import torch
import torch.distributions as D

from typing import Union


def make_multi_normal(
    mean: torch.Tensor, std: Union[float, torch.Tensor]
) -> D.Distribution:
    if isinstance(std, float):
        std = torch.tensor(std, device=mean.device)

    if std.shape == ():
        std = std.expand(mean.shape)

    return D.Independent(D.Normal(mean, std), reinterpreted_batch_ndims=1)


def make_tanh_transformed(
    mean: torch.Tensor, std: Union[float, torch.Tensor]
) -> D.Distribution:
    if isinstance(std, float):
        std = torch.tensor(std, device=mean.device)

    if std.shape == ():
        std = std.expand(mean.shape)

    return D.Independent(
        D.TransformedDistribution(
            base_distribution=D.Normal(mean, std),
            transforms=[D.TanhTransform(cache_size=1)],
        ),
        reinterpreted_batch_ndims=1,
    )


def make_truncated_normal(
    mean: torch.Tensor, std: Union[float, torch.Tensor]
) -> D.Distribution:
    if isinstance(std, float):
        std = torch.tensor(std, device=mean.device)

    if std.shape == ():
        std = std.expand(mean.shape)

    return D.Independent(
        TruncatedNormal(
            mean,
            std,
            -1.0,
            1.0,
        ),
        reinterpreted_batch_ndims=1,
    )


# From https://github.com/pytorch/rl/blob/main/torchrl/modules/distributions/continuous.py
import math
from numbers import Number

import torch
from torch.distributions import constraints, Distribution
from torch.distributions.utils import broadcast_all

CONST_SQRT_2 = math.sqrt(2)
CONST_INV_SQRT_2PI = 1 / math.sqrt(2 * math.pi)
CONST_INV_SQRT_2 = 1 / math.sqrt(2)
CONST_LOG_INV_SQRT_2PI = math.log(CONST_INV_SQRT_2PI)
CONST_LOG_SQRT_2PI_E = 0.5 * math.log(2 * math.pi * math.e)


class TruncatedStandardNormal(Distribution):
    """Truncated Standard Normal distribution.

    Source: https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
    """

    arg_constraints = {
        "a": constraints.real,
        "b": constraints.real,
    }
    has_rsample = True
    eps = 1e-6

    def __init__(self, a, b, validate_args=None):
        self.a, self.b = broadcast_all(a, b)
        if isinstance(a, Number) and isinstance(b, Number):
            batch_shape = torch.Size()
        else:
            batch_shape = self.a.size()
        super(TruncatedStandardNormal, self).__init__(
            batch_shape, validate_args=validate_args
        )
        if self.a.dtype != self.b.dtype:
            raise ValueError("Truncation bounds types are different")
        if any(
            (self.a >= self.b)
            .view(
                -1,
            )
            .tolist()
        ):
            raise ValueError("Incorrect truncation range")
        eps = self.eps
        self._dtype_min_gt_0 = eps
        self._dtype_max_lt_1 = 1 - eps
        self._little_phi_a = self._little_phi(self.a)
        self._little_phi_b = self._little_phi(self.b)
        self._big_phi_a = self._big_phi(self.a)
        self._big_phi_b = self._big_phi(self.b)
        self._Z = (self._big_phi_b - self._big_phi_a).clamp(eps, 1 - eps)
        self._log_Z = self._Z.log()
        little_phi_coeff_a = torch.nan_to_num(self.a, nan=math.nan)
        little_phi_coeff_b = torch.nan_to_num(self.b, nan=math.nan)
        self._lpbb_m_lpaa_d_Z = (
            self._little_phi_b * little_phi_coeff_b
            - self._little_phi_a * little_phi_coeff_a
        ) / self._Z
        self._mean = -(self._little_phi_b - self._little_phi_a) / self._Z
        self._variance = (
            1
            - self._lpbb_m_lpaa_d_Z
            - ((self._little_phi_b - self._little_phi_a) / self._Z) ** 2
        )
        self._entropy = CONST_LOG_SQRT_2PI_E + self._log_Z - 0.5 * self._lpbb_m_lpaa_d_Z

    @constraints.dependent_property
    def support(self):
        return constraints.interval(self.a, self.b)

    @property
    def mean(self):
        return self._mean

    @property
    def variance(self):
        return self._variance

    def entropy(self):
        return self._entropy

    @property
    def auc(self):
        return self._Z

    @staticmethod
    def _little_phi(x):
        return (-(x**2) * 0.5).exp() * CONST_INV_SQRT_2PI

    def _big_phi(self, x):
        phi = 0.5 * (1 + (x * CONST_INV_SQRT_2).erf())
        return phi.clamp(self.eps, 1 - self.eps)

    @staticmethod
    def _inv_big_phi(x):
        return CONST_SQRT_2 * (2 * x - 1).erfinv()

    def cdf(self, value):
        if self._validate_args:
            self._validate_sample(value)
        return ((self._big_phi(value) - self._big_phi_a) / self._Z).clamp(0, 1)

    def icdf(self, value):
        y = self._big_phi_a + value * self._Z
        y = y.clamp(self.eps, 1 - self.eps)
        return self._inv_big_phi(y)

    def log_prob(self, value):
        if self._validate_args:
            self._validate_sample(value)
        return CONST_LOG_INV_SQRT_2PI - self._log_Z - (value**2) * 0.5

    def rsample(self, sample_shape=None):
        if sample_shape is None:
            sample_shape = torch.Size([])
        shape = self._extended_shape(sample_shape)
        p = torch.empty(shape, device=self.a.device).uniform_(
            self._dtype_min_gt_0, self._dtype_max_lt_1
        )
        return self.icdf(p)


class TruncatedNormal(TruncatedStandardNormal):
    """Truncated Normal distribution.

    https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
    """

    has_rsample = True

    def __init__(self, loc, scale, a, b, validate_args=None):
        scale = scale.clamp_min(self.eps)
        self.loc, self.scale, a, b = broadcast_all(loc, scale, a, b)
        self._non_std_a = a
        self._non_std_b = b
        a = (a - self.loc) / self.scale
        b = (b - self.loc) / self.scale
        super(TruncatedNormal, self).__init__(a, b, validate_args=validate_args)
        self._log_scale = self.scale.log()
        self._mean = self._mean * self.scale + self.loc
        self._variance = self._variance * self.scale**2
        self._entropy += self._log_scale

    def _to_std_rv(self, value):
        return (value - self.loc) / self.scale

    def _from_std_rv(self, value):
        return value * self.scale + self.loc

    def cdf(self, value):
        return super(TruncatedNormal, self).cdf(self._to_std_rv(value))

    def icdf(self, value):
        sample = self._from_std_rv(super().icdf(value))

        # clamp data but keep gradients
        sample_clip = torch.stack(
            [sample.detach(), self._non_std_a.detach().expand_as(sample)], 0
        ).max(0)[0]
        sample_clip = torch.stack(
            [sample_clip, self._non_std_b.detach().expand_as(sample)], 0
        ).min(0)[0]
        sample.data.copy_(sample_clip)
        return sample

    def log_prob(self, value):
        value = self._to_std_rv(value)
        return super(TruncatedNormal, self).log_prob(value) - self._log_scale