# -*- coding: utf-8 -*-
"""
Created on Mon Jul 26 08:34:59 2010

Author: josef-pktd

changes:
added offset and zero-inflated version of Poisson
 - kind of ok, need better test cases,
 - a nan in ZIP bse, need to check hessian calculations
 - found error in ZIP loglike
 - all tests pass with

Issues
------
* If true model is not zero-inflated then numerical Hessian for ZIP has zeros
  for the inflation probability and is not invertible.
  -> hessian inverts and bse look ok if row and column are dropped, pinv also works
* GenericMLE: still get somewhere (where?)
   "CacheWriteWarning: The attribute 'bse' cannot be overwritten"
* bfgs is too fragile, doesn't come back
* `nm` is slow but seems to work
* need good start_params and their use in genericmle needs to be checked for
  consistency, set as attribute or method (called as attribute)
* numerical hessian needs better scaling

* check taking parts out of the loop, e.g. factorial(endog) could be precalculated


"""
from __future__ import print_function
import numpy as np
from scipy import stats
from scipy.misc import factorial
import statsmodels.api as sm
from statsmodels.base.model import GenericLikelihoodModel

def maxabs(arr1, arr2):
    return np.max(np.abs(arr1 - arr2))

def maxabsrel(arr1, arr2):
    return np.max(np.abs(arr2 / arr1 - 1))

class NonlinearDeltaCov(object):
    '''Asymptotic covariance by Deltamethod

    the function is designed for 2d array, with rows equal to
    the number of equations and columns equal to the number
    of parameters. 1d params work by chance ?

    fun: R^{m*k) -> R^{m}  where m is number of equations and k is
    the number of parameters.

    equations follow Greene

    '''
    def __init__(self, fun, params, cov_params):
        self.fun = fun
        self.params = params
        self.cov_params = cov_params

    def grad(self, params=None, **kwds):
        if params is None:
            params = self.params
        kwds.setdefault('epsilon', 1e-4)
        from statsmodels.tools.numdiff import approx_fprime
        return approx_fprime(params, self.fun, **kwds)

    def cov(self):
        g = self.grad()
        covar = np.dot(np.dot(g, self.cov_params), g.T)
        return covar

    def expected(self):
        # rename: misnomer, this is the MLE of the fun
        return self.fun(self.params)

    def wald(self, value):
        m = self.expected()
        v = self.cov()
        df = np.size(m)
        diff = m - value
        lmstat = np.dot(np.dot(diff.T, np.linalg.inv(v)), diff)
        return lmstat, stats.chi2.sf(lmstat, df)




class PoissonGMLE(GenericLikelihoodModel):
    '''Maximum Likelihood Estimation of Poisson Model

    This is an example for generic MLE which has the same
    statistical model as discretemod.Poisson.

    Except for defining the negative log-likelihood method, all
    methods and results are generic. Gradients and Hessian
    and all resulting statistics are based on numerical
    differentiation.

    '''

    # copied from discretemod.Poisson
    def nloglikeobs(self, params):
        """
        Loglikelihood of Poisson model

        Parameters
        ----------
        params : array-like
            The parameters of the model.

        Returns
        -------
        The log likelihood of the model evaluated at `params`

        Notes
        --------
        .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right]
        """
        XB = np.dot(self.exog, params)
        endog = self.endog
        return np.exp(XB) -  endog*XB + np.log(factorial(endog))

    def predict_distribution(self, exog):
        '''return frozen scipy.stats distribution with mu at estimated prediction
        '''
        if not hasattr(self, result):
            raise ValueError
        else:
            mu = np.exp(np.dot(exog, params))
            return stats.poisson(mu, loc=0)



class PoissonOffsetGMLE(GenericLikelihoodModel):
    '''Maximum Likelihood Estimation of Poisson Model

    This is an example for generic MLE which has the same
    statistical model as discretemod.Poisson but adds offset

    Except for defining the negative log-likelihood method, all
    methods and results are generic. Gradients and Hessian
    and all resulting statistics are based on numerical
    differentiation.

    '''

    def __init__(self, endog, exog=None, offset=None, missing='none', **kwds):
        # let them be none in case user wants to use inheritance
        if not offset is None:
            if offset.ndim == 1:
                offset = offset[:,None] #need column
            self.offset = offset.ravel()
        else:
            self.offset = 0.
        super(PoissonOffsetGMLE, self).__init__(endog, exog, missing=missing,
                **kwds)

#this was added temporarily for bug-hunting, but shouldn't be needed
#    def loglike(self, params):
#        return -self.nloglikeobs(params).sum(0)

    # original copied from discretemod.Poisson
    def nloglikeobs(self, params):
        """
        Loglikelihood of Poisson model

        Parameters
        ----------
        params : array-like
            The parameters of the model.

        Returns
        -------
        The log likelihood of the model evaluated at `params`

        Notes
        --------
        .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right]
        """

        XB = self.offset + np.dot(self.exog, params)
        endog = self.endog
        nloglik = np.exp(XB) -  endog*XB + np.log(factorial(endog))
        return nloglik

class PoissonZiGMLE(GenericLikelihoodModel):
    '''Maximum Likelihood Estimation of Poisson Model

    This is an example for generic MLE which has the same statistical model
    as discretemod.Poisson but adds offset and zero-inflation.

    Except for defining the negative log-likelihood method, all
    methods and results are generic. Gradients and Hessian
    and all resulting statistics are based on numerical
    differentiation.

    There are numerical problems if there is no zero-inflation.

    '''

    def __init__(self, endog, exog=None, offset=None, missing='none', **kwds):
        # let them be none in case user wants to use inheritance

        super(PoissonZiGMLE, self).__init__(endog, exog, missing=missing,
                **kwds)
        if not offset is None:
            if offset.ndim == 1:
                offset = offset[:,None] #need column
            self.offset = offset.ravel()  #which way?
        else:
            self.offset = 0.

        #TODO: it's not standard pattern to use default exog
        if exog is None:
            self.exog = np.ones((self.nobs,1))
        self.nparams = self.exog.shape[1]
        #what's the shape in regression for exog if only constant
        self.start_params = np.hstack((np.ones(self.nparams), 0))
        self.cloneattr = ['start_params']
        #needed for t_test and summary
        self.exog_names.append('zi')


    # original copied from discretemod.Poisson
    def nloglikeobs(self, params):
        """
        Loglikelihood of Poisson model

        Parameters
        ----------
        params : array-like
            The parameters of the model.

        Returns
        -------
        The log likelihood of the model evaluated at `params`

        Notes
        --------
        .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right]
        """
        beta = params[:-1]
        gamm = 1 / (1 + np.exp(params[-1]))  #check this
        # replace with np.dot(self.exogZ, gamma)
        #print(np.shape(self.offset), self.exog.shape, beta.shape
        XB = self.offset + np.dot(self.exog, beta)
        endog = self.endog
        nloglik = -np.log(1-gamm) + np.exp(XB) -  endog*XB + np.log(factorial(endog))
        nloglik[endog==0] = - np.log(gamm + np.exp(-nloglik[endog==0]))

        return nloglik



if __name__ == '__main__':

    #Example:
    np.random.seed(98765678)
    nobs = 1000
    rvs = np.random.randn(nobs,6)
    data_exog = rvs
    data_exog = sm.add_constant(data_exog, prepend=False)
    xbeta = 1 + 0.1*rvs.sum(1)
    data_endog = np.random.poisson(np.exp(xbeta))
    #print(data_endog

    modp = MyPoisson(data_endog, data_exog)
    resp = modp.fit()
    print(resp.params)
    print(resp.bse)

    from statsmodels.discretemod import Poisson
    resdp = Poisson(data_endog, data_exog).fit()
    print('\ncompare with discretemod')
    print('compare params')
    print(resdp.params - resp.params)
    print('compare bse')
    print(resdp.bse - resp.bse)

    gmlp = sm.GLM(data_endog, data_exog, family=sm.families.Poisson())
    resgp = gmlp.fit()
    ''' this creates a warning, bug bse is double defined ???
    c:\josef\eclipsegworkspace\statsmodels-josef-experimental-gsoc\scikits\statsmodels\decorators.py:105: CacheWriteWarning: The attribute 'bse' cannot be overwritten
      warnings.warn(errmsg, CacheWriteWarning)
    '''
    print('\ncompare with GLM')
    print('compare params')
    print(resgp.params - resp.params)
    print('compare bse')
    print(resgp.bse - resp.bse)

    lam = np.exp(np.dot(data_exog, resp.params))
    '''mean of Poisson distribution'''
    predmean = stats.poisson.stats(lam,moments='m')
    print(np.max(np.abs(predmean - lam)))

    fun = lambda params: np.exp(np.dot(data_exog.mean(0), params))

    lamcov = NonlinearDeltaCov(fun, resp.params, resdp.cov_params())
    print(lamcov.cov().shape)
    print(lamcov.cov())

    print('analytical')
    xm = data_exog.mean(0)
    print(np.dot(np.dot(xm, resdp.cov_params()), xm.T) * \
            np.exp(2*np.dot(data_exog.mean(0), resp.params)))

    ''' cov of linear transformation of params
    >>> np.dot(np.dot(xm, resdp.cov_params()), xm.T)
    0.00038904130127582825
    >>> resp.cov_params(xm)
    0.00038902428119179394
    >>> np.dot(np.dot(xm, resp.cov_params()), xm.T)
    0.00038902428119179394
    '''

    print(lamcov.wald(1.))
    print(lamcov.wald(2.))
    print(lamcov.wald(2.6))

    do_bootstrap = False
    if do_bootstrap:
        m,s,r = resp.bootstrap(method='newton')
        print(m)
        print(s)
        print(resp.bse)


    print('\ncomparison maxabs, masabsrel')
    print('discr params', maxabs(resdp.params, resp.params), maxabsrel(resdp.params, resp.params))
    print('discr bse   ', maxabs(resdp.bse, resp.bse), maxabsrel(resdp.bse, resp.bse))
    print('discr bsejac', maxabs(resdp.bse, resp.bsejac), maxabsrel(resdp.bse, resp.bsejac))
    print('discr bsejhj', maxabs(resdp.bse, resp.bsejhj), maxabsrel(resdp.bse, resp.bsejhj))
    print('')
    print('glm params  ', maxabs(resdp.params, resp.params), maxabsrel(resdp.params, resp.params))
    print('glm bse     ', maxabs(resdp.bse, resp.bse), maxabsrel(resdp.bse, resp.bse))

