目录
一、函数解释
如果输入x，输出是y，则求y关于x的导数（梯度）：
def grad(outputs, inputs, grad_outputs=None, retain_graph=None, create_graph=False,
only_inputs=True, allow_unused=False):
r"""Computes and returns the sum of gradients of outputs w.r.t. the inputs.
``grad_outputs`` should be a sequence of length matching ``output``
containing the pre-computed gradients w.r.t. each of the outputs. If an
output doesn't require_grad, then the gradient can be ``None``).
If ``only_inputs`` is ``True``, the function will only return a list of gradients
w.r.t the specified inputs. If it's ``False``, then gradient w.r.t. all remaining
leaves will still be computed, and will be accumulated into their ``.grad``
attribute.
Arguments:
outputs (sequence of Tensor): outputs of the differentiated function.
inputs (sequence of Tensor): Inputs w.r.t. which the gradient will be
returned (and not accumulated into ``.grad``).
grad_outputs (sequence of Tensor): Gradients w.r.t. each output.
None values can be specified for scalar Tensors or ones that don't require
grad. If a None value would be acceptable for all grad_tensors, then this
argument is optional. Default: None.
retain_graph (bool, optional): If ``False``, the graph used to compute the grad
will be freed. Note that in nearly all cases setting this option to ``True``
is not needed and often can be worked around in a much more efficient
way. Defaults to the value of ``create_graph``.
create_graph (bool, optional): If ``True``, graph of the derivative will
be constructed, allowing to compute higher order derivative products.
Default: ``False``.
allow_unused (bool, optional): If ``False``, specifying inputs that were not
used when computing outputs (and therefore their grad is always zero)
is an error. Defaults to ``False``.
"""
if not only_inputs:
warnings.warn("only_inputs argument is deprecated and is ignored now "
"(defaults to True). To accumulate gradient for other "
"parts of the graph, please use torch.autograd.backward.")
outputs = (outputs,) if isinstance(outputs, torch.Tensor) else tuple(outputs)
inputs = (inputs,) if isinstance(inputs, torch.Tensor) else tuple(inputs)
if grad_outputs is None:
grad_outputs = [None] * len(outputs)
elif isinstance(grad_outputs, torch.Tensor):
grad_outputs = [grad_outputs]
else:
grad_outputs = list(grad_outputs)
grad_outputs = _make_grads(outputs, grad_outputs)
if retain_graph is None:
retain_graph = create_graph
return Variable._execution_engine.run_backward(
outputs, grad_outputs, retain_graph, create_graph,
inputs, allow_unused)二、代码范例(y=x^2)
import torch
x = torch.randn(3, 4).requires_grad_(True)
for i in range(3):
for j in range(4):
x[i][j] = i + j
y = x ** 2
print(x)
print(y)
weight = torch.ones(y.size())
print(weight)
dydx = torch.autograd.grad(outputs=y,
inputs=x,
grad_outputs=weight,
retain_graph=True,
create_graph=True,
only_inputs=True)
"""(x**2)' = 2*x """
print(dydx[0])
d2ydx2 = torch.autograd.grad(outputs=dydx[0],
inputs=x,
grad_outputs=weight,
retain_graph=True,
create_graph=True,
only_inputs=True)
print(d2ydx2[0])
x是：
tensor([[0., 1., 2., 3.],
[1., 2., 3., 4.],
[2., 3., 4., 5.]], grad_fn=<CopySlices>)y = x的平方：
tensor([[ 0., 1., 4., 9.],
[ 1., 4., 9., 16.],
[ 4., 9., 16., 25.]], grad_fn=<PowBackward0>)weight：
tensor([[1., 1., 1., 1.],
[1., 1., 1., 1.],
[1., 1., 1., 1.]])dydx就是(一阶导数)，得到结果还需要乘以weight：
tensor([[ 0., 2., 4., 6.],
[ 2., 4., 6., 8.],
[ 4., 6., 8., 10.]], grad_fn=<ThMulBackward>)d2ydx2就是(二阶导数），得到结果还需要乘以weight：
tensor([[2., 2., 2., 2.],
[2., 2., 2., 2.],
[2., 2., 2., 2.]], grad_fn=<ThMulBackward>)是不是很简单呢～
