"""

Created on Tue Dec 20 20:24:20 2011

Author: Josef Perktold
License: BSD-3

"""

import numpy as np

from statsmodels.regression.linear_model import GLS, OLS, WLS


def atleast_2dcols(x):
    x = np.asarray(x)
    if x.ndim == 1:
        x = x[:, None]
    return x


class GLSHet2(GLS):
    """WLS with heteroscedasticity that depends on explanatory variables

    note: mixing GLS sigma and weights for heteroscedasticity might not make
    sense

    I think rewriting following the pattern of GLSAR is better
    stopping criteria: improve in GLSAR also, e.g. change in rho

    """

    def __init__(self, endog, exog, exog_var, sigma=None):
        self.exog_var = atleast_2dcols(exog_var)
        super(self.__class__, self).__init__(endog, exog, sigma=sigma)

    def fit(self, lambd=1.):
        # maybe iterate
        # preliminary estimate
        res_gls = GLS(self.endog, self.exog, sigma=self.sigma).fit()
        res_resid = OLS(res_gls.resid**2, self.exog_var).fit()
        # or  log-link
        # res_resid = OLS(np.log(res_gls.resid**2), self.exog_var).fit()
        # here I could use whiten and current instance instead of delegating
        # but this is easier
        # see pattern of GLSAR, calls self.initialize and self.fit
        res_wls = WLS(self.endog, self.exog, weights=1./res_resid.fittedvalues).fit()

        res_wls._results.results_residual_regression = res_resid
        return res_wls


class GLSHet(WLS):
    """
    A regression model with an estimated heteroscedasticity.

    A subclass of WLS, that additionally estimates the weight matrix as a
    function of additional explanatory variables.

    Parameters
    ----------
    endog : array_like
    exog : array_like
    exog_var : array_like, 1d or 2d
        regressors, explanatory variables for the variance
    weights : array_like or None
        If weights are given, then they are used in the first step estimation.
    link : link function or None
        If None, then the variance is assumed to be a linear combination of
        the exog_var. If given, then ...  not tested yet

    *extra attributes*

    history : dict
       contains the parameter estimates in both regression for each iteration

    result instance has

    results_residual_regression : OLS result instance
        result of heteroscedasticity estimation

    except for fit_iterative all methods are inherited from WLS.

    Notes
    -----
    GLSHet is considered to be experimental.

    `fit` is just standard WLS fit for fixed weights
    `fit_iterative` updates the estimate for weights, see its docstring

    The two alternative for handling heteroscedasticity in the data are to
    use heteroscedasticity robust standard errors or estimating the
    heteroscedasticity
    Estimating heteroscedasticity and using weighted least squares produces
    smaller confidence intervals for the estimated parameters then the
    heteroscedasticity robust standard errors if the heteroscedasticity is
    correctly specified. If the heteroscedasticity is incorrectly specified
    then the estimated covariance is inconsistent.

    Stock and Watson for example argue in favor of using OLS with
    heteroscedasticity robust standard errors instead of GLSHet sind we are
    seldom sure enough about the correct specification (in economics).

    GLSHet has asymptotically the same distribution as WLS if the true
    weights are know. In both cases the asymptotic distribution of the
    parameter estimates is the normal distribution.

    The assumption of the model:

    y = X*beta + u,
    with E(u) = 0, E(X*u)=0, var(u_i) = z_i*gamma
    or for vector of all observations Sigma = diag(Z*gamma)

    where
    y : endog (nobs)
    X : exog  (nobs, k_vars)
    Z : exog_var (nobs, k_vars2)
    beta, gamma estimated parameters

    If a link is specified, then the heteroscedasticity is

    var(u_i) = link.inverse(z_i*gamma), or
    link(var(u_i)) = z_i*gamma

    for example for log-linkg
    var(u_i) = exp(z_i*gamma)


    Usage : see example ....

    TODO: test link option
    """
    def __init__(self, endog, exog, exog_var=None, weights=None, link=None):
        self.exog_var = atleast_2dcols(exog_var)
        if weights is None:
            weights = np.ones(endog.shape)
        if link is not None:
            self.link = link
            self.linkinv = link.inverse   # as defined in families.links
        else:
            self.link = lambda x: x  # no transformation
            self.linkinv = lambda x: x

        super(self.__class__, self).__init__(endog, exog, weights=weights)

    def iterative_fit(self, maxiter=3):
        """
        Perform an iterative two-step procedure to estimate a WLS model.

        The model is assumed to have heteroskedastic errors.
        The variance is estimated by OLS regression of the link transformed
        squared residuals on Z, i.e.::

           link(sigma_i) = x_i*gamma.

        Parameters
        ----------
        maxiter : int, optional
            the number of iterations

        Notes
        -----
        maxiter=1: returns the estimated based on given weights
        maxiter=2: performs a second estimation with the updated weights,
                   this is 2-step estimation
        maxiter>2: iteratively estimate and update the weights

        TODO: possible extension stop iteration if change in parameter
            estimates is smaller than x_tol

        Repeated calls to fit_iterative, will do one redundant pinv_wexog
        calculation. Calling fit_iterative(maxiter) ones does not do any
        redundant recalculations (whitening or calculating pinv_wexog).
        """

        import collections
        self.history = collections.defaultdict(list)  # not really necessary
        res_resid = None  # if maxiter < 2 no updating
        for i in range(maxiter):
            # pinv_wexog is cached
            if hasattr(self, "pinv_wexog"):
                del self.pinv_wexog
            # self.initialize()
            # print 'wls self',
            results = self.fit()
            self.history["self_params"].append(results.params)
            if not i == maxiter-1:  # s kip for last iteration, could break instead
                # print 'ols',
                self.results_old = results  # for debugging
                # estimate heteroscedasticity
                res_resid = OLS(self.link(results.resid**2), self.exog_var).fit()
                self.history["ols_params"].append(res_resid.params)
                # update weights
                self.weights = 1./self.linkinv(res_resid.fittedvalues)
                self.weights /= self.weights.max()  # not required
                self.weights[self.weights < 1e-14] = 1e-14  # clip
                # print 'in iter', i, self.weights.var() # debug, do weights change
                self.initialize()

        # note results is the wrapper, results._results is the results instance
        results._results.results_residual_regression = res_resid
        return results
