"""
Testing for Theil-Sen module (sklearn.linear_model.theil_sen)
"""

# Author: Florian Wilhelm <florian.wilhelm@gmail.com>
# License: BSD 3 clause

from __future__ import division, print_function, absolute_import

import os
import sys
from contextlib import contextmanager
import numpy as np
from numpy.testing import assert_array_equal, assert_array_less
from numpy.testing import assert_array_almost_equal, assert_warns
from scipy.linalg import norm
from scipy.optimize import fmin_bfgs
from nose.tools import raises, assert_almost_equal
from sklearn.utils import ConvergenceWarning
from sklearn.linear_model import LinearRegression, TheilSenRegressor
from sklearn.linear_model.theil_sen import _spatial_median, _breakdown_point
from sklearn.linear_model.theil_sen import _modified_weiszfeld_step
from sklearn.utils.testing import assert_greater, assert_less


@contextmanager
def no_stdout_stderr():
    old_stdout = sys.stdout
    old_stderr = sys.stderr
    sys.stdout = open(os.devnull, 'w')
    sys.stderr = open(os.devnull, 'w')
    yield
    sys.stdout.flush()
    sys.stderr.flush()
    sys.stdout = old_stdout
    sys.stderr = old_stderr


def gen_toy_problem_1d(intercept=True):
    random_state = np.random.RandomState(0)
    # Linear model y = 3*x + N(2, 0.1**2)
    w = 3.
    if intercept:
        c = 2.
        n_samples = 50
    else:
        c = 0.1
        n_samples = 100
    x = random_state.normal(size=n_samples)
    noise = 0.1 * random_state.normal(size=n_samples)
    y = w * x + c + noise
    # Add some outliers
    if intercept:
        x[42], y[42] = (-2, 4)
        x[43], y[43] = (-2.5, 8)
        x[33], y[33] = (2.5, 1)
        x[49], y[49] = (2.1, 2)
    else:
        x[42], y[42] = (-2, 4)
        x[43], y[43] = (-2.5, 8)
        x[53], y[53] = (2.5, 1)
        x[60], y[60] = (2.1, 2)
        x[72], y[72] = (1.8, -7)
    return x[:, np.newaxis], y, w, c


def gen_toy_problem_2d():
    random_state = np.random.RandomState(0)
    n_samples = 100
    # Linear model y = 5*x_1 + 10*x_2 + N(1, 0.1**2)
    X = random_state.normal(size=(n_samples, 2))
    w = np.array([5., 10.])
    c = 1.
    noise = 0.1 * random_state.normal(size=n_samples)
    y = np.dot(X, w) + c + noise
    # Add some outliers
    n_outliers = n_samples // 10
    ix = random_state.randint(0, n_samples, size=n_outliers)
    y[ix] = 50 * random_state.normal(size=n_outliers)
    return X, y, w, c


def gen_toy_problem_4d():
    random_state = np.random.RandomState(0)
    n_samples = 10000
    # Linear model y = 5*x_1 + 10*x_2  + 42*x_3 + 7*x_4 + N(1, 0.1**2)
    X = random_state.normal(size=(n_samples, 4))
    w = np.array([5., 10., 42., 7.])
    c = 1.
    noise = 0.1 * random_state.normal(size=n_samples)
    y = np.dot(X, w) + c + noise
    # Add some outliers
    n_outliers = n_samples // 10
    ix = random_state.randint(0, n_samples, size=n_outliers)
    y[ix] = 50 * random_state.normal(size=n_outliers)
    return X, y, w, c


def test_modweiszfeld_step_1d():
    X = np.array([1., 2., 3.]).reshape(3, 1)
    # Check startvalue is element of X and solution
    median = 2.
    new_y = _modified_weiszfeld_step(X, median)
    assert_array_almost_equal(new_y, median)
    # Check startvalue is not the solution
    y = 2.5
    new_y = _modified_weiszfeld_step(X, y)
    assert_array_less(median, new_y)
    assert_array_less(new_y, y)
    # Check startvalue is not the solution but element of X
    y = 3.
    new_y = _modified_weiszfeld_step(X, y)
    assert_array_less(median, new_y)
    assert_array_less(new_y, y)
    # Check that a single vector is identity
    X = np.array([1., 2., 3.]).reshape(1, 3)
    y = X[0, ]
    new_y = _modified_weiszfeld_step(X, y)
    assert_array_equal(y, new_y)


def test_modweiszfeld_step_2d():
    X = np.array([0., 0., 1., 1., 0., 1.]).reshape(3, 2)
    y = np.array([0.5, 0.5])
    # Check first two iterations
    new_y = _modified_weiszfeld_step(X, y)
    assert_array_almost_equal(new_y, np.array([1 / 3, 2 / 3]))
    new_y = _modified_weiszfeld_step(X, new_y)
    assert_array_almost_equal(new_y, np.array([0.2792408, 0.7207592]))
    # Check fix point
    y = np.array([0.21132505, 0.78867497])
    new_y = _modified_weiszfeld_step(X, y)
    assert_array_almost_equal(new_y, y)


def test_spatial_median_1d():
    X = np.array([1., 2., 3.]).reshape(3, 1)
    true_median = 2.
    _, median = _spatial_median(X)
    assert_array_almost_equal(median, true_median)
    # Test larger problem and for exact solution in 1d case
    random_state = np.random.RandomState(0)
    X = random_state.randint(100, size=(1000, 1))
    true_median = np.median(X.ravel())
    _, median = _spatial_median(X)
    assert_array_equal(median, true_median)


def test_spatial_median_2d():
    X = np.array([0., 0., 1., 1., 0., 1.]).reshape(3, 2)
    _, median = _spatial_median(X, max_iter=100, tol=1.e-6)

    def cost_func(y):
        dists = np.array([norm(x - y) for x in X])
        return np.sum(dists)

    # Check if median is solution of the Fermat-Weber location problem
    fermat_weber = fmin_bfgs(cost_func, median, disp=False)
    assert_array_almost_equal(median, fermat_weber)
    # Check when maximum iteration is exceeded a warning is emitted
    assert_warns(ConvergenceWarning, _spatial_median, X, max_iter=30, tol=0.)


def test_theil_sen_1d():
    X, y, w, c = gen_toy_problem_1d()
    # Check that Least Squares fails
    lstq = LinearRegression().fit(X, y)
    assert_greater(np.abs(lstq.coef_ - w), 0.9)
    # Check that Theil-Sen works
    theil_sen = TheilSenRegressor(random_state=0).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, w, 1)
    assert_array_almost_equal(theil_sen.intercept_, c, 1)


def test_theil_sen_1d_no_intercept():
    X, y, w, c = gen_toy_problem_1d(intercept=False)
    # Check that Least Squares fails
    lstq = LinearRegression(fit_intercept=False).fit(X, y)
    assert_greater(np.abs(lstq.coef_ - w - c), 0.5)
    # Check that Theil-Sen works
    theil_sen = TheilSenRegressor(fit_intercept=False,
                                  random_state=0).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, w + c, 1)
    assert_almost_equal(theil_sen.intercept_, 0.)


def test_theil_sen_2d():
    X, y, w, c = gen_toy_problem_2d()
    # Check that Least Squares fails
    lstq = LinearRegression().fit(X, y)
    assert_greater(norm(lstq.coef_ - w), 1.0)
    # Check that Theil-Sen works
    theil_sen = TheilSenRegressor(max_subpopulation=1e3,
                                  random_state=0).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, w, 1)
    assert_array_almost_equal(theil_sen.intercept_, c, 1)


def test_calc_breakdown_point():
    bp = _breakdown_point(1e10, 2)
    assert_less(np.abs(bp - 1 + 1/(np.sqrt(2))), 1.e-6)


@raises(ValueError)
def test_checksubparams_negative_subpopulation():
    X, y, w, c = gen_toy_problem_1d()
    TheilSenRegressor(max_subpopulation=-1, random_state=0).fit(X, y)


@raises(ValueError)
def test_checksubparams_too_few_subsamples():
    X, y, w, c = gen_toy_problem_1d()
    TheilSenRegressor(n_subsamples=1, random_state=0).fit(X, y)


@raises(ValueError)
def test_checksubparams_too_many_subsamples():
    X, y, w, c = gen_toy_problem_1d()
    TheilSenRegressor(n_subsamples=101, random_state=0).fit(X, y)


@raises(ValueError)
def test_checksubparams_n_subsamples_if_less_samples_than_features():
    random_state = np.random.RandomState(0)
    n_samples, n_features = 10, 20
    X = random_state.normal(size=(n_samples, n_features))
    y = random_state.normal(size=n_samples)
    TheilSenRegressor(n_subsamples=9, random_state=0).fit(X, y)


def test_subpopulation():
    X, y, w, c = gen_toy_problem_4d()
    theil_sen = TheilSenRegressor(max_subpopulation=250,
                                  random_state=0).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, w, 1)
    assert_array_almost_equal(theil_sen.intercept_, c, 1)


def test_subsamples():
    X, y, w, c = gen_toy_problem_4d()
    theil_sen = TheilSenRegressor(n_subsamples=X.shape[0],
                                  random_state=0).fit(X, y)
    lstq = LinearRegression().fit(X, y)
    # Check for exact the same results as Least Squares
    assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 9)


def test_verbosity():
    X, y, w, c = gen_toy_problem_1d()
    # Check that Theil-Sen can be verbose
    with no_stdout_stderr():
        TheilSenRegressor(verbose=True, random_state=0).fit(X, y)
        TheilSenRegressor(verbose=True,
                          max_subpopulation=10,
                          random_state=0).fit(X, y)


def test_theil_sen_parallel():
    X, y, w, c = gen_toy_problem_2d()
    # Check that Least Squares fails
    lstq = LinearRegression().fit(X, y)
    assert_greater(norm(lstq.coef_ - w), 1.0)
    # Check that Theil-Sen works
    theil_sen = TheilSenRegressor(n_jobs=-1,
                                  random_state=0,
                                  max_subpopulation=2e3).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, w, 1)
    assert_array_almost_equal(theil_sen.intercept_, c, 1)


def test_less_samples_than_features():
    random_state = np.random.RandomState(0)
    n_samples, n_features = 10, 20
    X = random_state.normal(size=(n_samples, n_features))
    y = random_state.normal(size=n_samples)
    # Check that Theil-Sen falls back to Least Squares if fit_intercept=False
    theil_sen = TheilSenRegressor(fit_intercept=False,
                                  random_state=0).fit(X, y)
    lstq = LinearRegression(fit_intercept=False).fit(X, y)
    assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 12)
    # Check fit_intercept=True case. This will not be equal to the Least
    # Squares solution since the intercept is calculated differently.
    theil_sen = TheilSenRegressor(fit_intercept=True, random_state=0).fit(X, y)
    y_pred = theil_sen.predict(X)
    assert_array_almost_equal(y_pred, y, 12)
