn(k, 1)) * (rng.rand(k, 1) + 1)
    y = np.dot(X, w)
    sigma = 0.2
    y += sigma * rng.rand(*y.shape)
    y = y.squeeze()

    with warnings.catch_warnings(record=True) as warning_list:
        warnings.simplefilter("always", UserWarning)
        lars_alphas, _, lars_coef = linear_model.lars_path(X, y,
                                                           method='lasso')
    assert_true(len(warning_list) > 0)
    assert_true(('Dropping a regressor' in warning_list[0].message.args[0])
                or ('Early stopping' in warning_list[0].message.args[0]))

    lasso_coef = np.zeros((w.shape[0], len(lars_alphas)))
    for i, model in enumerate(linear_model.lasso_path(X, y, alphas=lars_alphas,
                                                      tol=1e-6)):
        lasso_coef[:, i] = model.coef_
    np.testing.assert_array_almost_equal(lars_coef, lasso_coef, decimal=1)


def test_lars_drop_for_good():
    # Create an ill-conditioned situation in which the LARS has to good
    # far in the path to converge, and check that LARS and coordinate
    # descent give the same answers
    X = [[10,     10,  0],
         [-1e-32,  0,  0],
         [1,       1,  1]]
    y = [100, -100, 1]
    lars = linear_model.LassoLars(.001, normalize=False)
    lars_coef_ = lars.fit(X, y).coef_
    lars_obj = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, lars_coef_)) ** 2
                + .1 * linalg.norm(lars_coef_, 1))
    coord_descent = linear_model.Lasso(.001, tol=1e-10, normalize=False)
    cd_coef_ = coord_descent.fit(X, y).coef_
    cd_obj = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, cd_coef_)) ** 2
              + .1 * linalg.norm(cd_coef_, 1))
    assert_array_almost_equal(lars_obj / cd_obj, 1.0, decimal=3)


def test_lars_add_features():
    """
    assure that at least some features get added if necessary

    test for 6d2b4c
    """
    # Hilbert matrix
    n = 5
    H = 1. / (np.arange(1, n + 1) + np.arange(n)[:, np.newaxis])
    clf = linear_model.Lars(fit_intercept=False).fit(
        H, np.arange(n))
    assert_true(np.all(np.isfinite(clf.coef_)))


def test_lars_n_nonzero_coefs(verbose=False):
    lars = linear_model.Lars(n_nonzero_coefs=6, verbose=verbose)
    lars.fit(X, y)
    assert_equal(len(lars.coef_.nonzero()[0]), 6)
    # The path should be of length 6 + 1 in a Lars going down to 6
    # non-zero coefs
    assert_equal(len(lars.alphas_), 7)


def test_multitarget():
    """
    Assure that estimators receiving multidimensional y do the right thing
    """
    X = diabetes.data
    Y = np.vstack([diabetes.target, diabetes.target ** 2]).T
    n_targets = Y.shape[1]

    for estimator in (linear_model.LassoLars(), linear_model.Lars()):
        estimator.fit(X, Y)
        alphas, active, coef, path = (estimator.alphas_, estimator.active_,
                                      estimator.coef_, estimator.coef_path_)
        for k in xrange(n_targets):
            estimator.fit(X, Y[:, k])
            assert_array_almost_equal(alphas[k], estimator.alphas_)
            assert_array_almost_equal(active[k], estimator.active_)
            assert_array_almost_equal(coef[k], estimator.coef_)
            assert_array_almost_equal(path[k], estimator.coef_path_)


def test_lars_cv():
    """ Test the LassoLarsCV object by checking that the optimal alpha
        increases as the number of samples increases.

        This property is not actualy garantied in general and is just a
        property of the given dataset, with the given steps chosen.
    """
    old_alpha = 0
    lars_cv = linear_model.LassoLarsCV()
    for length in (400, 200, 100):
        X = diabetes.data[:length]
        y = diabetes.target[:length]
        lars_cv.fit(X, y)
        np.testing.assert_array_less(old_alpha, lars_cv.alpha_)
        old_alpha = lars_cv.alpha_


def test_lasso_lars_ic():
    """ Test the LassoLarsIC object by checking that
        - some good features are selected.
        - alpha_bic > alpha_aic
        - n_nonzero_bic < n_nonzero_aic
    """
    lars_bic = linear_model.LassoLarsIC('bic')
    lars_aic = linear_model.LassoLarsIC('aic')
    rng = np.random.RandomState(42)
    X = diabetes.data
    y = diabetes.target
    X = np.c_[X, rng.randn(X.shape[0], 4)]  # add 4 bad features
    lars_bic.fit(X, y)
    lars_aic.fit(X, y)
    nonzero_bic = np.where(lars_bic.coef_)[0]
    nonzero_aic = np.where(lars_aic.coef_)[0]
    assert_greater(lars_bic.alpha_, lars_aic.alpha_)
    assert_less(len(nonzero_bic), len(nonzero_aic))
    assert_less(np.max(nonzero_bic), diabetes.data.shape[1])

    # test error on unknown IC
    lars_broken = linear_model.LassoLarsIC('<unknown>')
    assert_raises(ValueError, lars_broken.fit, X, y)


if __name__ == '__main__':
    import nose
    nose.runmodule()
