# -*- coding: utf-8 -*-
"""
Created on Sun Apr 20 17:12:53 2014

author: Josef Perktold

"""

import numpy as np
from numpy.testing import assert_allclose, assert_equal

from statsmodels.regression.linear_model import OLS, WLS
from statsmodels.sandbox.regression.predstd import wls_prediction_std
from statsmodels.regression._prediction import get_prediction


def test_predict_se():
    # this test doesn't use reference values
    # checks conistency across options, and compares to direct calculation

    # generate dataset
    nsample = 50
    x1 = np.linspace(0, 20, nsample)
    x = np.c_[x1, (x1 - 5)**2, np.ones(nsample)]
    np.random.seed(0)#9876789) #9876543)
    beta = [0.5, -0.01, 5.]
    y_true2 = np.dot(x, beta)
    w = np.ones(nsample)
    w[int(nsample * 6. / 10):] = 3
    sig = 0.5
    y2 = y_true2 + sig * w * np.random.normal(size=nsample)
    x2 = x[:,[0,2]]

    # estimate OLS
    res2 = OLS(y2, x2).fit()

    #direct calculation
    covb = res2.cov_params()
    predvar = res2.mse_resid + (x2 * np.dot(covb, x2.T).T).sum(1)
    predstd = np.sqrt(predvar)

    prstd, iv_l, iv_u = wls_prediction_std(res2)
    np.testing.assert_almost_equal(prstd, predstd, 15)

    #stats.t.isf(0.05/2., 50 - 2)
    q = 2.0106347546964458
    ci_half = q * predstd
    np.testing.assert_allclose(iv_u, res2.fittedvalues + ci_half, rtol=1e-12)
    np.testing.assert_allclose(iv_l, res2.fittedvalues - ci_half, rtol=1e-12)

    prstd, iv_l, iv_u = wls_prediction_std(res2, x2[:3,:])
    np.testing.assert_equal(prstd, prstd[:3])
    np.testing.assert_allclose(iv_u, res2.fittedvalues[:3] + ci_half[:3],
                               rtol=1e-12)
    np.testing.assert_allclose(iv_l, res2.fittedvalues[:3] - ci_half[:3],
                               rtol=1e-12)


    # check WLS
    res3 = WLS(y2, x2, 1. / w).fit()

    #direct calculation
    covb = res3.cov_params()
    predvar = res3.mse_resid * w + (x2 * np.dot(covb, x2.T).T).sum(1)
    predstd = np.sqrt(predvar)

    prstd, iv_l, iv_u = wls_prediction_std(res3)
    np.testing.assert_almost_equal(prstd, predstd, 15)

    #stats.t.isf(0.05/2., 50 - 2)
    q = 2.0106347546964458
    ci_half = q * predstd
    np.testing.assert_allclose(iv_u, res3.fittedvalues + ci_half, rtol=1e-12)
    np.testing.assert_allclose(iv_l, res3.fittedvalues - ci_half, rtol=1e-12)

    # testing shapes of exog
    prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1:,:], weights=3.)
    np.testing.assert_equal(prstd, prstd[-1])
    prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,:], weights=3.)
    np.testing.assert_equal(prstd, prstd[-1])

    prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=3.)
    np.testing.assert_equal(prstd, prstd[-2:])

    prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=[3, 3])
    np.testing.assert_equal(prstd, prstd[-2:])

    prstd, iv_l, iv_u = wls_prediction_std(res3, x2[:3,:])
    np.testing.assert_equal(prstd, prstd[:3])
    np.testing.assert_allclose(iv_u, res3.fittedvalues[:3] + ci_half[:3],
                               rtol=1e-12)
    np.testing.assert_allclose(iv_l, res3.fittedvalues[:3] - ci_half[:3],
                               rtol=1e-12)


    #use wrong size for exog
    #prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,0], weights=3.)
    np.testing.assert_raises(ValueError, wls_prediction_std, res3, x2[-1,0],
                             weights=3.)

    # check some weight values
    sew1 = wls_prediction_std(res3, x2[-3:,:])[0]**2
    for wv in np.linspace(0.5, 3, 5):

        sew = wls_prediction_std(res3, x2[-3:,:], weights=1. / wv)[0]**2
        np.testing.assert_allclose(sew, sew1 + res3.scale * (wv - 1))


class TestWLSPrediction(object):

    @classmethod
    def setup_class(cls):

        # from example wls.py

        nsample = 50
        x = np.linspace(0, 20, nsample)
        X = np.column_stack((x, (x - 5)**2))
        from statsmodels.tools.tools import add_constant
        X = add_constant(X)
        beta = [5., 0.5, -0.01]
        sig = 0.5
        w = np.ones(nsample)
        w[int(nsample * 6. / 10):] = 3
        y_true = np.dot(X, beta)
        e = np.random.normal(size=nsample)
        y = y_true + sig * w * e
        X = X[:,[0,1]]


        # ### WLS knowing the true variance ratio of heteroscedasticity

        mod_wls = WLS(y, X, weights=1./w)
        cls.res_wls = mod_wls.fit()


    def test_ci(self):
        res_wls = self.res_wls
        prstd, iv_l, iv_u = wls_prediction_std(res_wls)
        pred_res = get_prediction(res_wls)
        ci = pred_res.conf_int(obs=True)

        assert_allclose(pred_res.se_obs, prstd, rtol=1e-13)
        assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13)

        sf = pred_res.summary_frame()

        col_names = ['mean', 'mean_se', 'mean_ci_lower', 'mean_ci_upper',
                      'obs_ci_lower', 'obs_ci_upper']
        assert_equal(sf.columns.tolist(), col_names)

        pred_res2 = res_wls.get_prediction()
        ci2 = pred_res2.conf_int(obs=True)

        assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13)
        assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13)

        sf2 = pred_res2.summary_frame()
        assert_equal(sf2.columns.tolist(), col_names)


    def test_glm(self):
        # prelimnimary, getting started with basic test for GLM.get_prediction
        from statsmodels.genmod.generalized_linear_model import GLM

        res_wls = self.res_wls
        mod_wls = res_wls.model
        y, X, wi = mod_wls.endog, mod_wls.exog, mod_wls.weights

        w_sqrt = np.sqrt(wi)  # notation wi is weights, `w` is var
        mod_glm = GLM(y * w_sqrt, X * w_sqrt[:,None])

        # compare using t distribution
        res_glm = mod_glm.fit(use_t=True)
        pred_glm = res_glm.get_prediction()
        sf_glm = pred_glm.summary_frame()

        pred_res_wls = res_wls.get_prediction()
        sf_wls = pred_res_wls.summary_frame()
        n_compare = 30   # in glm with predict wendog
        assert_allclose(sf_glm.values[:n_compare],
                        sf_wls.values[:n_compare, :4])

        # compare using normal distribution

        res_glm = mod_glm.fit() # default use_t=False
        pred_glm = res_glm.get_prediction()
        sf_glm = pred_glm.summary_frame()

        res_wls = mod_wls.fit(use_t=False)
        pred_res_wls = res_wls.get_prediction()
        sf_wls = pred_res_wls.summary_frame()
        assert_allclose(sf_glm.values[:n_compare],
                        sf_wls.values[:n_compare, :4])

        # function for parameter transformation
        # should be separate test method
        from statsmodels.genmod._prediction import params_transform_univariate
        rates = params_transform_univariate(res_glm.params, res_glm.cov_params())

        rates2 = np.column_stack((np.exp(res_glm.params),
                                  res_glm.bse * np.exp(res_glm.params),
                                  np.exp(res_glm.conf_int())))
        assert_allclose(rates.summary_frame().values, rates2, rtol=1e-13)

        from statsmodels.genmod.families import links

        # with identity transform
        pt = params_transform_univariate(res_glm.params, res_glm.cov_params(), link=links.identity())

        assert_allclose(pt.tvalues, res_glm.tvalues, rtol=1e-13)
        assert_allclose(pt.se_mean, res_glm.bse, rtol=1e-13)
        ptt = pt.t_test()
        assert_allclose(ptt[0], res_glm.tvalues, rtol=1e-13)
        assert_allclose(ptt[1], res_glm.pvalues, rtol=1e-13)
