class Linear(Module):
    r"""Applies a linear transformation to the incoming data: :math:`y = xA^T + b`
    This module supports :ref:`TensorFloat32<tf32_on_ampere>`.
    Args:
        in_features: size of each input sample
        out_features: size of each output sample
        bias: If set to ``False``, the layer will not learn an additive bias.
            Default: ``True``
    Shape:
        - Input: :math:`(N, *, H_{in})` where :math:`*` means any number of
          additional dimensions and :math:`H_{in} = \text{in\_features}`
        - Output: :math:`(N, *, H_{out})` where all but the last dimension
          are the same shape as the input and :math:`H_{out} = \text{out\_features}`.
    Attributes:
        weight: the learnable weights of the module of shape
            :math:`(\text{out\_features}, \text{in\_features})`. The values are
            initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`, where
            :math:`k = \frac{1}{\text{in\_features}}`
        bias:   the learnable bias of the module of shape :math:`(\text{out\_features})`.
                If :attr:`bias` is ``True``, the values are initialized from
                :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
                :math:`k = \frac{1}{\text{in\_features}}`
    Examples::
        >>> m = nn.Linear(20, 30)
        >>> input = torch.randn(128, 20)
        >>> output = m(input)
        >>> print(output.size())
        torch.Size([128, 30])
    """
    __constants__ = ['in_features', 'out_features']
    in_features: int
    out_features: int
    weight: Tensor
 
    def __init__(self, in_features: int, out_features: int, bias: bool = True) -> None:
        super(Linear, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.weight = Parameter(torch.Tensor(out_features, in_features))
        if bias:
            self.bias = Parameter(torch.Tensor(out_features))
        else:
            self.register_parameter('bias', None)
        self.reset_parameters()
 
    def reset_parameters(self) -> None:
        init.kaiming_uniform_(self.weight, a=math.sqrt(5))
        if self.bias is not None:
            fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
            bound = 1 / math.sqrt(fan_in)
            init.uniform_(self.bias, -bound, bound)
 
    def forward(self, input: Tensor) -> Tensor:
        return F.linear(input, self.weight, self.bias)
 
    def extra_repr(self) -> str:
        return 'in_features={}, out_features={}, bias={}'.format(
            self.in_features, self.out_features, self.bias is not None
        )
 
 
# This class exists solely for Transformer; it has an annotation stating
# that bias is never None, which appeases TorchScript

import torch
 
# 隨機初始化一個shape為(128,20)的Tensor
x = torch.randn(128,20)
# 構造線性變換函數(shù)y = xA^T + b,且參數(shù)(20,30)指的是A的shape,則A.weight的shape就是(30,20)了
y= torch.nn.Linear(20,30)
output = y(x)
# 按照以上邏輯使用torch中的簡單乘法函數(shù)進行檢驗，結果很顯然與上述符合
# 下面的y.weight可以理解為一個shape為(30,20)的一個可學習的矩陣，.t()表示轉置
# y.bias若為TRUE，則bias是一個Tensor，且其shape為out_features,在該程序中應為30
# 更加細致的表達一下y = (128 * 20) * (30 * 20)^T + (if bias (1,30) ,else: 0)
ans = torch.mm(x,y.weight.t())+y.bias
print('ans.shape:\n',ans.shape)
print(torch.equal(ans,output))

Linear(in_features: int, out_features: int, bias: bool = True, device: Any | None = None, dtype: Any | None = None)

import torch
input = torch.randn(30, 20, 10)  # [30, 20, 10]
linear = torch.nn.Linear(10, 15)  # (*, 10) --> (*, 15)
output = linear(input)
print(output.size()) # 輸出 [30, 20, 15]