# Inherit from Function
class LinearFunction(Function):

  # Note that both forward and backward are @staticmethods
  @staticmethod
  # bias is an optional argument
  def forward(ctx, input, weight, bias=None):
    # ctx在這里類似self，ctx的屬性可以在backward中調用
    ctx.save_for_backward(input, weight, bias)
    output = input.mm(weight.t())
    if bias is not None:
      output += bias.unsqueeze(0).expand_as(output)
    return output

  # This function has only a single output, so it gets only one gradient
  @staticmethod
  def backward(ctx, grad_output):
    # This is a pattern that is very convenient - at the top of backward
    # unpack saved_tensors and initialize all gradients w.r.t. inputs to
    # None. Thanks to the fact that additional trailing Nones are
    # ignored, the return statement is simple even when the function has
    # optional inputs.
    input, weight, bias = ctx.saved_tensors
    grad_input = grad_weight = grad_bias = None

    # These needs_input_grad checks are optional and there only to
    # improve efficiency. If you want to make your code simpler, you can
    # skip them. Returning gradients for inputs that don't require it is
    # not an error.
    if ctx.needs_input_grad[0]:
      grad_input = grad_output.mm(weight)
    if ctx.needs_input_grad[1]:
      grad_weight = grad_output.t().mm(input)
    if bias is not None and ctx.needs_input_grad[2]:
      grad_bias = grad_output.sum(0).squeeze(0)

    return grad_input, grad_weight, grad_bias

#調用自定義的自動求導函數(shù)
linear = LinearFunction.apply(*args) #前向傳播
linear.backward()#反向傳播
linear.grad_fn.apply(*args)#反向傳播

class MulConstant(Function):
  @staticmethod
  def forward(ctx, tensor, constant):
    # ctx is a context object that can be used to stash information
    # for backward computation
    ctx.constant = constant
    return tensor * constant

  @staticmethod
  def backward(ctx, grad_output):
    # We return as many input gradients as there were arguments.
    # Gradients of non-Tensor arguments to forward must be None.
    return grad_output * ctx.constant, None

grad_x =t.autograd.grad(y, x, create_graph=True)

grad_grad_x = t.autograd.grad(grad_x[0],x)

class Linear(nn.Module):
  def __init__(self, input_features, output_features, bias=True):
    super(Linear, self).__init__()
    self.input_features = input_features
    self.output_features = output_features

    # nn.Parameter is a special kind of Tensor, that will get
    # automatically registered as Module's parameter once it's assigned
    # as an attribute. Parameters and buffers need to be registered, or
    # they won't appear in .parameters() (doesn't apply to buffers), and
    # won't be converted when e.g. .cuda() is called. You can use
    # .register_buffer() to register buffers.
    # (很重要?。?！參數(shù)一定需要梯度！)nn.Parameters require gradients by default.
    self.weight = nn.Parameter(torch.Tensor(output_features, input_features))
    if bias:
      self.bias = nn.Parameter(torch.Tensor(output_features))
    else:
      # You should always register all possible parameters, but the
      # optional ones can be None if you want.
      self.register_parameter('bias', None)

    # Not a very smart way to initialize weights
    self.weight.data.uniform_(-0.1, 0.1)
    if bias is not None:
      self.bias.data.uniform_(-0.1, 0.1)

  def forward(self, input):
    # See the autograd section for explanation of what happens here.
    return LinearFunction.apply(input, self.weight, self.bias)

  def extra_repr(self):
    # (Optional)Set the extra information about this module. You can test
    # it by printing an object of this class.
    return 'in_features={}, out_features={}, bias={}'.format(
      self.in_features, self.out_features, self.bias is not None