# -*- coding: utf-8 -*-
""" Transformation Classes as generators for Archimedean copulas


Created on Wed Jan 27 14:33:40 2021

Author: Josef Perktold
License: BSD-3

"""

import numpy as np
from scipy.special import expm1


# not used yet
class Transforms(object):

    def __init__(self):
        pass


class TransfFrank(Transforms):

    def evaluate(self, t, theta):
        t = np.asarray(t)
        return - (np.log(-expm1(-theta*t)) - np.log(-expm1(-theta)))
        # return - np.log(expm1(-theta*t) / expm1(-theta))

    def inverse(self, phi, theta):
        phi = np.asarray(phi)
        return -np.log1p(np.exp(-phi) * expm1(-theta)) / theta

    def deriv(self, t, theta):
        t = np.asarray(t)
        tmp = np.exp(-t*theta)
        return -theta * tmp/(tmp - 1)

    def deriv2(self, t, theta):
        t = np.asarray(t)
        tmp = np.exp(theta * t)
        d2 = - theta**2 * tmp / (tmp - 1)**2
        return d2

    def is_completly_monotonic(self, theta):
        # range of theta for which it is copula for d>2 (more than 2 rvs)
        return theta > 0 & theta < 1


class TransfClayton(Transforms):

    def _checkargs(self, theta):
        return theta > 0

    def evaluate(self, t, theta):
        return np.power(t, -theta) - 1.

    def inverse(self, phi, theta):
        return np.power(1 + phi, -1/theta)

    def deriv(self, t, theta):
        return -theta * np.power(t, -theta-1)

    def deriv2(self, t, theta):
        return theta * (theta + 1) * np.power(t, -theta-2)

    def is_completly_monotonic(self, theta):
        return theta > 0


class TransfGumbel(Transforms):
    '''
    requires theta >=1
    '''

    def _checkargs(self, theta):
        return theta >= 1

    def evaluate(self, t, theta):
        return np.power(-np.log(t), theta)

    def inverse(self, phi, theta):
        return np.exp(-np.power(phi, 1. / theta))

    def deriv(self, t, theta):
        return - theta * (-np.log(t))**(theta - 1) / t

    def deriv2(self, t, theta):
        tmp1 = np.log(t)
        d2 = (theta*(-1)**(1 + theta) * tmp1**(theta-1) * (1 - theta) +
              theta*(-1)**(1 + theta)*tmp1**theta)/(t**2*tmp1)
        # d2 = (theta * tmp1**(-1 + theta) * (1 - theta) + theta * tmp1**theta
        #       ) / (t**2 * tmp1)

        return d2

    def is_completly_monotonic(self, theta):
        return theta > 1


class TransfIndep(Transforms):

    def evaluate(self, t, *args):
        t = np.asarray(t)
        return -np.log(t)

    def inverse(self, phi, *args):
        phi = np.asarray(phi)
        return np.exp(-phi)

    def deriv(self, t, *args):
        t = np.asarray(t)
        return - 1./t

    def deriv2(self, t, *args):
        t = np.asarray(t)
        return 1. / t**2


class _TransfPower(Transforms):
    """generic multivariate Archimedean copula with additional power transforms

    Nelson p.144, equ. 4.5.2

    experimental, not yet tested and used
    """

    def __init__(self, transform):
        self.transform = transform

    def evaluate(self, t, alpha, beta, *tr_args):
        t = np.asarray(t)

        phi = np.power(self.transform.evaluate(np.power(t, alpha), *tr_args),
                       beta)
        return phi

    def inverse(self, phi, alpha, beta, *tr_args):
        phi = np.asarray(phi)
        transf = self.transform
        phi_inv = np.power(transf.evaluate(np.power(phi, 1. / beta), *tr_args),
                           1. / alpha)
        return phi_inv