def _no_grad_trunc_normal(
    tensor: torch.Tensor,
    mean: float,
    std: float,
    a: float,
    b: float,
) -> torch.Tensor:
    """Initializes the input tensor with a truncated normal distribution.

    This method is based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf

    Args:
        tensor:
            The tensor to initialize.
        mean:
            Mean of the distribution.
        std:
            Standard deviation of the distribution.
        a:
            Minimum value of the distribution, values below will be clamped.
        b:
            Maximum value of the distribution, values above will be clamped.

    """

    def norm_cdf(x):
        # Computes standard normal cumulative distribution function
        return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0

    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,
        )

    with torch.no_grad():
        # 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)
        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(2.0))
        tensor.add_(mean)

        # Clamp to ensure it's in the proper range
        tensor.clamp_(min=a, max=b)
        return tensor
Initializes the input tensor with a truncated normal distribution.

    This method is based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf

    Args:
        tensor:
            The tensor to initialize.
        mean:
            Mean of the distribution.
        std:
            Standard deviation of the distribution.
        a:
            Minimum value of the distribution, values below will be clamped.
        b:
            Maximum value of the distribution, values above will be clamped.

    
lightly/models/utils.py