# The implementation is adopted from timm (version: 0.6.11),
# made publicly available under the Apache 2.0 License at
# https://github.com/rwightman/pytorch-image-models/blob/main/timm/models/layers/weight_init.py
import math
import warnings

import torch
from torch.nn.init import _calculate_fan_in_and_fan_out


def _trunc_normal_(tensor, mean, std, a, b):
    # Cut & paste from PyTorch official master until it's in a few official releases - RW
    # Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
    def norm_cdf(x):
        # Computes standard normal cumulative distribution function
        return (1. + math.erf(x / math.sqrt(2.))) / 2.

    if (mean < a - 2 * std) or (mean > b + 2 * std):
        warnings.warn(
            'mean is more than 2 std from [a, b] in nn.init.trunc_normal_. '
            'The distribution of values may be incorrect.',
            stacklevel=2)

    # Values are generated by using a truncated uniform distribution and
    # then using the inverse CDF for the normal distribution.
    # Get upper and lower cdf values
    l = norm_cdf((a - mean) / std)  # noqa
    u = norm_cdf((b - mean) / std)

    # Uniformly fill tensor with values from [l, u], then translate to
    # [2l-1, 2u-1].
    tensor.uniform_(2 * l - 1, 2 * u - 1)

    # Use inverse cdf transform for normal distribution to get truncated
    # standard normal
    tensor.erfinv_()

    # Transform to proper mean, std
    tensor.mul_(std * math.sqrt(2.))
    tensor.add_(mean)

    # Clamp to ensure it's in the proper range
    tensor.clamp_(min=a, max=b)
    return tensor


def trunc_normal_(tensor, mean=0., std=1., a=-2., b=2.):
    # type: (Tensor, float, float, float, float) -> Tensor
    r"""Fills the input Tensor with values drawn from a truncated
    normal distribution. The values are effectively drawn from the
    normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
    with values outside :math:`[a, b]` redrawn until they are within
    the bounds. The method used for generating the random values works
    best when :math:`a \leq \text{mean} \leq b`.

    NOTE: this impl is similar to the PyTorch trunc_normal_, the bounds [a, b] are
    applied while sampling the normal with mean/std applied, therefore a, b args
    should be adjusted to match the range of mean, std args.

    Args:
        tensor: an n-dimensional `torch.Tensor`
        mean: the mean of the normal distribution
        std: the standard deviation of the normal distribution
        a: the minimum cutoff value
        b: the maximum cutoff value
    Examples:
        >>> w = torch.empty(3, 5)
        >>> nn.init.trunc_normal_(w)
    """
    with torch.no_grad():
        return _trunc_normal_(tensor, mean, std, a, b)


def trunc_normal_tf_(tensor, mean=0., std=1., a=-2., b=2.):
    # type: (Tensor, float, float, float, float) -> Tensor
    r"""Fills the input Tensor with values drawn from a truncated
    normal distribution. The values are effectively drawn from the
    normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
    with values outside :math:`[a, b]` redrawn until they are within
    the bounds. The method used for generating the random values works
    best when :math:`a \leq \text{mean} \leq b`.

    NOTE: this 'tf' variant behaves closer to Tensorflow / JAX impl where the
    bounds [a, b] are applied when sampling the normal distribution with mean=0, std=1.0
    and the result is subsquently scaled and shifted by the mean and std args.

    Args:
        tensor: an n-dimensional `torch.Tensor`
        mean: the mean of the normal distribution
        std: the standard deviation of the normal distribution
        a: the minimum cutoff value
        b: the maximum cutoff value
    Examples:
        >>> w = torch.empty(3, 5)
        >>> nn.init.trunc_normal_(w)
    """
    with torch.no_grad():
        _trunc_normal_(tensor, 0, 1.0, a, b)
        tensor.mul_(std).add_(mean)
    return tensor


def variance_scaling_(tensor, scale=1.0, mode='fan_in', distribution='normal'):
    fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
    if mode == 'fan_in':
        denom = fan_in
    elif mode == 'fan_out':
        denom = fan_out
    elif mode == 'fan_avg':
        denom = (fan_in + fan_out) / 2
    else:
        raise ValueError(f'invalid mode {mode}')

    variance = scale / denom

    if distribution == 'truncated_normal':
        # constant is stddev of standard normal truncated to (-2, 2)
        trunc_normal_tf_(tensor, std=math.sqrt(variance) / .87962566103423978)
    elif distribution == 'normal':
        with torch.no_grad():
            tensor.normal_(std=math.sqrt(variance))
    elif distribution == 'uniform':
        bound = math.sqrt(3 * variance)
        with torch.no_grad():
            tensor.uniform_(-bound, bound)
    else:
        raise ValueError(f'invalid distribution {distribution}')


def lecun_normal_(tensor):
    variance_scaling_(tensor, mode='fan_in', distribution='truncated_normal')
