# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""PowerTransform Bijector"""
from mindspore.ops import operations as P
from ..distribution._utils.utils import check_greater_equal_zero
from ..distribution._utils.custom_ops import exp_generic, log_generic
from .bijector import Bijector


class PowerTransform(Bijector):
    r"""
    PowerTransform Bijector.
    This Bijector performs the operation:

    .. math::
        Y = g(X) = (1 + X * c)^{1 / c}, X >= -1 / c

    where c >= 0 is the power.

    The power transform maps inputs from `[-1/c, inf]` to `[0, inf]`.

    This Bijector is equivalent to the :class:`mindspore.nn.probability.bijector.Exp` bijector when `c=0`.

    Args:
        power (float, list, numpy.ndarray, Tensor): The scale factor. Default: ``0`` .
        name (str): The name of the bijector. Default: ``'PowerTransform'`` .

    Note:
        The dtype of `power` must be float.

    Raises:
        ValueError: When `power` is less than 0 or is not known statically.
        TypeError: When the dtype of `power` is not float.

    Supported Platforms:
        ``Ascend`` ``GPU``

    Examples:
        >>> import mindspore
        >>> import mindspore.nn as nn
        >>> import mindspore.nn.probability.bijector as msb
        >>> from mindspore import Tensor
        >>> # To initialize a PowerTransform bijector of power 0.5.
        >>> powertransform = msb.PowerTransform(0.5)
        >>> value = Tensor([1, 2, 3], dtype=mindspore.float32)
        >>> ans1 = powertransform.forward(value)
        >>> print(ans1.shape)
        (3,)
        >>> ans2 = powertransform.inverse(value)
        >>> print(ans2.shape)
        (3,)
        >>> ans3 = powertransform.forward_log_jacobian(value)
        >>> print(ans3.shape)
        (3,)
        >>> ans4 = powertransform.inverse_log_jacobian(value)
        >>> print(ans4.shape)
        (3,)
    """

    def __init__(self,
                 power=0.,
                 name='PowerTransform'):
        param = dict(locals())
        param['param_dict'] = {'power': power}
        super(PowerTransform, self).__init__(name=name, param=param)
        self._power = self._add_parameter(power, 'power')
        check_greater_equal_zero(self._power, 'Power')

        self.pow = P.Pow()
        self.dtypeop = P.DType()
        self.cast = P.Cast()
        self.equal_base = P.Equal()
        self.exp = exp_generic
        self.expm1 = P.Expm1()
        self.fill = P.Fill()
        self.log = log_generic
        self.log1p = P.Log1p()
        self.select_base = P.Select()
        self.shape = P.Shape()

    @property
    def power(self):
        """
        Return the power parameter of the bijector.

        Returns:
            Tensor, the power parameter of the bijector.
        """
        return self._power

    def extend_repr(self):
        """Display instance object as string."""
        if self.is_scalar_batch:
            str_info = 'power = {}'.format(self.power)
        else:
            str_info = 'batch_shape = {}'.format(self.batch_shape)
        return str_info

    def _forward(self, x):
        """
        Evaluate the forward mapping.
        """
        x = self._check_value_dtype(x)
        power_local = self.cast_param_by_value(x, self.power)

        # broad cast the value of x and power
        ones = self.fill(self.dtypeop(power_local),
                         self.shape(x + power_local), 1.)
        power_local = power_local * ones
        x = x * ones
        safe_power = self.select_base(self.equal_base(power_local, P.ZerosLike()(power_local)),
                                      ones,
                                      power_local)

        forward_v = self.select_base(self.equal_base(power_local, P.ZerosLike()(power_local)),
                                     self.exp(x),
                                     self.exp(self.log1p(x * safe_power) / safe_power))
        return forward_v

    def _inverse(self, y):
        """
        Evaluate the inverse mapping.
        """
        y = self._check_value_dtype(y)
        power_local = self.cast_param_by_value(y, self.power)

        # broad cast the value of x and power
        ones = self.fill(self.dtypeop(power_local),
                         self.shape(y + power_local), 1.)
        power_local = power_local * ones
        y = y * ones
        safe_power = self.select_base(self.equal_base(power_local, P.ZerosLike()(power_local)),
                                      ones,
                                      power_local)

        inverse_v = self.select_base(self.equal_base(power_local, P.ZerosLike()(power_local)),
                                     self.log(y),
                                     self.expm1(self.log(y) * safe_power) / safe_power)

        return inverse_v

    def _forward_log_jacobian(self, x):
        r"""
        .. math:
            if c == 0:
                f(x) = e^x
                f'(x) = e^x
                \log(f'(x)) = \log(e^x) = x
            else:
                f(x) = e^\frac{\log(xc + 1)}{c}
                f'(x) = e^\frac{\log(xc + 1)}{c} * \frac{1}{xc + 1}
                \log(f'(x)) =  (\frac{1}{c} - 1) * \log(xc + 1)
        """
        x = self._check_value_dtype(x)
        power_local = self.cast_param_by_value(x, self.power)

        # broad cast the value of x and power
        ones = self.fill(self.dtypeop(power_local),
                         self.shape(x + power_local), 1.)
        power_local = power_local * ones
        x = x * ones

        forward_log_j = self.select_base(self.equal_base(power_local, P.ZerosLike()(power_local)),
                                         x,
                                         (1. / power_local - 1) * self.log1p(x * power_local))

        return forward_log_j

    def _inverse_log_jacobian(self, y):
        r"""
        .. math:
            if c == 0:
                f(x) = \log(x)
                f'(x) = \frac{1}{x}
                \log(f'(x)) = \log(\frac{1}{x}) = -\log(x)
            else:
                f(x) = \frac{e^\log(y)*c + 1}{c}
                f'(x) = \frac{e^c\log(y)}{y}
                \log(f'(x)) =  \log(\frac{e^c\log(y)}{y}) = (c-1) * \log(y)
        """
        y = self._check_value_dtype(y)
        power_local = self.cast_param_by_value(y, self.power)
        inverse_log_j = (power_local - 1) * self.log(y)
        return inverse_log_j
